**Technologies**

**Chapter 1**

Provisional chapter

**Inert and Reactive Working Fluids for Closed Power**

DOI: 10.5772/intechopen.79290

Inert and Reactive Working Fluids for Closed Power

**Cycles: Present Knowledge, Applications and Open**

The possibility of selecting the working fluid of a closed power cycle represents one of the most important levers to maximise the efficiency and to optimise the design of this technology. This chapter is intended to provide a description of the present state of knowledge on the effects that fluid thermo-physical properties, such as molecular complexity and molecular mass, have on the design and performance of cycle components. With a view to allow for accounting for multicomponent inert and reactive working fluids along the optimisation process, the chapter then presents the main outstanding scientific

Keywords: closed thermodynamic cycle, working fluid, inert and reactive mixture,

The history of power production systems has been marked by the deployment of two main technologies: the water cycle and the open gas cycle. Both the engines owe their development to the possible exploitation of the traditional high-grade heat sources (i.e. characterised by a high maximum temperature and a huge thermal power), represented by the heat of combustion of fossil fuels. The achievement of a minimum acceptable efficiency level of these technologies requires the availability of a high thermal power, in the case of water cycles, and the achievement of a sufficiently high maximum temperature of the gaseous working fluid, in the

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

thermodynamic properties, transformations, thermal stability

Cycles: Present Knowledge, Applications and Open

Silvia Lasala, Romain Privat and Jean-Noël Jaubert

Silvia Lasala, Romain Privat and Jean-Noël Jaubert

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.79290

barriers which need to be overcome.

**Researches**

Abstract

1. Introduction

case of gas cycles.

Researches

#### **Inert and Reactive Working Fluids for Closed Power Cycles: Present Knowledge, Applications and Open Researches** Inert and Reactive Working Fluids for Closed Power Cycles: Present Knowledge, Applications and Open Researches

DOI: 10.5772/intechopen.79290

Silvia Lasala, Romain Privat and Jean-Noël Jaubert Silvia Lasala, Romain Privat and Jean-Noël Jaubert

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.79290

#### Abstract

The possibility of selecting the working fluid of a closed power cycle represents one of the most important levers to maximise the efficiency and to optimise the design of this technology. This chapter is intended to provide a description of the present state of knowledge on the effects that fluid thermo-physical properties, such as molecular complexity and molecular mass, have on the design and performance of cycle components. With a view to allow for accounting for multicomponent inert and reactive working fluids along the optimisation process, the chapter then presents the main outstanding scientific barriers which need to be overcome.

Keywords: closed thermodynamic cycle, working fluid, inert and reactive mixture, thermodynamic properties, transformations, thermal stability

## 1. Introduction

The history of power production systems has been marked by the deployment of two main technologies: the water cycle and the open gas cycle. Both the engines owe their development to the possible exploitation of the traditional high-grade heat sources (i.e. characterised by a high maximum temperature and a huge thermal power), represented by the heat of combustion of fossil fuels. The achievement of a minimum acceptable efficiency level of these technologies requires the availability of a high thermal power, in the case of water cycles, and the achievement of a sufficiently high maximum temperature of the gaseous working fluid, in the case of gas cycles.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Nowadays, the recognised necessity of reducing the environmental impact of power 'production' processes has imposed the exploitation of non-traditional heat sources either recovered from industrial processes or made available by renewable energies (geothermal, biomass and solar thermal energy). These are typically characterised by a lower thermal power and a lower maximum temperature than thermal sources generated by the combustion of fossil fuels.

heat sources (liquid, gaseous or two-phase streams) which generally make the use of water cycles unsuitable. The thermodynamic properties of water, in fact, entail the necessity of adopting complex and expensive plant configurations, preventing from their use in lowtemperature and low-power applications [1]. In these cases, the design of simple turbines and the occurrence of a single-phase vapour expansion are aspects of primary importance which direct the use of molecules being more complex and heavier than water, currently represented

Inert and Reactive Working Fluids for Closed Power Cycles: Present Knowledge, Applications and Open Researches

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5

Organic fluids are most conveniently used as subcritical working fluids in power production plants designed to recover heat wasted by industrial processes and many other low-mediumtemperature applications. Organic fluids are used up to 400 C, due to their limited thermal stability. Macchi has presented [2] a 'grey zone' of applications, characterised by an heat source temperature of 300–400 C and a power output of 8–50 MW, where organic fluids could

Furthermore, the production of high-power outputs is conveniently associated with the use of either water or CO2 cycles, giving preference to CO2 for the high-temperature applications represented by solar energy (solar tower technology) and nuclear energy (IV generation of

Moreover, it is worth highlighting that, besides the already attested application of hightemperature CO2 power cycles, this technology may also be considered as a viable solution for the exploitation of medium-temperature heat sources (300–600 C), competing with organic

The optimal choice between fluids for power systems designed to exploit mediumtemperature and low-medium heat sources is thus not straightforward. The preferential use of a specific fluid in a particular range of power outputs and source temperatures results, in fact, from the techno-economical optimisation of these technologies, which maximises their efficiency and minimises their costs according to the specific constraints imposed by each application. Thermodynamic properties (in particular, specific molar heat capacities and critical properties) and the molar mass of each fluid influence the performance of the thermody-

The nature of a selected pure working fluid does influence the performance of power cycles in the way its thermo-physical properties affect the thermodynamics of the cycle, turbomachines and heat exchanger efficiencies. Subsections 2.1.1 and 2.1.2 briefly introduce the foundations of

2.1.1. Effect of fluid molecular complexity and mass on the performance and design of turbomachines A preliminary classification of working fluids can be performed according to their molecular weight (first criterion) and to their molecular complexity (second criterion), the latter being related to the degrees of freedom of the molecule and, thus, to their molar heat capacity.

In general, one could erroneously think that more complex molecules are characterised, at all time, by a higher molecular weight. Although this is observable in the majority of cases, such a

by organic fluids (hydrocarbons, fluorocarbons and siloxanes) [2].

compete with water cycles.

nuclear reactors) [3].

fluids and water [1].

such a statement.

namic cycle and the design of components.

The efficient and economical recovery of these low-temperature thermal energies is made possible by the use of closed cycles in which the working fluid can be properly selected. Depending on the heat capacities of both the thermal source to be exploited and the cold sink where cycle heat is discharged, the use of different working fluids might be indeed more or less convenient, in terms of both energy conversion efficiency and components design.

Together with the optimisation of the cycle configuration ('process-design' approach), the possibility to define the optimal working fluid for each application ('product-design' approach) represents the greatest degree of flexibility to reduce the irreversibilities of any of these energy conversion processes and, thus, to maximise their efficiency.

Despite the pivotal role represented by the optimal selection of the working fluid, the scientific knowledge level on physicochemical thermodynamic and transport properties, thermal stability and environmental characteristics of fluids do merely allow the reliable utilisation of purecomponent fluids.

This chapter aims, firstly, to present a review of the present knowledge level on this topic and, secondly, to highlight the main scientific gaps which currently limit the assessment of the energy potential of closed cycles operating with inert and reactive mixtures as working fluids.

## 2. The state of the art on working fluids for closed power cycles

Two main criteria exist to differentiate between working fluids, depending on whether they are pure or multicomponent, inert or reactive fluids. According to these classifications, inert fluids may be pure or multicomponent (typically binary) fluids, while reactive fluids may only be multicomponent fluids, as they are mixtures by definition. The advantage represented by the use of optimal inert fluids mainly lies in the possibility of reducing the irreversibilities occurring along the cycle; differently, reactive fluids may allow the substantial increase of the energy 'produced' during fluid expansion, thanks to the conversion of the chemical energy (other than the physical one) of the reactive fluid.

#### 2.1. Inert pure fluids

Nowadays, pure fluids are mainly used as working fluids, among which water represents the pioneer for power cycles. Even now, water is the fluid which is mostly used in a closed thermodynamic cycle, in particular, in the Rankine cycle. The thermodynamic conversion of non-traditional thermal sources (geothermal, biomass, solar thermal and industrial waste heat recovery) is associated to a wide variety of powers, thermal grades and physical states of the heat sources (liquid, gaseous or two-phase streams) which generally make the use of water cycles unsuitable. The thermodynamic properties of water, in fact, entail the necessity of adopting complex and expensive plant configurations, preventing from their use in lowtemperature and low-power applications [1]. In these cases, the design of simple turbines and the occurrence of a single-phase vapour expansion are aspects of primary importance which direct the use of molecules being more complex and heavier than water, currently represented by organic fluids (hydrocarbons, fluorocarbons and siloxanes) [2].

Nowadays, the recognised necessity of reducing the environmental impact of power 'production' processes has imposed the exploitation of non-traditional heat sources either recovered from industrial processes or made available by renewable energies (geothermal, biomass and solar thermal energy). These are typically characterised by a lower thermal power and a lower maximum temperature than thermal sources generated by the combustion of fossil fuels.

The efficient and economical recovery of these low-temperature thermal energies is made possible by the use of closed cycles in which the working fluid can be properly selected. Depending on the heat capacities of both the thermal source to be exploited and the cold sink where cycle heat is discharged, the use of different working fluids might be indeed more or

Together with the optimisation of the cycle configuration ('process-design' approach), the possibility to define the optimal working fluid for each application ('product-design' approach) represents the greatest degree of flexibility to reduce the irreversibilities of any of

Despite the pivotal role represented by the optimal selection of the working fluid, the scientific knowledge level on physicochemical thermodynamic and transport properties, thermal stability and environmental characteristics of fluids do merely allow the reliable utilisation of pure-

This chapter aims, firstly, to present a review of the present knowledge level on this topic and, secondly, to highlight the main scientific gaps which currently limit the assessment of the energy potential of closed cycles operating with inert and reactive mixtures as working fluids.

Two main criteria exist to differentiate between working fluids, depending on whether they are pure or multicomponent, inert or reactive fluids. According to these classifications, inert fluids may be pure or multicomponent (typically binary) fluids, while reactive fluids may only be multicomponent fluids, as they are mixtures by definition. The advantage represented by the use of optimal inert fluids mainly lies in the possibility of reducing the irreversibilities occurring along the cycle; differently, reactive fluids may allow the substantial increase of the energy 'produced' during fluid expansion, thanks to the conversion of the chemical energy (other than

Nowadays, pure fluids are mainly used as working fluids, among which water represents the pioneer for power cycles. Even now, water is the fluid which is mostly used in a closed thermodynamic cycle, in particular, in the Rankine cycle. The thermodynamic conversion of non-traditional thermal sources (geothermal, biomass, solar thermal and industrial waste heat recovery) is associated to a wide variety of powers, thermal grades and physical states of the

2. The state of the art on working fluids for closed power cycles

less convenient, in terms of both energy conversion efficiency and components design.

these energy conversion processes and, thus, to maximise their efficiency.

component fluids.

4 Organic Rankine Cycle Technology for Heat Recovery

the physical one) of the reactive fluid.

2.1. Inert pure fluids

Organic fluids are most conveniently used as subcritical working fluids in power production plants designed to recover heat wasted by industrial processes and many other low-mediumtemperature applications. Organic fluids are used up to 400 C, due to their limited thermal stability. Macchi has presented [2] a 'grey zone' of applications, characterised by an heat source temperature of 300–400 C and a power output of 8–50 MW, where organic fluids could compete with water cycles.

Furthermore, the production of high-power outputs is conveniently associated with the use of either water or CO2 cycles, giving preference to CO2 for the high-temperature applications represented by solar energy (solar tower technology) and nuclear energy (IV generation of nuclear reactors) [3].

Moreover, it is worth highlighting that, besides the already attested application of hightemperature CO2 power cycles, this technology may also be considered as a viable solution for the exploitation of medium-temperature heat sources (300–600 C), competing with organic fluids and water [1].

The optimal choice between fluids for power systems designed to exploit mediumtemperature and low-medium heat sources is thus not straightforward. The preferential use of a specific fluid in a particular range of power outputs and source temperatures results, in fact, from the techno-economical optimisation of these technologies, which maximises their efficiency and minimises their costs according to the specific constraints imposed by each application. Thermodynamic properties (in particular, specific molar heat capacities and critical properties) and the molar mass of each fluid influence the performance of the thermodynamic cycle and the design of components.

The nature of a selected pure working fluid does influence the performance of power cycles in the way its thermo-physical properties affect the thermodynamics of the cycle, turbomachines and heat exchanger efficiencies. Subsections 2.1.1 and 2.1.2 briefly introduce the foundations of such a statement.

#### 2.1.1. Effect of fluid molecular complexity and mass on the performance and design of turbomachines

A preliminary classification of working fluids can be performed according to their molecular weight (first criterion) and to their molecular complexity (second criterion), the latter being related to the degrees of freedom of the molecule and, thus, to their molar heat capacity.

In general, one could erroneously think that more complex molecules are characterised, at all time, by a higher molecular weight. Although this is observable in the majority of cases, such a conclusion is not universally correct. For example, carbon dioxide is characterised by a higher molecular complexity and a lower molecular weight with respect to krypton. This is shown in Table 1. The same table allows another similar comparison, between perfluorohexane and 1-undecanol, the former being heavier and molecularly simpler than the latter.

Molecular complexity influences the design and performance of a thermodynamic cycle, in such a way that complexity affects the degree of freedom of the molecule itself and, thus, the change in the thermodynamic properties of the fluid in response to energy interactions with the environment. In particular, a higher molecular complexity entails a lower adiabatic index, γ = cp/cv (see Table 1) and, thus, a weaker temperature modification of the fluid, at a given pressure ratio, and a more important pressure change, at a fixed temperature ratio. Along an isentropic compression or expansion of molecules in the ideal gas state, temperature and pressure ratios are related by means of the molecular complexity:

$$(T\_2/T\_1 = (P\_2/P\_1)^{\frac{\gamma \tau}{\gamma}} = (v\_2/v\_1)^{1\gamma} \tag{1}$$

specific heat capacity resulting from more complex or lighter molecules, the higher the number

Inert and Reactive Working Fluids for Closed Power Cycles: Present Knowledge, Applications and Open Researches

Moreover, it is possible to show that the radial dimensions of turbomachines depend only on the molecular complexity, the pressure and the temperature of the fluid. In particular, and contrary to axial extension, cross-sectional areas are minimised by the use of complex mole-

To reduce the design complexity of turbomachines and to increase their efficiency (limiting the number of stages, the variation of volumetric flow and avoiding the occurrence of supersonic conditions), it is thus preferable to adopt simple and heavy fluids. The higher radial dimensions of turbomachines that would result from the use of simple molecules could be reduced

It is worth highlighting that the molecular complexity determines, in particular, the inclination of saturation vapour curve in the T-s diagram: the increase in temperature or in pressure results, respectively, in an increase or a decrease in saturated-vapour entropy. Depending on whether the influence of temperature or that of pressure overrides, the saturated-vapour curve slopes positively or negatively in the T-s plane (Figure 2(a) and (c)). In the case of (c), which concerns complex molecules, the expansion of saturated-vapour fluids in saturated Rankine cycles favourably occurs in the superheated vapour phase (the so-called 'dry' expansion), avoiding the inefficient expansion of the fluid in the two-phase region. Herein, a simple

approach to allow for distinguishing between these two families of fluids is presented.

dPsat <sup>P</sup>sat <sup>¼</sup> <sup>B</sup>

dssat gas ¼ c • p dT <sup>T</sup> -RdPsat

dssat gas dT <sup>¼</sup> <sup>1</sup>

dssat gas dT <sup>¼</sup> <sup>1</sup>

and substituting it into Eq. (3), it is possible to deduce

Equation (6) shows that when the combination of c•

Antoine equation in the reduced variables, ln Psat

or, defining B\* = B/Tc,

c•

Assuming, for simplicity, that the vapour behaves as a perfect gas, it is possible to write that

Considering the Antoine equation for saturation pressure, ln(Psat) = A - B/T, and its differential form:

<sup>T</sup> <sup>c</sup> • <sup>p</sup> -<sup>R</sup> <sup>B</sup> T

<sup>T</sup> <sup>c</sup> • <sup>p</sup> -<sup>R</sup> <sup>B</sup><sup>∗</sup> Tr

<sup>p</sup> <sup>¼</sup> <sup>R</sup> � <sup>B</sup><sup>∗</sup>=Tr, the saturation vapour curve is vertical in the plane T-s. Practically, it is possible to observe the existence of an average value for B\* common to most of fluids. Considering

> r <sup>¼</sup> <sup>A</sup><sup>∗</sup>

<sup>P</sup>sat (3)

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7

<sup>T</sup><sup>2</sup> dT (4)

(5)

(6)

<sup>p</sup> and of Tr of the fluid is such that


of stages of the turbomachine.

by an increasing fluid pressure.

cules that would reduce the volumetric flow of the stream.

By way of example, Table 1 reports the temperature (or molar volume) and pressure changes, for each considered fluid, resulting from, respectively, pressure and temperature modifications. It can be observed, from Table 1, that complex molecules lead to compressions and expansions characterised by high optimal pressure ratios, high molar volume ratios and, thus, poorer turbomachine efficiencies.

Considering the expansion or the compression of different fluids characterised by equal temperature profiles, it is possible to state that turbomachines specific work, w, results to be proportional to the mass heat capacity of the fluid, cp, and, thus, to its molecular complexity, γ, and molar weight, M:

$$w \propto \overline{c}\_p = \frac{\mathcal{V}}{\mathcal{V}^{-1}M} \tag{2}$$

The axial size of turbomachines is influenced by the molecular complexity and the molar mass: as the maximum enthalpy change per stage of a turbomachine is limited, the higher the


Table 1. Main characteristics of working fluids characterised by different molecular weight and molecular complexity.

specific heat capacity resulting from more complex or lighter molecules, the higher the number of stages of the turbomachine.

Moreover, it is possible to show that the radial dimensions of turbomachines depend only on the molecular complexity, the pressure and the temperature of the fluid. In particular, and contrary to axial extension, cross-sectional areas are minimised by the use of complex molecules that would reduce the volumetric flow of the stream.

To reduce the design complexity of turbomachines and to increase their efficiency (limiting the number of stages, the variation of volumetric flow and avoiding the occurrence of supersonic conditions), it is thus preferable to adopt simple and heavy fluids. The higher radial dimensions of turbomachines that would result from the use of simple molecules could be reduced by an increasing fluid pressure.

It is worth highlighting that the molecular complexity determines, in particular, the inclination of saturation vapour curve in the T-s diagram: the increase in temperature or in pressure results, respectively, in an increase or a decrease in saturated-vapour entropy. Depending on whether the influence of temperature or that of pressure overrides, the saturated-vapour curve slopes positively or negatively in the T-s plane (Figure 2(a) and (c)). In the case of (c), which concerns complex molecules, the expansion of saturated-vapour fluids in saturated Rankine cycles favourably occurs in the superheated vapour phase (the so-called 'dry' expansion), avoiding the inefficient expansion of the fluid in the two-phase region. Herein, a simple approach to allow for distinguishing between these two families of fluids is presented.

Assuming, for simplicity, that the vapour behaves as a perfect gas, it is possible to write that

$$ds\_{\rm gas}^{\rm sat} = c\_p^\bullet \frac{dT}{T} \cdot R \frac{dP^{\rm sat}}{P^{\rm sat}} \tag{3}$$

Considering the Antoine equation for saturation pressure, ln(Psat) = A - B/T, and its differential form:

$$\frac{dP^{sat}}{P^{sat}} = \frac{B}{T^2}dT\tag{4}$$

and substituting it into Eq. (3), it is possible to deduce

$$\frac{d\mathbf{s}\_{gas}^{sat}}{dT} = \frac{1}{T} \left( \mathbf{c}\_p^\bullet \cdot \mathbf{R} \, \frac{B}{T} \right) \tag{5}$$

or, defining B\* = B/Tc,

conclusion is not universally correct. For example, carbon dioxide is characterised by a higher molecular complexity and a lower molecular weight with respect to krypton. This is shown in Table 1. The same table allows another similar comparison, between perfluorohexane and

Molecular complexity influences the design and performance of a thermodynamic cycle, in such a way that complexity affects the degree of freedom of the molecule itself and, thus, the change in the thermodynamic properties of the fluid in response to energy interactions with the environment. In particular, a higher molecular complexity entails a lower adiabatic index, γ = cp/cv (see Table 1) and, thus, a weaker temperature modification of the fluid, at a given pressure ratio, and a more important pressure change, at a fixed temperature ratio. Along an isentropic compression or expansion of molecules in the ideal gas state, temperature and

γ-1

By way of example, Table 1 reports the temperature (or molar volume) and pressure changes, for each considered fluid, resulting from, respectively, pressure and temperature modifications. It can be observed, from Table 1, that complex molecules lead to compressions and expansions characterised by high optimal pressure ratios, high molar volume ratios and, thus,

Considering the expansion or the compression of different fluids characterised by equal temperature profiles, it is possible to state that turbomachines specific work, w, results to be proportional to the mass heat capacity of the fluid, cp, and, thus, to its molecular complexity,

<sup>w</sup> <sup>∝</sup>cp <sup>¼</sup> <sup>γ</sup>

Fluid He Kr CO2 CH4 C6F14 C11H24O

M (g/mol) 3.02 83.8 44.01 16.05 338.04 172.31

v,T¼298:15 K=R(�) 1.500 1.500 3.479 3.291 30.474 31.009

p,T¼298:15 K=<sup>R</sup> (�) 2.500 2.500 4.479 4.291 31.474 32.009

<sup>θ</sup>• <sup>¼</sup> <sup>γ</sup>• ð Þ -<sup>1</sup> <sup>=</sup>γ• 0.400 0.400 0.223 0.233 0.032 0.031 T2=T1; v2=v1 (with P2=P1 ¼ 4) 1.74; 0.44 1.74; 0.44 1.48; 0.37 1.41; 0.35 1.06; 0.26 1.06; 0.26 P2=P1 (with T2=T1 ¼ 1:25) 1.75 1.75 2.72 2.61 1122.28 1264.85

<sup>v</sup> 1.667 1.667 1.287 1.304 1.033 1.032

Table 1. Main characteristics of working fluids characterised by different molecular weight and molecular complexity.

The axial size of turbomachines is influenced by the molecular complexity and the molar mass: as the maximum enthalpy change per stage of a turbomachine is limited, the higher the

γ-1 R

Helium Krypton Carbon dioxide Methane Perfluorohexane 1-Undecanol

<sup>γ</sup> ¼ ð Þ v2=v1

<sup>1</sup>-<sup>γ</sup> (1)

<sup>M</sup> (2)

1-undecanol, the former being heavier and molecularly simpler than the latter.

T2=T1 ¼ ð Þ P2=P1

pressure ratios are related by means of the molecular complexity:

poorer turbomachine efficiencies.

6 Organic Rankine Cycle Technology for Heat Recovery

γ, and molar weight, M:

c•

c•

<sup>γ</sup>• <sup>¼</sup> <sup>c</sup>• <sup>p</sup> =c•

$$\frac{d\mathbf{s}\_{gas}^{sat}}{dT} = \frac{1}{T} \left( \mathbf{c}\_p^\bullet \text{-} \mathbf{R} \frac{B^\*}{T\_r} \right) \tag{6}$$

Equation (6) shows that when the combination of c• <sup>p</sup> and of Tr of the fluid is such that c• <sup>p</sup> <sup>¼</sup> <sup>R</sup> � <sup>B</sup><sup>∗</sup>=Tr, the saturation vapour curve is vertical in the plane T-s. Practically, it is possible to observe the existence of an average value for B\* common to most of fluids. Considering Antoine equation in the reduced variables, ln Psat r <sup>¼</sup> <sup>A</sup><sup>∗</sup> - B<sup>∗</sup>=Tr, and letting it pass through the critical point (Pr = 1, Tr = 1), it follows that A\* = B\* ; optimising B\* for different fluids in the reduced temperature domain Tr ∈ (0.75; 1), it is possible to observe that, for most common fluids, B\* ∿ 7 (see Figure 1).

A very rough criterion to distinguish between fluids characterised by positively or negatively sloped saturation vapour curves consists in considering the saturation vapour curve in the temperature range identified by Tr ∈ [0.65; 0.85] and comparing the perfect gas heat capacity of the fluid, c• <sup>p</sup> , calculated at the intermediate temperature defined by 0.75�Tc, with the two limits <sup>R</sup>�B\* /Tr = 70 J/mol/K (with B\* = 7 and Tr = 0.85) and <sup>R</sup>�B\* /Tr = 90 J/mol/K (with B\* = 7 and Tr = 0.65): fluids having a c• <sup>p</sup> (Tr = 0.75) > 90 J/mol/K are typically characterised by a retrograde saturation vapour curve, while fluids having c• <sup>p</sup> (Tr = 0.75) < 70 J/mol/K most likely have a non-retrograde saturation vapour curve. Fluids with c• <sup>p</sup> (Tr = 0.75) ∈ [70 J/mol/K; 90 J/mol/K] have, in general, quasi-isentropic saturation vapour curves (Figure 2(b)).

Beside the positive effect that the use of complex molecules has on dry expansions, they also entail the convenient similar gradient of vapour and liquid isobars, in the T-s plane (see Figure 2). Complex fluids are thus particularly suitable to exploit variable temperature heat sources.

#### 2.1.2. Effect of fluid molecular complexity and mass on the performance and design of heat exchangers

The nature of the working fluid also affects the design of heat exchangers. Two aspects have to be considered in sizing heat exchangers: the capacity of the adopted fluid to exchange heat and the mechanical power consumed by compressors to enable the fluid flowing through the heat exchanger.

It is possible to show [4] that the most important parameter of an optimal heat transfer fluid is the molar mass, which should preferably be low (light molecule) to allow the maximisation of heat exchange coefficients. Heavy molecules would instead entail the adoption of heavy and expensive heat exchangers.

Figure 1. Parameter B\* which minimises, for 90 considered fluids, the objective function P <sup>i</sup> Psat <sup>r</sup> ð Þ Ti - exp B<sup>∗</sup> - <sup>B</sup><sup>∗</sup> ð Þ <sup>=</sup>Tr,i � �<sup>2</sup> . Critical properties and saturation pressures, Psat <sup>r</sup> ð Þ Ti , have been extracted from the NIST standard reference database 23, Refprop 9.1.

Figure 2. T-s diagrams of water (a) with isobars 5–35 MPa, R11, (b) and toluene (c) with isobars 0.5–6.5 MPa. For the sake of completeness, the red arrows indicate an isentropic expansion for the three considered fluids, from their saturated-

Inert and Reactive Working Fluids for Closed Power Cycles: Present Knowledge, Applications and Open Researches

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9

vapour state.

Inert and Reactive Working Fluids for Closed Power Cycles: Present Knowledge, Applications and Open Researches http://dx.doi.org/10.5772/intechopen.79290 9

critical point (Pr = 1, Tr = 1), it follows that A\* = B\*

fluids, B\* ∿ 7 (see Figure 1).

8 Organic Rankine Cycle Technology for Heat Recovery

/Tr = 70 J/mol/K (with B\*

vapour curve, while fluids having c•

saturation vapour curve. Fluids with c•

quasi-isentropic saturation vapour curves (Figure 2(b)).

the fluid, c•

fluids having a c•

<sup>R</sup>�B\*

sources.

exchanger.

Refprop 9.1.

expensive heat exchangers.

Critical properties and saturation pressures, Psat

reduced temperature domain Tr ∈ (0.75; 1), it is possible to observe that, for most common

A very rough criterion to distinguish between fluids characterised by positively or negatively sloped saturation vapour curves consists in considering the saturation vapour curve in the temperature range identified by Tr ∈ [0.65; 0.85] and comparing the perfect gas heat capacity of

Beside the positive effect that the use of complex molecules has on dry expansions, they also entail the convenient similar gradient of vapour and liquid isobars, in the T-s plane (see Figure 2). Complex fluids are thus particularly suitable to exploit variable temperature heat

2.1.2. Effect of fluid molecular complexity and mass on the performance and design of heat exchangers The nature of the working fluid also affects the design of heat exchangers. Two aspects have to be considered in sizing heat exchangers: the capacity of the adopted fluid to exchange heat and the mechanical power consumed by compressors to enable the fluid flowing through the heat

It is possible to show [4] that the most important parameter of an optimal heat transfer fluid is the molar mass, which should preferably be low (light molecule) to allow the maximisation of heat exchange coefficients. Heavy molecules would instead entail the adoption of heavy and

Figure 1. Parameter B\* which minimises, for 90 considered fluids, the objective function P

= 7 and Tr = 0.85) and <sup>R</sup>�B\*

<sup>p</sup> , calculated at the intermediate temperature defined by 0.75�Tc, with the two limits

<sup>p</sup> (Tr = 0.75) > 90 J/mol/K are typically characterised by a retrograde saturation

; optimising B\* for different fluids in the

= 7 and Tr = 0.65):

/Tr = 90 J/mol/K (with B\*

<sup>p</sup> (Tr = 0.75) < 70 J/mol/K most likely have a non-retrograde

<sup>p</sup> (Tr = 0.75) ∈ [70 J/mol/K; 90 J/mol/K] have, in general,

<sup>i</sup> Psat

<sup>r</sup> ð Þ Ti , have been extracted from the NIST standard reference database 23,

<sup>r</sup> ð Þ Ti - exp B<sup>∗</sup> - <sup>B</sup><sup>∗</sup> ð Þ <sup>=</sup>Tr,i � �<sup>2</sup>

.

Figure 2. T-s diagrams of water (a) with isobars 5–35 MPa, R11, (b) and toluene (c) with isobars 0.5–6.5 MPa. For the sake of completeness, the red arrows indicate an isentropic expansion for the three considered fluids, from their saturatedvapour state.

Moreover, the low optimal compression ratios resulting from the use of simple molecules allow the reduction of the pressure levels of the fluid crossing the heat exchangers and, thus, of their sizes and investment costs.

2.2.2. CO2 condensation cycles

2.2.3. Major scientific obstacles

2.2.3.1. Thermodynamics of mixtures

triple points and saturation properties.

the reliable use of multicomponent working fluids.

To exploit high-temperature heat sources (e.g. solar, nuclear and coal power plants) in the presence of low-temperature cooling sinks at less than 15–20 C, carbon dioxide is usually proposed as an optimal working fluid in transcritical power cycles because of its critical properties, natural availability, corrosion-neutral properties and simpler turbomachinery

Inert and Reactive Working Fluids for Closed Power Cycles: Present Knowledge, Applications and Open Researches

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11

However, when the available cooling source is, for example, air at ambient temperature (e.g. concentrated-solar-power technologies located in desert areas), CO2 transcritical cycles cannot be used since the low critical temperature of pure CO2, 31 C, prevents CO2 from condensation when air temperature is higher than 30 C. To beneficiate from the use of transcritical cycles, instead of the more compression power consumer Brayton ones, it is useful to increase the critical temperature of pure CO2 to 40–50 C by adding a small quantity of a properly selected second component (inorganic compounds such as TiCl4, TiBr4, SnCl4, SnBr4, VCl4, VBr4, GeCl4, fluorocarbons such as C6F14, etc.) to carbon dioxide [5–7]. In [5], it is shown how the critical temperature of the system may be increased by adding a small molar amount of C6F14 or TiCl4 to CO2. Similarly, the increase of the critical point of fluids allowed by the use of mixtures could also enable the more efficient use of condensing cycles instead of supercritical ones in very low-temperature applications. A typical example is represented by power cycles which reject their thermal heat into a stream of liquefied natural gas (cool source of the cycle), in order to convert it from liquid to vapour phase, from ambient temperature to 150 C [8]. Currently, the use of particularly efficient pure fluids (e.g. nitrogen, argon, oxygen), which are fluids which critical temperature is lower than the minimum temperature achieved by the cycle, has been mainly proposed. Mixing one of these low critical temperature components with a small amount of a high critical temperature one (e.g. krypton) could allow the improvement of an increase of the critical temperature of the fluid and

design compared to helium Brayton cycles and water Rankine cycles.

thus the lower-power consuming compression of a liquid instead of a gas.

Nowadays, the scale of the deployment of mixtures does not yet reflect the numerousness of

Despite the resources allocated in this research domain over the past years, this research topic still encounters some major scientific obstacles, described in the following sections 2.2.3.1– 2.2.3.3, which feed the uncertainty surrounding the results of these studies and which limit

The design of multicomponent working fluids requires mixing pure fluids characterised by some very different thermodynamic properties, which are typically critical coordinates or

Mixing different pure fluids (which generally involves two species) may result in a multicomponent system which thermodynamic properties highly deviate from those of each

studies undertaken to evaluate the potential of using multicomponent working fluids.

#### 2.1.3. Further considerations

As mentioned in Section 2.1.1, usually complex fluids are heavy fluids and, vice versa, simple fluids are light fluids. It is thus not straightforward to select an optimal fluid even considering only guidelines reported in Sections 2.1.1.

According to conclusions of Sections 2.1.1 and 2.1.2, it is always convenient to use simple molecules, from the point of view of the design and performance of both turbomachines and heat exchangers. However, the opposite effect that the molar mass of the fluid has on heat exchangers and turbomachines implies the necessity of solving a techno-economical optimisation problem.

## 2.2. Inert mixtures

There exist applications (an ensemble of hot and cold thermal sources and thermodynamic cycles) in which restricting the search for a working fluid in the range of available pure fluids highly limits the efficiency of the energy system. It is for this reason that, with the increasing interest to exploit a wider variety of thermal sources (other than combustion sources), in the 1990s, researchers started envisaging the possibility of using inert mixtures as working fluids, considering the selection of their composition as the most effective lever for the optimal design of closed thermodynamic cycles. The following two cases of closed power cycles represent blatant examples of the importance of utilising mixtures instead of pure working fluids to better optimise the heat exchange between working fluid and hot source and to reduce the power required for fluid compression.

#### 2.2.1. Organic Rankine cycles

Cycles based on organic components, also called ORC (organic Rankine cycles), are mostly operated in subcritical modes (Rankine cycles). In such configurations, the isothermal evaporation and condensation of a pure fluid is the most efficient solution when the heat source and the cold sink present an isothermal profile. However, heat sources and/or sinks are usually available to these cycles with a variable temperature profile: typical heat sources are flue gases discharged by internal combustion power cycles (i.e. Brayton, Diesel and Otto engines), gaseous biomass combustion products, geothermal fluids and liquid solar fluids; variable temperature sinks are usually represented by liquid water heated for cogeneration purposes and/or cooling air used in the condenser.

In the case of variable temperature heat sources, the flexible adjustment of the composition of a zeotropic working fluid could allow the thermodynamically optimal matching between the variable temperature profile of the working fluid, characterised by a temperature glide, and the one of the thermal sources.

## 2.2.2. CO2 condensation cycles

Moreover, the low optimal compression ratios resulting from the use of simple molecules allow the reduction of the pressure levels of the fluid crossing the heat exchangers and, thus, of

As mentioned in Section 2.1.1, usually complex fluids are heavy fluids and, vice versa, simple fluids are light fluids. It is thus not straightforward to select an optimal fluid even considering

According to conclusions of Sections 2.1.1 and 2.1.2, it is always convenient to use simple molecules, from the point of view of the design and performance of both turbomachines and heat exchangers. However, the opposite effect that the molar mass of the fluid has on heat exchangers and turbomachines implies the necessity of solving a techno-economical optimisa-

There exist applications (an ensemble of hot and cold thermal sources and thermodynamic cycles) in which restricting the search for a working fluid in the range of available pure fluids highly limits the efficiency of the energy system. It is for this reason that, with the increasing interest to exploit a wider variety of thermal sources (other than combustion sources), in the 1990s, researchers started envisaging the possibility of using inert mixtures as working fluids, considering the selection of their composition as the most effective lever for the optimal design of closed thermodynamic cycles. The following two cases of closed power cycles represent blatant examples of the importance of utilising mixtures instead of pure working fluids to better optimise the heat exchange between working fluid and hot source and to reduce the

Cycles based on organic components, also called ORC (organic Rankine cycles), are mostly operated in subcritical modes (Rankine cycles). In such configurations, the isothermal evaporation and condensation of a pure fluid is the most efficient solution when the heat source and the cold sink present an isothermal profile. However, heat sources and/or sinks are usually available to these cycles with a variable temperature profile: typical heat sources are flue gases discharged by internal combustion power cycles (i.e. Brayton, Diesel and Otto engines), gaseous biomass combustion products, geothermal fluids and liquid solar fluids; variable temperature sinks are usually represented by liquid water heated for cogeneration purposes and/or

In the case of variable temperature heat sources, the flexible adjustment of the composition of a zeotropic working fluid could allow the thermodynamically optimal matching between the variable temperature profile of the working fluid, characterised by a temperature glide, and

their sizes and investment costs.

10 Organic Rankine Cycle Technology for Heat Recovery

only guidelines reported in Sections 2.1.1.

power required for fluid compression.

2.2.1. Organic Rankine cycles

cooling air used in the condenser.

the one of the thermal sources.

2.1.3. Further considerations

tion problem.

2.2. Inert mixtures

To exploit high-temperature heat sources (e.g. solar, nuclear and coal power plants) in the presence of low-temperature cooling sinks at less than 15–20 C, carbon dioxide is usually proposed as an optimal working fluid in transcritical power cycles because of its critical properties, natural availability, corrosion-neutral properties and simpler turbomachinery design compared to helium Brayton cycles and water Rankine cycles.

However, when the available cooling source is, for example, air at ambient temperature (e.g. concentrated-solar-power technologies located in desert areas), CO2 transcritical cycles cannot be used since the low critical temperature of pure CO2, 31 C, prevents CO2 from condensation when air temperature is higher than 30 C. To beneficiate from the use of transcritical cycles, instead of the more compression power consumer Brayton ones, it is useful to increase the critical temperature of pure CO2 to 40–50 C by adding a small quantity of a properly selected second component (inorganic compounds such as TiCl4, TiBr4, SnCl4, SnBr4, VCl4, VBr4, GeCl4, fluorocarbons such as C6F14, etc.) to carbon dioxide [5–7]. In [5], it is shown how the critical temperature of the system may be increased by adding a small molar amount of C6F14 or TiCl4 to CO2.

Similarly, the increase of the critical point of fluids allowed by the use of mixtures could also enable the more efficient use of condensing cycles instead of supercritical ones in very low-temperature applications. A typical example is represented by power cycles which reject their thermal heat into a stream of liquefied natural gas (cool source of the cycle), in order to convert it from liquid to vapour phase, from ambient temperature to 150 C [8]. Currently, the use of particularly efficient pure fluids (e.g. nitrogen, argon, oxygen), which are fluids which critical temperature is lower than the minimum temperature achieved by the cycle, has been mainly proposed. Mixing one of these low critical temperature components with a small amount of a high critical temperature one (e.g. krypton) could allow the improvement of an increase of the critical temperature of the fluid and thus the lower-power consuming compression of a liquid instead of a gas.

#### 2.2.3. Major scientific obstacles

Nowadays, the scale of the deployment of mixtures does not yet reflect the numerousness of studies undertaken to evaluate the potential of using multicomponent working fluids.

Despite the resources allocated in this research domain over the past years, this research topic still encounters some major scientific obstacles, described in the following sections 2.2.3.1– 2.2.3.3, which feed the uncertainty surrounding the results of these studies and which limit the reliable use of multicomponent working fluids.

#### 2.2.3.1. Thermodynamics of mixtures

The design of multicomponent working fluids requires mixing pure fluids characterised by some very different thermodynamic properties, which are typically critical coordinates or triple points and saturation properties.

Mixing different pure fluids (which generally involves two species) may result in a multicomponent system which thermodynamic properties highly deviate from those of each pure component that forms the mixture. Such a deviation quantifies the level of non-ideality of the mixture (i.e. the importance of molecular interactions) and, thus, the difficulty in modelling its thermodynamic properties. An extreme typical example is represented by binary mixtures of type III (according to the classification of van Konynenburg and Scott) which present a specific composition range for which critical pressure achieves infinitely high values [5, 9].

power or, even worse, the occurrence of serious faults in fundamental components, such as turbines or heat exchangers. Moreover, as a general rule, the greater the thermal stability, the greater the maximum temperature at which the fluid can be used and the better the perfor-

Inert and Reactive Working Fluids for Closed Power Cycles: Present Knowledge, Applications and Open Researches

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13

Different approaches have been proposed so far to assess the thermal stability of pure fluids [17]. However, all experimental laboratories that investigate the thermal stability of fluids only focus on pure fluids, and, at present, an experimental technology being able to test the thermal

Researches undertaken during the last years on working fluids have ignored the promising results published by a dozen scientists in the years 1960–1990 which reversibly proposed reactive working fluids for mainly military, spatial and power production applications.

Over that period, four reactive systems (P4 ⇄ 2P2, Al2Cl6 ⇄ 2AlCl3, 2NOCl ⇄ 2NO + Cl2, N2O4 ⇄ 2NO2 ⇄ 2NO + O2) and two generalised reacting schemes (A2 ⇄ 2A; 2A ⇄ 2B + C) have been considered. Preliminary results obtained in these studies have shown that the utilisation of certain reactive fluids (N2O4, NOCl) rather than pure fluids and inert mixtures can lead to the increase of the conversion efficiency of power cycles of more than 10 percentage points [18–20]. In particular, it has been observed [18, 19, 21–24] that such an improvement follows from the specific evolution of the equilibrium composition of the reactive fluid and from the involvement of the energy of reaction; more precisely, authors attested that the presence of a proper chemical reaction leads to the increase of the power output, resulting from the augmented (1) energy released by the fluid during expansion and (2) energy exchanged in heat exchangers, thanks to the increased heat capacity and coefficients of heat exchange of reactive fluids.

It can be easily shown that the adoption of reactive fluids characterised by an exothermic reaction (ΔRH� < 0) along fluid expansion leads to an increased production of produced work (δw):

Despite the promising results revealed by these studies on reactive fluids, nonetheless obtained under simplification assumptions of perfect gas mixtures, researches on reactive working fluids have been abandoned at their preliminary stage of development. Many scientific obstacles, in fact, limited and still limit the applicative study of reactive working fluids.

ð7Þ

stability of mixtures is still absent according to authors' knowledge.

mance of the power plant.

2.3. Reactive fluids

The main issue affecting applied thermodynamics concerns the absence of a universal model (equation of state) which enables the reliable prediction of thermodynamic properties of mixtures characterised by a more or less pronounced level of non-ideality, without relying on experimental data. Still today, in fact, all the available equations of state contain parameters which need to be calibrated or, at least, validated over experimental data [10, 11].

However, the level of empiricism of thermodynamic models (mostly cubic and molecular-based equations of state) is decreasing over the years, meaning that parameters, which account for the incapability of the thermodynamic theory to model the reality, are more and more representative of physical quantities. For example, the modelisation of mixture properties by means of cubic equations of state requires the use of mixing rules to account for molecular interactions.

The application of more theoretically grounded mixing rules (e.g. the latest excess Helmholtz energy-based mixing rules instead of quadratic van der Waals mixing rules) enables the more accurate and reliable calculation of thermodynamic properties of mixtures [12, 13]. The same consideration also applies to molecular-based models [14, 15].

A typically recognised problem is the unreliable calculation of the critical region and twophase thermodynamic properties of multicomponent working fluids intended for closed power cycles, by currently available thermodynamic models and, also, simulation tools based on inappropriate available algorithms.

Furthermore, the uncertainty of measurement of some thermodynamic properties (e.g. specific heat capacities or vapour-liquid equilibrium properties of highly non-ideal mixtures) is still too high to enable their reliable use for calibrating and validating models.

#### 2.2.3.2. Transport properties of mixtures in two phase

The available scientific results on forced convection vaporisation or condensation of zeotropic mixtures are very limited. Many studies have analysed the performance of heat exchangers crossed by zeotropic fluids, without providing information on the local conditions in the evaporating streams [16].

The lack of information on transport properties actually feeds the overall uncertainty affecting heat exchangers sizing, on the one hand, and pressure drops evaluation, on the other.

#### 2.2.3.3. Thermal stability of mixtures

The thermal stability of a working fluid or a mixture represents its capability to preserve all its main physical properties unchanged because of the heating. This is a key parameter for the selected working fluid in a power plant, since even a partial decomposition may cause loss of power or, even worse, the occurrence of serious faults in fundamental components, such as turbines or heat exchangers. Moreover, as a general rule, the greater the thermal stability, the greater the maximum temperature at which the fluid can be used and the better the performance of the power plant.

Different approaches have been proposed so far to assess the thermal stability of pure fluids [17]. However, all experimental laboratories that investigate the thermal stability of fluids only focus on pure fluids, and, at present, an experimental technology being able to test the thermal stability of mixtures is still absent according to authors' knowledge.

#### 2.3. Reactive fluids

pure component that forms the mixture. Such a deviation quantifies the level of non-ideality of the mixture (i.e. the importance of molecular interactions) and, thus, the difficulty in modelling its thermodynamic properties. An extreme typical example is represented by binary mixtures of type III (according to the classification of van Konynenburg and Scott) which present a specific composition range for which critical pressure achieves infinitely high values [5, 9].

The main issue affecting applied thermodynamics concerns the absence of a universal model (equation of state) which enables the reliable prediction of thermodynamic properties of mixtures characterised by a more or less pronounced level of non-ideality, without relying on experimental data. Still today, in fact, all the available equations of state contain parameters

However, the level of empiricism of thermodynamic models (mostly cubic and molecular-based equations of state) is decreasing over the years, meaning that parameters, which account for the incapability of the thermodynamic theory to model the reality, are more and more representative of physical quantities. For example, the modelisation of mixture properties by means of cubic

The application of more theoretically grounded mixing rules (e.g. the latest excess Helmholtz energy-based mixing rules instead of quadratic van der Waals mixing rules) enables the more accurate and reliable calculation of thermodynamic properties of mixtures [12, 13]. The same

A typically recognised problem is the unreliable calculation of the critical region and twophase thermodynamic properties of multicomponent working fluids intended for closed power cycles, by currently available thermodynamic models and, also, simulation tools based

Furthermore, the uncertainty of measurement of some thermodynamic properties (e.g. specific heat capacities or vapour-liquid equilibrium properties of highly non-ideal mixtures) is still too

The available scientific results on forced convection vaporisation or condensation of zeotropic mixtures are very limited. Many studies have analysed the performance of heat exchangers crossed by zeotropic fluids, without providing information on the local conditions in the

The lack of information on transport properties actually feeds the overall uncertainty affecting

The thermal stability of a working fluid or a mixture represents its capability to preserve all its main physical properties unchanged because of the heating. This is a key parameter for the selected working fluid in a power plant, since even a partial decomposition may cause loss of

heat exchangers sizing, on the one hand, and pressure drops evaluation, on the other.

which need to be calibrated or, at least, validated over experimental data [10, 11].

equations of state requires the use of mixing rules to account for molecular interactions.

consideration also applies to molecular-based models [14, 15].

high to enable their reliable use for calibrating and validating models.

on inappropriate available algorithms.

12 Organic Rankine Cycle Technology for Heat Recovery

evaporating streams [16].

2.2.3.3. Thermal stability of mixtures

2.2.3.2. Transport properties of mixtures in two phase

Researches undertaken during the last years on working fluids have ignored the promising results published by a dozen scientists in the years 1960–1990 which reversibly proposed reactive working fluids for mainly military, spatial and power production applications.

Over that period, four reactive systems (P4 ⇄ 2P2, Al2Cl6 ⇄ 2AlCl3, 2NOCl ⇄ 2NO + Cl2, N2O4 ⇄ 2NO2 ⇄ 2NO + O2) and two generalised reacting schemes (A2 ⇄ 2A; 2A ⇄ 2B + C) have been considered. Preliminary results obtained in these studies have shown that the utilisation of certain reactive fluids (N2O4, NOCl) rather than pure fluids and inert mixtures can lead to the increase of the conversion efficiency of power cycles of more than 10 percentage points [18–20].

In particular, it has been observed [18, 19, 21–24] that such an improvement follows from the specific evolution of the equilibrium composition of the reactive fluid and from the involvement of the energy of reaction; more precisely, authors attested that the presence of a proper chemical reaction leads to the increase of the power output, resulting from the augmented (1) energy released by the fluid during expansion and (2) energy exchanged in heat exchangers, thanks to the increased heat capacity and coefficients of heat exchange of reactive fluids.

It can be easily shown that the adoption of reactive fluids characterised by an exothermic reaction (ΔRH� < 0) along fluid expansion leads to an increased production of produced work (δw):

$$\begin{aligned} \delta \boldsymbol{w}^{\leftarrow} \overset{\text{AdS}}{=} \mathop{\mathrm{d}\hbar}\_{\underset{\text{Perfect}}{\text{Perfect}}} &= \mathop{\mathrm{c}}\_{\underset{\text{igna}}{}} \mathop{\mathrm{d}T} + \left(\frac{\partial \hbar}{\partial P}\right)\_{\underset{\text{To}}{}} \mathop{\mathrm{d}P}\_{} + \Delta\_{\kappa} H^{\alpha} \frac{d\dot{\xi}}{\dot{\eta}\dot{\eta}} \\ &= \mathop{\mathrm{c}}\_{\underset{\text{e}}{}} \mathop{\mathrm{d}T}\_{} + \Delta\_{\kappa} H^{\alpha} \frac{d\dot{\xi}}{\dot{\eta}\dot{\eta}} \\ &\overset{\text{def}}{}\_{\underset{\text{supobian}}{}} \end{aligned} \tag{7}$$

Despite the promising results revealed by these studies on reactive fluids, nonetheless obtained under simplification assumptions of perfect gas mixtures, researches on reactive working fluids have been abandoned at their preliminary stage of development. Many scientific obstacles, in fact, limited and still limit the applicative study of reactive working fluids.

## 2.3.1. Major scientific obstacles

Knowledge gaps listed in Section 2.2.3, which regard the thermodynamics, transport properties and thermal stability of mixtures, clearly represent barriers for the deployment of reversible reactive working fluids too, as they are, by definition, mixtures. Moreover, the extensive analysis of the potentiality offered by the specific use of these fluids would also require addressing the specific lacks briefly described subsequently.

• definition of a predictive and universal thermodynamic model for mixtures;

cp, cv molar heat capacity at constant pressure and constant volume

• experimental and theoretical assessment of mixture thermal stability;

and design.

Acknowledgements

cation of this chapter.

Nomenclature

T temperature

h molar enthalpy s molar entropy

m\_ mass flow rate M molar weight

v molar volume

R universal gas constant

c critical property r reduced property

A, B, A\*, B\* parameters w specific work

Subscripts

ΔRH� enthalpy of reaction

ξ\_ rate of extent of reaction

P pressure

Symbols

• experimental and theoretical investigation of the transport properties of mixtures;

• comprehension of the effects that reactive fluid characteristics have on cycle performance

Inert and Reactive Working Fluids for Closed Power Cycles: Present Knowledge, Applications and Open Researches

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15

The authors wish to thank ASME IGTI ORC Power Systems—KCORC for funding the publi-

## 2.3.1.1. Thermodynamics of adiabatic expanding and compressing fluids, which undergo reversible and instantaneous reactions

So far, thermodynamic transformations of fluids in expanders and compressors have only been studied under the assumption of inert fluid. The preliminary researches on reactive fluids do not report any indication about the thermodynamic treatment of the expansion/compression of a reactive fluid.

Different from inert (iso-composition) gaseous adiabatic expansions, which are isentropic in the case of zero thermodynamic losses, reactive expanding fluids need to be modelled as a series of infinitesimal expansions, of pressure variation dP, each one subdivided into two transformations: (1) iso-composition adiabatic expansion, from pressure P to pressure P + dP; and (2) adiabatic isobar reaction, at the pressure P + dP.

No one theoretical reference has been found in the study that analyses this thermodynamic transformation.

#### 2.3.1.2. Theoretical comprehension of the dependence of cycle performance and design on the type of chemical reaction

There exist many types of chemical reactions which, in the direction of their spontaneous evolution, may be characterised by a fast or a slow kinetics, by an increasing or a decreasing number of moles and which may be exothermic or endothermic. The effect of the occurrence of a reaction during fluid expansion or compression, fluid heating or cooling depends on its characteristics, which can beneficiate or disadvantage the efficiency of the energy conversion process.

With the aim of expanding the research of optimal working fluids to reactive mixtures, it is necessary to preliminarily address these points.

## 3. Conclusion

This chapter aims to boost researches devoted to the comprehension of the impact on power cycles of the characteristics of their working fluid. To this end, the chapter presents the state of the art on pure and multicomponent inert and reactive working fluids, highlighting the major scientific obstacles that nowadays primarily need to be overcome in order to allow a thorough research of the best working fluid for each application of closed power cycles:


## Acknowledgements

The authors wish to thank ASME IGTI ORC Power Systems—KCORC for funding the publication of this chapter.

## Nomenclature

#### Symbols

2.3.1. Major scientific obstacles

14 Organic Rankine Cycle Technology for Heat Recovery

instantaneous reactions

a reactive fluid.

transformation.

chemical reaction

process.

3. Conclusion

addressing the specific lacks briefly described subsequently.

and (2) adiabatic isobar reaction, at the pressure P + dP.

necessary to preliminarily address these points.

Knowledge gaps listed in Section 2.2.3, which regard the thermodynamics, transport properties and thermal stability of mixtures, clearly represent barriers for the deployment of reversible reactive working fluids too, as they are, by definition, mixtures. Moreover, the extensive analysis of the potentiality offered by the specific use of these fluids would also require

2.3.1.1. Thermodynamics of adiabatic expanding and compressing fluids, which undergo reversible and

So far, thermodynamic transformations of fluids in expanders and compressors have only been studied under the assumption of inert fluid. The preliminary researches on reactive fluids do not report any indication about the thermodynamic treatment of the expansion/compression of

Different from inert (iso-composition) gaseous adiabatic expansions, which are isentropic in the case of zero thermodynamic losses, reactive expanding fluids need to be modelled as a series of infinitesimal expansions, of pressure variation dP, each one subdivided into two transformations: (1) iso-composition adiabatic expansion, from pressure P to pressure P + dP;

No one theoretical reference has been found in the study that analyses this thermodynamic

2.3.1.2. Theoretical comprehension of the dependence of cycle performance and design on the type of

There exist many types of chemical reactions which, in the direction of their spontaneous evolution, may be characterised by a fast or a slow kinetics, by an increasing or a decreasing number of moles and which may be exothermic or endothermic. The effect of the occurrence of a reaction during fluid expansion or compression, fluid heating or cooling depends on its characteristics, which can beneficiate or disadvantage the efficiency of the energy conversion

With the aim of expanding the research of optimal working fluids to reactive mixtures, it is

This chapter aims to boost researches devoted to the comprehension of the impact on power cycles of the characteristics of their working fluid. To this end, the chapter presents the state of the art on pure and multicomponent inert and reactive working fluids, highlighting the major scientific obstacles that nowadays primarily need to be overcome in order to allow a thorough

research of the best working fluid for each application of closed power cycles:


#### Subscripts


#### Superscripts


#### Accents

— specific mass property

## Author details

Silvia Lasala\*, Romain Privat and Jean-Noël Jaubert

Address all correspondence to: silvia.lasala@univ-lorraine.fr

Ecole Nationale Supérieure des Industries Chimiques, Laboratoire Réactions et Génie des Procédés, Université de Lorraine, Nancy, France

[8] Invernizzi CM, Iora P. The exploitation of the physical exergy of liquid natural gas by closed power thermodynamic cycles. An overview. Energy. 2016;105:2-15. Available from:

Inert and Reactive Working Fluids for Closed Power Cycles: Present Knowledge, Applications and Open Researches

http://dx.doi.org/10.5772/intechopen.79290

17

[9] Privat R, Jaubert J-N. Classification of global fluid-phase equilibrium behaviors in binary systems. Chemical Engineering Research and Design. 2013;91(10):1807-1839. Available

[10] Lasala S, Chiesa P, Privat R, Jaubert J-N. Optimizing thermodynamic models: The relevance of molar fraction uncertainties. Journal of Chemical & Engineering Data. 2017 Feb 9;

[11] Lasala S, Chiesa P, Privat R, Jaubert J-N. Modeling the thermodynamics of fluids treated by CO2 capture processes with Peng-Robinson + residual Helmholtz energy-based mixing rules. Industrial and Engineering Chemistry Research. 2017;56(8). Available from: http://

[12] Lasala S, Chiesa P, Privat R, Jaubert J-N. VLE properties of CO2–based binary systems containing N2, O2 and Ar: Experimental measurements and modelling results with advanced cubic equations of state. Fluid Phase Equilibria. 2016;428:18-31. Available from:

[13] Lasala S. Advanced Cubic Equations of State for Accurate Modelling of Fluid Mixtures.

[14] Economou IG. Statistical associating fluid theory: A successful model for the calculation of thermodynamic and phase equilibrium properties of complex fluid mixtures. Industrial and Engineering Chemistry Research. 2002;41(5):953-962. Available from: http://doi.org/

[15] Tan SP, Adidharma H, Radosz M. Recent advances and applications of statistical associating fluid theory. Industrial and Engineering Chemistry Research. 2008;47(21):8063-8082.

[16] Incropera FP, DeWitt DP, Bergman TL, Lavine AS. Fundamentals of Heat and Mass

[17] Invernizzi CM, Bonalumi D. 05 – Thermal stability of organic fluids for organic Rankine cycle systems. In: Organic Rankine Cycle (ORC) Power Systems. 2017. pp. 121-151. Avail-

[18] Stochl RJ. Potential Performance Improvemet Using a Reacting Gas (Nitrogen Tetroxide)

[19] Angelino G. Performance of N2O4 gas cycles for solar power applications. Proc Inst Mech Eng 1847–1982 (vols 1–196). 1979;193:313-320. Available from: https://doi.org/10.1243/

[20] Huang HM, Govind R. Use of dissociating gases in Brayton cycle space power systems. Industrial and Engineering Chemistry Research. 1988;27:803-810. Available from: https://

as the Working Fluid in a Closed Brayton Cycle - NASA TM-79322; 1979

Application to CO2 Capture Systems. Italy: Politecnico di Milano; 2016

62(2):825-832. Available from: http://doi.org/10.1021/acs.jced.6b00853

https://doi.org/10.1016/j.energy.2015.09.020

doi.org/10.1021/acs.iecr.6b04190

10.1021/ie0102201

https://doi.org/10.1016/j.fluid.2016.05.015

Available from: http://doi.org/10.1021/ie8008764

PIME\_PROC\_1979\_193\_033\_02

doi.org/10.1021/ie00077a015

Transfer. Vol. 6, Water. 2007. 997 p. ISBN: 978–0471457282

able from: http://doi.org/10.1016/B978-0-08-100510-1.00005-3

from: https://doi.org/10.1016/j.cherd.2013.06.026

## References


[8] Invernizzi CM, Iora P. The exploitation of the physical exergy of liquid natural gas by closed power thermodynamic cycles. An overview. Energy. 2016;105:2-15. Available from: https://doi.org/10.1016/j.energy.2015.09.020

Superscripts

Accents

Author details

References

100510-1.00001-6

09.125

• perfect gas property sat saturation property

16 Organic Rankine Cycle Technology for Heat Recovery

— specific mass property

Silvia Lasala\*, Romain Privat and Jean-Noël Jaubert

Procédés, Université de Lorraine, Nancy, France

from: https://doi.org/10.13182/NT06-A3734

lavoro in cicli termodinamici. 2017

Address all correspondence to: silvia.lasala@univ-lorraine.fr

Ecole Nationale Supérieure des Industries Chimiques, Laboratoire Réactions et Génie des

[1] Astolfi M, Alfani D, Lasala S, Macchi E. Comparison between ORC and CO2 power systems for the exploitation of low-medium temperature heat sources. Energy. 2018

[2] Macchi E. 1 – Theoretical basis of the organic Rankine cycle. In: Organic Rankine Cycle (ORC) Power Systems. 2017. pp. 3-24. Available from: https://doi.org/10.1016/B978-0-08-

[3] Dostal V, Hejzlar P, Driscoll MJ. The supercritical carbon dioxide power cycle: Comparison to other advanced power cycles. Nuclear Technology. 2006;154(3):283-301. Available

[4] El-Wakil MM. Nuclear Power Engineering. New York, USA: Mc Graw-Hill; 1962. 556 p.

[5] Lasala S, Bonalumi D, Macchi E, Privat R, Jaubert JN. The design of CO2-based working fluids for high-temperature heat source power cycles. In: Energy Procedia. 2017. pp. 947-

[6] Lasala S, Invernizzi C, Iora P, Chiesa P, Macchi E. Thermal stability analysis of Perfluorohexane. Energy Procedia. 2015;75. Available from: https://doi.org/10.1016/j.egypro.2017.

[7] Bonalumi D, Macchi E, Lasala S. Miscele a base di anidride carbonica come fluido di

954. Available from: https://doi.org/10.1016/j.egypro.2017.09.125


[21] Huang SH, Radosz M. Equation of state for small, large, polydisperse and associating molecules. Industrial and Engineering Chemistry Research. 1990;29:2284-2294. Available from: http://doi.org/10.1021/ie00107a014

**Chapter 2**

Provisional chapter

**Effects of the Working Fluid Charge in Organic Rankine**

DOI: 10.5772/intechopen.78026

It is well known that organic Rankine cycle (ORC) power systems often operate in conditions differing from the nominal design point due to variations of the heat source and heat sink conditions. Similar to a vapor compression cycle, the system operation (e.g., subcooling level, pump cavitation) and performance (e.g., heat exchanger effectiveness) of an ORC are affected by the working fluid charge. This chapter presents a discussion of the effects of the charge inventory in ORC systems. In particular, both numerical and experimental aspects are presented. The importance of properly predicting the total amount of working fluid charge for optimizing design and off-design conditions is highlighted. Furthermore, an overview on state-of-the-art modeling approaches is also

Keywords: off-design, working fluid charge, modeling, subcooling, charge-sensitive

Organic Rankine cycle (ORC) systems are widely acknowledged as one of the most suitable technologies for harvesting medium- to low-grade heat sources (i.e., below 300�C) from both renewable sources (e.g., geothermal and solar) and waste heat [1]. Nowadays, the total power capacity installed worldwide is estimated to be above 2.7 GWe, as reported by Tartière et al. in the ORC World Map [2, 3]. Furthermore, there has been a continuous increase in research activity related to ORC-based power systems over the last decades that has demonstrated the

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

value of this technology and its potential to improve energy sustainability [4].

Effects of the Working Fluid Charge in Organic Rankine

**Cycle Power Systems: Numerical and Experimental**

Cycle Power Systems: Numerical and Experimental

Davide Ziviani, Rémi Dickes, Vincent Lemort,

Davide Ziviani, Rémi Dickes, Vincent Lemort,

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

James E. Braun and Eckhard A. Groll

James E. Braun and Eckhard A. Groll

http://dx.doi.org/10.5772/intechopen.78026

Abstract

presented.

1. Introduction

**Analyses**

Analyses


#### **Effects of the Working Fluid Charge in Organic Rankine Cycle Power Systems: Numerical and Experimental Analyses** Effects of the Working Fluid Charge in Organic Rankine Cycle Power Systems: Numerical and Experimental Analyses

DOI: 10.5772/intechopen.78026

Davide Ziviani, Rémi Dickes, Vincent Lemort, James E. Braun and Eckhard A. Groll Davide Ziviani, Rémi Dickes, Vincent Lemort, James E. Braun and Eckhard A. Groll

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.78026

#### Abstract

[21] Huang SH, Radosz M. Equation of state for small, large, polydisperse and associating molecules. Industrial and Engineering Chemistry Research. 1990;29:2284-2294. Available

[22] Cheung H. Dissociating gas as a working fluid for space plant. Energy Convers. 1968;8:

[23] Hasah MZ, Martin RC. Use of dissociating gases as primary coolants and working fluids in power cycles for fusion reactors. IASMiRT; 1989. Available from: https://repository.lib. ncsu.edu/bitstream/handle/1840.20/29799/DC\_250636.pdf?sequence=1&isAllowed=y [24] Jacobs TA, Lloyd JR. The influence of the equilibrium dissociation of a diatomic gas on Brayton-cycle performance. Journal of Applied Mechanics. 1963:288-290. Available from:

125-128. Available from: https://doi.org/10.1016/0013-7480(68)90114-9

from: http://doi.org/10.1021/ie00107a014

18 Organic Rankine Cycle Technology for Heat Recovery

https://doi.org/10.1115/1.3636527

It is well known that organic Rankine cycle (ORC) power systems often operate in conditions differing from the nominal design point due to variations of the heat source and heat sink conditions. Similar to a vapor compression cycle, the system operation (e.g., subcooling level, pump cavitation) and performance (e.g., heat exchanger effectiveness) of an ORC are affected by the working fluid charge. This chapter presents a discussion of the effects of the charge inventory in ORC systems. In particular, both numerical and experimental aspects are presented. The importance of properly predicting the total amount of working fluid charge for optimizing design and off-design conditions is highlighted. Furthermore, an overview on state-of-the-art modeling approaches is also presented.

Keywords: off-design, working fluid charge, modeling, subcooling, charge-sensitive

## 1. Introduction

Organic Rankine cycle (ORC) systems are widely acknowledged as one of the most suitable technologies for harvesting medium- to low-grade heat sources (i.e., below 300�C) from both renewable sources (e.g., geothermal and solar) and waste heat [1]. Nowadays, the total power capacity installed worldwide is estimated to be above 2.7 GWe, as reported by Tartière et al. in the ORC World Map [2, 3]. Furthermore, there has been a continuous increase in research activity related to ORC-based power systems over the last decades that has demonstrated the value of this technology and its potential to improve energy sustainability [4].

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Generally, ORCs are designed and optimized for steady-state operating conditions, unless mobile applications are considered. However, in the vast majority of stationary applications (e.g., solar thermal power, geothermal, waste heat recovery, and combined heat and power), the heat source and heat sink conditions are subjected to fluctuations and the ORC systems often operate at part-load or off-design conditions. To this end, numerical and experimental studies on off-design ORC performance have been published in the scientific literature, as outlined by Dickes et al. [5]. Similar to vapor compression systems, ORC performance is sensitive to working fluid charge and an incorrect charge level affects the system performance, especially under part-load conditions. Yet, very limited work can be found on the impact of working fluid charge on off-design operations. In fact, besides the research conducted by the Authors [6–8], only two additional studies could be found in the literature. Liu et al. [9] discussed the effect of different working fluid charge masses on the system performance. Experimental and numerical analyses were carried out to identify the optimal working fluid charge. Pan et al. [10] analyzed the impact of the working fluid charge on the length distribution of the different zones in the heat exchangers under several operating conditions. Furthermore, different void fraction models and heat transfer correlations were compared to assess their impact on the working fluid mass estimations in the heat exchangers.

The present chapter discusses the relationship between working fluid charge and performance in ORC systems under different operating conditions. Furthermore, the fundamentals of deterministic numerical methods to account for working fluid charge in ORC simulations are also described.

of the unit. The costs associated with the working fluid and possible working fluid losses due to leaks can be significant, especially in large-scale systems (up to 10% of the plant cost) [12]. With respect to the system behavior, when the operating conditions shift from design to offdesign, the working fluid charge migrates within the system, altering the transition between single-to two-phase heat transfer regimes inside the heat exchangers. If the system is overcharged, typically the length (or, equivalently, the spatial fraction) of the subcooled zone in the evaporator increases, reducing both the capacity and degree of superheating. However, if the system is under-charged, one of the drawbacks is the decrease of subcooling at the condenser outlet, which may cause the pump to cavitate [13]. Additionally, a liquid receiver can be installed before the pump, as shown in Figure 1, in order to compensate for charge migration during off-design conditions, especially in large scale ORC systems. Nevertheless, a non-

Figure 1. General schematic of a regenerative organic Rankine cycle system. An independent lubricant oil loop is also

Effects of the Working Fluid Charge in Organic Rankine Cycle Power Systems: Numerical and Experimental…

http://dx.doi.org/10.5772/intechopen.78026

21

The estimation of the optimum charge level is particularly challenging when additional aspects of the normal ORC operation are considered. In particular, lubricant oil may be pre-mixed with the working fluid to ensure the correct functioning of positive displacement expanders. In other cases, oil-separators are utilized to separate the working fluid from the lubricant oil at the expander outlet. However, oil entrainment in the vapor and oil solubility affect the distribution of charge in the system. Furthermore, non-condensable gases can also be present inside the system, which can impact the operation of the ORCs by altering the condensing pressure [14]. Based on the aforementioned reasoning, appropriate numerical methodologies are required to predict the performance of the system and to account for the total working fluid charge in a deterministic way such that the system model resembles the actual behavior of the system. Experimental results are also necessary to validate such numerical methods and to conduct additional analyses. Therefore, in the following sections, the state-of-the-art numerical methods utilized to simulate ORC systems are described and their limitations are also highlighted.

proper charge level may completely empty or flood the liquid receiver.

included for completeness. Typical location of the sensors is also shown.

## 2. Importance of working fluid charge in ORC systems

A general sub-critical ORC with an internal heat exchanger (or regenerator), as shown in Figure 1, is considered as an example to understand the effect of working fluid charge. Although this chapter focuses on sub-critical ORC systems, the principles and the methodologies discussed hereafter can be extended to transcritical cycles and other cycle configurations [11]. By referring to Figure 1, the system consists of three heat exchangers (e.g., brazed plate heat exchangers), a pump (either centrifugal or volumetric type), a positive displacement expander (e.g., scroll type), a liquid receiver (or buffer tank), and line sets (or pipelines) between each component. Depending on the type of expander (e.g., single- and twin-screw, swash plate, or scroll), a dedicated oil-injection loop with an additional pump may be present in the system (see Figure 1). An oil separator is typically installed after the expander to avoid accumulation of the lubricant oil inside the heat exchangers, where hot spots may occur.

The operation of a sub-critical ORC encompasses several aspects that are common to refrigeration systems, such as the control of the subcooling at the condenser outlet and the degree of superheating at the evaporator outlet, single- and two-phase heat transfer in the heat exchangers, as well as working fluid leaks. The amount of working fluid charged into the system has a direct effect on the performance, the flexibility, as well as on the operational costs Effects of the Working Fluid Charge in Organic Rankine Cycle Power Systems: Numerical and Experimental… http://dx.doi.org/10.5772/intechopen.78026 21

Generally, ORCs are designed and optimized for steady-state operating conditions, unless mobile applications are considered. However, in the vast majority of stationary applications (e.g., solar thermal power, geothermal, waste heat recovery, and combined heat and power), the heat source and heat sink conditions are subjected to fluctuations and the ORC systems often operate at part-load or off-design conditions. To this end, numerical and experimental studies on off-design ORC performance have been published in the scientific literature, as outlined by Dickes et al. [5]. Similar to vapor compression systems, ORC performance is sensitive to working fluid charge and an incorrect charge level affects the system performance, especially under part-load conditions. Yet, very limited work can be found on the impact of working fluid charge on off-design operations. In fact, besides the research conducted by the Authors [6–8], only two additional studies could be found in the literature. Liu et al. [9] discussed the effect of different working fluid charge masses on the system performance. Experimental and numerical analyses were carried out to identify the optimal working fluid charge. Pan et al. [10] analyzed the impact of the working fluid charge on the length distribution of the different zones in the heat exchangers under several operating conditions. Furthermore, different void fraction models and heat transfer correlations were compared to assess

their impact on the working fluid mass estimations in the heat exchangers.

2. Importance of working fluid charge in ORC systems

lubricant oil inside the heat exchangers, where hot spots may occur.

described.

20 Organic Rankine Cycle Technology for Heat Recovery

The present chapter discusses the relationship between working fluid charge and performance in ORC systems under different operating conditions. Furthermore, the fundamentals of deterministic numerical methods to account for working fluid charge in ORC simulations are also

A general sub-critical ORC with an internal heat exchanger (or regenerator), as shown in Figure 1, is considered as an example to understand the effect of working fluid charge. Although this chapter focuses on sub-critical ORC systems, the principles and the methodologies discussed hereafter can be extended to transcritical cycles and other cycle configurations [11]. By referring to Figure 1, the system consists of three heat exchangers (e.g., brazed plate heat exchangers), a pump (either centrifugal or volumetric type), a positive displacement expander (e.g., scroll type), a liquid receiver (or buffer tank), and line sets (or pipelines) between each component. Depending on the type of expander (e.g., single- and twin-screw, swash plate, or scroll), a dedicated oil-injection loop with an additional pump may be present in the system (see Figure 1). An oil separator is typically installed after the expander to avoid accumulation of the

The operation of a sub-critical ORC encompasses several aspects that are common to refrigeration systems, such as the control of the subcooling at the condenser outlet and the degree of superheating at the evaporator outlet, single- and two-phase heat transfer in the heat exchangers, as well as working fluid leaks. The amount of working fluid charged into the system has a direct effect on the performance, the flexibility, as well as on the operational costs

Figure 1. General schematic of a regenerative organic Rankine cycle system. An independent lubricant oil loop is also included for completeness. Typical location of the sensors is also shown.

of the unit. The costs associated with the working fluid and possible working fluid losses due to leaks can be significant, especially in large-scale systems (up to 10% of the plant cost) [12].

With respect to the system behavior, when the operating conditions shift from design to offdesign, the working fluid charge migrates within the system, altering the transition between single-to two-phase heat transfer regimes inside the heat exchangers. If the system is overcharged, typically the length (or, equivalently, the spatial fraction) of the subcooled zone in the evaporator increases, reducing both the capacity and degree of superheating. However, if the system is under-charged, one of the drawbacks is the decrease of subcooling at the condenser outlet, which may cause the pump to cavitate [13]. Additionally, a liquid receiver can be installed before the pump, as shown in Figure 1, in order to compensate for charge migration during off-design conditions, especially in large scale ORC systems. Nevertheless, a nonproper charge level may completely empty or flood the liquid receiver.

The estimation of the optimum charge level is particularly challenging when additional aspects of the normal ORC operation are considered. In particular, lubricant oil may be pre-mixed with the working fluid to ensure the correct functioning of positive displacement expanders. In other cases, oil-separators are utilized to separate the working fluid from the lubricant oil at the expander outlet. However, oil entrainment in the vapor and oil solubility affect the distribution of charge in the system. Furthermore, non-condensable gases can also be present inside the system, which can impact the operation of the ORCs by altering the condensing pressure [14].

Based on the aforementioned reasoning, appropriate numerical methodologies are required to predict the performance of the system and to account for the total working fluid charge in a deterministic way such that the system model resembles the actual behavior of the system. Experimental results are also necessary to validate such numerical methods and to conduct additional analyses. Therefore, in the following sections, the state-of-the-art numerical methods utilized to simulate ORC systems are described and their limitations are also highlighted.

## 3. Charge-sensitive ORC modeling approaches

Modeling of ORC systems is typically performed for steady-state conditions using purely thermodynamic considerations. Assumptions are made regarding the minimum temperature difference (i.e., the pinch point) between the working fluid and the heat source and heat sink fluids. The degrees of subcooling at the pump inlet and superheat at the expander inlet are set, as well as the condensing and evaporating temperatures. Constant values of isentropic efficiency for the pump and expander are often assumed. Then, the cycle is solved by computing the enthalpy of the working fluid at each state point and assuming the pump and expander to be adiabatic. This type of simplified model works well as an initial working fluid screening tool and to broadly assess cycle performance trends. However, in such a model, the physical characteristics of the system components are not taken into account. It follows that a more detailed model is necessary to study the behavior of a real ORC system in off-design conditions. Such a detailed model also typically estimates the steady-state response of the system, although dynamic models have been constructed from similar considerations [15]. For the scope of this chapter, the following discussions will be limited to steady-state modeling.

A detailed ORC model such as the one described above can give information about off-design performance, working fluid charge sensitivity, migration of charge between operating points, pressure drops, and the impact of working fluid transport properties on the heat transfer processes. Although, it only applies to the exact system being modeled, it provides a general framework (see for example ORCmKit library [19]) whereby other systems can be simulated by

Effects of the Working Fluid Charge in Organic Rankine Cycle Power Systems: Numerical and Experimental…

http://dx.doi.org/10.5772/intechopen.78026

23

While constructing a charge-sensitive model, a number of challenges, both numerical and

• Since the entire ORC model is obtained by connecting several sub-models representing the system components and a number of residuals are necessary to ensure a physicallymeaningful solution, a robust solution scheme is required to perform charge-sensitive

• Due to the presence of multiple heat transfer mechanisms, pressure drops, and flow regimes inside the heat exchangers, it is important to properly identify the convective heat transfer coefficients in multi-zone heat exchangers and understand how the working fluid

• The charge estimation inside the heat exchangers relies on the proper knowledge of spatial fraction occupied by each zone (i.e., single-phase liquid or vapor, two-phase) as well as the estimation of the working fluid density. In the case of single-phase zones, such calculation is straightforward. However, in the case of two-phase zones, the density depends on the pressure, temperature, quality, and flow regime through the void fraction.

• Difficulties in accounting all the system volumes (e.g., valves, sight glasses, filters, sensors,

• Correctness of the model in predicting the total working fluid charge with different

• Uncertainties associated with the exact amount of working fluid charge present in the

In order to address the majority of these modeling aspects, general guidelines for developing charge-sensitive models are discussed in the following section. Among these aspects, heat transfer correlations and the length of each zone inside the heat exchangers account for the majority of the inaccuracy in charge estimations. However, it will be shown in Section 4.3 that the solubility of working fluid in oil can also be significant. A charge tuning scheme can be applied to improve the accuracy of charge estimation, as outlined in Section 3.3. Experimental

results from a test case will be used to address the last three bullet points in Section 4.

adjusting the geometric parameters of the model.

simulations with reasonable computational efforts.

charge can improve the reliability of estimating such coefficients.

Void fraction models directly impact the charge estimation.

• Presence of a liquid receiver in the system.

• Estimation of working fluid dissolved in lubricant oil.

and line sets).

working fluids.

actual system.

thermophysical, need to be considered:

#### 3.1. Definition of a mechanistic model for ORC system

Detailed off-design models of ORC systems are built by connecting together different submodels for each component of the system and are implicitly solved by driving to zero a number of residuals to ensure that the solution is within a physical domain. Such detailed models are based upon the extensive literature available for vapor compression cooling and heat pumping systems [16, 17]. A recent overview of off-design steady-state performance studies and modeling applied to ORC systems can be found in [8].

Generally, an ORC system model can be regarded as mechanistic if the inputs and the known parameters are similar to those an ORC operator would know in practice. The model then uses physical principles and empirical or semi-empirical component models to simulate system performance given these parameters, inputs and boundary conditions. An ORC system model requires knowledge of the pump and expander displacements, the heat exchangers geometry, and the total system volume. Such a model receives as inputs the working fluid type, the inlet temperature and mass flow rate of the source and sink fluids, the rotational speeds of the pump and expander, and the condenser exit subcooling or the total working fluid charge in the system. A truly mechanistic model is charge-sensitive, meaning the total refrigerant charge is known, but the condenser exit subcooling is determined by the ORC operation [5]. In fact, if the condenser exit subcooling is fixed within the simulation, an assumption is made regarding the system state, which is not known in a real system. Outputs of the model include rotating equipment efficiency, system efficiency, heat transfer rates, condensing and evaporating temperatures, and net power production. In addition, a Second Law analysis can also be applied to estimate the system irreversibilities [18].

A detailed ORC model such as the one described above can give information about off-design performance, working fluid charge sensitivity, migration of charge between operating points, pressure drops, and the impact of working fluid transport properties on the heat transfer processes. Although, it only applies to the exact system being modeled, it provides a general framework (see for example ORCmKit library [19]) whereby other systems can be simulated by adjusting the geometric parameters of the model.

While constructing a charge-sensitive model, a number of challenges, both numerical and thermophysical, need to be considered:


3. Charge-sensitive ORC modeling approaches

22 Organic Rankine Cycle Technology for Heat Recovery

3.1. Definition of a mechanistic model for ORC system

estimate the system irreversibilities [18].

studies and modeling applied to ORC systems can be found in [8].

Modeling of ORC systems is typically performed for steady-state conditions using purely thermodynamic considerations. Assumptions are made regarding the minimum temperature difference (i.e., the pinch point) between the working fluid and the heat source and heat sink fluids. The degrees of subcooling at the pump inlet and superheat at the expander inlet are set, as well as the condensing and evaporating temperatures. Constant values of isentropic efficiency for the pump and expander are often assumed. Then, the cycle is solved by computing the enthalpy of the working fluid at each state point and assuming the pump and expander to be adiabatic. This type of simplified model works well as an initial working fluid screening tool and to broadly assess cycle performance trends. However, in such a model, the physical characteristics of the system components are not taken into account. It follows that a more detailed model is necessary to study the behavior of a real ORC system in off-design conditions. Such a detailed model also typically estimates the steady-state response of the system, although dynamic models have been constructed from similar considerations [15]. For the scope of this chapter, the following discussions will be limited to steady-state modeling.

Detailed off-design models of ORC systems are built by connecting together different submodels for each component of the system and are implicitly solved by driving to zero a number of residuals to ensure that the solution is within a physical domain. Such detailed models are based upon the extensive literature available for vapor compression cooling and heat pumping systems [16, 17]. A recent overview of off-design steady-state performance

Generally, an ORC system model can be regarded as mechanistic if the inputs and the known parameters are similar to those an ORC operator would know in practice. The model then uses physical principles and empirical or semi-empirical component models to simulate system performance given these parameters, inputs and boundary conditions. An ORC system model requires knowledge of the pump and expander displacements, the heat exchangers geometry, and the total system volume. Such a model receives as inputs the working fluid type, the inlet temperature and mass flow rate of the source and sink fluids, the rotational speeds of the pump and expander, and the condenser exit subcooling or the total working fluid charge in the system. A truly mechanistic model is charge-sensitive, meaning the total refrigerant charge is known, but the condenser exit subcooling is determined by the ORC operation [5]. In fact, if the condenser exit subcooling is fixed within the simulation, an assumption is made regarding the system state, which is not known in a real system. Outputs of the model include rotating equipment efficiency, system efficiency, heat transfer rates, condensing and evaporating temperatures, and net power production. In addition, a Second Law analysis can also be applied to


In order to address the majority of these modeling aspects, general guidelines for developing charge-sensitive models are discussed in the following section. Among these aspects, heat transfer correlations and the length of each zone inside the heat exchangers account for the majority of the inaccuracy in charge estimations. However, it will be shown in Section 4.3 that the solubility of working fluid in oil can also be significant. A charge tuning scheme can be applied to improve the accuracy of charge estimation, as outlined in Section 3.3. Experimental results from a test case will be used to address the last three bullet points in Section 4.

#### 3.2. Overall charge-sensitive model description

As aforementioned, the individual components are properly arranged to form the overall cycle model. By referring to the ORC schematic of Figure 1, two general approaches can be identified to assemble the cycle models, which are shown as block diagrams in Figures 2 and 3, respectively. By looking at the two diagrams, it appears evident that the major cycle components, that is, heat exchangers, pump and expander, are arranged in the same fashion. The major difference is the approach adopted to account for the line sets connecting the active components and, therefore, the associated pressure drops and heat losses. The approach shown in Figure 2 retains the physical description of the cycle with the line set sub-models placed between two consecutive cycle components. It follows that an accurate description of each line set, including internal and external diameters as well as equivalent length, is required. Whereas, in the block diagram of Figure 3, the line set losses are lumped into two single artificial components representing high- and low-pressure sides of the systems. These lumped components are placed at the outlet of the evaporator and the condenser, respectively.

Each block diagram also determines the required initial guess values and the residual to be driven to zero to solve the system. In particular, in the case of the block diagram of Figure 2, the five initial guesses are the pump inlet specific enthalpy (hpump,suc), the pump inlet and outlet pressures (ppump,suc, ppump,dis), the expander inlet specific enthalpy (hexp ,suc), and the expander outlet pressure (pexp ,suc). Such guesses are chosen because of the presence of the regenerator in

> the cycle and to ensure stability of the code. Given the set of guess values, an iteration of the cycle model consists of solving the components in the following order: pump and pump discharge line set, expander and expander discharge line set, regenerator and regenerator exit line sets for liquid and vapor sides, evaporator and expander suction line set, and condenser and pump suction line set. The solution of the cycle model is enforced by five residuals. In particular, four residuals ensure the continuity of thermodynamic states between two consec-

> Figure 3. Block diagram showing the solver architecture of the charge-sensitive ORC model proposed by Dickes et al. [8]. The inputs are indicated in blue, the outputs in brown, the parameters in green, the iteration variables in red and the

Effects of the Working Fluid Charge in Organic Rankine Cycle Power Systems: Numerical and Experimental…

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25

Δ<sup>1</sup> ¼ hpump,suc � hlineset,pump, out; Δ<sup>2</sup> ¼ ppump,suc � plineset,pump, out Δ<sup>3</sup> ¼ hexp ,suc � hlineset, exp , out; Δ<sup>4</sup> ¼ pexp ,suc � plineset, exp , out

The fifth residual is associated with the total system charge, which is estimated by summing all

where the mass of working fluid for each component is given by mwf , component ¼ Vcomponentrwf. Particular attention has to be given to computing the averaged density of the working fluid, rwf , to account for single-, two-phase conditions for both pure working fluids or mixtures, as will be discussed in more detail in Section 3.3. Furthermore, it can also be mentioned that the

i

<sup>Δ</sup>5, charge <sup>¼</sup> mevap <sup>þ</sup> mcond <sup>þ</sup> mregen <sup>þ</sup> mpump <sup>þ</sup> <sup>m</sup>exp <sup>þ</sup> mtank <sup>þ</sup><sup>X</sup>

(1)

mlineset,i � mwf (2)

utive components. These are:

model residuals in violet.

the charge contributions:

Figure 2. Block diagram showing how the individual component models are arranged to form the overall ORC model. Variables are updated as they pass through each component (adapted from [7]).

Effects of the Working Fluid Charge in Organic Rankine Cycle Power Systems: Numerical and Experimental… http://dx.doi.org/10.5772/intechopen.78026 25

3.2. Overall charge-sensitive model description

24 Organic Rankine Cycle Technology for Heat Recovery

As aforementioned, the individual components are properly arranged to form the overall cycle model. By referring to the ORC schematic of Figure 1, two general approaches can be identified to assemble the cycle models, which are shown as block diagrams in Figures 2 and 3, respectively. By looking at the two diagrams, it appears evident that the major cycle components, that is, heat exchangers, pump and expander, are arranged in the same fashion. The major difference is the approach adopted to account for the line sets connecting the active components and, therefore, the associated pressure drops and heat losses. The approach shown in Figure 2 retains the physical description of the cycle with the line set sub-models placed between two consecutive cycle components. It follows that an accurate description of each line set, including internal and external diameters as well as equivalent length, is required. Whereas, in the block diagram of Figure 3, the line set losses are lumped into two single artificial components representing high- and low-pressure sides of the systems. These lumped components are placed at the outlet of the evaporator and the condenser, respectively. Each block diagram also determines the required initial guess values and the residual to be driven to zero to solve the system. In particular, in the case of the block diagram of Figure 2, the five initial guesses are the pump inlet specific enthalpy (hpump,suc), the pump inlet and outlet pressures (ppump,suc, ppump,dis), the expander inlet specific enthalpy (hexp ,suc), and the expander outlet pressure (pexp ,suc). Such guesses are chosen because of the presence of the regenerator in

Figure 2. Block diagram showing how the individual component models are arranged to form the overall ORC model.

Variables are updated as they pass through each component (adapted from [7]).

Figure 3. Block diagram showing the solver architecture of the charge-sensitive ORC model proposed by Dickes et al. [8]. The inputs are indicated in blue, the outputs in brown, the parameters in green, the iteration variables in red and the model residuals in violet.

the cycle and to ensure stability of the code. Given the set of guess values, an iteration of the cycle model consists of solving the components in the following order: pump and pump discharge line set, expander and expander discharge line set, regenerator and regenerator exit line sets for liquid and vapor sides, evaporator and expander suction line set, and condenser and pump suction line set. The solution of the cycle model is enforced by five residuals. In particular, four residuals ensure the continuity of thermodynamic states between two consecutive components. These are:

$$\begin{aligned} \Delta\_1 &= h\_{\text{pump,suc}} - h\_{\text{lineest,pump,out}}; \quad \Delta\_2 = p\_{\text{pump,suc}} - p\_{\text{lineest,pump,out}} \\ \Delta\_3 &= h\_{\text{exp},\text{suc}} - h\_{\text{lineest,exp},\text{out}}; \quad \Delta\_4 = p\_{\text{exp},\text{suc}} - p\_{\text{lineest,exp},\text{out}} \end{aligned} \tag{1}$$

The fifth residual is associated with the total system charge, which is estimated by summing all the charge contributions:

$$
\Delta\_{5, \text{charge}} = m\_{\text{evap}} + m\_{\text{cond}} + m\_{\text{regen}} + m\_{\text{pump}} + m\_{\text{exp}} + m\_{\text{turb}} + \sum\_{i} m\_{\text{lineest},i} - m\_{\text{wf}} \tag{2}
$$

where the mass of working fluid for each component is given by mwf , component ¼ Vcomponentrwf. Particular attention has to be given to computing the averaged density of the working fluid, rwf , to account for single-, two-phase conditions for both pure working fluids or mixtures, as will be discussed in more detail in Section 3.3. Furthermore, it can also be mentioned that the fifth residual associated with the total charge, Δ5, charge, is usually replaced by the difference between the imposed and calculated condenser exit subcooling in many off-design simulation models proposed in literature.

and serves as a mass damping device during off-design conditions. In most cases, the liquid receiver is modeled by neglecting heat losses to the environment as well as potential hydrostatic effects due to the height of liquid (i.e., the pressure is considered to be uniform inside the liquid receiver). Nevertheless, it is not straightforward to predict the mass of liquid stored inside the tank at any operating condition with a steady-state model. In an experimental setup, a level sensor could be used to monitor the liquid level inside the tank. However, in commercial ORC systems, this may not be a viable option. Recently, Dickes et al. [8] proposed a liquid receiver model by introducing four hypotheses that resulted in the following constraints for calculating the mass of

Effects of the Working Fluid Charge in Organic Rankine Cycle Power Systems: Numerical and Experimental…

where Vtank is the total volume of the liquid receiver, Ltank is the liquid level, rsat,l and rsat, <sup>v</sup> are the saturated liquid and vapor densities at the supply pressure, respectively. Under normal operating conditions and optimal charge, the receiver should be partially filled with liquid. If the charge is not proper or the ORC system is operating at strong off-design conditions, the receiver can be either full or empty of liquid. Furthermore, such mathematical formulation may result in numerical issues due to a discontinuity in the mass estimation when the fluid

The line sets (or pipelines) connect the different system components and carry the working fluid. The line sets consist of piping, valves, fittings, sight glasses, filters and other elements and are also associated with pressure drops and heat losses. As mentioned at the beginning of this section, two different modeling approaches can be employed to estimate the working fluid charge carried by the line sets as well as the thermodynamic states at inlet and outlet of each line set. By referring to Figure 2, a total of six line sets is considered. In particular, each line set can carry single-phase or two-phase working fluid and they are modeled as an equivalent tube having inner and outer diameters. An equivalent length that accounts for straight sections (Lstraight) and all the fittings (Leq,fittings) is computed by using the method of loss coefficients proposed by Munson et al. [24]. Distinction is made in the calculation of pressure drops to account for single and two-phase flow conditions. In the case of single-phase flow, the pressure drop for a certain line set having a certain internal diameter is computed by introducing the

> <sup>P</sup>Lstraight <sup>þ</sup> <sup>P</sup>Leq,fittings ID

where v is the working fluid velocity. Under two-phase conditions, the Lockhart-Martinelli

method for two-phase frictional pressure drop in tubes [25] is used. That is:

if htank,su < hsatðptank,su, x ¼ 0Þ

http://dx.doi.org/10.5772/intechopen.78026

(4)

27

if htank,su > hsatðptank,su, x ¼ 1Þ

rlineset,suv<sup>2</sup> 2

� � (5)

if xtank,su ¼ 0 if xtank,su ∈½0, 1�

working fluid inside the liquid receiver:

8 >>>><

>>>>:

Vtankrtank,su

Vtankrsat,<sup>v</sup> Vtankrtank,su

reaches its saturated liquid state (i.e., xtank,su ¼ 0) [8].

<sup>Δ</sup>plineset, <sup>1</sup>φ,ID¼const <sup>¼</sup> <sup>f</sup>

Vtank Ltankrsat,<sup>l</sup> þ ð Þ 1 � Ltank rsat,<sup>l</sup> � �

mreceiver ¼

Darcy friction factor:

In the case of the block diagram of Figure 3, the model iterates on the evaporator outlet specific enthalpy (hevap,ex), pump inlet and outlet pressures (ppump,su, ppump,ex), and condenser outlet subcooling (ΔTsc). The residuals to be minimized are the condenser outlet specific enthalpy, the evaporator outlet specific enthalpy, the expander rotational speed, and the total system charge:

$$
\Delta\_1 = 1 - \frac{h\_{\rm cd,ex,2}}{h\_{\rm cd,ex,2}}; \quad \Delta\_2 = 1 - \frac{h\_{\rm cp,ex,2}}{h\_{\rm cp,ex,2}}; \quad \Delta\_3 = 1 - \frac{N\_{\rm exp,2}}{N\_{\rm exp}}; \quad \Delta\_4 = 1 - \frac{m\_{\rm wf,2}}{m\_{\rm wf}} \tag{3}
$$

where the total working fluid charge is calculated by employing an analogous expression to that one appearing in Eq. (2).

In both solution schemes, the resulting problem to be solved is multi-dimensional, leading to possible convergence issues when the charge is imposed. To increase the robustness of the model, a multi-stage solver can be employed to run the simulations. Dickes et al. [8] described these ad-hoc solvers in detail. The thermophysical properties of the working fluid can be retrieved either from CoolProp [20] or REFPROP [21].

In order to simulate the entire cycle, different sub-models are required to characterize each of the components. In the context of charge-sensitive modeling, the heat exchangers typically have the largest volumes in the system and are subjected to varying flow regimes, as outlined in Section 3.3. However, pump, expander, liquid receiver, and line sets also require proper modeling. Particular emphasis is given to estimate the working fluid charge in each of these components. For an extensive description and examples of these models, the reader is invited to referred to [5–8, 19].

As a general overview, the rotating equipment is modeled by using one or more of the following approaches: (i) a performance map based on experimental data (black box models); (ii) physics-based models with empirically determined parameters (gray box models); (iii) entirely physics-based models (white box models). Semi-empirical models are usually preferred as a compromise between physical-characteristics (e.g., under- over-expansion/compression, pressure drops, heat transfer and mechanical losses) and computational cost. Regarding the charge estimation of rotating equipment, the mass of working fluid is computed by knowing the internal volume of the machine and by computing an average density. This simplified approach is usually reasonable given the relatively small internal volumes of pumps and expanders compared to heat exchangers and other volumes of the system. However, especially in the case of oil lubricated positive displacement expanders, high pressures and temperatures may lead to dissolved refrigerant in the oil that could be accounted for using solubility data of the refrigerant-oil mixture [16, 22, 23].

A liquid receiver (or buffer tank) can be installed in an ORC system at the condenser outlet. Under normal operating conditions, the liquid receiver ensures a saturated liquid at the condenser outlet

and serves as a mass damping device during off-design conditions. In most cases, the liquid receiver is modeled by neglecting heat losses to the environment as well as potential hydrostatic effects due to the height of liquid (i.e., the pressure is considered to be uniform inside the liquid receiver). Nevertheless, it is not straightforward to predict the mass of liquid stored inside the tank at any operating condition with a steady-state model. In an experimental setup, a level sensor could be used to monitor the liquid level inside the tank. However, in commercial ORC systems, this may not be a viable option. Recently, Dickes et al. [8] proposed a liquid receiver model by introducing four hypotheses that resulted in the following constraints for calculating the mass of working fluid inside the liquid receiver:

fifth residual associated with the total charge, Δ5, charge, is usually replaced by the difference between the imposed and calculated condenser exit subcooling in many off-design simulation

In the case of the block diagram of Figure 3, the model iterates on the evaporator outlet specific enthalpy (hevap,ex), pump inlet and outlet pressures (ppump,su, ppump,ex), and condenser outlet subcooling (ΔTsc). The residuals to be minimized are the condenser outlet specific enthalpy, the evaporator outlet specific enthalpy, the expander rotational speed, and the total system

where the total working fluid charge is calculated by employing an analogous expression to

In both solution schemes, the resulting problem to be solved is multi-dimensional, leading to possible convergence issues when the charge is imposed. To increase the robustness of the model, a multi-stage solver can be employed to run the simulations. Dickes et al. [8] described these ad-hoc solvers in detail. The thermophysical properties of the working fluid can be

In order to simulate the entire cycle, different sub-models are required to characterize each of the components. In the context of charge-sensitive modeling, the heat exchangers typically have the largest volumes in the system and are subjected to varying flow regimes, as outlined in Section 3.3. However, pump, expander, liquid receiver, and line sets also require proper modeling. Particular emphasis is given to estimate the working fluid charge in each of these components. For an extensive description and examples of these models, the reader is invited

As a general overview, the rotating equipment is modeled by using one or more of the following approaches: (i) a performance map based on experimental data (black box models); (ii) physics-based models with empirically determined parameters (gray box models); (iii) entirely physics-based models (white box models). Semi-empirical models are usually preferred as a compromise between physical-characteristics (e.g., under- over-expansion/compression, pressure drops, heat transfer and mechanical losses) and computational cost. Regarding the charge estimation of rotating equipment, the mass of working fluid is computed by knowing the internal volume of the machine and by computing an average density. This simplified approach is usually reasonable given the relatively small internal volumes of pumps and expanders compared to heat exchangers and other volumes of the system. However, especially in the case of oil lubricated positive displacement expanders, high pressures and temperatures may lead to dissolved refrigerant in the oil that could be accounted for using

A liquid receiver (or buffer tank) can be installed in an ORC system at the condenser outlet. Under normal operating conditions, the liquid receiver ensures a saturated liquid at the condenser outlet

; <sup>Δ</sup><sup>3</sup> <sup>¼</sup> <sup>1</sup> � <sup>N</sup>exp ,<sup>2</sup>

Nexp

; <sup>Δ</sup><sup>4</sup> <sup>¼</sup> <sup>1</sup> � mwf ,<sup>2</sup>

mwf

(3)

models proposed in literature.

26 Organic Rankine Cycle Technology for Heat Recovery

<sup>Δ</sup><sup>1</sup> <sup>¼</sup> <sup>1</sup> � hcd,ex, <sup>2</sup>

that one appearing in Eq. (2).

to referred to [5–8, 19].

hcd,ex, <sup>2</sup>

retrieved either from CoolProp [20] or REFPROP [21].

solubility data of the refrigerant-oil mixture [16, 22, 23].

; <sup>Δ</sup><sup>2</sup> <sup>¼</sup> <sup>1</sup> � hev,ex, <sup>2</sup>

hev,ex, <sup>2</sup>

charge:

$$m\_{\text{reciver}} = \begin{cases} V\_{\text{tank}} \rho\_{\text{tank,su}} & \text{if } h\_{\text{tank,su}} < h\_{\text{stl}} (p\_{\text{tank,su}}, \mathbf{x} = \mathbf{0}) \\ V\_{\text{tank}} \left[ L\_{\text{tank}} \rho\_{\text{sstl}} + (1 - L\_{\text{tank}}) \rho\_{\text{sstl}} \right] & \text{if } \mathbf{x}\_{\text{tank,su}} = \mathbf{0} \\ V\_{\text{tank}} \rho\_{\text{sst,v}} & \text{if } \mathbf{x}\_{\text{tank,su}} \in [0, 1] \\ V\_{\text{tank}} \rho\_{\text{tank,su}} & \text{if } h\_{\text{tank,su}} > h\_{\text{stl}} (p\_{\text{tank,su}}, \mathbf{x} = 1) \end{cases} \tag{4}$$

where Vtank is the total volume of the liquid receiver, Ltank is the liquid level, rsat,l and rsat, <sup>v</sup> are the saturated liquid and vapor densities at the supply pressure, respectively. Under normal operating conditions and optimal charge, the receiver should be partially filled with liquid. If the charge is not proper or the ORC system is operating at strong off-design conditions, the receiver can be either full or empty of liquid. Furthermore, such mathematical formulation may result in numerical issues due to a discontinuity in the mass estimation when the fluid reaches its saturated liquid state (i.e., xtank,su ¼ 0) [8].

The line sets (or pipelines) connect the different system components and carry the working fluid. The line sets consist of piping, valves, fittings, sight glasses, filters and other elements and are also associated with pressure drops and heat losses. As mentioned at the beginning of this section, two different modeling approaches can be employed to estimate the working fluid charge carried by the line sets as well as the thermodynamic states at inlet and outlet of each line set. By referring to Figure 2, a total of six line sets is considered. In particular, each line set can carry single-phase or two-phase working fluid and they are modeled as an equivalent tube having inner and outer diameters. An equivalent length that accounts for straight sections (Lstraight) and all the fittings (Leq,fittings) is computed by using the method of loss coefficients proposed by Munson et al. [24]. Distinction is made in the calculation of pressure drops to account for single and two-phase flow conditions. In the case of single-phase flow, the pressure drop for a certain line set having a certain internal diameter is computed by introducing the Darcy friction factor:

$$\Delta p\_{\text{lineest, 1q, ID=const}} = f \frac{\sum L\_{\text{straight}} + \sum L\_{\text{eq, fitting}}}{ID} \left(\frac{\rho\_{\text{lineest, su}} \upsilon^2}{2}\right) \tag{5}$$

where v is the working fluid velocity. Under two-phase conditions, the Lockhart-Martinelli method for two-phase frictional pressure drop in tubes [25] is used. That is:

$$
\Delta p\_{\text{lineest}, 2\uprho, \text{ID}=\text{const}} = -\left(\frac{dp}{dz}\right)\_F \left(\sum L\_{\text{straight}} + \sum L\_{\text{eq, fitting}}\right) \tag{6}
$$

changes in both evaporator and condenser and different phases co-exist during these processes. An internal heat exchanger (or regenerator) can be present in the system to improve the cycle thermal efficiency [11]. The heat exchangers account for the majority of the volume in an ORC system and therefore, it is particularly important to have reliable models to predict the

Effects of the Working Fluid Charge in Organic Rankine Cycle Power Systems: Numerical and Experimental…

To predict the different zones inside an HEX, three different numerical methods can be used: moving-boundary [7, 8], finite-volume (or discretized) [16], and hybrid approach [26]. The main advantage of moving-boundary models is their fast computation time and good accuracy. Finitevolume models provide greater spatial resolution but can be computationally expensive. Hybrid models represent a compromise between the former methods. By considering the movingboundary model as an example, the heat exchanger can be divided in multiple zones, as shown in Figure 4. Each zone is characterized by a heat transfer coefficient and heat transfer area through which a certain heat transfer process occurs. By knowing the inlet conditions of both streams, the effective heat transfer rate between the hot and cold streams is calculated by enforcing that the total surface area occupied by the different zones is equal to the geometrical surface area of the heat exchanger [8]. It follows that the total working fluid mass inside the heat exchanger (mHEX)

can be calculated as the sum of the working fluid mass associated with each zone:

mwf ,HEX <sup>¼</sup> <sup>X</sup>

N

i¼1

where wi is the volume fraction occupied by the i-th zone in the heat exchanger, and r<sup>i</sup> is the mean density of working fluid in the i-th zone. In order to ensure a correct estimation of the working fluid charge, the knowledge of the zone division (or in other words, correct estimation of the heat transfer rates) and the evaluation of the working fluid density under both single- and two-phase conditions are required. In particular, the latter implies the selection of the proper void fraction model that characterizes both boiling and condensing processes.

Various heat exchanger types are employed in ORC systems (e.g., brazed plate heat exchangers, fin and tubes, shell and tubes, etc.) and a number of state-of-the-art heat transfer correlations are available in the literature that are used to predict the convective heat transfer

Figure 4. Schematic of counterflow HEX model simulated by moving boundary method showing phase boundaries

(solid lines) and zone boundaries (dashed lines).

rið Þ wiVHEX (13)

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29

heat transfer rate, zone lengths, and working fluid charge.

The heat losses though the line sets to the surroundings can be calculated with the effectiveness-NTU method [17], as given in Eq. (7), where NTUlineset can be either specified or obtained by regression using experimental data.

$$T\_{\text{lineest},\text{ex}} = T\_{\text{amb}} - e^{(-NTl\_{\text{lineest}})} (T\_{\text{amb}} - T\_{\text{lineest},\text{su}}) \tag{7}$$

A more simplified approach is proposed in Figure 3, where the line sets and associated losses are lumped in the high- and the low-pressure lines by using single fictitious components placed at the outlet of the evaporator and the condenser, respectively. The pressure losses are computed as a linear function of the working fluid kinetic energy with two coefficients to be calibrated using experimental data. That is:

$$
\Delta p\_{\text{lineset}} = \mathcal{K} \left( \frac{m\_{wf}^2}{\rho\_{\text{lineset},su}} \right) + B \tag{8}
$$

The ambient losses are modeled by introducing an overall heat transfer coefficient of the line set (UAlineset), which is the sum of the thermal resistance of the pipe, the thermal resistance associated with insulation and the convective UA values associated with the inside and outside of the line set:

$$Q\_{lineest} = UA\_{lineest}(T\_{lineest,su} - T\_{amb})\tag{9}$$

$$LIA\_{lineet} = \left(\frac{1}{LIA\_{ID}} + \frac{1}{LIA\_{OD}} + R\_{lineet} + R\_{insolution}\right)^{-1} \tag{10}$$

The working fluid charge of each line set is calculated in a manner that is similar to the approach that will be presented for each zone of the heat exchangers (see Section 3.3). In the case of single-phase working fluid, the mass of working fluid is calculated as

$$m\_{\text{lineset}} = V\_{\text{lineset}} \rho\_{\text{lineset}} \tag{11}$$

where rlineset is the average between inlet and outlet densities of a line set. If a line set is considered adiabatic, then rlineset � rlineset,su. Under two-phase conditions, the average density of the working fluid is obtained by introducing an average void fraction over the length of the line set (αlineset). Mathematically, this can be expressed as:

$$
\rho\_{linset} = \alpha\_{linset} \rho\_{sat, v} + (1 - \alpha\_{linset}) \rho\_{sat, l} \tag{12}
$$

#### 3.3. Working fluid charge in heat exchangers

An ORC system operates between a heat source and heat sink by using heat exchangers (HEX) for the heat input and rejection processes, respectively. The working fluid undergoes phase changes in both evaporator and condenser and different phases co-exist during these processes. An internal heat exchanger (or regenerator) can be present in the system to improve the cycle thermal efficiency [11]. The heat exchangers account for the majority of the volume in an ORC system and therefore, it is particularly important to have reliable models to predict the heat transfer rate, zone lengths, and working fluid charge.

<sup>Δ</sup>plineset,<sup>2</sup>φ,ID¼const ¼ � dp

Tlineset,ex ¼ Tamb � e

UAlineset <sup>¼</sup> <sup>1</sup>

line set (αlineset). Mathematically, this can be expressed as:

3.3. Working fluid charge in heat exchangers

UAID þ

case of single-phase working fluid, the mass of working fluid is calculated as

Δplineset ¼ K

by regression using experimental data.

28 Organic Rankine Cycle Technology for Heat Recovery

calibrated using experimental data. That is:

line set:

dz � �

F

The heat losses though the line sets to the surroundings can be calculated with the effectiveness-NTU method [17], as given in Eq. (7), where NTUlineset can be either specified or obtained

A more simplified approach is proposed in Figure 3, where the line sets and associated losses are lumped in the high- and the low-pressure lines by using single fictitious components placed at the outlet of the evaporator and the condenser, respectively. The pressure losses are computed as a linear function of the working fluid kinetic energy with two coefficients to be

> m2 wf rlineset,su !

The ambient losses are modeled by introducing an overall heat transfer coefficient of the line set (UAlineset), which is the sum of the thermal resistance of the pipe, the thermal resistance associated with insulation and the convective UA values associated with the inside and outside of the

> 1 UAOD

The working fluid charge of each line set is calculated in a manner that is similar to the approach that will be presented for each zone of the heat exchangers (see Section 3.3). In the

where rlineset is the average between inlet and outlet densities of a line set. If a line set is considered adiabatic, then rlineset � rlineset,su. Under two-phase conditions, the average density of the working fluid is obtained by introducing an average void fraction over the length of the

An ORC system operates between a heat source and heat sink by using heat exchangers (HEX) for the heat input and rejection processes, respectively. The working fluid undergoes phase

<sup>X</sup>Lstraight <sup>þ</sup>XLeq,fittings � �

Qlineset ¼ UAlinesetð Þ Tlineset,su � Tamb (9)

mlineset ¼ Vlinesetrlineset (11)

rlineset ¼ αlinesetrsat, <sup>v</sup> þ ð Þ 1 � αlineset rsat,l (12)

þ Rlineset þ Rinsulation

� ��<sup>1</sup>

ð Þ �NTUlineset ð Þ Tamb � Tlineset,su (7)

þ B (8)

(6)

(10)

To predict the different zones inside an HEX, three different numerical methods can be used: moving-boundary [7, 8], finite-volume (or discretized) [16], and hybrid approach [26]. The main advantage of moving-boundary models is their fast computation time and good accuracy. Finitevolume models provide greater spatial resolution but can be computationally expensive. Hybrid models represent a compromise between the former methods. By considering the movingboundary model as an example, the heat exchanger can be divided in multiple zones, as shown in Figure 4. Each zone is characterized by a heat transfer coefficient and heat transfer area through which a certain heat transfer process occurs. By knowing the inlet conditions of both streams, the effective heat transfer rate between the hot and cold streams is calculated by enforcing that the total surface area occupied by the different zones is equal to the geometrical surface area of the heat exchanger [8]. It follows that the total working fluid mass inside the heat exchanger (mHEX) can be calculated as the sum of the working fluid mass associated with each zone:

$$m\_{wf,HEX} = \sum\_{i=1}^{N} \rho\_i(w\_i V\_{HEX}) \tag{13}$$

where wi is the volume fraction occupied by the i-th zone in the heat exchanger, and r<sup>i</sup> is the mean density of working fluid in the i-th zone. In order to ensure a correct estimation of the working fluid charge, the knowledge of the zone division (or in other words, correct estimation of the heat transfer rates) and the evaluation of the working fluid density under both single- and two-phase conditions are required. In particular, the latter implies the selection of the proper void fraction model that characterizes both boiling and condensing processes.

Various heat exchanger types are employed in ORC systems (e.g., brazed plate heat exchangers, fin and tubes, shell and tubes, etc.) and a number of state-of-the-art heat transfer correlations are available in the literature that are used to predict the convective heat transfer

Figure 4. Schematic of counterflow HEX model simulated by moving boundary method showing phase boundaries (solid lines) and zone boundaries (dashed lines).

coefficients in each zone. However, these correlations are often purely empirical and calibrated to fit experimental data and multiple correlations may be available for the same type of heat exchanger and working fluid. Furthermore, these correlations are typically derived for refrigeration systems, which present different operating conditions than ORCs. It follows that such correlations are likely to over-predict or under-predict the actual heat transfer coefficient within a certain zone, even though the overall predictions of the heat transfer rate may be reasonable. Nevertheless, errors in predictions of heat transfer within individual zones can lead to significant errors in charge estimations [8]. To improve the accuracy in predicting the heat transfer coefficients in the different zones, empirical parameters of these correlations should be fitted with experimental results by using identification methods [8].

The accuracy of the heat transfer predictions alone does not ensure the correctness of the charge estimation. In fact, as already indicated in Eq. (14), under two-phase conditions, the density is a function of the thermodynamic conditions as well as the flow pattern characterizing each phase. The void fraction, α, is an essential parameter associated with two-phase flow and it is related to the fluid quality, x. Based on the void fraction, the working fluid mass of a two-phase zone having length L and cross section Ac is calculated as:

$$m\_{\rm wf, 2\,\text{op}} = m\_{\rm wf, v} + m\_{\rm wf, l} = A\_c \left( \rho\_v \int\_0^L \alpha(\mathbf{x}) dl + \rho\_l \int\_0^L [1 - \alpha(\mathbf{x})] dl \right) \tag{14}$$

The study considered a total of 360 charge-sensitive simulations including 40 experimental data points, 4 tuning methods, 5 void fraction correlations, and 72 heat exchanger models. It was concluded that the total working fluid charge estimation is mainly affected by the adjusting (or tuning) method applied to the convective heat transfer coefficient rather than the void fraction model. However, a trade-off between the two aspects exists since higher accuracy in the thermal performance predictions led to a large scatter of the charge inventory predictions.

Effects of the Working Fluid Charge in Organic Rankine Cycle Power Systems: Numerical and Experimental…

http://dx.doi.org/10.5772/intechopen.78026

31

4. Experimental considerations on working fluid charge with pure working

In Section 3, the numerical aspects to be considered while developing a charge-sensitive ORC model have been discussed. However, in order to understand the usefulness of the model in predicting a real ORC behavior, it is necessary to consider experimental data. To this end, in the following sub-sections, several aspects related to analyzing different charge levels using

Steady-state operation of an ORC system can be detected by adopting for example the conditions proposed by Woodland et al. [15]. Alternatively, the methodology described by Dickes et al. [5] could also be employed. Due to the fact that experimental data is subject to different uncertainties, possible errors or sensor malfunction, a post-treatment data can be performed to identify possible outliers by using the open-source GPExp library [27]. Furthermore, a reconciliation method can also be applied to correct the measured data affected by measurement

Uncertainty propagation from the measured system properties to the calculated quantities is usually performed according to the method described by Figliola and Beasley [29]. In particular, it is important to discuss the uncertainties associated with the total system charges, which are often not thoroughly accounted for when reporting experimental results of ORC systems. In general, there are several sources of uncertainty in the measurement of the total system charge, such as inaccuracy of the scale used to weight the supply cylinder, leakage of working fluid from the system during operation, small portions of working fluid occupying charging hoses, small losses in system charge due to purging of charging hoses, stacked uncertainties due to the summing of several incremental charging steps. In experimental test rigs, the uncertainty due to purging of system charging hoses can be eliminated by leaving all charging hoses connected and full of working fluid during all tests and incremental charge conditions. Leakage of working fluid from the system during operation can be neglected after ensuring that repeated tests at the same conditions, but several days apart, yield approximately the same condenser subcooling. The main sources of uncertainty in the working fluid charge level are the inaccuracy of the scale and the stacked uncertainties due to several incremental steps in adding or subtracting charge. As an example, if a scale has a known resolution of 0.005 kg, and a measurement uncertainty of ten times the resolution or 0.045 kg is

error propagation to satisfy physical system constraints (e.g., energy balances) [28].

both experimental and charge-sensitive model results are presented.

fluids and zeotropic mixtures

4.1. Data reduction and charge uncertainties

To be further noted is that the void fraction αð Þx is integrated along the length of the zone as a function of the working fluid quality. A common simplification is to assume a uniform heat flux in the two-phase zone, that is, a linear evolution of the quality along the length of the zone. However, a more appropriate approach would require evaluation of the effective spatial evolution of the quality in the heat exchanger for example by discretizing the two-phase zone into multiple sub-cells (e.g., by employing a hybrid heat exchanger model) [8]. Similar to the convective heat transfer correlations, several void fraction models can be found in the scientific literature [8, 10] that lead to different values of the mean density under two-phase conditions. An example of investigation of the combined effect of different convective heat transfer correlations and void fraction models on the total charge estimation is shown in Figure 5 that is based on the work done by Dickes et al. [8].

Figure 5. Working fluid charge predictions for different void fraction models as well as three adjusting methods to tune the convective heat transfer correlations [8].

The study considered a total of 360 charge-sensitive simulations including 40 experimental data points, 4 tuning methods, 5 void fraction correlations, and 72 heat exchanger models. It was concluded that the total working fluid charge estimation is mainly affected by the adjusting (or tuning) method applied to the convective heat transfer coefficient rather than the void fraction model. However, a trade-off between the two aspects exists since higher accuracy in the thermal performance predictions led to a large scatter of the charge inventory predictions.

## 4. Experimental considerations on working fluid charge with pure working fluids and zeotropic mixtures

In Section 3, the numerical aspects to be considered while developing a charge-sensitive ORC model have been discussed. However, in order to understand the usefulness of the model in predicting a real ORC behavior, it is necessary to consider experimental data. To this end, in the following sub-sections, several aspects related to analyzing different charge levels using both experimental and charge-sensitive model results are presented.

#### 4.1. Data reduction and charge uncertainties

coefficients in each zone. However, these correlations are often purely empirical and calibrated to fit experimental data and multiple correlations may be available for the same type of heat exchanger and working fluid. Furthermore, these correlations are typically derived for refrigeration systems, which present different operating conditions than ORCs. It follows that such correlations are likely to over-predict or under-predict the actual heat transfer coefficient within a certain zone, even though the overall predictions of the heat transfer rate may be reasonable. Nevertheless, errors in predictions of heat transfer within individual zones can lead to significant errors in charge estimations [8]. To improve the accuracy in predicting the heat transfer coefficients in the different zones, empirical parameters of these correlations

The accuracy of the heat transfer predictions alone does not ensure the correctness of the charge estimation. In fact, as already indicated in Eq. (14), under two-phase conditions, the density is a function of the thermodynamic conditions as well as the flow pattern characterizing each phase. The void fraction, α, is an essential parameter associated with two-phase flow and it is related to the fluid quality, x. Based on the void fraction, the working fluid mass of a

> ð L

0 @

To be further noted is that the void fraction αð Þx is integrated along the length of the zone as a function of the working fluid quality. A common simplification is to assume a uniform heat flux in the two-phase zone, that is, a linear evolution of the quality along the length of the zone. However, a more appropriate approach would require evaluation of the effective spatial evolution of the quality in the heat exchanger for example by discretizing the two-phase zone into multiple sub-cells (e.g., by employing a hybrid heat exchanger model) [8]. Similar to the convective heat transfer correlations, several void fraction models can be found in the scientific literature [8, 10] that lead to different values of the mean density under two-phase conditions. An example of investigation of the combined effect of different convective heat transfer correlations and void fraction models on the total charge estimation is shown in Figure 5 that is

Figure 5. Working fluid charge predictions for different void fraction models as well as three adjusting methods to tune

αð Þx dl þ r<sup>l</sup>

ð L

½ � 1 � αð Þx dl

1

A (14)

0

0

should be fitted with experimental results by using identification methods [8].

two-phase zone having length L and cross section Ac is calculated as:

mwf ,2<sup>φ</sup> ¼ mwf ,v þ mwf ,l ¼ Ac r<sup>v</sup>

based on the work done by Dickes et al. [8].

30 Organic Rankine Cycle Technology for Heat Recovery

the convective heat transfer correlations [8].

Steady-state operation of an ORC system can be detected by adopting for example the conditions proposed by Woodland et al. [15]. Alternatively, the methodology described by Dickes et al. [5] could also be employed. Due to the fact that experimental data is subject to different uncertainties, possible errors or sensor malfunction, a post-treatment data can be performed to identify possible outliers by using the open-source GPExp library [27]. Furthermore, a reconciliation method can also be applied to correct the measured data affected by measurement error propagation to satisfy physical system constraints (e.g., energy balances) [28].

Uncertainty propagation from the measured system properties to the calculated quantities is usually performed according to the method described by Figliola and Beasley [29]. In particular, it is important to discuss the uncertainties associated with the total system charges, which are often not thoroughly accounted for when reporting experimental results of ORC systems. In general, there are several sources of uncertainty in the measurement of the total system charge, such as inaccuracy of the scale used to weight the supply cylinder, leakage of working fluid from the system during operation, small portions of working fluid occupying charging hoses, small losses in system charge due to purging of charging hoses, stacked uncertainties due to the summing of several incremental charging steps. In experimental test rigs, the uncertainty due to purging of system charging hoses can be eliminated by leaving all charging hoses connected and full of working fluid during all tests and incremental charge conditions. Leakage of working fluid from the system during operation can be neglected after ensuring that repeated tests at the same conditions, but several days apart, yield approximately the same condenser subcooling. The main sources of uncertainty in the working fluid charge level are the inaccuracy of the scale and the stacked uncertainties due to several incremental steps in adding or subtracting charge. As an example, if a scale has a known resolution of 0.005 kg, and a measurement uncertainty of ten times the resolution or 0.045 kg is conservatively assumed, the uncertainty of the total system charge (ucharge) can be estimated as a function of the number of consecutive charging steps, nsteps, as:

$$
\mu\_{\text{charge}} = \sqrt{\left(0.045\right)^2 \cdot n\_{\text{steps}}} \tag{15}
$$

4.3. Total working fluid charge model predictions

R134a-R245fa (0.625–0.375)

One of the main purposes of a charge-sensitive model is to predict the total charge of a certain ORC system for which it has been developed and its behavior (e.g., evaporating and condensing temperatures, subcooling and superheating). This needs to hold true also under the circumstances that the system is under-charged or over-charged as well as if the working fluid is changed, that is, drop-in replacement. To this end, the same ORC system considered in Section 4.2 is used as an example [6]. The charge-sensitive model is employed to simulate three different working fluids (i.e., R134a, R245fa, and R134a-R245fa (0.635–0.375)) at three different charge levels, without any tuning. The untuned model prediction of the system charge versus the measured charge for all the test points is shown in Figure 7. It can be seen that even without tuning, the model predictions are reasonably accurate due to the fact that the heat

Figure 6. Measured second law efficiency versus condenser exit subcooling for each working fluid. The contour shows the working fluid charge and the size of the markers is proportional to the expander rotational speed (data from [6]).

Working fluid Charge [kg] Source temperature [�C] Expander speed range [rpm] Pump speed range [rpm]

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20.4 80, 100 1200–3000 1000 22.7 100 1500–2300 1000

29.5 80, 100 1000–2000 300–500 31.8 80, 100 1000–2000 300–500

24.9 80, 100 1000–1500 500–1000 27.2 80, 100 1000–2500 500–1000 29.5 80, 100 1000–2200 500–1000

R134a 18.1 80, 100 2800–3000 1000

R245fa 27.4 80, 100 1000–2000 300–500

Table 1. Summary of experimental test matrix to investigate the effect of working fluid charge [6].

As reported by Woodland [6], given a system charge of 18.1 kg, the relative uncertainty in system charge assuming a maximum of 8 charge steps is still less than 1%. Therefore, a high degree of confidence can be placed on the measured system charge level. More challenging is determining the actual charge inside the heat exchangers, which would require active measurements of their weight during operation.

In the case of a zeotropic mixture, for example, R134a-R245fa (0.625–0.375), uncertainty in the charge level of each component of the binary mixture results in some uncertainties in the concentration of the mixture, which is an important parameter in computing the thermophysical properties of the mixture. However, even with the conservative estimate on the charge uncertainty previously mentioned, the resulting relative uncertainty in the concentration is ≤0.004, which results in a relative uncertainty of 1% or less, depending on which component concentration is considered. Depending on the mixture considered, the sensitivity of the mixture thermodynamic properties to the concentration can be much smaller for single-phase states than the sensitivity to temperature. For example, in the case of R134a-R245fa, the sensitivity of enthalpy to the concentration uncertainty is two orders of magnitude less than the sensitivity to the temperature uncertainty for single-phase states [6]. As a result, the measured concentration of the working fluid is not a dominant factor in measurement uncertainty in this case.

#### 4.2. Effect of charge variations in an ORC system

To conduct a working fluid charge study, it is desired to explore a wide range of working conditions, different working fluids, and several charge levels. In the current available literature, only the study published by Woodland [6] meets all of these criteria, and, therefore, it is used hereafter as an example. In particular, three working fluids were chosen to investigate low grade waste heat recovery by means of an ORC: R134a, R245fa, and the zeotropic mixture R134a-R245fa (0.625–0.375). In addition, two heat source temperatures, and several charge levels of the working fluids were considered. The range of conditions tested experimentally for each working fluid is summarized in Table 1. A complete description of the ORC system can be found in [6] and its schematic is shown in Figure 1. The effect of the working fluid charge on the ORC system performance is shown in Figure 6, where the Second Law efficiency, defined as the ratio of the system net power to the total exergy rate available, is plotted as a function of the subcooling level for different operating conditions. It can be seen that for a given working fluid and heat source inlet temperature, there exists an optimum charge level that maximizes the Second Law efficiency (i.e., power output) of the system. Furthermore, for each working fluid, the efficiency tends to be higher at lower subcooling due to lower condensing pressures dictated by lower fluid charge.

Effects of the Working Fluid Charge in Organic Rankine Cycle Power Systems: Numerical and Experimental… http://dx.doi.org/10.5772/intechopen.78026 33


Table 1. Summary of experimental test matrix to investigate the effect of working fluid charge [6].

Figure 6. Measured second law efficiency versus condenser exit subcooling for each working fluid. The contour shows the working fluid charge and the size of the markers is proportional to the expander rotational speed (data from [6]).

#### 4.3. Total working fluid charge model predictions

conservatively assumed, the uncertainty of the total system charge (ucharge) can be estimated as

As reported by Woodland [6], given a system charge of 18.1 kg, the relative uncertainty in system charge assuming a maximum of 8 charge steps is still less than 1%. Therefore, a high degree of confidence can be placed on the measured system charge level. More challenging is determining the actual charge inside the heat exchangers, which would require active mea-

In the case of a zeotropic mixture, for example, R134a-R245fa (0.625–0.375), uncertainty in the charge level of each component of the binary mixture results in some uncertainties in the concentration of the mixture, which is an important parameter in computing the thermophysical properties of the mixture. However, even with the conservative estimate on the charge uncertainty previously mentioned, the resulting relative uncertainty in the concentration is ≤0.004, which results in a relative uncertainty of 1% or less, depending on which component concentration is considered. Depending on the mixture considered, the sensitivity of the mixture thermodynamic properties to the concentration can be much smaller for single-phase states than the sensitivity to temperature. For example, in the case of R134a-R245fa, the sensitivity of enthalpy to the concentration uncertainty is two orders of magnitude less than the sensitivity to the temperature uncertainty for single-phase states [6]. As a result, the measured concentration of the working fluid is not a dominant factor in measurement uncer-

To conduct a working fluid charge study, it is desired to explore a wide range of working conditions, different working fluids, and several charge levels. In the current available literature, only the study published by Woodland [6] meets all of these criteria, and, therefore, it is used hereafter as an example. In particular, three working fluids were chosen to investigate low grade waste heat recovery by means of an ORC: R134a, R245fa, and the zeotropic mixture R134a-R245fa (0.625–0.375). In addition, two heat source temperatures, and several charge levels of the working fluids were considered. The range of conditions tested experimentally for each working fluid is summarized in Table 1. A complete description of the ORC system can be found in [6] and its schematic is shown in Figure 1. The effect of the working fluid charge on the ORC system performance is shown in Figure 6, where the Second Law efficiency, defined as the ratio of the system net power to the total exergy rate available, is plotted as a function of the subcooling level for different operating conditions. It can be seen that for a given working fluid and heat source inlet temperature, there exists an optimum charge level that maximizes the Second Law efficiency (i.e., power output) of the system. Furthermore, for each working fluid, the efficiency tends to be higher at lower subcooling due to lower condensing pressures

q

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð Þ <sup>0</sup>:<sup>045</sup> <sup>2</sup> � nsteps

(15)

a function of the number of consecutive charging steps, nsteps, as:

surements of their weight during operation.

32 Organic Rankine Cycle Technology for Heat Recovery

4.2. Effect of charge variations in an ORC system

tainty in this case.

dictated by lower fluid charge.

ucharge ¼

One of the main purposes of a charge-sensitive model is to predict the total charge of a certain ORC system for which it has been developed and its behavior (e.g., evaporating and condensing temperatures, subcooling and superheating). This needs to hold true also under the circumstances that the system is under-charged or over-charged as well as if the working fluid is changed, that is, drop-in replacement. To this end, the same ORC system considered in Section 4.2 is used as an example [6]. The charge-sensitive model is employed to simulate three different working fluids (i.e., R134a, R245fa, and R134a-R245fa (0.635–0.375)) at three different charge levels, without any tuning. The untuned model prediction of the system charge versus the measured charge for all the test points is shown in Figure 7. It can be seen that even without tuning, the model predictions are reasonably accurate due to the fact that the heat

Figure 7. Parity plot showing the ability of the charge-sensitive model to predict the total working fluid charge without any charge tuning.

charge-sensitive ORC system modeling. An empirical two-point charge tuning equation that incorporates a linear function of the length of the subcooled section in the condenser (Lcond,sc)

Figure 8. Heat exchanger length fraction (a) and breakdown of component charge (b) versus condenser exit subcooling when the total charge is imposed as model input. Pump speed = 1000 rpm, expander speed = 2000 rpm, source temperature = 100�C, source and sink fluid flow rates are 0.45 and 1 kg/s, respectively. The charge calculation is untuned.

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35

where Cm, <sup>0</sup> and Cm, <sup>1</sup> are the regression parameters to be estimated by linear regression. The estimated correction term from Eq. (16) is added to the total working fluid charge computed by

In this chapter, the effects of the total working fluid charge on the performance and operation of an ORC system have been discussed. In particular, both numerical and experimental have been used to demonstrate the importance of considering the charge inventory when analyzing off-design conditions of the ORC system. Under-charging or over-charging the system has a direct effect on the spatial distribution of the different zones inside the heat exchangers. Additional aspects such as oil solubility can also have non-negligible impact on the system performance. A detailed mechanistic model of the ORC allows identification of optimal charge level. However, charge-tuning is always required to account for inaccuracies and uncertainties associated with the modeling assumptions. In fact, two-phase heat transfer correlations and void fraction models directly affect the charge inventory estimations. The analysis of the charge inventory of ORC systems is also particularly important when considering drop-in replacements such as HFOs and their blends. The size of the heat exchangers as well as the piping system require an optimal working fluid charge to ensure proper behavior of the ORC

mwf ,meas � mwf , calc ¼ Cm, <sup>0</sup> þ Cm,1Lcond,sc (16)

can be employed:

5. Conclusions

the model to give an unbiased estimate [17].

at both design and off-design conditions.

exchanger volumes as well as the liquid line sets have been accounted for. These liquid volumes remain constant across all experimental tests and therefore set the baseline charge level of the system. However, the model does not predict the variability in charge well for all cases. For R134a, the trend in system charge is captured well, but with increased underprediction of the charge at higher charge levels. For R245fa, the trend is not captured well. A general increase is observed, but the underprediction is significant. For the zeotropic mixture, no trend is visible at all in the charge prediction. Variability in the predicted charge is due to the changing liquid lengths in the heat exchangers, the void fraction of two-phase flow, and the solubility of the working fluid in the lubricant oil. In particular, if the boundary conditions of the ORC are fixed then an increase in the working fluid charge in the system leads to a decrease in the two-phase zone in the condenser (resp. subcooled zone), as shown in Figure 8(a). If the void fraction model and the heat transfer coefficient of the two-phase zone are not estimated correctly, the charge of the subcooled region can be largely under predicted due to the rapid increase in liquid level inside the condenser, as shown in Figure 8(b). Solubility of the working fluid in the oil was not considered in the model. However, it can have a significant impact on prediction of the total system charge. In fact, if an oil separator is present in the ORC system, the working fluid dissolved in the lubricant oil could be up to 10% of the total charge depending on the solubility of the working fluid-lubricant oil mixture [6].

#### 4.4. Charge tuning schemes

As shown in Figure 8, the estimation of working fluid charge in system modeling is usually biased due to inaccurate estimation of system volumes, ambiguous flow patterns under twophase flow conditions, solubility of working fluid in the lubricant oil, etc. A charge-tuning scheme can be used to eliminate the bias. Although such methods have been widely used for vapor compression heat pumping cycles [16, 17], they have not been employed in

Effects of the Working Fluid Charge in Organic Rankine Cycle Power Systems: Numerical and Experimental… http://dx.doi.org/10.5772/intechopen.78026 35

Figure 8. Heat exchanger length fraction (a) and breakdown of component charge (b) versus condenser exit subcooling when the total charge is imposed as model input. Pump speed = 1000 rpm, expander speed = 2000 rpm, source temperature = 100�C, source and sink fluid flow rates are 0.45 and 1 kg/s, respectively. The charge calculation is untuned.

charge-sensitive ORC system modeling. An empirical two-point charge tuning equation that incorporates a linear function of the length of the subcooled section in the condenser (Lcond,sc) can be employed:

$$m\_{\text{uf}, \text{meas}} - m\_{\text{uf}, \text{calc}} = \mathbb{C}\_{m, 0} + \mathbb{C}\_{m, 1} \text{L}\_{\text{cond}, sc} \tag{16}$$

where Cm, <sup>0</sup> and Cm, <sup>1</sup> are the regression parameters to be estimated by linear regression. The estimated correction term from Eq. (16) is added to the total working fluid charge computed by the model to give an unbiased estimate [17].

#### 5. Conclusions

exchanger volumes as well as the liquid line sets have been accounted for. These liquid volumes remain constant across all experimental tests and therefore set the baseline charge level of the system. However, the model does not predict the variability in charge well for all cases. For R134a, the trend in system charge is captured well, but with increased underprediction of the charge at higher charge levels. For R245fa, the trend is not captured well. A general increase is observed, but the underprediction is significant. For the zeotropic mixture, no trend is visible at all in the charge prediction. Variability in the predicted charge is due to the changing liquid lengths in the heat exchangers, the void fraction of two-phase flow, and the solubility of the working fluid in the lubricant oil. In particular, if the boundary conditions of the ORC are fixed then an increase in the working fluid charge in the system leads to a decrease in the two-phase zone in the condenser (resp. subcooled zone), as shown in Figure 8(a). If the void fraction model and the heat transfer coefficient of the two-phase zone are not estimated correctly, the charge of the subcooled region can be largely under predicted due to the rapid increase in liquid level inside the condenser, as shown in Figure 8(b). Solubility of the working fluid in the oil was not considered in the model. However, it can have a significant impact on prediction of the total system charge. In fact, if an oil separator is present in the ORC system, the working fluid dissolved in the lubricant oil could be up to 10% of the total charge

Figure 7. Parity plot showing the ability of the charge-sensitive model to predict the total working fluid charge without

As shown in Figure 8, the estimation of working fluid charge in system modeling is usually biased due to inaccurate estimation of system volumes, ambiguous flow patterns under twophase flow conditions, solubility of working fluid in the lubricant oil, etc. A charge-tuning scheme can be used to eliminate the bias. Although such methods have been widely used for vapor compression heat pumping cycles [16, 17], they have not been employed in

depending on the solubility of the working fluid-lubricant oil mixture [6].

4.4. Charge tuning schemes

any charge tuning.

34 Organic Rankine Cycle Technology for Heat Recovery

In this chapter, the effects of the total working fluid charge on the performance and operation of an ORC system have been discussed. In particular, both numerical and experimental have been used to demonstrate the importance of considering the charge inventory when analyzing off-design conditions of the ORC system. Under-charging or over-charging the system has a direct effect on the spatial distribution of the different zones inside the heat exchangers. Additional aspects such as oil solubility can also have non-negligible impact on the system performance. A detailed mechanistic model of the ORC allows identification of optimal charge level. However, charge-tuning is always required to account for inaccuracies and uncertainties associated with the modeling assumptions. In fact, two-phase heat transfer correlations and void fraction models directly affect the charge inventory estimations. The analysis of the charge inventory of ORC systems is also particularly important when considering drop-in replacements such as HFOs and their blends. The size of the heat exchangers as well as the piping system require an optimal working fluid charge to ensure proper behavior of the ORC at both design and off-design conditions.

## Conflict of interest

The Authors declare no conflict of interest.

sc subcooled

wf working fluid

\*, Rémi Dickes<sup>2</sup>

\*Address all correspondence to: dziviani@purdue.edu

22:168-186. DOI: 10.1016/j.rser.2013.01.028

81:552-562. DOI: 10.1016/j.rser.2017.08.028

Procedia. 2017;129:2-9. DOI: 10.1016/j.egypro.2017.09.159

Energy. 2017;123:710-727. DOI: 10.1016/j.energy.2017.01.130

ture and scroll expander [Thesis]. Purdue University; 2015

simulation tool. Energies. 2016;9:389. DOI: 10.3390/en9060389

, Vincent Lemort<sup>2</sup>

1 Ray W. Herrick Laboratories, School of Mechanical Engineering, Purdue University,

Effects of the Working Fluid Charge in Organic Rankine Cycle Power Systems: Numerical and Experimental…

2 Thermodynamics Laboratory, Aerospace and Mechanical Engineering Department,

[1] Quoilin S, van den Broek M, Declaye S, Dewallef P, Lemort V.: Techno-economic survey of organic Rankine cycle (ORC) systems. Renewable and Sustainable Energy Reviews. 2013;

[2] Tartier T. ORC World Map [Internet]. 2016. Available from: http://www.orc-world-map.org/

[3] Tartièr T, Astolfi M. A world overview of the organic Rankine cycle market. Energy

[4] Imran M, Haglind F, Asim M, Alvi ZJ. Resent research trends in organic Rankine cycle technology: A bibliometric approach. Renewable and Sustainable Energy Reviews. 2018;

[5] Dickes R, Dumont O, Daccord R, Quoilin S, Lemort V. Modelling of organic Rankine cycle power systems in off-design conditions: An experimentally-validated comparative study.

[6] Woodland BJ. Methods of increasing net work output of organic Rankine cycles for lowgrade waste heat recovery with a detailed analysis using a zeotropic working fluid mix-

[7] Ziviani D, Woodland BJ, Georges E, Groll EA, Braun JE, Horton WT, van den Broek M, De Paepe M. Development and a validation of a charge sensitive organic Rankine cycle (ORC)

, James E. Braun<sup>1</sup> and Eckhard A. Groll<sup>1</sup>

http://dx.doi.org/10.5772/intechopen.78026

37

su supply

Author details

Davide Ziviani<sup>1</sup>

References

West Lafayette, IN, USA

University of Liège, Liège, Belgium

[Accessed: March 17, 2018]

## Nomenclature


sc subcooled

su supply

Conflict of interest

Nomenclature

A area, [m<sup>2</sup>

m mass, [kg]

The Authors declare no conflict of interest.

36 Organic Rankine Cycle Technology for Heat Recovery

]

c tuning coefficient, [�]

C regression coefficient, [�] h specific enthalpy, [kJ/kg]

N rotational speed, [rpm]

Nu Nusselt number, [�]

Q heat transfer rate, [W]

R Thermal resistance, [K/W]

Re Reynolds number, [�]

UA heat conductance, [W/K]

]

]

T temperature, [K]

V volume, [m3

x quality, [�]

meas measured

α void fraction, [�] r density, [kg/m<sup>3</sup>

p pressure, [Pa]

calc calculated cond condenser evap evaporator

ex exit

exp. expander

Subscripts

wf working fluid

## Author details

Davide Ziviani<sup>1</sup> \*, Rémi Dickes<sup>2</sup> , Vincent Lemort<sup>2</sup> , James E. Braun<sup>1</sup> and Eckhard A. Groll<sup>1</sup>

\*Address all correspondence to: dziviani@purdue.edu

1 Ray W. Herrick Laboratories, School of Mechanical Engineering, Purdue University, West Lafayette, IN, USA

2 Thermodynamics Laboratory, Aerospace and Mechanical Engineering Department, University of Liège, Liège, Belgium

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Energy. 2018;212:1262-1281. DOI: 10.1016/j.apenergy.2018.01.004

131:884-896. DOI: 10.1016/j.applthermaleng.2017.16.017

2017. pp. 173-249. DOI: 10.1016/B978-0-08-100510-1.00007-7

DOI: 10.1016/j.enconman.2017.06.009

38 Organic Rankine Cycle Technology for Heat Recovery

11.096

2017.10.054

DOI: 10.1016/j.ijrefrig.2009.06.009

ijrefrig.2013.10.007

https://github.com/orcmkit


**Chapter 3**

**Provisional chapter**

**Expanders for Organic Rankine Cycle Technology**

**Expanders for Organic Rankine Cycle Technology**

DOI: 10.5772/intechopen.78720

The overall power conversion efficiency of organic Rankine cycle (ORC) systems is highly sensitive to the isentropic efficiency of expansion machines. No expansion machine type is universally ideal as every machine has its own advantages and disadvantages and is suitable for a comparatively narrow range of operations of the highest efficiency. Therefore, an optimum selection of an expansion machine type is important for a financially viable ORC implementation. This chapter presents the mode of operation, technical feasibility, and challenges in the application of turbo-expanders (radial inflow, radial outflow, and axial machines) and volumetric expansion machines (scroll, screw, piston, and vane) for use in ORC systems. It can be concluded that different machines are suitable for a different range of power output in commercial applications. In general, volumetric machines are suitable for 50 kWe and below but turbomachines are more suitable

**Keywords:** turbomachines, volumetric expanders, organic Rankine cycle, expansion

Organic Rankine (ORC) cycle-based systems have gained popularity in the last 2 decades for heat to power conversion in various applications. In comparison with the traditional Rankine cycle, the ORC-based power systems allow the flexibility to choose working fluids and expansion machines, as an additional degree of freedom, allowing optimal configurations both from the thermodynamic as well as techno-economic aspects. ORC systems can be designed to optimally convert waste heat from internal combustion engine (ICE) exhaust, geothermal heat sources, biomass applications, solar thermal applications, and other thermal

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Fuhaid Alshammari, Muhammad Usman and

Fuhaid Alshammari, Muhammad Usman and

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

for power outputs higher than 50 kWe.

machines, isentropic efficiency

http://dx.doi.org/10.5772/intechopen.78720

Apostolos Pesyridis

Apostolos Pesyridis

**Abstract**

**1. Introduction**

#### **Expanders for Organic Rankine Cycle Technology Expanders for Organic Rankine Cycle Technology**

DOI: 10.5772/intechopen.78720

Fuhaid Alshammari, Muhammad Usman and Apostolos Pesyridis Fuhaid Alshammari, Muhammad Usman and Apostolos Pesyridis

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.78720

#### **Abstract**

The overall power conversion efficiency of organic Rankine cycle (ORC) systems is highly sensitive to the isentropic efficiency of expansion machines. No expansion machine type is universally ideal as every machine has its own advantages and disadvantages and is suitable for a comparatively narrow range of operations of the highest efficiency. Therefore, an optimum selection of an expansion machine type is important for a financially viable ORC implementation. This chapter presents the mode of operation, technical feasibility, and challenges in the application of turbo-expanders (radial inflow, radial outflow, and axial machines) and volumetric expansion machines (scroll, screw, piston, and vane) for use in ORC systems. It can be concluded that different machines are suitable for a different range of power output in commercial applications. In general, volumetric machines are suitable for 50 kWe and below but turbomachines are more suitable for power outputs higher than 50 kWe.

**Keywords:** turbomachines, volumetric expanders, organic Rankine cycle, expansion machines, isentropic efficiency

#### **1. Introduction**

Organic Rankine (ORC) cycle-based systems have gained popularity in the last 2 decades for heat to power conversion in various applications. In comparison with the traditional Rankine cycle, the ORC-based power systems allow the flexibility to choose working fluids and expansion machines, as an additional degree of freedom, allowing optimal configurations both from the thermodynamic as well as techno-economic aspects. ORC systems can be designed to optimally convert waste heat from internal combustion engine (ICE) exhaust, geothermal heat sources, biomass applications, solar thermal applications, and other thermal

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

gradient-based sources like ocean thermal energy conversion (OTEC). The maintenance-free automated operation and relatively smaller installation and operational costs compared to Rankine cycles make them ideal for commercial use specifically in <10 MW-scale applications.

**2.1. Turbo-expanders**

In the turbo-expander operation, a high-pressure fluid is directed from the evaporator outlet to the turbine inlet, where the high static pressure of the fluid is converted into high-flow velocity when it passes through nozzles. The high-velocity fluid then transfers its momentum to an array of moving blades, while passing through them. The moving blades are attached to a shaft which is connected to a generator to convert the mechanical energy into electrical energy. Turbines used in ORC application are generally different from expansion machines used for air, steam, and other gases because, in steam cycles, the enthalpy drop is much higher than that in ORCs. Thus, fewer turbine stages are required in ORCs; therefore, cheaper and lighter turbines are the result. However, the dense vapour properties vary largely from ideal gas behaviour and the speed of sound is much lower than in lighter gases or steam, which influences the nozzle design [2]. The low speed of sound in dense molecule fluids often causes turbines to operate in transonic and supersonic modes. As a result, a highly dissipative system of shockwaves is common in these machines which complicate the design and sacrifice

Expanders for Organic Rankine Cycle Technology http://dx.doi.org/10.5772/intechopen.78720 43

Turbo-expanders have two main categories: axial turbines and radial turbines, as differentiated in **Figure 1** (adapted from [4]). The main difference between the two categories is the way the working fluid flows in relation to the shaft. In axial turbines, the flow of the working fluid is parallel to the shaft, whereas, in radial turbines, it is radial to the shaft at the inlet converting

Selection of the suitable turbine (axial or radial) depends mainly on the operating conditions and corresponding enthalpy drop required. At low mass flow rates, the blades of the axial turbine become very small which results in a significant efficiency drop due to the difficulty of maintaining small tip clearance between the blades and the casing. Therefore, axial turbines are always preferred in a large-scale application where the mass flow rate is high and pressure ratio is small. In contrast, radial turbines are employed with applications of low mass

performance specifically during off-design operations [3].

**Figure 1.** Schematic of axial flow (left) and radial inflow (right) turbines.

to axial at the outlet of the turbine.

ORC power systems generally comprise four major components, namely: evaporator, condenser, pump, and expander. The evaporator and condenser are primarily heat exchangers, appropriately sized for a certain duty to operate with specified fluids at specific operating conditions. The current state of the art can be considered sufficient enough to support the technological requirements to ensure the availability of heat exchangers to be used as evaporators and condensers. The pumps have also been well developed and can be bought off the shelf to fulfil the requirements of the ORC system. However, the expander can be considered as the most technically advanced component of an ORC system. The expander is the machine which extracts the energy from the expansion of high-pressure vapour resulting in low pressure while passing through its inlet to the outlet port and converts fluid energy to mechanical power (rotational or reciprocating), which is then often converted to electrical power via direct or indirect coupling to a generator. Organic Rankine cycles, in general, have low thermodynamic efficiency due to limited temperature differences between the heat source and heat sink streams. Therefore, the efficiency of the overall cycle is highly sensitive to the efficiency of the expansion machine [1]. Therefore, the selection of an appropriate expander for a certain ORC application is of great importance to avoid further efficiency reductions and for commercial viability. Depending on the application, operating conditions (temperature, pressure, and mass flow rate), working fluid, and power levels, different types of expansion machines can be used.

## **2. Primary classification of expanders**

In general, the expansion machines are classified based on the nature of their operation. They are broadly classified as either turbo-machine or volumetric-type machines. The turbo-machines in this case refer to turbines of the dynamic or velocity type. They convert the dynamic pressure or high-velocity fluid momentum into mechanical energy while passing through a series of blades. The leaving fluid has generally low pressure and an overall enthalpy drop occurs while passing through machines. Turbomachines are more commonly used for medium to large-scale applications and are well known for their higher efficiency. For smaller power output (<50 kWe), volumetric machines are frequently the preferred choice.

The volumetric-type machines are also known as positive displacement machines. They operate on a principle of force application on a movable mechanical component to extract power. The pressurized fluid is introduced into a chamber and the chamber volume is increased as a net force is applied by a compressed fluid. When the chamber reaches its maximum expansion volume, the low-pressure fluid is released out of expander. The volumetric machines are often equipped with valves to control the inlet and outlet flow of fluid and synchronization with expanding chamber. The volumetric expanders are suitable for smaller power output and often derived from heating, ventilation, air-conditioning and cooling (HVAC) compressors modified to operate in reverse. Both turbomachines and volumetric expanders have their own advantages and disadvantages along with several types available for each main category.

#### **2.1. Turbo-expanders**

gradient-based sources like ocean thermal energy conversion (OTEC). The maintenance-free automated operation and relatively smaller installation and operational costs compared to Rankine cycles make them ideal for commercial use specifically in <10 MW-scale applications. ORC power systems generally comprise four major components, namely: evaporator, condenser, pump, and expander. The evaporator and condenser are primarily heat exchangers, appropriately sized for a certain duty to operate with specified fluids at specific operating conditions. The current state of the art can be considered sufficient enough to support the technological requirements to ensure the availability of heat exchangers to be used as evaporators and condensers. The pumps have also been well developed and can be bought off the shelf to fulfil the requirements of the ORC system. However, the expander can be considered as the most technically advanced component of an ORC system. The expander is the machine which extracts the energy from the expansion of high-pressure vapour resulting in low pressure while passing through its inlet to the outlet port and converts fluid energy to mechanical power (rotational or reciprocating), which is then often converted to electrical power via direct or indirect coupling to a generator. Organic Rankine cycles, in general, have low thermodynamic efficiency due to limited temperature differences between the heat source and heat sink streams. Therefore, the efficiency of the overall cycle is highly sensitive to the efficiency of the expansion machine [1]. Therefore, the selection of an appropriate expander for a certain ORC application is of great importance to avoid further efficiency reductions and for commercial viability. Depending on the application, operating conditions (temperature, pressure, and mass flow rate), working fluid, and power levels, different types of expansion machines can be used.

In general, the expansion machines are classified based on the nature of their operation. They are broadly classified as either turbo-machine or volumetric-type machines. The turbo-machines in this case refer to turbines of the dynamic or velocity type. They convert the dynamic pressure or high-velocity fluid momentum into mechanical energy while passing through a series of blades. The leaving fluid has generally low pressure and an overall enthalpy drop occurs while passing through machines. Turbomachines are more commonly used for medium to large-scale applications and are well known for their higher efficiency. For smaller power out-

The volumetric-type machines are also known as positive displacement machines. They operate on a principle of force application on a movable mechanical component to extract power. The pressurized fluid is introduced into a chamber and the chamber volume is increased as a net force is applied by a compressed fluid. When the chamber reaches its maximum expansion volume, the low-pressure fluid is released out of expander. The volumetric machines are often equipped with valves to control the inlet and outlet flow of fluid and synchronization with expanding chamber. The volumetric expanders are suitable for smaller power output and often derived from heating, ventilation, air-conditioning and cooling (HVAC) compressors modified to operate in reverse. Both turbomachines and volumetric expanders have their own advantages and disadvantages along with several types available for each main category.

put (<50 kWe), volumetric machines are frequently the preferred choice.

**2. Primary classification of expanders**

42 Organic Rankine Cycle Technology for Heat Recovery

In the turbo-expander operation, a high-pressure fluid is directed from the evaporator outlet to the turbine inlet, where the high static pressure of the fluid is converted into high-flow velocity when it passes through nozzles. The high-velocity fluid then transfers its momentum to an array of moving blades, while passing through them. The moving blades are attached to a shaft which is connected to a generator to convert the mechanical energy into electrical energy.

Turbines used in ORC application are generally different from expansion machines used for air, steam, and other gases because, in steam cycles, the enthalpy drop is much higher than that in ORCs. Thus, fewer turbine stages are required in ORCs; therefore, cheaper and lighter turbines are the result. However, the dense vapour properties vary largely from ideal gas behaviour and the speed of sound is much lower than in lighter gases or steam, which influences the nozzle design [2]. The low speed of sound in dense molecule fluids often causes turbines to operate in transonic and supersonic modes. As a result, a highly dissipative system of shockwaves is common in these machines which complicate the design and sacrifice performance specifically during off-design operations [3].

Turbo-expanders have two main categories: axial turbines and radial turbines, as differentiated in **Figure 1** (adapted from [4]). The main difference between the two categories is the way the working fluid flows in relation to the shaft. In axial turbines, the flow of the working fluid is parallel to the shaft, whereas, in radial turbines, it is radial to the shaft at the inlet converting to axial at the outlet of the turbine.

Selection of the suitable turbine (axial or radial) depends mainly on the operating conditions and corresponding enthalpy drop required. At low mass flow rates, the blades of the axial turbine become very small which results in a significant efficiency drop due to the difficulty of maintaining small tip clearance between the blades and the casing. Therefore, axial turbines are always preferred in a large-scale application where the mass flow rate is high and pressure ratio is small. In contrast, radial turbines are employed with applications of low mass

**Figure 1.** Schematic of axial flow (left) and radial inflow (right) turbines.

flow rate and high-pressure ratios such as turbochargers and ORC systems. For small flow rates, the radial turbines present more efficient performance due to their lower sensitivity to the blade profile than the axial ones. In addition, ORC applications employ high-density fluids which necessitate a more robust turbine due to the increased blade loading. In such conditions, radial turbines are favourable as the blades are rigidly attached to the hub. Due to the radius reduction from rotor inlet to the exit, radial turbines can handle a single-stage expansion ratio of 9:1, while axial turbines require at least two stages. Therefore, radial turbines are also favourable when the system size is taken into account.

*2.1.1. Radial inflow turbines*

as follows: r1

as nozzle exit diameter, D<sup>4</sup>

b3

as volute inlet radius, r2

inlet radius, r5t as rotor exit tip radius, r5h as rotor exit hub radius, b2

procedure, various designers use their own, bespoke techniques.

turbines specifically for small-scale units over axial machines listed below:

machines often require separate blade and rotor manufacturing.

can help to reduce the overall cost.

axial might need three stages).

age effects.

**Figure 3** presents the meridional view and overall architecture of the turbine stage in a radial inflow turbine (RIT), which are sometimes also referred to as inward flow radial (IFR 90). As it can be observed, the high-pressure fluid enters the casing (volute) inlet and initial flow direction is primarily radial which is converted to the tangential direction circumferentially at the rotor inlet stage where it, also, contains both radial and tangential components. While passing through the rotor the flow loses its tangential component. The leaving flow must have minimum swirl flow at rotor exit. Furthermore, the direction of flow is converted from radial at the inlet to axial at rotor exit where ideally, there is no radial component. The geometric parameters mentioned in **Figure 3** are obtained from the design process and they are defined

as stator inlet radius, r<sup>3</sup>

The design procedure of radial inflow turbines involves, in simplified form, the steps illustrated in **Figure 4**, which presents a typical path followed. Although there is no single correct

The design process of turbines (not only limited to the radial machines) often utilize the concept of mean-line flow which provides a preliminary or baseline one-dimensional design. The techniques assume the properties and parameters to be lumped and focus mainly on the inlet and outlet of cascades. The flow is assumed to be uniform and unidirectional and estimation at the centre line of flow can provide average flow characteristics of the fluid. The outcomes of a mean-line model are linked with blade design often based on experiences from NACA databases and statistical models. The overall design is transformed to a computer-aided design (CAD) model which can be used for three-dimensional computational fluid dynamic (CFD) analysis based on Reynolds average Navier-Stokes (RANS) calculations. The resulting analysis helps in the final tweaks of the fluid dynamic design and to achieve optimum performance. The detailed design and optimization techniques can be found in [6–8] for understanding the radial turbine performance. The authors in [4, 8] compiled a list of advantages of using radial

**1.** Radial inflow machines are often manufactured as single piece cast or forged whereas axial

**2.** Single-piece rotors are more robust, stiff, and have enhanced rotor-dynamic stability which

**3.** RITs can offer better off-design performance when variable geometry nozzles are used. **4.** Downsizing the axial machines for small-scale ORC applications requires blades to be very small and numerous, which increases the wetted area and frictional losses and blade block-

**5.** The running clearance necessary between rotor tip and casing becomes a significant frac-

**6.** RITs support larger pressure ratios in a single stage (up to 10 is common for RIT but the

tion of the blade height which means higher proportionate leakage losses.

as rotor inlet tip diameter and ξ as clearance.

as stator exit radius, r<sup>4</sup>

Expanders for Organic Rankine Cycle Technology http://dx.doi.org/10.5772/intechopen.78720

as nozzle inlet diameter,

as rotor

45

However, generally speaking, axial turbines offer better performance at off-design conditions. Moreover, axial turbines present higher efficiency than radial turbines in large-scale applications such large gas turbines, due to the elimination of the flow turning in the meridional plane. In addition, the disc of the axial turbine is protected at high temperatures since only the blades are exposed to the heat. In radial turbines, on the other hand, both the blades and the disc are exposed to the heat since the expansion takes place at both inducer and exducer of the impeller. However, it is worth mentioning that ORC turbines operate usually at low temperatures where concerns about high temperature are significantly lower compared to other applications. The selection of the optimum configuration had been often related to two dimensionless parameters, that is, specific speed and specific diameter, which are based on the volumetric flow and enthalpy drop. **Figure 2** (adapted from [5] commonly known as Balje diagram) presents the selection map and suggests the use of axial flow machines for large specific speeds which correspond to larger flow rate. However, these diagrams should be used with caution as they were essentially developed for incompressible flow. Despite limitations, they are useful to provide initial information which can be further cross-checked by high fidelity models at later stages.

The radial turbines generally involved radial inflow configuration but recent advances in turbine development have also made the use of radial outflow turbines available in ORC technology which is discussed separately, below.

**Figure 2.** Turbines selection maps based on performance with respect to specific speed and specific diameter.

#### *2.1.1. Radial inflow turbines*

flow rate and high-pressure ratios such as turbochargers and ORC systems. For small flow rates, the radial turbines present more efficient performance due to their lower sensitivity to the blade profile than the axial ones. In addition, ORC applications employ high-density fluids which necessitate a more robust turbine due to the increased blade loading. In such conditions, radial turbines are favourable as the blades are rigidly attached to the hub. Due to the radius reduction from rotor inlet to the exit, radial turbines can handle a single-stage expansion ratio of 9:1, while axial turbines require at least two stages. Therefore, radial tur-

However, generally speaking, axial turbines offer better performance at off-design conditions. Moreover, axial turbines present higher efficiency than radial turbines in large-scale applications such large gas turbines, due to the elimination of the flow turning in the meridional plane. In addition, the disc of the axial turbine is protected at high temperatures since only the blades are exposed to the heat. In radial turbines, on the other hand, both the blades and the disc are exposed to the heat since the expansion takes place at both inducer and exducer of the impeller. However, it is worth mentioning that ORC turbines operate usually at low temperatures where concerns about high temperature are significantly lower compared to other applications. The selection of the optimum configuration had been often related to two dimensionless parameters, that is, specific speed and specific diameter, which are based on the volumetric flow and enthalpy drop. **Figure 2** (adapted from [5] commonly known as Balje diagram) presents the selection map and suggests the use of axial flow machines for large specific speeds which correspond to larger flow rate. However, these diagrams should be used with caution as they were essentially developed for incompressible flow. Despite limitations, they are useful to provide initial information which can be further cross-checked by high fidelity models at later stages.

The radial turbines generally involved radial inflow configuration but recent advances in turbine development have also made the use of radial outflow turbines available in ORC

**Figure 2.** Turbines selection maps based on performance with respect to specific speed and specific diameter.

bines are also favourable when the system size is taken into account.

44 Organic Rankine Cycle Technology for Heat Recovery

technology which is discussed separately, below.

**Figure 3** presents the meridional view and overall architecture of the turbine stage in a radial inflow turbine (RIT), which are sometimes also referred to as inward flow radial (IFR 90). As it can be observed, the high-pressure fluid enters the casing (volute) inlet and initial flow direction is primarily radial which is converted to the tangential direction circumferentially at the rotor inlet stage where it, also, contains both radial and tangential components. While passing through the rotor the flow loses its tangential component. The leaving flow must have minimum swirl flow at rotor exit. Furthermore, the direction of flow is converted from radial at the inlet to axial at rotor exit where ideally, there is no radial component. The geometric parameters mentioned in **Figure 3** are obtained from the design process and they are defined as follows: r1 as volute inlet radius, r2 as stator inlet radius, r<sup>3</sup> as stator exit radius, r<sup>4</sup> as rotor inlet radius, r5t as rotor exit tip radius, r5h as rotor exit hub radius, b2 as nozzle inlet diameter, b3 as nozzle exit diameter, D<sup>4</sup> as rotor inlet tip diameter and ξ as clearance.

The design procedure of radial inflow turbines involves, in simplified form, the steps illustrated in **Figure 4**, which presents a typical path followed. Although there is no single correct procedure, various designers use their own, bespoke techniques.

The design process of turbines (not only limited to the radial machines) often utilize the concept of mean-line flow which provides a preliminary or baseline one-dimensional design. The techniques assume the properties and parameters to be lumped and focus mainly on the inlet and outlet of cascades. The flow is assumed to be uniform and unidirectional and estimation at the centre line of flow can provide average flow characteristics of the fluid. The outcomes of a mean-line model are linked with blade design often based on experiences from NACA databases and statistical models. The overall design is transformed to a computer-aided design (CAD) model which can be used for three-dimensional computational fluid dynamic (CFD) analysis based on Reynolds average Navier-Stokes (RANS) calculations. The resulting analysis helps in the final tweaks of the fluid dynamic design and to achieve optimum performance. The detailed design and optimization techniques can be found in [6–8] for understanding the radial turbine performance. The authors in [4, 8] compiled a list of advantages of using radial turbines specifically for small-scale units over axial machines listed below:


#### *2.1.2. Radial outflow turbines*

The flow direction in a radial outflow turbine (ROT) is opposite to that of the radial inflow machine. The flow enters the ROT at the centre, near the axis of rotation, axially, and then it travels outwards in the radial direction while passing through arrays of rotor and stator blades. **Figure 5**, adapted from the works of [9], presents the schematic of radial outflow turbines which are also known as centrifugal turbines.

The low speed of sound in organic fluids requires supersonic or at least transonic flows which lead to losses due to shock formation and interaction. The large volumetric expansion of organic fluids requires larger areas at the exit of turbines for the reduction in losses. The ROTs can have the inherent feature of enlargement in the area as the flow moves in a radial direction which means supersonic flows can be avoided and losses can be reduced to end up with high-efficiency turbines.

The ROTs allow the adoption of multi-stator-rotor ring arrangements in the radial direction maintaining low peripheral speeds, resulting in low mechanical stresses, lower bearing losses, and simple connections of generator and grid. Furthermore, full-admission inlet stages can be adapted. The simplicity of multistage assembly allows tighter tolerances and thus losses can

Expanders for Organic Rankine Cycle Technology http://dx.doi.org/10.5772/intechopen.78720 47

The disadvantages of ROTs include slightly lower efficiencies compared to RITs as large a surface area is in contact with fluid during flow. Furthermore, for heavy-/large-molecule working fluids, the first stage often has insufficient flow passage area due to the inherent square root proportionality of radius to area, therefore, limiting the turbine application for high-temperature applications. ROTs are more suitable for small-scale applications compared

The axial turbines are characterized by the primary flow of the working fluid which is in axial direction and parallel to the rotational axis. Axial machines are more suitable for larger flow rates, which mean having larger specific speeds as per the Balje diagram (**Figure 2**). In ORC technology, these machines are often suitable for medium-to-large power outputs in single or multistage configurations ranging from one to five. The isentropic efficiencies of axial machines in nominal operations range from 80 to 90% [2]. The axial machines are the most commonly used turbomachine for power production, approximately 70% of power generated

be reduced. The detailed design and analysis of ROTs are presented in [9, 10].

to micro-/mini-ORC applications.

**Figure 5.** Schematic of radial outflow turbine.

*2.1.3. Axial turbines*

**Figure 3.** Meridional view (left) and architecture of turbine stage (right).

**Figure 4.** The fluid dynamic design process of turbine design.

**Figure 5.** Schematic of radial outflow turbine.

*2.1.2. Radial outflow turbines*

46 Organic Rankine Cycle Technology for Heat Recovery

high-efficiency turbines.

turbines which are also known as centrifugal turbines.

**Figure 3.** Meridional view (left) and architecture of turbine stage (right).

**Figure 4.** The fluid dynamic design process of turbine design.

The flow direction in a radial outflow turbine (ROT) is opposite to that of the radial inflow machine. The flow enters the ROT at the centre, near the axis of rotation, axially, and then it travels outwards in the radial direction while passing through arrays of rotor and stator blades. **Figure 5**, adapted from the works of [9], presents the schematic of radial outflow

The low speed of sound in organic fluids requires supersonic or at least transonic flows which lead to losses due to shock formation and interaction. The large volumetric expansion of organic fluids requires larger areas at the exit of turbines for the reduction in losses. The ROTs can have the inherent feature of enlargement in the area as the flow moves in a radial direction which means supersonic flows can be avoided and losses can be reduced to end up with

> The ROTs allow the adoption of multi-stator-rotor ring arrangements in the radial direction maintaining low peripheral speeds, resulting in low mechanical stresses, lower bearing losses, and simple connections of generator and grid. Furthermore, full-admission inlet stages can be adapted. The simplicity of multistage assembly allows tighter tolerances and thus losses can be reduced. The detailed design and analysis of ROTs are presented in [9, 10].

> The disadvantages of ROTs include slightly lower efficiencies compared to RITs as large a surface area is in contact with fluid during flow. Furthermore, for heavy-/large-molecule working fluids, the first stage often has insufficient flow passage area due to the inherent square root proportionality of radius to area, therefore, limiting the turbine application for high-temperature applications. ROTs are more suitable for small-scale applications compared to micro-/mini-ORC applications.

#### *2.1.3. Axial turbines*

The axial turbines are characterized by the primary flow of the working fluid which is in axial direction and parallel to the rotational axis. Axial machines are more suitable for larger flow rates, which mean having larger specific speeds as per the Balje diagram (**Figure 2**). In ORC technology, these machines are often suitable for medium-to-large power outputs in single or multistage configurations ranging from one to five. The isentropic efficiencies of axial machines in nominal operations range from 80 to 90% [2]. The axial machines are the most commonly used turbomachine for power production, approximately 70% of power generated is based on these machines as the preferred expander type of large power units. One of the limitations of axial machines is that considering large-stage expansion ratios, the axial channel undergoes span-wise enlargements with a negative impact on performance. Furthermore, highly supersonic conditions may be found at stator exit and converging-diverging nozzle arrangement, which may not be conducive for good off-design performance. Despite their few limitations, axial machines are adapted in large-scale applications in power plants using steam or Brayton cycles and they are also popular in nuclear power applications along with megawatt-scale power output in ORC applications.

are often soluble in working fluid and can be circulated in the complete ORC cycle or only in the expander by means of separation mechanisms where oil is removed and re-circulated in the expander. The oil separation systems incur the cost of extra equipment and add to system complexity. The complete circulation might have detrimental effects on heat exchanger performance. In order to mitigate these issues, working fluids with good lubricant properties are preferred. Oil-free expanders have also been developed and the lubrication for their bearings

Expanders for Organic Rankine Cycle Technology http://dx.doi.org/10.5772/intechopen.78720 49

**Figure 6** adapted from [13] presents the under- and over-expansion losses. The volumetric machines have fixed volumetric ratio, so the thermodynamic cycle must be designed for optimum expansion ratio. It might be possible that a higher pressure ratio may theoretically lead to higher efficiency but the over-expansion losses will limit the overall performance so the close match between cycle and machine expansion ratio must exist. In recent years, volumetric expanders have received a great deal of attention in small-scale systems due to their good

Scroll expanders consist of two spirals: an orbiting scroll and fixed scroll as presented in **Figure 7** adapted from [14]. The orbiting scroll moves along with the fixed scroll within tight tolerances. The working fluid moves in from the centre and moves outwards inside the chamber between the orbiting and moving scroll. They are widely used as they can be derived from a scroll compressor, thereby, reducing the machine cost. Scroll expander can be either compliant or constrained. In the former, a lubrication system is required in order to reduce the friction between the contacting sidewalls. In the latter, lubrication is not required due to the existence of the linking mechanism between the rotating and fixed scrolls. In addition, there

Scroll expanders usually operate at low power output applications (<10 kWe) due to their limited speed. In addition, they are preferred in small-scale applications due to their low parts count, which reduces the level of noise, increases the reliability, and makes them more cost

is no need for exhaust valves which results in noise reduction.

**Figure 6.** The under expansion (left) and over expansion (right) losses.

is done by the application of grease [12].

off-design performance.

*2.2.1. Scroll expanders*

Axial machines are adaptable and a list is populated by [11] to highlight the reasons for their flexibility.


The design and performance evaluation of axial machines is performed in a similar manner as for radial machines and details of which can be found in works of [11]. However, the simple correlations of efficiency prediction for gas and steam turbines are not strictly valid for ORC applications.

## **2.2. Volumetric expanders**

Volumetric expanders can be classified into four main categories: scroll, screw, piston, and rotary vane. Unlike turbo-expanders where the fluid movement is continuous, in volumetric expanders, it is cyclic. An inherent characteristic of this type of expanders is the fixed volume expansion ratio. They operate by trapping a fixed volume of the fluid and displacing this volume into the discharge of the machine, resulting in mechanical work due to the pressure drop. Therefore, they are also called displacement expanders.

Contrary to turbines, some volumetric expanders may have valves at inlet and outlet ports. The compressed fluid is fed into a chamber and inlet valves are closed, the expansion process starts, and at the end of the expansion, the outlet valve is opened to release the low-pressure fluid. These might be useful to control the timing and flow through an expander but it incurs significant losses. Piston-type expanders often have valves, scroll machines may also have these valves, but in general, screw, scroll, and vane type-expanders operate without valves.

Another peculiarity of volumetric expanders is related to their lubrication requirement. As they operate on the principle of changing volumetric capacity, there must exist some parts which are moving in contact with other surfaces to increase the volume for expansion. The contact movement adds friction which increases the wear, tear, and heat of the surfaces. Lubricant oil is often circulated especially in scroll- and screw-type expanders, which reduce the friction and also help seal the clearances and reduce leakage losses. The lubricant oils used are often soluble in working fluid and can be circulated in the complete ORC cycle or only in the expander by means of separation mechanisms where oil is removed and re-circulated in the expander. The oil separation systems incur the cost of extra equipment and add to system complexity. The complete circulation might have detrimental effects on heat exchanger performance. In order to mitigate these issues, working fluids with good lubricant properties are preferred. Oil-free expanders have also been developed and the lubrication for their bearings is done by the application of grease [12].

**Figure 6** adapted from [13] presents the under- and over-expansion losses. The volumetric machines have fixed volumetric ratio, so the thermodynamic cycle must be designed for optimum expansion ratio. It might be possible that a higher pressure ratio may theoretically lead to higher efficiency but the over-expansion losses will limit the overall performance so the close match between cycle and machine expansion ratio must exist. In recent years, volumetric expanders have received a great deal of attention in small-scale systems due to their good off-design performance.

#### *2.2.1. Scroll expanders*

is based on these machines as the preferred expander type of large power units. One of the limitations of axial machines is that considering large-stage expansion ratios, the axial channel undergoes span-wise enlargements with a negative impact on performance. Furthermore, highly supersonic conditions may be found at stator exit and converging-diverging nozzle arrangement, which may not be conducive for good off-design performance. Despite their few limitations, axial machines are adapted in large-scale applications in power plants using steam or Brayton cycles and they are also popular in nuclear power applications along with

Axial machines are adaptable and a list is populated by [11] to highlight the reasons for their

**1.** Pressure can be as high as 300 bar (supercritical cycle) or too low (few hundredths of a bar,

**2.** Overall pressure ratio could be as high as several thousand or as low as 1.0002 in wind

**3.** The diameters could be ranging from few centimetres to 100 m in wind turbine applications.

The design and performance evaluation of axial machines is performed in a similar manner as for radial machines and details of which can be found in works of [11]. However, the simple correlations of efficiency prediction for gas and steam turbines are not strictly valid for ORC

Volumetric expanders can be classified into four main categories: scroll, screw, piston, and rotary vane. Unlike turbo-expanders where the fluid movement is continuous, in volumetric expanders, it is cyclic. An inherent characteristic of this type of expanders is the fixed volume expansion ratio. They operate by trapping a fixed volume of the fluid and displacing this volume into the discharge of the machine, resulting in mechanical work due to the pressure

Contrary to turbines, some volumetric expanders may have valves at inlet and outlet ports. The compressed fluid is fed into a chamber and inlet valves are closed, the expansion process starts, and at the end of the expansion, the outlet valve is opened to release the low-pressure fluid. These might be useful to control the timing and flow through an expander but it incurs significant losses. Piston-type expanders often have valves, scroll machines may also have these valves, but in general, screw, scroll, and vane type-expanders operate without valves.

Another peculiarity of volumetric expanders is related to their lubrication requirement. As they operate on the principle of changing volumetric capacity, there must exist some parts which are moving in contact with other surfaces to increase the volume for expansion. The contact movement adds friction which increases the wear, tear, and heat of the surfaces. Lubricant oil is often circulated especially in scroll- and screw-type expanders, which reduce the friction and also help seal the clearances and reduce leakage losses. The lubricant oils used

drop. Therefore, they are also called displacement expanders.

megawatt-scale power output in ORC applications.

last stages of the steam cycle).

48 Organic Rankine Cycle Technology for Heat Recovery

flexibility.

turbines.

applications.

**2.2. Volumetric expanders**

Scroll expanders consist of two spirals: an orbiting scroll and fixed scroll as presented in **Figure 7** adapted from [14]. The orbiting scroll moves along with the fixed scroll within tight tolerances. The working fluid moves in from the centre and moves outwards inside the chamber between the orbiting and moving scroll. They are widely used as they can be derived from a scroll compressor, thereby, reducing the machine cost. Scroll expander can be either compliant or constrained. In the former, a lubrication system is required in order to reduce the friction between the contacting sidewalls. In the latter, lubrication is not required due to the existence of the linking mechanism between the rotating and fixed scrolls. In addition, there is no need for exhaust valves which results in noise reduction.

Scroll expanders usually operate at low power output applications (<10 kWe) due to their limited speed. In addition, they are preferred in small-scale applications due to their low parts count, which reduces the level of noise, increases the reliability, and makes them more cost

**Figure 6.** The under expansion (left) and over expansion (right) losses.

**Figure 7.** Operation of the scroll expander.

effective. Scroll expanders have a volumetric ratio between 1.5 and 5 and maximum power output reported of 12 kW [15]. Moreover, scroll expanders can have high efficiency as 80% at different operating conditions. Furthermore, the off-design operation of scroll machines was presented in the works of [16] and **Figure 8** adapted from [15] presents the accounting of losses of scroll machine when operated at various pressure ratios.

The results suggest that the highest efficiency is achieved when the scroll machine is operating at a built-in pressure ratio of 4–7. Furthermore, it can be inferred that decline in performance is more rapid for underexpansion when compared with overexpansion. This suggests that a slightly oversized machine will be a better choice for varying load applications. The primary operation range for scroll machines is from 0.5 kWe to 10 kWe output power range. Scroll machines are primarily derived from refrigeration and HVAC compressor units. They could be in various sealing conditions, for instance, hermetic, semi-hermetic, and open-drive configurations. Hermetic-type machines contain electric machines sealed in a single casing along with the compressor/expander. The working fluids may come in contact with electric coils and help to cool down the electrical systems. The machine is not supposed to be opened for services. The semi-hermetic configuration allows the machine to be dismantled for servicing and open-drive systems have generators/motors completely separate from the expander/compressor. The generator/motor is connected to expansion machine by a belt or magnetic coupling allowing the sealing to be limited to expansion machine components only. Technological enhancements to increase the volumetric ratio are being pursued; one of the ways to increase the built-in volume ratio is by utilizing variable thickness walls. However, no such commercial unit is available yet. The operating speeds in general for scroll machines are around 3600 RPM so the generators can be directly coupled to them.

of twin screw expander. The synchronized movement of intermeshing rotors generates volume profiles that originate at one end of the rotor and terminate at another end. The working fluid is expanded in that meshed chamber. Screw expanders can be applied in systems with power outputs up to 1 MW. Lubrication is required in screw expanders due to the direct contact between the rotors. However, lubrication can be omitted if a fluid with lubrication specification is adopted. Like scroll expanders, screw expanders can operate with wet work-

Expanders for Organic Rankine Cycle Technology http://dx.doi.org/10.5772/intechopen.78720 51

The rotor clearance is below 50 μm so the leakage losses are comparatively small, thus reducing friction losses. Screw machines exhibit in general medium levels of noise and high costs.

ing fluids since they can accept large mass fractions.

**Figure 9.** Schematic of a twin screw expander.

**Figure 8.** Variation in efficiency as a function of pressure ratio.

#### *2.2.2. Screw expanders*

Screw expanders are composed of two helical rotors designed with an accurate profile to trap the required amount of the working fluid. **Figure 9** (adapted from [17]) presents a schematic

**Figure 8.** Variation in efficiency as a function of pressure ratio.

effective. Scroll expanders have a volumetric ratio between 1.5 and 5 and maximum power output reported of 12 kW [15]. Moreover, scroll expanders can have high efficiency as 80% at different operating conditions. Furthermore, the off-design operation of scroll machines was presented in the works of [16] and **Figure 8** adapted from [15] presents the accounting of

The results suggest that the highest efficiency is achieved when the scroll machine is operating at a built-in pressure ratio of 4–7. Furthermore, it can be inferred that decline in performance is more rapid for underexpansion when compared with overexpansion. This suggests that a slightly oversized machine will be a better choice for varying load applications. The primary operation range for scroll machines is from 0.5 kWe to 10 kWe output power range. Scroll machines are primarily derived from refrigeration and HVAC compressor units. They could be in various sealing conditions, for instance, hermetic, semi-hermetic, and open-drive configurations. Hermetic-type machines contain electric machines sealed in a single casing along with the compressor/expander. The working fluids may come in contact with electric coils and help to cool down the electrical systems. The machine is not supposed to be opened for services. The semi-hermetic configuration allows the machine to be dismantled for servicing and open-drive systems have generators/motors completely separate from the expander/compressor. The generator/motor is connected to expansion machine by a belt or magnetic coupling allowing the sealing to be limited to expansion machine components only. Technological enhancements to increase the volumetric ratio are being pursued; one of the ways to increase the built-in volume ratio is by utilizing variable thickness walls. However, no such commercial unit is available yet. The operating speeds in general for scroll machines

losses of scroll machine when operated at various pressure ratios.

**Figure 7.** Operation of the scroll expander.

50 Organic Rankine Cycle Technology for Heat Recovery

are around 3600 RPM so the generators can be directly coupled to them.

Screw expanders are composed of two helical rotors designed with an accurate profile to trap the required amount of the working fluid. **Figure 9** (adapted from [17]) presents a schematic

*2.2.2. Screw expanders*

**Figure 9.** Schematic of a twin screw expander.

of twin screw expander. The synchronized movement of intermeshing rotors generates volume profiles that originate at one end of the rotor and terminate at another end. The working fluid is expanded in that meshed chamber. Screw expanders can be applied in systems with power outputs up to 1 MW. Lubrication is required in screw expanders due to the direct contact between the rotors. However, lubrication can be omitted if a fluid with lubrication specification is adopted. Like scroll expanders, screw expanders can operate with wet working fluids since they can accept large mass fractions.

The rotor clearance is below 50 μm so the leakage losses are comparatively small, thus reducing friction losses. Screw machines exhibit in general medium levels of noise and high costs. The volumetric ratio can be from 2 to 8. Expander power output ranges from 1.5 kW up to 1 MW. The isentropic efficiencies have been reported to be as high as 70% [15]. They can operate at higher RPM configurations than scroll machines, and a gearbox may be required if the machine is operating above 5000 RPM, which is not uncommon for screw machines. In general screw, machines are suitable for power applications from 5 to 50 kW in ORC applications. **Figure 10** (adapted from [18]) presents the selection maps of working fluids for operation with screw machines based on evaporation and condensing temperatures.

#### *2.2.3. Piston expanders*

The working fluid enters the piston expander when the piston is around the top dead centre (TDC) and the inlet valve is then closed. The fluid expands as the piston is pushed by the internal pressure; the energy is transferred to the central crankshaft by connecting rod. The exit valve is opened up at bottom dead centre and expanded working fluid starts moving out of the chamber as the piston moves back to TDC as shown in **Figure 11**.

lower mass flow rates. Piston expanders can operate under two-phase conditions of the working fluid. However, they are heavy and suffer from noise and vibration. However, like some volumetric expanders, lubrication is required in piston expanders but entails the difficulty of implementation because the oil should be mixed with the working fluid, which reduces the efficiency of the cycle. The piston expanders mainly suffer from the requirement for weight balancing, torque impulse, heavy weight, precise valve operation, and a large number of parts

Expanders for Organic Rankine Cycle Technology http://dx.doi.org/10.5772/intechopen.78720 53

Rotary vane expanders are operated based on Wankel concept. **Figure 12** adapted from [19] presents the working of a vane expander. Working fluid enters the expander at the location having small clearance. A rotor with moveable vanes is attached to a rotor which is in close proximity to the casing in asymmetric orientation. The rotation of the rotor allows the vanes to move outwards while trapping working fluid, as the rotation angle increases the volume

Their reported power output ranges from few watts to 2.2 kW. As some volumetric expanders, they can be directly attached to the generator due to their low rotational speeds. They are usually preferred to reduce the system costs because of their simple design and low manufacturing costs, higher torque, and higher volumetric efficiency. In addition, they are mechanically simple and available commercially. In addition, they are characterized by small vibration, low acoustic impact, and simple and reliable structure. However, they exhibit lower isentropic efficiencies compared to other volumetric expanders due to leakages and higher friction losses. Furthermore, the machine must be lubricated to minimize wear and enhance sealing. **Figure 13** presents a picture of actual vane expander and the size can be estimated from the figure. Despite their popularity for micro-scale applications, they have certain technical limitations. The volumetric ratio is limited with commonly reported values of 3–7. The maximum temperature at the inlet is also limited to around 140°C. To ensure the vane movement in the groove and to still minimize the leakage, a tight tolerance is maintained. If a very hightemperature working fluid is passing through it, the expansion of vanes might cause them to stick and the machine will cease its operation. This limits the use of vane expanders for

bound by consecutive vanes increases and expansion of working fluid occurs.

[4] but they have mature manufacturing technology available.

**Figure 11.** Pressure-volume diagram of piston expander.

*2.2.4. Rotary vane expanders*

high-temperature applications [12].

The piston expanders can have a single piston or multiple piston-cylinder arrangements. The designs are also not limited to the piston-connecting rod and crank-based systems. Linear piston expanders are gaining popularity where a single piston may oscillate in a cylinder and operate in two volume chambers at opposite ends. Apart from the aforementioned, axial configuration, rolling pistons, and swash plates are some of the different types of piston expanders.

Pistons expanders are known to have lower isentropic efficiencies compared to corresponding turbomachines, for example. The maximum reported efficiency is 76% and the average is reported to be around 50% [15]. Piston expanders are characterized by relatively large pressure ratios of 6–14. Due to the low power outputs, such types of volumetric expanders are preferred in small- and micro-scale applications. In general, the output of the expander around 2 kW is reported but one of the works has reported 18.6 kW with steam as the working fluid [15]. Unlike the previous categories of volumetric expanders, piston expanders are adopted with inlet and discharge valves to control the suction and discharge processes. However, for the latter process, exhaust ports can be applied instead of valves which lead to larger work and

**Figure 10.** Selection maps for screw expander application.

**Figure 11.** Pressure-volume diagram of piston expander.

lower mass flow rates. Piston expanders can operate under two-phase conditions of the working fluid. However, they are heavy and suffer from noise and vibration. However, like some volumetric expanders, lubrication is required in piston expanders but entails the difficulty of implementation because the oil should be mixed with the working fluid, which reduces the efficiency of the cycle. The piston expanders mainly suffer from the requirement for weight balancing, torque impulse, heavy weight, precise valve operation, and a large number of parts [4] but they have mature manufacturing technology available.

#### *2.2.4. Rotary vane expanders*

The volumetric ratio can be from 2 to 8. Expander power output ranges from 1.5 kW up to 1 MW. The isentropic efficiencies have been reported to be as high as 70% [15]. They can operate at higher RPM configurations than scroll machines, and a gearbox may be required if the machine is operating above 5000 RPM, which is not uncommon for screw machines. In general screw, machines are suitable for power applications from 5 to 50 kW in ORC applications. **Figure 10** (adapted from [18]) presents the selection maps of working fluids for opera-

The working fluid enters the piston expander when the piston is around the top dead centre (TDC) and the inlet valve is then closed. The fluid expands as the piston is pushed by the internal pressure; the energy is transferred to the central crankshaft by connecting rod. The exit valve is opened up at bottom dead centre and expanded working fluid starts moving out

The piston expanders can have a single piston or multiple piston-cylinder arrangements. The designs are also not limited to the piston-connecting rod and crank-based systems. Linear piston expanders are gaining popularity where a single piston may oscillate in a cylinder and operate in two volume chambers at opposite ends. Apart from the aforementioned, axial configuration, rolling pistons, and swash plates are some of the different types of piston expanders. Pistons expanders are known to have lower isentropic efficiencies compared to corresponding turbomachines, for example. The maximum reported efficiency is 76% and the average is reported to be around 50% [15]. Piston expanders are characterized by relatively large pressure ratios of 6–14. Due to the low power outputs, such types of volumetric expanders are preferred in small- and micro-scale applications. In general, the output of the expander around 2 kW is reported but one of the works has reported 18.6 kW with steam as the working fluid [15]. Unlike the previous categories of volumetric expanders, piston expanders are adopted with inlet and discharge valves to control the suction and discharge processes. However, for the latter process, exhaust ports can be applied instead of valves which lead to larger work and

tion with screw machines based on evaporation and condensing temperatures.

of the chamber as the piston moves back to TDC as shown in **Figure 11**.

**Figure 10.** Selection maps for screw expander application.

*2.2.3. Piston expanders*

52 Organic Rankine Cycle Technology for Heat Recovery

Rotary vane expanders are operated based on Wankel concept. **Figure 12** adapted from [19] presents the working of a vane expander. Working fluid enters the expander at the location having small clearance. A rotor with moveable vanes is attached to a rotor which is in close proximity to the casing in asymmetric orientation. The rotation of the rotor allows the vanes to move outwards while trapping working fluid, as the rotation angle increases the volume bound by consecutive vanes increases and expansion of working fluid occurs.

Their reported power output ranges from few watts to 2.2 kW. As some volumetric expanders, they can be directly attached to the generator due to their low rotational speeds. They are usually preferred to reduce the system costs because of their simple design and low manufacturing costs, higher torque, and higher volumetric efficiency. In addition, they are mechanically simple and available commercially. In addition, they are characterized by small vibration, low acoustic impact, and simple and reliable structure. However, they exhibit lower isentropic efficiencies compared to other volumetric expanders due to leakages and higher friction losses. Furthermore, the machine must be lubricated to minimize wear and enhance sealing. **Figure 13** presents a picture of actual vane expander and the size can be estimated from the figure. Despite their popularity for micro-scale applications, they have certain technical limitations. The volumetric ratio is limited with commonly reported values of 3–7. The maximum temperature at the inlet is also limited to around 140°C. To ensure the vane movement in the groove and to still minimize the leakage, a tight tolerance is maintained. If a very hightemperature working fluid is passing through it, the expansion of vanes might cause them to stick and the machine will cease its operation. This limits the use of vane expanders for high-temperature applications [12].

liquid droplets during the expansion process which can lead to erosion problems. ORC systems utilizing variable heat source conditions (flow rate or temperature) are specifically prone to two-phase fluid admittance in expansion machines. Although the degree of superheating is continuously monitored by control systems, under severe fluctuating heat source conditions, which are typical for an automobile engine operating in an urban driving cycle, the tight control of the degree of superheating becomes difficult even for state-of-the-art control schemes. The influx of the liquid phase becomes unavoidable in such cases. Furthermore, the trilateral flash cycles are considered thermodynamically beneficial [21, 22] but they need expansion

Expanders for Organic Rankine Cycle Technology http://dx.doi.org/10.5772/intechopen.78720 55

The turbo-expanders have very limited capability to handle multiphase flows. Major erosion problems arise when liquid droplets strike the rotor blades. Thin liquid films may form on the stator and then larger droplets are shed which accelerate along the high-velocity gas molecules towards the rotor blades. The velocity of droplets is not immensely high due to their large inertia but when fast-moving rotor blades are hit the change in momentum can cause tremendous localized forces and cause the erosion of rotor blades specifically at leading edges and near the tip due to higher tangential velocities [23]. Some coatings can slow down the erosion process but increase the expander cost and complexity. Water drainage systems and blade heating

systems to prevent liquid flow are very difficult to implement for small-scale systems.

Volumetric machines are generally more tolerant to admission liquid phase primarily due to lower component velocities involved. Scroll and screw machines are well known for the capability of flooded expansion. Recent research [24] compared the experimental results of a 2 kW-class scroll machine for superheated expansion and flooded expansion. The results indicate that system can run smoothly for flooded expansion and even at conditions where both inlet and outlet of the expander have two-phase conditions. The net power output was observed to be lower as the cycle work output is reduced thermodynamically. However, it was not possible to report the isentropic efficiency in the multiphase expansion regime as instrumentation capability was limited. Furthermore, a significant quantity of oil was used to test the liquid flooded expansion in the scroll machine in the works of [25] and only a modest decrease in performance was observed. It was also discovered that liquid injection can reduce the leakage losses in scroll machines and can be a promising solution for trilateral flash-cycle

Screw expanders are particularly popular for their potential use in trilateral flash cycles. Screw machines have been tested with flooded expansion in various studies. Up to 0.1 mass fraction of liquid oil was used to test the performance of the expander in [27] and it was reported that the presence of liquid oil helps to seal the clearance volumes at lower operational speeds and as throttling losses become dominant at higher rotational speeds. The authors concluded that further work with low-viscosity working fluids and impact of gases and liquid working fluid along with lubricants needs to be pursued. The authors in [28] compared dry expansion and water-flooded expansion and concluded that water-flooded machines are preferable to dry-running machines for all circumferential speeds but oil-flooded expansion was beneficial for lower speeds. It was also proposed in the literature [29] that screw expanders can be built no larger than current gas compressors to work as two-phase expanders with far higher efficiencies than were believed to be possible for trilateral flash cycles. If the liquid-flooded working fluid can also act as the lubricant instead of oil, the expander and cycle performance

machines which are capable of handling multiphase fluids.

expanders for the smaller scale [26].

**Figure 12.** Operation of a rotary vane expander.

**Figure 13.** Photograph of the actual vane expander from the works of [20].

## **3. Multiphase expansion capability**

Working fluids with a positive temperature-entropy slope or at least isentropic expansion capability are preferred for organic Rankine cycle applications to avoid the formation of liquid droplets during the expansion process which can lead to erosion problems. ORC systems utilizing variable heat source conditions (flow rate or temperature) are specifically prone to two-phase fluid admittance in expansion machines. Although the degree of superheating is continuously monitored by control systems, under severe fluctuating heat source conditions, which are typical for an automobile engine operating in an urban driving cycle, the tight control of the degree of superheating becomes difficult even for state-of-the-art control schemes. The influx of the liquid phase becomes unavoidable in such cases. Furthermore, the trilateral flash cycles are considered thermodynamically beneficial [21, 22] but they need expansion machines which are capable of handling multiphase fluids.

The turbo-expanders have very limited capability to handle multiphase flows. Major erosion problems arise when liquid droplets strike the rotor blades. Thin liquid films may form on the stator and then larger droplets are shed which accelerate along the high-velocity gas molecules towards the rotor blades. The velocity of droplets is not immensely high due to their large inertia but when fast-moving rotor blades are hit the change in momentum can cause tremendous localized forces and cause the erosion of rotor blades specifically at leading edges and near the tip due to higher tangential velocities [23]. Some coatings can slow down the erosion process but increase the expander cost and complexity. Water drainage systems and blade heating systems to prevent liquid flow are very difficult to implement for small-scale systems.

Volumetric machines are generally more tolerant to admission liquid phase primarily due to lower component velocities involved. Scroll and screw machines are well known for the capability of flooded expansion. Recent research [24] compared the experimental results of a 2 kW-class scroll machine for superheated expansion and flooded expansion. The results indicate that system can run smoothly for flooded expansion and even at conditions where both inlet and outlet of the expander have two-phase conditions. The net power output was observed to be lower as the cycle work output is reduced thermodynamically. However, it was not possible to report the isentropic efficiency in the multiphase expansion regime as instrumentation capability was limited. Furthermore, a significant quantity of oil was used to test the liquid flooded expansion in the scroll machine in the works of [25] and only a modest decrease in performance was observed. It was also discovered that liquid injection can reduce the leakage losses in scroll machines and can be a promising solution for trilateral flash-cycle expanders for the smaller scale [26].

Screw expanders are particularly popular for their potential use in trilateral flash cycles. Screw machines have been tested with flooded expansion in various studies. Up to 0.1 mass fraction of liquid oil was used to test the performance of the expander in [27] and it was reported that the presence of liquid oil helps to seal the clearance volumes at lower operational speeds and as throttling losses become dominant at higher rotational speeds. The authors concluded that further work with low-viscosity working fluids and impact of gases and liquid working fluid along with lubricants needs to be pursued. The authors in [28] compared dry expansion and water-flooded expansion and concluded that water-flooded machines are preferable to dry-running machines for all circumferential speeds but oil-flooded expansion was beneficial for lower speeds. It was also proposed in the literature [29] that screw expanders can be built no larger than current gas compressors to work as two-phase expanders with far higher efficiencies than were believed to be possible for trilateral flash cycles. If the liquid-flooded working fluid can also act as the lubricant instead of oil, the expander and cycle performance

**3. Multiphase expansion capability**

**Figure 12.** Operation of a rotary vane expander.

54 Organic Rankine Cycle Technology for Heat Recovery

**Figure 13.** Photograph of the actual vane expander from the works of [20].

Working fluids with a positive temperature-entropy slope or at least isentropic expansion capability are preferred for organic Rankine cycle applications to avoid the formation of can increase substantially in organic Rankine cycle trilateral flash cycles [30]. The multiphase expansion capability of reciprocating expanders still needs to be investigated in detail with a focus on the throttling losses through the inlet valves.

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2013;**22**:168-186

## **4. Conclusion**

It is evident that no expander technology is perfect; each type of machine has its own advantages and disadvantages. Based on the literature survey and experiences in commercial applications of ORCs, it is clear that efficiency and cost are a function of power output. In general, efficiency increases and cost reduces per kW as the power output is increased. In the context of the presented text in the chapter, it can be concluded that in general volumetric machines are suitable for smaller power output systems. Vane-type expanders are suitable for power outputs below 1.5 kWe, and scroll machines are suitable in the range of 1–5 kWe. Screw machines are suitable for the range of 5–50 kWe. Piston expanders are suitable for larger pressure ratios between 5 and 20 kWe. Turbomachines are suitable for larger-scale systems or if the cost of manufacturing is reduced then they can replace the volumetric machine with their single-stage expansion capability and high comparative efficiencies. In general, radial inflow machines are suitable from 30 to 500 kWe; recent advances in the industry have also successfully implemented radial machines in the MWe range. Axial machines are, however, the dominant type in the MW power range. Radial outflow machines appear to be competitive in the small-scale range below 50 kWe where radial inflow machines require higher rotational speeds.

## **Author details**

Fuhaid Alshammari, Muhammad Usman and Apostolos Pesyridis\*

\*Address all correspondence to: a.pesyridis@brunel.ac.uk

Department of Mechanical, Aerospace and Civil Engineering, Centre for Advanced Powertrain and Fuels (CAPF), Brunel University London, Uxbridge, United Kingdom

## **References**


[3] Colonna P, Harinck J, Rebay S, Guardone A. Real-gas effects in organic Rankine cycle turbine nozzles. Journal of Propulsion and Power [Internet]. Mar 1, 2008;**24**(2):282-294. DOI: 10.2514/1.29718

can increase substantially in organic Rankine cycle trilateral flash cycles [30]. The multiphase expansion capability of reciprocating expanders still needs to be investigated in detail with a

It is evident that no expander technology is perfect; each type of machine has its own advantages and disadvantages. Based on the literature survey and experiences in commercial applications of ORCs, it is clear that efficiency and cost are a function of power output. In general, efficiency increases and cost reduces per kW as the power output is increased. In the context of the presented text in the chapter, it can be concluded that in general volumetric machines are suitable for smaller power output systems. Vane-type expanders are suitable for power outputs below 1.5 kWe, and scroll machines are suitable in the range of 1–5 kWe. Screw machines are suitable for the range of 5–50 kWe. Piston expanders are suitable for larger pressure ratios between 5 and 20 kWe. Turbomachines are suitable for larger-scale systems or if the cost of manufacturing is reduced then they can replace the volumetric machine with their single-stage expansion capability and high comparative efficiencies. In general, radial inflow machines are suitable from 30 to 500 kWe; recent advances in the industry have also successfully implemented radial machines in the MWe range. Axial machines are, however, the dominant type in the MW power range. Radial outflow machines appear to be competitive in the small-scale

range below 50 kWe where radial inflow machines require higher rotational speeds.

Department of Mechanical, Aerospace and Civil Engineering, Centre for Advanced Powertrain and Fuels (CAPF), Brunel University London, Uxbridge, United Kingdom

[1] Ibarra M, Rovira A, Alarcón-Padilla D-C, Blanco J. Performance of a 5 kWe organic Rankine cycle at part-load operation. Applied Energy [Internet]. May 2014;**120**:147-158. Available from: http://linkinghub.elsevier.com/retrieve/pii/S0306261914000865 [Accessed:

[2] Colonna P, Casati E, Trapp C, Mathijssen T, Larjola J, Turunen-Saaresti T, et al. Organic Rankine cycle power systems: From the concept to current technology, applications and an outlook to the future. Journal of Engineering for Gas Turbines and Power [Internet]. 2015;**137**(October):1-19. Available from: http://gasturbinespower.asmedigitalcollection.

Fuhaid Alshammari, Muhammad Usman and Apostolos Pesyridis\*

\*Address all correspondence to: a.pesyridis@brunel.ac.uk

asme.org/article.aspx?doi=10.1115/1.4029884

focus on the throttling losses through the inlet valves.

56 Organic Rankine Cycle Technology for Heat Recovery

**4. Conclusion**

**Author details**

**References**

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[27] Nikolov A, Brümmer A. Investigating a small oil-flooded twin-screw expander for wasteheat utilisation in organic Rankine cycle systems. Energies. 2017;**10**(7):869. DOI:10.3390/

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[28] Gräßer M, Brümmer A. Influence of liquid in clearances on the operational behaviour of twin screw expanders. IOP Conference Series Materials Science and Engineering.

[29] Smith IK, Stošič N, Aldis CA. Development of the trilateral flash cycle system: Part 3: The design of high-efficiency two-phase screw expanders. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy [Internet]. 1996;**210**(1):75-93 Available from: http://pia.sagepub.com/content/210/1/75%5Cnhttp://pia.sagepub.com/

[30] Ziviani D, Groll EA, Braun JE, De Paepe M, van den Broek M. Analysis of an organic Rankine cycle with liquid-flooded expansion and internal regeneration (ORCLFE). Energy

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[15] Imran M, Usman M, Lee DH, Park BS. Volumetric expanders for low grade & waste heat recovery applications. Renewable and Sustainable Energy Reviews. 2016. DOI: 10.1016/j.

[16] Lemort V, Declaye S, Quoilin S. Experimental characterization of a hermetic scroll expander for use in a micro-scale Rankine cycle. Proceedings of the Institution of Mecha-

[17] Smith IK, Stosic N. Prospects for energy conversion effeiciency improvement by use of twin screw two phase expander. In: 2nd Int Heat Power Cycles Conf. Paris, France; 2001.

[18] Quoilin S, Sart-tilman C. Expansion machine and fluid selection for the organic Rankine cycle. In: 7th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics July 19-21, 2010, Antalya, Turkey. 2010. http://hdl.handle.net/2268/62997

[19] Imran M, Usman M, Lee DH, Park BS. Volumetric expanders for low grade & waste heat recovery applications. Renewable and Sustainable Energy Reviews [Internet]. May 2016;**57**:1090-1109. Available from: http://www.sciencedirect.com/science/article/pii/

[20] Farrokhi M, Noie SH, Akbarzadeh AA. Preliminary experimental investigation of a natural gas-fired ORC-based micro-CHP system for residential buildings. Applied Thermal Engineering [Internet]. Aug 1, 2014;**69**(1-2):221-229. Available from: https://www.scien-

[21] Astolfi M. Technical options for organic Rankine cycle systems. Organic Rankine Cycle

[22] DiPippo R. Ideal thermal efficiency for geothermal binary plants. Geothermics [Internet]. Jun 2007;**36**(3):276-285. Available from: http://www.sciencedirect.com/science/article/pii/

[23] Rossi P, Raheem A, Abhari RS. Numerical model of liquid film formation and breakup in last stage of a low-pressure steam turbine. Journal of Engineering for Gas Turbines and Power [Internet]. 2017;**140**(3):32602. Available from: http://gasturbinespower.asmedigi-

[24] Sun H, Qin J, Hung TC, Lin CH, Lin YF. Performance comparison of organic Rankine cycle with expansion from superheated zone or two-phase zone based on temperature utilization rate of heat source. Energy [Internet]. 2018;**149**:566-576. DOI: 10.1016/j.

[25] Bell IH, Lemort V, Groll EA, Braun JE, King GB, Horton WT. Liquid flooded compression and expansion in scroll machines – Part II: Experimental testing and model validation. International Journal of Refrigeration [Internet]. 2012;**35**(7):1890-1900. DOI: 10.1016/j.

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**Section 2**

**Dynamic Models**

**Section 2**

**Dynamic Models**

**Chapter 4**

Provisional chapter

**Modeling for Organic Rankine Cycle Waste Heat**

DOI: 10.5772/intechopen.78997

This chapter introduces the modeling of organic Rankine cycle waste heat recovery (ORC-WHR) system. The main goal of this chapter is to give an overview of ORC-WHR system modeling, especially focus on the heat exchanger models due to its key role in the ORC-WHR system development. Six heat exchanger models considered in this chapter includes static model, 0D dynamic model, 1D finite volume model, 1D moving boundary model, 2D & 3D model. Model complexity, accuracy, and computation time are analyzed for the six heat exchanger models. More importantly, the heat exchanger model selection is discussed based on different phase of ORC-WHR system development, which facilitates the development of ORC-WHR system, and reduces the system development cost. In addition, a full ORC-WHR system model is presented as a modeling example including

heat exchanger model, expander model, valve model and pump model.

Keywords: modeling, overview, heat exchanger, organic Rankine cycle, waste heat

As the virtual representation of the ORC-WHR system, ORC-WHR model is a great tool to reduce the cost and time of system development. The ORC-WHR model can be categorized based on the heat exchanger modeling method as shown in Figure 1. Based on whether the model includes Ordinary Differential Equations (ODEs) or not, the heat exchanger models can be classified as dynamic model (w/ODEs) and static model (w/o ODEs). Under the dynamic category, the models are further classified based on the model dimension (0D, 1D, 2D and 3D). Under the 1D category, the models can be classified based on the concept of modeling (moving

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Modeling for Organic Rankine Cycle Waste Heat

**Recovery System Development**

Recovery System Development

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

Bin Xu, Adamu Yebi and Zoran Filipi

Bin Xu, Adamu Yebi and Zoran Filipi

http://dx.doi.org/10.5772/intechopen.78997

Abstract

recovery

1. Introduction

boundary model and finite volume model).

#### **Modeling for Organic Rankine Cycle Waste Heat Recovery System Development** Modeling for Organic Rankine Cycle Waste Heat Recovery System Development

DOI: 10.5772/intechopen.78997

Bin Xu, Adamu Yebi and Zoran Filipi Bin Xu, Adamu Yebi and Zoran Filipi

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.78997

#### Abstract

This chapter introduces the modeling of organic Rankine cycle waste heat recovery (ORC-WHR) system. The main goal of this chapter is to give an overview of ORC-WHR system modeling, especially focus on the heat exchanger models due to its key role in the ORC-WHR system development. Six heat exchanger models considered in this chapter includes static model, 0D dynamic model, 1D finite volume model, 1D moving boundary model, 2D & 3D model. Model complexity, accuracy, and computation time are analyzed for the six heat exchanger models. More importantly, the heat exchanger model selection is discussed based on different phase of ORC-WHR system development, which facilitates the development of ORC-WHR system, and reduces the system development cost. In addition, a full ORC-WHR system model is presented as a modeling example including heat exchanger model, expander model, valve model and pump model.

Keywords: modeling, overview, heat exchanger, organic Rankine cycle, waste heat recovery

## 1. Introduction

As the virtual representation of the ORC-WHR system, ORC-WHR model is a great tool to reduce the cost and time of system development. The ORC-WHR model can be categorized based on the heat exchanger modeling method as shown in Figure 1. Based on whether the model includes Ordinary Differential Equations (ODEs) or not, the heat exchanger models can be classified as dynamic model (w/ODEs) and static model (w/o ODEs). Under the dynamic category, the models are further classified based on the model dimension (0D, 1D, 2D and 3D). Under the 1D category, the models can be classified based on the concept of modeling (moving boundary model and finite volume model).

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Figure 1. Heat exchanger modeling methods in ORC-WHR application.

Figure 2. 0D heat exchanger dynamic model diagram.

Generally, static modeling method only considers the energy balance of heat exchanger (i.e. the heat release from the heat sources equals to the heat absorption by the working fluid) [1–3]. Due to the static models lacking ODEs, there is no time varying parameter. Thus, this method can only analyze the steady state condition.

component development, control development and power optimization. The advantage of the dynamic model is its transient capability, which can predict the component performance over transient operating condition, evaluate the control strategies, and assist power optimization at

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65

The ORC-WHR system model includes four main components and other supporting components. The four main components include evaporator, expander, condenser, and working fluid pump as shown in Figure 5. The other supporting components include valves, pipes, reservoir, feed pump, etc. The four main components exist in all the ORC-WHR system and the number

of supporting components depend on the specific applications. There are several challenges in the ORC-WHR system modeling:

Figure 3. 1D heat exchanger finite volume model diagram.

Figure 4. 1D heat exchanger moving boundary model diagram.

transient conditions.

Figure 5. ORC-WHR system diagram.

On the contrary, dynamic modeling methods are capable of simulating the transient conditions and provide the parameter vector that changes along the time vector. 0D model [4, 5] lumps the parameter in a single point as shown in Figure 2 and the parameter is the same in any location of heat exchanger. For example, the heat source temperature is the same between the location near the exhaust gas inlet and the location near the exhaust gas outlet of heat exchanger. 1D model considers the one dimension in the direction of flow path. Two typical 1D models are finite volume model [6–8] and moving boundary model [9–11] as shown in Figures 3 and 4, respectively. For instance, the heat source temperature is different at different location of the flow path. The 2D and 3D models consider not only one dimension in the flow path direction, but also the directions perpendicular to the flow path axis.

The model is critical in the ORC-WHR system development. Static modeling method is utilized to analyze the energy flow and cycle efficiency at the beginning phase of the ORC system development. With the help of static models, heat sources selection, working fluid screening, expander machine selection, and cycle efficiency calculation can be roughly conducted. Dynamic models are developed in later phase of ORC-WHR system development to help Modeling for Organic Rankine Cycle Waste Heat Recovery System Development http://dx.doi.org/10.5772/intechopen.78997 65

Figure 3. 1D heat exchanger finite volume model diagram.

Figure 4. 1D heat exchanger moving boundary model diagram.

component development, control development and power optimization. The advantage of the dynamic model is its transient capability, which can predict the component performance over transient operating condition, evaluate the control strategies, and assist power optimization at transient conditions.

The ORC-WHR system model includes four main components and other supporting components. The four main components include evaporator, expander, condenser, and working fluid pump as shown in Figure 5. The other supporting components include valves, pipes, reservoir, feed pump, etc. The four main components exist in all the ORC-WHR system and the number of supporting components depend on the specific applications.

There are several challenges in the ORC-WHR system modeling:

Figure 5. ORC-WHR system diagram.

Generally, static modeling method only considers the energy balance of heat exchanger (i.e. the heat release from the heat sources equals to the heat absorption by the working fluid) [1–3]. Due to the static models lacking ODEs, there is no time varying parameter. Thus, this method

On the contrary, dynamic modeling methods are capable of simulating the transient conditions and provide the parameter vector that changes along the time vector. 0D model [4, 5] lumps the parameter in a single point as shown in Figure 2 and the parameter is the same in any location of heat exchanger. For example, the heat source temperature is the same between the location near the exhaust gas inlet and the location near the exhaust gas outlet of heat exchanger. 1D model considers the one dimension in the direction of flow path. Two typical 1D models are finite volume model [6–8] and moving boundary model [9–11] as shown in Figures 3 and 4, respectively. For instance, the heat source temperature is different at different location of the flow path. The 2D and 3D models consider not only one dimension in the flow

The model is critical in the ORC-WHR system development. Static modeling method is utilized to analyze the energy flow and cycle efficiency at the beginning phase of the ORC system development. With the help of static models, heat sources selection, working fluid screening, expander machine selection, and cycle efficiency calculation can be roughly conducted. Dynamic models are developed in later phase of ORC-WHR system development to help

path direction, but also the directions perpendicular to the flow path axis.

can only analyze the steady state condition.

Figure 2. 0D heat exchanger dynamic model diagram.

64 Organic Rankine Cycle Technology for Heat Recovery

Figure 1. Heat exchanger modeling methods in ORC-WHR application.

The first modeling challenge is the heat exchanger modeling method selection. Heat exchanger is the key component of the system and there are several available modeling methods. The modeling process is time-consuming. Thus, it is extremely important to choose the right modeling method before diving into the modeling details.

<sup>m</sup>\_ hscp, hsðThs,in � Ths, outÞ ¼ <sup>m</sup>\_ <sup>f</sup> hf , out � hf ,in (1)

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hf ,in <sup>¼</sup> map pf ,evap,Tf ,in (2)

hf , out <sup>¼</sup> map pf ,evap,Tf , out (3)

dt <sup>¼</sup> <sup>m</sup>\_ hscp,hsðThs,in � Ths, outÞ � Ahs,wUhs,wð Þ Ths � Tw (4)

(5)

(6)

where m\_ hs is heat source mass flow rate, cp, hs is the heat source heat capacity, Ths,in=Ths, out are heat source heat exchanger inlet/outlet temperature, hf ,in and hf , out are the working fluid enthalpy at heat exchanger inlet and outlet. They can be calculated based on the working fluid

where Tf ,in, Tf , out are working fluid heat exchanger inlet/outlet temperature, pf ,evap is working fluid evaporation pressure. Different from static heat exchanger model, dynamic heat exchanger model considers the ODEs in the governing equations. In addition, the wall dynamics are included in the governing equations. Take 0D dynamic model as an example. Assuming there is not pressure drop across the heat exchanger, pressure dynamics are fast dynamics and can be neglected in the energy balance equation. The heat exchanger energy balance then include three

dt ¼ �m\_ <sup>f</sup> hf , out � hf ,in <sup>þ</sup> Af ,wUf ,w Tw � Tf

dt <sup>¼</sup> Ahs,wUhs,wð Þ� Ths � Tw Awf ,wUwf ,w Tw � Tf

where Ahs,w, Uhs,w are the heat transfer area and heat transfer coefficient between heat source and wall. The wall is the medium separating the heat source and working fluid. Af ,w, Uf ,w are

The 0D dynamic model has three equations in energy balance, whereas static model only has one equation in energy balance. Besides more equations in 0D dynamic model, each equation has more terms than that from static model. In addition, the working fluid mass balance equation is another equation in the 0D dynamic model as presented in Eq. (7). Thus 0D dynamic model is more complex than the static model and the 0D dynamic model requires

the heat transfer area and heat transfer coefficient between working fluid and wall.

thermodynamic table as follows:

equations:

Heat source energy balance:

Working fluid energy balance:

Wall energy balance:

mhscp,hs

dThs

mf dhf

dTw

mwcp,w

more time and effort in modeling.

The second challenge is the fidelity of the model or assumptions to be made. The more assumptions to be made, the less fidelity the model will be. On the other hand, the less assumptions require more modeling time and effort. Thus, there is a trade-off between the model fidelity and modeling effort. However, the smart choose of assumptions might significantly reduce the modeling time and effort depending on the purposes of the model.

The third challenge is the system model integration [7] and robustness. After the component models are finished, the component models need to be integrated together to simulate the entire ORC-WHR system. The inputs and outputs of the connected models must be compatible to each other. In addition, the robustness of the integrated model could be a problem in highly transient operating conditions such as ORC system warmup, cool down, or heat source fast step change, etc. Moreover, the coupling dynamics of working fluid temperature, pressure and phase change increases the difficulty of system model robustness improvement.

Section 2 gives an overview of the ORC-WHR system model and discusses the heat exchanger model comparison and selection at different phases of ORC-WHR system development. Section 3 presents the details of a finite volume heat exchanger model, expander model, valve model and pump model as an ORC-WHR system model example.

## 2. Overview of the ORC-WHR modeling

This section gives an overview of the ORC-WHR system modeling methods in terms of model complexity, accuracy, and computation time. With the modeling overview, it is easier to find the right modeling method in certain ORC-WHR system development phase. Among the four main components, pump model and expander model are generally simple compared with the heat exchanger model and there is no many choices respective to the pump and expander modeling methods. Heat exchanger model is the most challenging one in many cases. Thus, this chapter mainly focus on the heat exchanger modeling methods comparison and evaluation.

#### 2.1. Heat exchanger model complexity

Model complexity indirectly represents the modeling time and effort required to build the model. The less complexity, the less modeling time and effort are required. In previous section, heat exchanger modeling methods are classified in Figure 1. In terms of model complexity, static heat exchanger model has the lowest complexity compared with dynamic model. The reason is that no ODE exists in the governing equations. All the equations are algebraic relation with energy balance. Using static method, the heat exchanger energy balance only has one equation and is given as follows:

$$
\dot{m}\_{\rm hs} \varepsilon\_{p,\rm hs} (T\_{\rm hs,in} - T\_{\rm hs,out}) = \dot{m}\_f \left( h\_{f,out} - h\_{f,in} \right) \tag{1}
$$

where m\_ hs is heat source mass flow rate, cp, hs is the heat source heat capacity, Ths,in=Ths, out are heat source heat exchanger inlet/outlet temperature, hf ,in and hf , out are the working fluid enthalpy at heat exchanger inlet and outlet. They can be calculated based on the working fluid thermodynamic table as follows:

$$\mathbf{h}\_{f,\text{in}} = \text{map}\left(\mathbf{p}\_{f,\text{evap},} \mathbf{T}\_{f,\text{in}}\right) \tag{2}$$

$$\mathbf{h}\_{f,out} = \text{map}\left(\mathbf{p}\_{f,evap\_r}\mathbf{T}\_{f,out}\right) \tag{3}$$

where Tf ,in, Tf , out are working fluid heat exchanger inlet/outlet temperature, pf ,evap is working fluid evaporation pressure. Different from static heat exchanger model, dynamic heat exchanger model considers the ODEs in the governing equations. In addition, the wall dynamics are included in the governing equations. Take 0D dynamic model as an example. Assuming there is not pressure drop across the heat exchanger, pressure dynamics are fast dynamics and can be neglected in the energy balance equation. The heat exchanger energy balance then include three equations:

Heat source energy balance:

The first modeling challenge is the heat exchanger modeling method selection. Heat exchanger is the key component of the system and there are several available modeling methods. The modeling process is time-consuming. Thus, it is extremely important to choose the right

The second challenge is the fidelity of the model or assumptions to be made. The more assumptions to be made, the less fidelity the model will be. On the other hand, the less assumptions require more modeling time and effort. Thus, there is a trade-off between the model fidelity and modeling effort. However, the smart choose of assumptions might signifi-

The third challenge is the system model integration [7] and robustness. After the component models are finished, the component models need to be integrated together to simulate the entire ORC-WHR system. The inputs and outputs of the connected models must be compatible to each other. In addition, the robustness of the integrated model could be a problem in highly transient operating conditions such as ORC system warmup, cool down, or heat source fast step change, etc. Moreover, the coupling dynamics of working fluid temperature, pressure and

Section 2 gives an overview of the ORC-WHR system model and discusses the heat exchanger model comparison and selection at different phases of ORC-WHR system development. Section 3 presents the details of a finite volume heat exchanger model, expander model, valve

This section gives an overview of the ORC-WHR system modeling methods in terms of model complexity, accuracy, and computation time. With the modeling overview, it is easier to find the right modeling method in certain ORC-WHR system development phase. Among the four main components, pump model and expander model are generally simple compared with the heat exchanger model and there is no many choices respective to the pump and expander modeling methods. Heat exchanger model is the most challenging one in many cases. Thus, this chapter

Model complexity indirectly represents the modeling time and effort required to build the model. The less complexity, the less modeling time and effort are required. In previous section, heat exchanger modeling methods are classified in Figure 1. In terms of model complexity, static heat exchanger model has the lowest complexity compared with dynamic model. The reason is that no ODE exists in the governing equations. All the equations are algebraic relation with energy balance. Using static method, the heat exchanger energy balance only

mainly focus on the heat exchanger modeling methods comparison and evaluation.

cantly reduce the modeling time and effort depending on the purposes of the model.

phase change increases the difficulty of system model robustness improvement.

model and pump model as an ORC-WHR system model example.

2. Overview of the ORC-WHR modeling

2.1. Heat exchanger model complexity

has one equation and is given as follows:

modeling method before diving into the modeling details.

66 Organic Rankine Cycle Technology for Heat Recovery

$$m\_{\rm hs}c\_{p,\rm hs}\frac{dT\_{\rm hs}}{dt} = \dot{m}\_{\rm hs}c\_{p,\rm hs}(T\_{\rm hs,in} - T\_{\rm hs,out}) - A\_{\rm hs,w}U\_{\rm hs,w}(T\_{\rm hs} - T\_w) \tag{4}$$

Working fluid energy balance:

$$m\_f \frac{d\mathbf{h}\_f}{dt} = -\dot{m}\_f \left(\mathbf{h}\_{f,out} - \mathbf{h}\_{f,in}\right) + A\_{f,w} \mathbf{U}\_{f,w} \left(T\_w - T\_f\right) \tag{5}$$

Wall energy balance:

$$m\_w c\_{p,w} \frac{dT\_w}{dt} = A\_{\text{hs,w}} \mathcal{U}\_{\text{hs,w}} (T\_{\text{hs}} - T\_w) - A\_{wf,w} \mathcal{U}\_{wf,w} \left( T\_w - T\_f \right) \tag{6}$$

where Ahs,w, Uhs,w are the heat transfer area and heat transfer coefficient between heat source and wall. The wall is the medium separating the heat source and working fluid. Af ,w, Uf ,w are the heat transfer area and heat transfer coefficient between working fluid and wall.

The 0D dynamic model has three equations in energy balance, whereas static model only has one equation in energy balance. Besides more equations in 0D dynamic model, each equation has more terms than that from static model. In addition, the working fluid mass balance equation is another equation in the 0D dynamic model as presented in Eq. (7). Thus 0D dynamic model is more complex than the static model and the 0D dynamic model requires more time and effort in modeling.

$$\frac{d\mathfrak{m}\_f}{dt} = \dot{\mathfrak{m}}\_{f,in} - \dot{\mathfrak{m}}\_{f,out} \tag{7}$$

usually utilized to assist basic energy balance between the heat sources and working fluid. This calculation only needs to give an estimate result and does not require high accurate model. In the static modeling process, many parameters are generally not considered such as heat transfer area and heat transfer coefficient in the heat exchanger, and heat loss from the heat exchanger to the ambient. Therefore, the static heat exchanger model accuracy is not high. 0D dynamic heat exchanger model makes less assumptions than the static model, which improves the model accuracy. To be specific, 0D model considers the heat transfer area and heat transfer coefficients in the heat exchanger. In addition, 0D model is generally validated by experimental data, which also increases the model accuracy compared with static model.

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1D finite volume model and moving boundary model have less assumptions than the 0D model in that they consider one more dimension than the 0D model. With 1D model, the parameters of working fluid, heat source and wall have different values at different location in the axis of flow path, whereas 0D model share the same value at different location. This one more dimension feature equips the 1D models with higher fidelity than the 0D model. Thus 1D models have higher accuracy than the 0D model. Between the two 1D models, finite volume model has finer discretization resolution than the moving boundary model (m vs. 3 in Figures 3 and 4). Therefore, as the number m goes larger, the 1D finite volume model could have

2D and 3D heat exchanger model have less assumption than the 1D or 0D heat exchanger

Overall, the accuracy rank of all the heat exchanger models are as follows: Static model < 0D dynamic model < 1D moving boundary model < 1D finite volume model < 2D & 3D heat

The computation time is very important if the model needs to run online or the model is implemented in computational costly algorithms offline like Dynamic Programming. Static model only has algebraic equations and is the fastest model among all the heat exchanger models. The computation time of 0D and 1D models can be evaluated by the number of ODEs of the corresponding model. As mentioned earlier this section, the 0D model has the least number of ODEs, followed by 1D moving boundary model and 1D finite volume model, respectively. Similarly, the 2D model has more ODEs than 1D model and less ODEs than 3D

Therefore, the computation time of all the heat exchanger models can be ranked as follows: static model <0D model <1D moving boundary model <1D finite volume model <2D & 3D

Selecting the right heat exchanger model at different phase of ORC-WHR system development

2.4. Model selection at different ORC-WHR system development phases

higher accuracy than the 1D moving boundary model.

models, which equips them with higher accuracy.

2.3. Heat exchanger model computation time

exchanger model.

model.

model.

has three benefits:

1D dynamic models share the same four governing equations (Eqs. (4-7)) with 0D in each discretized cell. The main difference is that 0D model has only one cell and 1D models have more than one cell. 1D dynamic models include finite volume model and moving boundary model. Finite volume model includes m discretized cells, each cell has the same volume. Moving boundary model includes three cells, each cell has different volume, which are determined by the phase of working fluid. There are three phases in the working fluid inside the heat exchanger including pure liquid, mixed (liquid & vapor) and pure vapor. Each phase occupies one cell in the moving boundary model. The governing Eqs. (4-7) are applied in each cell of 1D finite volume model and moving boundary model. Therefore, the 1D heat exchanger models has more equations than the 0D heat exchanger model. In terms of model complexity, 1D heat exchanger models are more complex than the 0D model. Even though both 0D and 1D models share similar governing equations, 1D models need to consider the boundary conditions between the adjacent cells, whereas 0D model only need to consider the boundary conditions at the heat exchanger inlet and outlet. Between the two 1D models, considering finite volume model generally has more than three cells, 1D moving boundary model has less governing equations than the 1D finite volume method and the number of different equations is (m-3)\*4. Even though finite volume model has more equations, different cells share equations, which means as long as Eqs. (4-7) are developed, finite volume model is almost done. However, moving boundary model three cells do not share exact Eqs. (4-7). In moving boundary model, Eqs. (4-7) are implemented into three cells. Due to the cell volume is not fixed, the equations requires further derivation and finally 12 different equations are derived. In other words, at different cell, Eqs. (4-7) have different formats. These derivation increases the model complexity of the moving boundary model and results in that moving boundary model complexity is higher than the finite volume model.

2D and 3D heat exchanger models are more complex than the 1D and 0D heat exchanger models and are generally modeled in CFD softwares (e.g. ANSYS, FLUENT, etc.).

Overall the heat exchanger model complexity rank can be given as follows: static model <0D dynamic model <1D dynamic finite volume model <1D dynamic moving boundary model <2D & 3D dynamic model.

#### 2.2. Heat exchanger model accuracy

Accuracy is the model characteristic that everyone wants to maximize, because it determines the value of the model in some sense. Unlike model complexity, model accuracy can be easily quantified. There is a reference to compare with the model prediction and the accuracy represents the error between the model prediction and the reference.

Static heat exchanger model is utilized in the concept phase in the ORC-WHR development. In the concept phase, no components are selected and no experiments are conducted. Thus, in general, there is no reference data to evaluate the accuracy of the static model. Static model is usually utilized to assist basic energy balance between the heat sources and working fluid. This calculation only needs to give an estimate result and does not require high accurate model. In the static modeling process, many parameters are generally not considered such as heat transfer area and heat transfer coefficient in the heat exchanger, and heat loss from the heat exchanger to the ambient. Therefore, the static heat exchanger model accuracy is not high.

0D dynamic heat exchanger model makes less assumptions than the static model, which improves the model accuracy. To be specific, 0D model considers the heat transfer area and heat transfer coefficients in the heat exchanger. In addition, 0D model is generally validated by experimental data, which also increases the model accuracy compared with static model.

1D finite volume model and moving boundary model have less assumptions than the 0D model in that they consider one more dimension than the 0D model. With 1D model, the parameters of working fluid, heat source and wall have different values at different location in the axis of flow path, whereas 0D model share the same value at different location. This one more dimension feature equips the 1D models with higher fidelity than the 0D model. Thus 1D models have higher accuracy than the 0D model. Between the two 1D models, finite volume model has finer discretization resolution than the moving boundary model (m vs. 3 in Figures 3 and 4). Therefore, as the number m goes larger, the 1D finite volume model could have higher accuracy than the 1D moving boundary model.

2D and 3D heat exchanger model have less assumption than the 1D or 0D heat exchanger models, which equips them with higher accuracy.

Overall, the accuracy rank of all the heat exchanger models are as follows: Static model < 0D dynamic model < 1D moving boundary model < 1D finite volume model < 2D & 3D heat exchanger model.

#### 2.3. Heat exchanger model computation time

dmf

68 Organic Rankine Cycle Technology for Heat Recovery

complexity is higher than the finite volume model.

& 3D dynamic model.

2.2. Heat exchanger model accuracy

1D dynamic models share the same four governing equations (Eqs. (4-7)) with 0D in each discretized cell. The main difference is that 0D model has only one cell and 1D models have more than one cell. 1D dynamic models include finite volume model and moving boundary model. Finite volume model includes m discretized cells, each cell has the same volume. Moving boundary model includes three cells, each cell has different volume, which are determined by the phase of working fluid. There are three phases in the working fluid inside the heat exchanger including pure liquid, mixed (liquid & vapor) and pure vapor. Each phase occupies one cell in the moving boundary model. The governing Eqs. (4-7) are applied in each cell of 1D finite volume model and moving boundary model. Therefore, the 1D heat exchanger models has more equations than the 0D heat exchanger model. In terms of model complexity, 1D heat exchanger models are more complex than the 0D model. Even though both 0D and 1D models share similar governing equations, 1D models need to consider the boundary conditions between the adjacent cells, whereas 0D model only need to consider the boundary conditions at the heat exchanger inlet and outlet. Between the two 1D models, considering finite volume model generally has more than three cells, 1D moving boundary model has less governing equations than the 1D finite volume method and the number of different equations is (m-3)\*4. Even though finite volume model has more equations, different cells share equations, which means as long as Eqs. (4-7) are developed, finite volume model is almost done. However, moving boundary model three cells do not share exact Eqs. (4-7). In moving boundary model, Eqs. (4-7) are implemented into three cells. Due to the cell volume is not fixed, the equations requires further derivation and finally 12 different equations are derived. In other words, at different cell, Eqs. (4-7) have different formats. These derivation increases the model complexity of the moving boundary model and results in that moving boundary model

2D and 3D heat exchanger models are more complex than the 1D and 0D heat exchanger

Overall the heat exchanger model complexity rank can be given as follows: static model <0D dynamic model <1D dynamic finite volume model <1D dynamic moving boundary model <2D

Accuracy is the model characteristic that everyone wants to maximize, because it determines the value of the model in some sense. Unlike model complexity, model accuracy can be easily quantified. There is a reference to compare with the model prediction and the accuracy

Static heat exchanger model is utilized in the concept phase in the ORC-WHR development. In the concept phase, no components are selected and no experiments are conducted. Thus, in general, there is no reference data to evaluate the accuracy of the static model. Static model is

models and are generally modeled in CFD softwares (e.g. ANSYS, FLUENT, etc.).

represents the error between the model prediction and the reference.

dt <sup>¼</sup> <sup>m</sup>\_ <sup>f</sup> ,in � <sup>m</sup>\_ <sup>f</sup> , out (7)

The computation time is very important if the model needs to run online or the model is implemented in computational costly algorithms offline like Dynamic Programming. Static model only has algebraic equations and is the fastest model among all the heat exchanger models. The computation time of 0D and 1D models can be evaluated by the number of ODEs of the corresponding model. As mentioned earlier this section, the 0D model has the least number of ODEs, followed by 1D moving boundary model and 1D finite volume model, respectively. Similarly, the 2D model has more ODEs than 1D model and less ODEs than 3D model.

Therefore, the computation time of all the heat exchanger models can be ranked as follows: static model <0D model <1D moving boundary model <1D finite volume model <2D & 3D model.

#### 2.4. Model selection at different ORC-WHR system development phases

Selecting the right heat exchanger model at different phase of ORC-WHR system development has three benefits:


The ORC-WHR system development procedures can be explained using the diagram shown in Figure 6. The system development starts from concept design, in which phase the heat sources selection, working fluid selection, expander selection, expander power output form (electrical or mechanical) and system configuration are roughly evaluated and determined. It is common that some of the selection may be not finalized, which needs further investigation in the latter phases of the development. In the concept phase, some general energy balance are calculated to evaluate the power output at different operating condition and different system configuration. There is no experimental data and the calculation is not necessarily to be very accurate. Thus, the static heat exchanger model fits this development phase. The model is not very accurate, but its accuracy is enough to generate a general estimation of energy balance between heat sources and working fluid, and power output value from the expander machine.

The third development phase is system integration phase, during which the ORC-WHR components hardware are connected in the test rig. During this phase, the model is not required. As the components are integrated into an entire system, the next step is to conduct the experiments. However, without control, the ORC-WHR system experiments are hard to conduct due to the coupling of working fluid temperature, evaporation pressure, and the transient

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The fourth development phase is the control development. The most important control in ORC-WHR system are the working fluid temperature control and evaporation pressure control. It is possible to develop the temperature and pressure control without a model (i.e. traditional PID feedback control). However, many simulation and experiments showed that the traditional PID feedback control cannot control the ORC-WHR system very well. Feedforward plus feedback or advanced controls (e.g. model predictive control) are proposed by many researchers in the field of ORC-WHR system. Both the feedforward and advanced controls require system models, either simple models or complex models. In the feedforward control, the highly accurate model helps improve the control performance. However, due to the combination with PID feedback control, the feedforward control model does not have to be very accurate. Because the feedback control helps correct the error brought by the feedforward control. Lower accuracy requirement helps reduce the modeling effort. Thus, static model or 0D model are common in feedforward control design. In advanced controls, the model accuracy has higher requirements than the feedforward control. It is because generally there is no feedback control to correct the model error. Accuracy is one of the constraints for advanced control and computation time is the other because the advanced control needs to run online. The accuracy constraint eliminates the possibility of selecting static model or 0D model and the computation time constraint eliminates the possibility of 1D finite volume model and 2D or 3D model. Thus, most of advanced controls developed for ORC-WHR system utilized 1D moving boundary model as the heat exchanger control-oriented model even though the moving

The fifth development phase is the power optimization phase. After the control development, the experiments can be conducted. However, there is still a gap to reach the system design goal, which is the selection of the optimal reference trajectories for working fluid temperature at the outlet of evaporator heat exchanger, evaporation pressure, condensation pressure, working fluid subcooling temperature at condenser outlet etc. The model helps identify the optimal reference trajectories corresponding to the maximum expander power or net power from the ORC-WHR system at varying heat sources operating conditions. There are three methods to achieve the power maximization goal: (1) develop a map or a correlation between the optimal reference and the inputs such as heat sources mass flow rate and temperature. The map or correlation is from the optimal results from the steady state analysis with the help of model. In this method, accuracy is the most important factor and model complexity is also important. Therefore, finite volume method fits this requirement very well. (2) Develop an optimal reference trajectory based on transient driving cycle. Compared with steady states, transient driving cycle optimization requires more computation time, especially for dynamic programming algorithm. Thus, computation time is the most important factor for the model. The model accuracy should not be too low. Therefore,

boundary model has relative high model complexity.

heat source.

After the concept phase, the component selection and development phase follows, during which the components hardware are selected based on the available products on the market or designed and manufactured. This is the first generation of the components selection, which may change several other generations based on the individual and integrated system experiments. Experimental data are collected from individual components. During this phase, the component models help the design of some components details such as the heat transfer area of heat exchanger, the nozzle area of turbine expander, the expansion ratio of piston expander, the size of the valve, the displacement of pump and the inner diameter of connected pipes. During this phase, the static model and 0D heat exchanger model help design the details of heat exchanger. The 0D model can be identified by the experimental data from the heat exchanger. The identified 0D model gives hints on updating the current heat exchanger generation to the next level by sweep some of key design parameters such as heat transfer area, section area of flow path, and length of flow path. The expander machine prototype can generate an efficiency or power map as a function of variables like expander speed, inlet pressure, outlet pressure, and expansion ratio. This map helps build either map-based or physics-based expander model.

Figure 6. ORC-WHR system development procedures.

The third development phase is system integration phase, during which the ORC-WHR components hardware are connected in the test rig. During this phase, the model is not required. As the components are integrated into an entire system, the next step is to conduct the experiments. However, without control, the ORC-WHR system experiments are hard to conduct due to the coupling of working fluid temperature, evaporation pressure, and the transient heat source.

1. Meeting the certain development phase goals;

The ORC-WHR system development procedures can be explained using the diagram shown in Figure 6. The system development starts from concept design, in which phase the heat sources selection, working fluid selection, expander selection, expander power output form (electrical or mechanical) and system configuration are roughly evaluated and determined. It is common that some of the selection may be not finalized, which needs further investigation in the latter phases of the development. In the concept phase, some general energy balance are calculated to evaluate the power output at different operating condition and different system configuration. There is no experimental data and the calculation is not necessarily to be very accurate. Thus, the static heat exchanger model fits this development phase. The model is not very accurate, but its accuracy is enough to generate a general estimation of energy balance between

heat sources and working fluid, and power output value from the expander machine.

After the concept phase, the component selection and development phase follows, during which the components hardware are selected based on the available products on the market or designed and manufactured. This is the first generation of the components selection, which may change several other generations based on the individual and integrated system experiments. Experimental data are collected from individual components. During this phase, the component models help the design of some components details such as the heat transfer area of heat exchanger, the nozzle area of turbine expander, the expansion ratio of piston expander, the size of the valve, the displacement of pump and the inner diameter of connected pipes. During this phase, the static model and 0D heat exchanger model help design the details of heat exchanger. The 0D model can be identified by the experimental data from the heat exchanger. The identified 0D model gives hints on updating the current heat exchanger generation to the next level by sweep some of key design parameters such as heat transfer area, section area of flow path, and length of flow path. The expander machine prototype can generate an efficiency or power map as a function of variables like expander speed, inlet pressure, outlet pressure, and expansion ratio. This map helps build either map-based or

2. Reducing the time and effort of modeling;

3. Reducing the cost of modeling.

70 Organic Rankine Cycle Technology for Heat Recovery

physics-based expander model.

Figure 6. ORC-WHR system development procedures.

The fourth development phase is the control development. The most important control in ORC-WHR system are the working fluid temperature control and evaporation pressure control. It is possible to develop the temperature and pressure control without a model (i.e. traditional PID feedback control). However, many simulation and experiments showed that the traditional PID feedback control cannot control the ORC-WHR system very well. Feedforward plus feedback or advanced controls (e.g. model predictive control) are proposed by many researchers in the field of ORC-WHR system. Both the feedforward and advanced controls require system models, either simple models or complex models. In the feedforward control, the highly accurate model helps improve the control performance. However, due to the combination with PID feedback control, the feedforward control model does not have to be very accurate. Because the feedback control helps correct the error brought by the feedforward control. Lower accuracy requirement helps reduce the modeling effort. Thus, static model or 0D model are common in feedforward control design. In advanced controls, the model accuracy has higher requirements than the feedforward control. It is because generally there is no feedback control to correct the model error. Accuracy is one of the constraints for advanced control and computation time is the other because the advanced control needs to run online. The accuracy constraint eliminates the possibility of selecting static model or 0D model and the computation time constraint eliminates the possibility of 1D finite volume model and 2D or 3D model. Thus, most of advanced controls developed for ORC-WHR system utilized 1D moving boundary model as the heat exchanger control-oriented model even though the moving boundary model has relative high model complexity.

The fifth development phase is the power optimization phase. After the control development, the experiments can be conducted. However, there is still a gap to reach the system design goal, which is the selection of the optimal reference trajectories for working fluid temperature at the outlet of evaporator heat exchanger, evaporation pressure, condensation pressure, working fluid subcooling temperature at condenser outlet etc. The model helps identify the optimal reference trajectories corresponding to the maximum expander power or net power from the ORC-WHR system at varying heat sources operating conditions. There are three methods to achieve the power maximization goal: (1) develop a map or a correlation between the optimal reference and the inputs such as heat sources mass flow rate and temperature. The map or correlation is from the optimal results from the steady state analysis with the help of model. In this method, accuracy is the most important factor and model complexity is also important. Therefore, finite volume method fits this requirement very well. (2) Develop an optimal reference trajectory based on transient driving cycle. Compared with steady states, transient driving cycle optimization requires more computation time, especially for dynamic programming algorithm. Thus, computation time is the most important factor for the model. The model accuracy should not be too low. Therefore, 0D model meets this criteria. (3) Directly optimize the power in the advanced control developed in the control development phase. In this case, no extra effort is needed in the power optimization phase. However, due to the computation time limitation of the online advanced control, the 'optimal' power calculated by the advanced control is local optimal rather than global optimal, which is the drawback of this third method.

The working fluid mass balance can be expressed as:

the wall and the fluid (working fluid or exhaust gas).

Aw, crosscp,wrwLw

Tw,t kð Þ <sup>þ</sup><sup>1</sup> ¼ Tw,t kð Þ þ

The wall energy balance is shown below:

w represents wall.

follows:

∂Af , crossr<sup>f</sup> ∂t þ

fluid and exhaust gas energy balance are expressed in the follow form:

∂ð Þ Acrossrh ∂t þ

dTw

the exhaust gas flows right to left and the working fluid flows left to right.

fluid energy balance Eq. (13), and exhaust gas energy balance Eq. (13).

∂m\_ <sup>f</sup>

where Across represents cross-sectional area, subscript f represents working fluid, r represents density, m\_ is mass flow rate, z represents spatial position in the axial direction. Mass flow balance in the exhaust gas side is ignored due to the exhaust gas fast dynamics. The working

∂mh\_

where p represent pressure, h represent enthalpy, d represents the effective flow path diameter, U represents the heat transfer coefficient, and ΔT represents temperature difference between

where cp represents heat capacity, L represents the length in axial direction, Af ,w represents the heat transfer area between working fluid and wall, Uf ,w represents the heat transfer coefficient between working fluid and wall. m<sup>η</sup> represents the heat exchanger efficiency multiplier, which accounts for heat loss to the ambient, Ae,w represents the heat transfer area between exhaust gas and wall, Ue,w is the heat transfer coefficient between exhaust gas and wall, and subscript

Figure 3 presents the finite volume method for heat exchanger modeling. The model includes m uniform volumetric cells. In each cell, the heat q flows from the exhaust gas through the wall to working fluid and governing Eqs. (8-10) are solved in each cell. In this counterflow design,

Eqs. (8) and (9) are simplified to ODE Eqs. (4) and (7). Eq. (10), Eq. (4) and Eq. (7) are solved as

where k is the time step indices, Δt is length of time step. Overall, there are four equations to be solved for each cell: wall energy balance Eq. (11), working fluid mass balance Eq. (12), working

Af ,wUf ,w,t kð ÞΔTf ,w,t kð Þ þ Ae,wUe,w,t kð ÞΔTe,w,t kð Þ Aw, crosscprwLw

ð Þ mh t kð Þ <sup>þ</sup><sup>1</sup> <sup>¼</sup> ð Þ mh t kð Þ <sup>þ</sup> <sup>m</sup>\_ in,t kð Þhin,t kð Þ � <sup>m</sup>\_ outhout,t kð Þ <sup>þ</sup> AUt kð ÞΔ<sup>T</sup> <sup>Δ</sup><sup>t</sup> (13)

mf ,t kð Þ <sup>þ</sup><sup>1</sup> <sup>¼</sup> mf ,t kð Þ <sup>þ</sup> <sup>m</sup>\_ <sup>f</sup> ,in,t kð Þ � <sup>m</sup>\_ <sup>f</sup> , out,t kð Þ <sup>Δ</sup><sup>t</sup> (12)

<sup>∂</sup><sup>z</sup> <sup>¼</sup> <sup>0</sup> (8)

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Modeling for Organic Rankine Cycle Waste Heat Recovery System Development

<sup>∂</sup><sup>z</sup> <sup>¼</sup> <sup>π</sup>dUΔ<sup>T</sup> (9)

Δt (11)

dt <sup>¼</sup> Af ,wUf ,wΔTf ,w <sup>þ</sup> <sup>m</sup>ηAe,wUe,wΔTe,w (10)

As long as the control development and power maximization phases are done, the experimental implementation phase does not require the model.

## 3. Modeling of ORC-WHR system

This section presents the details of a full ORC-WHR system model, aiming to provide an example of modeling of entire ORC-WHR system. The configuration of the example system is shown in Figure 7. The tail pipe (TP) exhaust gas from an internal combustion engine is considered as heat source. Electrified turbine expander is chosen as expander machine. One valve is installed upstream of turbine expander to protect turbine from liquid working fluid during the system warmup or highly transient engine conditions. Another valve is installed in the bypass of turbine to allow working fluid bypass the turbine and also controls the working fluid evaporation pressure.

#### 3.1. Heat exchanger modeling

Two heat exchangers exist in the ORC system including evaporator and condenser. In this chapter, only TP evaporator model is presented and the condenser is modeled using the same method. Two assumptions made in the TP evaporator model: (i) axial heat conduction are not considered in all three medium (working fluid, wall and TP exhaust gas), (ii) the wall temperature gradient in the radial direction is neglected, and (iii) pressure drop across the heat exchanger is not considered.

Figure 7. ORC-WHR system diagram.

The working fluid mass balance can be expressed as:

0D model meets this criteria. (3) Directly optimize the power in the advanced control developed in the control development phase. In this case, no extra effort is needed in the power optimization phase. However, due to the computation time limitation of the online advanced control, the 'optimal' power calculated by the advanced control is local optimal rather than

As long as the control development and power maximization phases are done, the experimen-

This section presents the details of a full ORC-WHR system model, aiming to provide an example of modeling of entire ORC-WHR system. The configuration of the example system is shown in Figure 7. The tail pipe (TP) exhaust gas from an internal combustion engine is considered as heat source. Electrified turbine expander is chosen as expander machine. One valve is installed upstream of turbine expander to protect turbine from liquid working fluid during the system warmup or highly transient engine conditions. Another valve is installed in the bypass of turbine to allow working fluid bypass the turbine and also controls the working

Two heat exchangers exist in the ORC system including evaporator and condenser. In this chapter, only TP evaporator model is presented and the condenser is modeled using the same method. Two assumptions made in the TP evaporator model: (i) axial heat conduction are not considered in all three medium (working fluid, wall and TP exhaust gas), (ii) the wall temperature gradient in the radial direction is neglected, and (iii) pressure drop across the heat

global optimal, which is the drawback of this third method.

tal implementation phase does not require the model.

3. Modeling of ORC-WHR system

72 Organic Rankine Cycle Technology for Heat Recovery

fluid evaporation pressure.

3.1. Heat exchanger modeling

exchanger is not considered.

Figure 7. ORC-WHR system diagram.

$$\frac{\partial A\_{f,cross} \rho\_f}{\partial t} + \frac{\partial \dot{m}\_f}{\partial z} = 0 \tag{8}$$

where Across represents cross-sectional area, subscript f represents working fluid, r represents density, m\_ is mass flow rate, z represents spatial position in the axial direction. Mass flow balance in the exhaust gas side is ignored due to the exhaust gas fast dynamics. The working fluid and exhaust gas energy balance are expressed in the follow form:

$$\frac{\partial(A\_{cross}\rho h)}{\partial t} + \frac{\partial \dot{m}h}{\partial z} = \pi d\mathcal{U}\Delta T \tag{9}$$

where p represent pressure, h represent enthalpy, d represents the effective flow path diameter, U represents the heat transfer coefficient, and ΔT represents temperature difference between the wall and the fluid (working fluid or exhaust gas).

The wall energy balance is shown below:

$$A\_{w,cross} \mathbf{c}\_{p,w} \rho\_w L\_w \frac{dT\_w}{dt} = A\_{f,w} \mathbf{U}\_{f,w} \Delta T\_{f,w} + m\_\eta A\_{e,w} \mathbf{U}\_{e,w} \Delta T\_{e,w} \tag{10}$$

where cp represents heat capacity, L represents the length in axial direction, Af ,w represents the heat transfer area between working fluid and wall, Uf ,w represents the heat transfer coefficient between working fluid and wall. m<sup>η</sup> represents the heat exchanger efficiency multiplier, which accounts for heat loss to the ambient, Ae,w represents the heat transfer area between exhaust gas and wall, Ue,w is the heat transfer coefficient between exhaust gas and wall, and subscript w represents wall.

Figure 3 presents the finite volume method for heat exchanger modeling. The model includes m uniform volumetric cells. In each cell, the heat q flows from the exhaust gas through the wall to working fluid and governing Eqs. (8-10) are solved in each cell. In this counterflow design, the exhaust gas flows right to left and the working fluid flows left to right.

Eqs. (8) and (9) are simplified to ODE Eqs. (4) and (7). Eq. (10), Eq. (4) and Eq. (7) are solved as follows:

$$T\_{w,t(k+1)} = T\_{w,t(k)} + \frac{A\_{f,w} \mathcal{U}\_{f,w,t(k)} \Delta T\_{f,w,t(k)} + A\_{\varepsilon,w} \mathcal{U}\_{\varepsilon,w,t(k)} \Delta T\_{\varepsilon,w,t(k)}}{A\_{w,\text{cross}} \varepsilon\_p \rho\_w L\_w} \Delta t \tag{11}$$

$$\mathbf{m}\_{f,t(k+1)} = \mathbf{m}\_{f,t(k)} + \left(\dot{\mathbf{m}}\_{f,\dot{\mathbf{m}},t(k)} - \dot{\mathbf{m}}\_{f,\text{out},t(k)}\right)\Delta t \tag{12}$$

$$\left(\left(m\mathbf{h}\right)\_{t(k+1)} - \left(m\mathbf{h}\right)\_{t(k)} + \left(\dot{m}\_{\text{in},t(k)}h\_{\text{in},t(k)} - \dot{m}\_{\text{out}}h\_{\text{out},t(k)} + AU\_{t(k)}\Delta T\right)\Delta t\right) \tag{13}$$

where k is the time step indices, Δt is length of time step. Overall, there are four equations to be solved for each cell: wall energy balance Eq. (11), working fluid mass balance Eq. (12), working fluid energy balance Eq. (13), and exhaust gas energy balance Eq. (13).

Heat transfer coefficients are calculated separately in working fluid side and exhaust gas side. In the exhaust gas side, at each time step, heat transfer coefficient is calculated once and all the m cells share the same value, which is only a function of time. Eq. (14) is the expression of friction factor for the concentric tubes [12]:

$$\mathcal{L}\_{\varepsilon} = \left( 1.8 \log\_{10} \left( Re\_{\varepsilon}^{\*} \right) - 1.5 \right)^{-2} \tag{14}$$

$$Re\_e^\* = Re\_e \frac{\left(1 + r\_d^2\right) \ln\left(r\_d\right) + (1 - r\_d)}{\left(1 + r\_d^2\right) \ln\left(r\_d\right)}\tag{15}$$

$$r\_d = \frac{d\_{in}}{d\_{out}}\tag{16}$$

Uf ,w,i ¼

Uf ,tp <sup>¼</sup> ð Þ <sup>1</sup> � <sup>x</sup> <sup>0</sup>:<sup>01</sup> ð Þþ <sup>1</sup> � <sup>x</sup> <sup>1</sup>:9x<sup>0</sup>:<sup>4</sup> <sup>r</sup><sup>f</sup> ,sat

The outlet enthalpy is calculated by isentropic efficiency as follows:

4

< :

3.2. Expander modeling

high expansion ratios (10–30).

modynamic table of the working fluid.

The turbine power is given as follows

ξ<sup>f</sup> ,i 8 � �Ref ,iPrf ,i

> ffiffiffiffiffi ξ<sup>f</sup> ,i 8 q

df Df � �<sup>0</sup>:<sup>5</sup>

During the evaporation process, both liquid and vapor phase exist. The heat transfer coefficient for this situation is calculated using a vertical tube two-phase heat transfer coefficient

expression as shown in Eq. (24) [13]. Uf ,w,sat and Uf ,w,vap are calculated from Eq. (22).

8 �2:<sup>2</sup>

<sup>þ</sup>x<sup>0</sup>:<sup>01</sup> Uf ,vap Uf ,sat

2 4

<sup>r</sup><sup>f</sup> ,vap !<sup>0</sup>:<sup>35</sup> <sup>2</sup>

@

The turbine is integrated with an electric generator in this work. However, it can also be mechanically connected to engine crank shaft through a gearbox. Turbine expander mass flow rate has a linear relationship to turbine inlet pressure, Eq. (25), due to the choked flow status at

Outlet temperature, Tout, is calculated from outlet enthalpy and outlet pressure using a ther-

Pr<sup>0</sup>:<sup>667</sup> <sup>f</sup> ,i � 1 � �

> þ 0:079 Re<sup>0</sup>:<sup>25</sup> f ;i

> > 3 5

> > > 1 A

m\_ in ¼ aturbpin þ bturb (25)

hout ¼ hin � ηisð Þ hin � hout,is (26)

<sup>η</sup>is <sup>¼</sup> map Nturb; pin=pout; Tin � � (27)

hout,is <sup>¼</sup> map sout; pout � � (28)

sin <sup>¼</sup> map hin; pin � � (30)

Tout <sup>¼</sup> map hout; pout � � (31)

sout ¼ sin (29)

3 5

http://dx.doi.org/10.5772/intechopen.78997

�<sup>2</sup>9 = ;

�0:<sup>5</sup> (24)

<sup>1</sup> <sup>þ</sup> 8 1ð Þ � <sup>x</sup> <sup>0</sup>:<sup>7</sup> <sup>r</sup><sup>f</sup> ,sat <sup>r</sup><sup>f</sup> ,vap !<sup>0</sup>:<sup>67</sup> <sup>0</sup>

kf ,i df ,i

Modeling for Organic Rankine Cycle Waste Heat Recovery System Development

(22)

75

(23)

1 þ 12:7

ξ<sup>f</sup> ,i ¼ 0:0075

where ξ is friction factor, din and dout are inner and outer diameters of concentric tube, respectively. The thermal conductivity of the exhaust gas is shown as follows:

$$k\_{1,\epsilon} = 1.07 + \frac{900}{Re\_{\epsilon}} - \frac{0.63}{(1 + 10Pr\_{\epsilon})} \tag{17}$$

$$Re\_{\varepsilon} = \frac{\dot{m}\_{\varepsilon} d\_{\varepsilon}}{A\_{\varepsilon, \text{cross}} \upsilon\_{d}} \tag{18}$$

$$Pr\_{\epsilon} = \frac{\upsilon\_{d,\epsilon} \varepsilon\_{p,\epsilon}}{k\_{\epsilon}} \tag{19}$$

where d is hydraulic diameter, vd is dynamic viscosity, Pr is Prandtl number. Nusselt number expression, Eq. (20), of a concentric tube with insulated outer pipe wall is selected based on the heat exchanger structure [13].

$$Nu\_{\varepsilon} = \frac{\left(\frac{\xi\_{\varepsilon}}{8}\right) \text{Re}\_{\varepsilon} Pr\_{\varepsilon}}{k\_{1,\varepsilon} + 12.7\sqrt{\frac{\xi\_{\varepsilon}}{8}} (Pr\_{\varepsilon}^{0.667} - 1)} \left[1 + \left(\frac{d\_{\varepsilon}}{l}\right)^{0.667}\right] \tag{20}$$

where l is length of the pipe in the heat exchanger. The heat transfer coefficient between exhaust gas and wall are calculated with Eq. (21) [14]. The experimental evaporator construction differs slightly from concentric tubes, so a heat transfer coefficient multiplier (mU) is applied.

$$\mathcal{U}L\_{\varepsilon,w} = m\_{\mathcal{U}} \frac{N\mu\_{\varepsilon}k\_{\varepsilon}}{d\_{\varepsilon}} \tag{21}$$

For the working fluid side heat transfer coefficients, they are not only time dependent, but also space dependent due to the phase change of working fluid along the heat exchanger. The single phase heat transfer coefficients are calculated in Eq. (22). The expression is chosen based on geometry structure of the heat exchanger [13].

Modeling for Organic Rankine Cycle Waste Heat Recovery System Development http://dx.doi.org/10.5772/intechopen.78997 75

$$\mathcal{U}\_{f,w,i} = \frac{\left(\frac{\xi\_{f,i}}{8}\right) \text{Re}\_{f,i} \text{Pr}\_{f,i}}{1 + 12.7 \sqrt{\frac{\xi\_{f,i}}{8}} \left(\text{Pr}\_{f,i}^{0.667} - 1\right)} \frac{\mathbf{k}\_{f,i}}{\mathbf{d}\_{f,i}} \tag{22}$$

$$
\xi\_{f,i} = 0.0075 \left( \frac{d\_f}{D\_f} \right)^{0.5} + \frac{0.079}{Re\_{f,i}^{0.25}} \tag{23}
$$

During the evaporation process, both liquid and vapor phase exist. The heat transfer coefficient for this situation is calculated using a vertical tube two-phase heat transfer coefficient expression as shown in Eq. (24) [13]. Uf ,w,sat and Uf ,w,vap are calculated from Eq. (22).

$$\begin{split} \mathbf{U}\_{f,tp} &= \left\{ (1-\mathbf{x})^{0.01} \left[ (1-\mathbf{x}) + \mathbf{1}.9\mathbf{x}^{0.4} \left( \frac{\rho\_{f,\text{sat}}}{\rho\_{f,\text{up}}} \right)^{0.35} \right]^{-2.2} \\ &+ \mathbf{x}^{0.01} \left[ \frac{\mathbf{U}\_{f,\text{up}}}{\mathbf{U}\_{f,\text{sat}}} \left( 1 + 8(1-\mathbf{x})^{0.7} \left( \frac{\rho\_{f,\text{sat}}}{\rho\_{f,\text{up}}} \right)^{0.67} \right) \right]^{-2} \right\}^{-0.5} \end{split} \tag{24}$$

#### 3.2. Expander modeling

Heat transfer coefficients are calculated separately in working fluid side and exhaust gas side. In the exhaust gas side, at each time step, heat transfer coefficient is calculated once and all the m cells share the same value, which is only a function of time. Eq. (14) is the expression of

e

� �ln rð Þþ <sup>d</sup> ð Þ <sup>1</sup> � rd <sup>1</sup> <sup>þ</sup> <sup>r</sup><sup>2</sup> d � �ln rð Þ<sup>d</sup>

� � � <sup>1</sup>:<sup>5</sup> � ��<sup>2</sup> (14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

<sup>ξ</sup><sup>e</sup> <sup>¼</sup> <sup>1</sup>:<sup>8</sup> log<sup>10</sup> Re<sup>∗</sup>

respectively. The thermal conductivity of the exhaust gas is shown as follows:

k1,e ¼ 1:07 þ

ξe 8 � �

k1,e þ 12:7

<sup>1</sup> <sup>þ</sup> <sup>r</sup><sup>2</sup> d

> rd <sup>¼</sup> din dout

where ξ is friction factor, din and dout are inner and outer diameters of concentric tube,

900 Ree

Ree <sup>¼</sup> <sup>m</sup>\_ ede Ae, crossvd

Pre <sup>¼</sup> vd,ecp,e ke

where d is hydraulic diameter, vd is dynamic viscosity, Pr is Prandtl number. Nusselt number expression, Eq. (20), of a concentric tube with insulated outer pipe wall is selected based on the

ReePre

Ue,w ¼ mU

For the working fluid side heat transfer coefficients, they are not only time dependent, but also space dependent due to the phase change of working fluid along the heat exchanger. The single phase heat transfer coefficients are calculated in Eq. (22). The expression is chosen based

Pr<sup>0</sup>:<sup>667</sup> <sup>e</sup> � <sup>1</sup> � �

where l is length of the pipe in the heat exchanger. The heat transfer coefficient between exhaust gas and wall are calculated with Eq. (21) [14]. The experimental evaporator construction differs slightly from concentric tubes, so a heat transfer coefficient multiplier (mU) is

> Nueke de

1 þ

de l � �<sup>0</sup>:<sup>667</sup> " #

ffiffiffi ξe 8 q

� <sup>0</sup>:<sup>63</sup> ð Þ 1 þ 10Pre

Re<sup>∗</sup> <sup>e</sup>¼ Ree

friction factor for the concentric tubes [12]:

74 Organic Rankine Cycle Technology for Heat Recovery

heat exchanger structure [13].

applied.

Nue ¼

on geometry structure of the heat exchanger [13].

The turbine is integrated with an electric generator in this work. However, it can also be mechanically connected to engine crank shaft through a gearbox. Turbine expander mass flow rate has a linear relationship to turbine inlet pressure, Eq. (25), due to the choked flow status at high expansion ratios (10–30).

$$
\dot{m}\_{\text{in}} = a\_{\text{turb}} p\_{\text{in}} + b\_{\text{turb}} \tag{25}
$$

The outlet enthalpy is calculated by isentropic efficiency as follows:

$$h\_{\rm out} = h\_{\rm in} - \eta\_{\rm is} (h\_{\rm in} - h\_{\rm out, is}) \tag{26}$$

$$\eta\_{is} = \text{map}\{\mathcal{N}\_{thrb}, p\_{in}/p\_{out}, T\_{in}\} \tag{27}$$

$$h\_{out,is} = \max(s\_{out}, p\_{out}) \tag{28}$$

$$\mathbf{s}\_{out} = \mathbf{s}\_{in} \tag{29}$$

$$s\_{\rm in} = \max\{h\_{\rm in}, p\_{\rm in}\} \tag{30}$$

Outlet temperature, Tout, is calculated from outlet enthalpy and outlet pressure using a thermodynamic table of the working fluid.

$$T\_{out} = \text{map}\{h\_{out}, p\_{out}\} \tag{31}$$

The turbine power is given as follows

$$P\_{\rm Turb} = \eta\_{conv} \eta\_{em} \eta\_{is} \dot{m}\_{in} (h\_{in} - h\_{out, is}) \tag{32}$$

4. Conclusion

Author details

References

Bin Xu\*, Adamu Yebi and Zoran Filipi

ences. 2011;54:2746-2753

2016;165:878-892

\*Address all correspondence to: xbin@clemson.edu

evaluation. SAE International 2012-01-1602; 2012

This chapter mainly focuses on the modeling of ORC-WHR system including the overview of model complexity, accuracy, computation time of different heat exchanger models such as static model, 0D model, 1D finite volume model, 1D moving boundary model etc. static heat exchanger model ends up popular in calculating the energy balance at the concept phase of the ORC-WHR system development. 0D model is suitable for the computational costly optimization algorithm like Dynamic Programming due to its less computation time compared with higher dimensional models like moving boundary model and finite volume model. Moving boundary model ends up with the best choice as a control model in advanced controls due to its low computation cost than finite volume model and higher accuracy than the 0D model, even though it has higher model complexity than 0D model and finite volume model. Finite volume model is the best choice to work as offline plant model due to its high accuracy and stability compared with moving boundary model and 0D model. 2D and 3D model is suitable for the heat exchanger component development due to their capability of revealing detailed information inside different locations of the heat exchanger. The ORC-WHR system model example presented in Section 3 shows the complete system model. After reading this chapter, the readers will be equipped with the basic understanding of ORC-WHR system model and

Modeling for Organic Rankine Cycle Waste Heat Recovery System Development

http://dx.doi.org/10.5772/intechopen.78997

77

how to start modeling in the ORC-WHR system development.

Department of Automotive Engineering, Clemson University, Greenville, SC, USA

[1] Wei MS, Fang JL, Ma CC, Danish SN. Waste heat recovery from heavy-duty diesel engine exhaust gases by medium temperature ORC system. Science China-Technological Sci-

[2] Arunachalam PN, Shen MQ, Tuner M, Tunestal P, Thern M. Waste heat recovery from multiple heat sources in a HD truck diesel engine using a Rankine cycle—A theoretical

[3] Grelet V, Reiche T, Lemort V, Nadri M, Dufour P. Transient performance evaluation of waste heat recovery Rankine cycle based system for heavy duty trucks. Applied Energy.

[4] Horst TA, Tegethoff W, Eilts P, Koehler J. Prediction of dynamic Rankine cycle waste heat recovery performance and fuel saving potential in passenger car applications considering

where turbine power electronics efficiency ηconv ¼ 0:99 and turbine electric motor efficiency ηem ¼ 0:95.

#### 3.3. Valve modeling

The turbine inlet valve and turbine bypass valve both experience vapor phase flow. They are modeled based on the compressible flow status: subsonic flow or supersonic flow [15]:

$$\begin{cases} \begin{aligned} &\text{If } \left(\frac{2}{\gamma+1}\right)^{\frac{\gamma}{\gamma-1}} \leq \frac{p\_{out}}{p\_{in}} \leq 1 \text{(subsonic)}:\\ &\text{If } 0 \leq \frac{p\_{out}}{p\_{in}} \leq \left(\frac{2}{\gamma+1}\right)^{\frac{\gamma}{\gamma-1}} \text{(supersonic)}:\\ &\text{If } 0 \leq \frac{p\_{out}}{p\_{in}} \leq \left(\frac{2}{\gamma+1}\right)^{\frac{\gamma}{\gamma-1}} \text{(supersonic)}: \quad \dot{m} = \text{OC}\_{d}A\_{0} \left(\frac{2}{\gamma+1}\right)^{\frac{\gamma+1}{2(\gamma-1)}} \sqrt{\gamma p\_{in}}\rho\_{in} \end{aligned} \end{cases} \end{cases}$$

where <sup>γ</sup> <sup>¼</sup> cp cv is heat capacity ratio. Assuming the working fluid experiences an isentropic process across the valve (hout ¼ hin), the outlet temperature is calculated:

$$T\_{out} = f\left(p\_{out}, h\_{out}\right) \tag{34}$$

#### 3.4. Pump modeling

The ORC-WHR system pumps maintain both working fluid mass flow and pressure. The pump is a positive displacement type, whereas the feed pump is an inline roller cell pump. The mass flow rate of the pump is interpolated from a 2-D map as shown in Eq. (35). Pump power consumption and outlet temperature are calculated from physics expressions via Eqs. (36, 37).

$$
\dot{m}\_{pump} = \max\{\mathcal{N}\_{pump}\} \tag{35}
$$

$$P\_{pump} = \frac{\dot{m}\_{pump}}{\rho} \frac{\left(p\_{out,pump} - p\_{in,pump}\right)}{\eta\_{is,pump}} \tag{36}$$

$$T\_{out,pump} = T\_{in,pump} + \frac{\left(1 - \eta\_{is,pump}\right)P\_{pump}}{\dot{m}\_{pump}c\_{p,pump}}\tag{37}$$

where r is the pump upstream working fluid density, pin, pump, pout, pump are upstream and downstream pressure respectively, cp,pump is the upstream specific heat capacity of the working fluid, ηis,pump is isentropic efficiency and is expressed as a function of pump mass flow rate. The empirical expression and coefficients are found in [8, 16].

$$\eta\_{is, pump} = 0.93 - 0.11 \log \left(\frac{\dot{m}\_{pump}}{\dot{m}\_{pump, max}}\right) - 0.2 \log \left(\frac{\dot{m}\_{pump}}{\dot{m}\_{pump, max}}\right)^2 - 0.06 \log \left(\frac{\dot{m}\_{pump}}{\dot{m}\_{pump, max}}\right)^3 \tag{38}$$

## 4. Conclusion

PTurb ¼ ηconvηemηism\_ inð Þ hin � hout,is (32)

2γ γ � 1

2 γþ1 � � <sup>γ</sup>þ<sup>1</sup>

cv is heat capacity ratio. Assuming the working fluid experiences an isentropic

pinrin

<sup>2</sup>ð Þ <sup>γ</sup>�<sup>1</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffi γpinrin p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

(33)

(36)

(37)

(38)

pout pin � �<sup>2</sup> γ � pout pin � �<sup>γ</sup>þ<sup>1</sup> γ

vu " # ut

� � (34)

� � (35)

� <sup>0</sup>:<sup>06</sup> log <sup>m</sup>\_ pump

m\_ pump,max � �<sup>3</sup>

where turbine power electronics efficiency ηconv ¼ 0:99 and turbine electric motor efficiency

The turbine inlet valve and turbine bypass valve both experience vapor phase flow. They are

Tout ¼ f pout; hout

The ORC-WHR system pumps maintain both working fluid mass flow and pressure. The pump is a positive displacement type, whereas the feed pump is an inline roller cell pump. The mass flow rate of the pump is interpolated from a 2-D map as shown in Eq. (35). Pump power consumption and outlet temperature are calculated from physics expressions via

m\_ pump ¼ map Npump

where r is the pump upstream working fluid density, pin, pump, pout, pump are upstream and downstream pressure respectively, cp,pump is the upstream specific heat capacity of the working fluid, ηis,pump is isentropic efficiency and is expressed as a function of pump mass flow rate. The

� <sup>0</sup>:<sup>2</sup> log <sup>m</sup>\_ pump

m\_ pump,max � �<sup>2</sup>

pout,pump � pin,pump � �

ηis,pump

1 � ηis,pump � �

m\_ pumpcp,pump

Ppump

modeled based on the compressible flow status: subsonic flow or supersonic flow [15]:

≤ 1ð Þ subsonic : m\_ ¼ OCdA<sup>0</sup>

process across the valve (hout ¼ hin), the outlet temperature is calculated:

Ppump <sup>¼</sup> <sup>m</sup>\_ pump r

Tout, pump ¼ Tin, pump þ

empirical expression and coefficients are found in [8, 16].

m\_ pump,max � �

<sup>η</sup>is, pump <sup>¼</sup> <sup>0</sup>:<sup>93</sup> � <sup>0</sup>:<sup>11</sup> log <sup>m</sup>\_ pump

ð Þ supersonic : m\_ ¼ OCdA<sup>0</sup>

ηem ¼ 0:95.

If <sup>2</sup> γþ1 � � <sup>γ</sup> γ�1 <sup>≤</sup> pout pin

where <sup>γ</sup> <sup>¼</sup> cp

Eqs. (36, 37).

8 >>>>><

>>>>>:

If <sup>0</sup> <sup>≤</sup> pout pin ≤

3.4. Pump modeling

2 γ þ 1 � � <sup>γ</sup> γ�1

76 Organic Rankine Cycle Technology for Heat Recovery

3.3. Valve modeling

This chapter mainly focuses on the modeling of ORC-WHR system including the overview of model complexity, accuracy, computation time of different heat exchanger models such as static model, 0D model, 1D finite volume model, 1D moving boundary model etc. static heat exchanger model ends up popular in calculating the energy balance at the concept phase of the ORC-WHR system development. 0D model is suitable for the computational costly optimization algorithm like Dynamic Programming due to its less computation time compared with higher dimensional models like moving boundary model and finite volume model. Moving boundary model ends up with the best choice as a control model in advanced controls due to its low computation cost than finite volume model and higher accuracy than the 0D model, even though it has higher model complexity than 0D model and finite volume model. Finite volume model is the best choice to work as offline plant model due to its high accuracy and stability compared with moving boundary model and 0D model. 2D and 3D model is suitable for the heat exchanger component development due to their capability of revealing detailed information inside different locations of the heat exchanger. The ORC-WHR system model example presented in Section 3 shows the complete system model. After reading this chapter, the readers will be equipped with the basic understanding of ORC-WHR system model and how to start modeling in the ORC-WHR system development.

## Author details

Bin Xu\*, Adamu Yebi and Zoran Filipi

\*Address all correspondence to: xbin@clemson.edu

Department of Automotive Engineering, Clemson University, Greenville, SC, USA

## References


interactions with vehicles' energy management. Energy Conversion and Management. 2014;78:438-451

**Chapter 5**

Provisional chapter

**Optimal Sizing of Waste Heat Recovery Systems for**

DOI: 10.5772/intechopen.78590

In this study, a methodology for optimal sizing of waste heat recovery (WHR) systems is presented. It deals with dynamic engine conditions. This study focuses on Euro-VI truck applications with a mechanically coupled Organic Rankine Cycle-based WHR system. An alternating optimization architecture is developed for optimal system sizing and control of the WHR system. The sizing problem is formulated as a fuel consumption and system cost optimization problem using a newly developed, scalable WHR system model. Constraints related to safe WHR operation and system mass are included in this methodology. The components scaled in this study are the expander and the EGR and exhaust gas evaporators. The WHR system size is optimized over a hot World Harmonized Transient Cycle (WHTC), which consists of urban, rural and highway driving conditions. The optimal component sizes are found to vary for these different driving conditions. By implementing a switching model predictive control (MPC) strategy on the optimally sized WHR system, its performance is validated. The net fuel consumption is found to be reduced by 1.1% as compared to the originally sized WHR system over the total WHTC.

Keywords: scalable models, component sizing, control, heavy-duty diesel engine

Heavy-duty (HD) engines are the workhorse in the transport sector. Driven by societal concerns about global warming and energy security, this sector faces enormous challenges to dramatically reduce green house gas emissions and fuel consumption over the upcoming decades. In the EU, CO2 legislation for HD vehicles is in preparation. For 2050, a 60% CO2

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Optimal Sizing of Waste Heat Recovery Systems for

**Dynamic Engine Conditions**

Dynamic Engine Conditions

http://dx.doi.org/10.5772/intechopen.78590

Abstract

1. Introduction

reduction sectorial target is set.

Emanuel Feru, Srajan Goyal and Frank Willems

Emanuel Feru, Srajan Goyal and Frank Willems

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter


#### **Optimal Sizing of Waste Heat Recovery Systems for Dynamic Engine Conditions** Optimal Sizing of Waste Heat Recovery Systems for Dynamic Engine Conditions

DOI: 10.5772/intechopen.78590

Emanuel Feru, Srajan Goyal and Frank Willems Emanuel Feru, Srajan Goyal and Frank Willems

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.78590

#### Abstract

interactions with vehicles' energy management. Energy Conversion and Management.

[5] Peralez J, Tona P, Sciarretta A, Dufour P, Nadri M. Optimal control of a vehicular organic Rankine cycle via dynamic programming with adaptive discretization grid. IFAC Pro-

[6] Xie H, Yang C. Dynamic behavior of Rankine cycle system for waste heat recovery of heavy duty diesel engines under driving cycle. Applied Energy. 2013;112:130-141

[7] Xu B, Rathod D, Kulkarni S, Yebi A, Filipi Z, Onori S, et al. Transient dynamic modeling and validation of an organic Rankine cycle waste heat recovery system for heavy duty

[8] Quoilin S, Aumann R, Grill A, Schuster A, Lemort V, Spliethoff H. Dynamic modeling and optimal control strategy of waste heat recovery organic Rankine cycles. Applied Energy.

[9] Peralez J, Tona P, Lepreux O, Sciarretta A, Voise L, Dufour P, et al. Improving the control performance of an organic Rankine cycle system for waste heat recovery from a heavyduty diesel engine using a model-based approach. In: 2013 IEEE 52nd Annual Conference

[10] Luong D, Tsao TC. Linear quadratic integral control of an organic Rankine cycle for waste heat recovery in heavy-duty diesel Powertrain. In: 2014 American Control Conference

[11] Yebi A, Xu B, Liu X, Shutty J, Anschel P, Filipi Z, et al. Estimation and predictive control of a parallel evaporator diesel engine waste heat recovery system. IEEE Transactions on

[12] Gnielinski V. Berechnung des Druckverlustes in glatten konzentrischen Ringspalten bei ausgebildeter laminarer und turbulenter isothermer Strömung. Chemie Ingenieur

[13] Blaß E, Chemieingenieurwesen GVu. VDI-Gesellschaft Verfahrenstechnik und Chemieingenieurwesen GVC: gestern, heute, morgen; eine Jubiläumsschrift anläßlich des Jahrestreffens der Verfahrensingenieure 1984 in München zum 50-jährigen Bestehen der GVC: Saur;

[14] Bergman TL, Incropera FP, Lavine AS. Fundamentals of Heat and Mass Transfer. Hobo-

[15] Weiss HH, Boshwirth L. A simple but efficient equipment for experimental determination of valve loss coefficient under compressible and steady flow conditions. In: International

[16] Vetter G. Rotierende Verdrängerpumpen für die Prozesstechnik. Vulkan-Verlag GmbH;

diesel engine applications. Applied Energy. 2017;205:260-279

on Decision and Control (Cdc); 2013. pp. 6830-6836

Control Systems Technology. 2017;PP:1-14

ken, New Jersey, USA: John Wiley & Sons; 2011

Compressor Engineering Conference; 1982. pp. 69-76

2014;78:438-451

78 Organic Rankine Cycle Technology for Heat Recovery

2011;88:2183-2190

(Acc); 2014. pp. 3147-3152

Technik. 2007;79:91-95

1984

2006

ceedings Volumes. 2014;47:5671-5678

In this study, a methodology for optimal sizing of waste heat recovery (WHR) systems is presented. It deals with dynamic engine conditions. This study focuses on Euro-VI truck applications with a mechanically coupled Organic Rankine Cycle-based WHR system. An alternating optimization architecture is developed for optimal system sizing and control of the WHR system. The sizing problem is formulated as a fuel consumption and system cost optimization problem using a newly developed, scalable WHR system model. Constraints related to safe WHR operation and system mass are included in this methodology. The components scaled in this study are the expander and the EGR and exhaust gas evaporators. The WHR system size is optimized over a hot World Harmonized Transient Cycle (WHTC), which consists of urban, rural and highway driving conditions. The optimal component sizes are found to vary for these different driving conditions. By implementing a switching model predictive control (MPC) strategy on the optimally sized WHR system, its performance is validated. The net fuel consumption is found to be reduced by 1.1% as compared to the originally sized WHR system over the total WHTC.

Keywords: scalable models, component sizing, control, heavy-duty diesel engine

#### 1. Introduction

Heavy-duty (HD) engines are the workhorse in the transport sector. Driven by societal concerns about global warming and energy security, this sector faces enormous challenges to dramatically reduce green house gas emissions and fuel consumption over the upcoming decades. In the EU, CO2 legislation for HD vehicles is in preparation. For 2050, a 60% CO2 reduction sectorial target is set.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

To meet these challenging targets for trucks, besides vehicle and logistic measures, increase of the powertrain efficiency is an important research area. In modern diesel engines, around 25% of the fuel energy is converted into heat and is wasted with the exhaust gases into the environment. Extracting this energy and converting it into useful propulsion energy will potentially lead to significant reductions in fuel consumption.

2. System description

tion catalyst (AMOX).

Figure 1. Scheme of the complete powertrain with WHR system [11].

Figure 1 shows the studied system, which is based on a 13 liter, 6 cylinder Euro-VI heavy-duty diesel engine. This engine is equipped with common rail fuel injection, a high-pressure exhaust gas recirculation (EGR) system, variable turbocharger geometry (VTG) and an aftertreatment system. This aftertreatment system consists of a diesel oxidation catalyst (DOC), a diesel particulate filter (DPF) and a selective catalytic reduction (SCR) system with ammonia oxida-

Optimal Sizing of Waste Heat Recovery Systems for Dynamic Engine Conditions

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A waste heat recovery system is installed that recovers heat from the EGR line as well as the line downstream of the aftertreatment system using an EGR and Exhaust Gas (EXH) evaporator, respectively. The working principle of this WHR system is based on an Organic Rankine Cycle (ORC). The working fluid is ethanol. It is pumped from the open reservoir, which is at ambient pressure, through the evaporators by two electrically driven pumps. In the evaporators, heat is extracted from the exhaust gases and is used to vaporize the ethanol. This vapor expands in the two-piston expander and generates mechanical power. Note that the expander is mechanically coupled to the engine crankshaft. The expander is said to operate safely if vapor state is maintained before the expander, that is, the working fluid must be in superheated state. The presence of droplets can damage the expander. After expansion, the working fluid is cooled in the condenser. The resulting liquid working fluid flows back to the reservoir, where it is stored at atmospheric pressure. For WHR system control, both pumps are used. A throttle valve ut at the expander inlet is also available to accommodate gear shifting. When the driver's requested power is less than the net power delivered by the WHR system, Preq ≤ Pwhr,

The Organic Rankine Cycle (ORC) seems a promising waste heat recovery (WHR) technology for heavy-duty applications [1, 2]. For future implementation, further optimization of the costbenefit ratio is crucial. More precisely, optimal sizing of the WHR system is necessary to maximize the WHR power output and fuel economy of the vehicle. However, this is challenging, since there are many factors that affect the optimality of WHR system size, including: driving conditions, system constraints, and the control strategy. In [3], it is shown that dynamic operating conditions play an important role for optimization of WHR systems, especially in truck applications. A huge gap was observed between predictions based on steady-state and dynamic conditions. Similar results are found in [4]: performance evaluation in steady-state operating points derived by driving cycle reduction tends to overestimate the fuel gain induced by the WHR system. In addition, the coupling between system and control design has to be dealt with.

In the literature, publications dedicated to topology design and architecture, control and integration with the powertrain system can be found for ORC-based WHR systems in automotive applications. The studied physics-based models [5–9] are based on stock component models, which are already available commercially. The size of the components is chosen based on the packaging requirements and cost. In summary, models with scalable components and component sizing approaches are lacking.

In this study, a new methodology is presented for optimal component sizing of WHR systems in the presence of highly dynamic engine conditions. The main goal is to minimize overall powertrain fuel consumption, while meeting safety constraints. This study is an extension of the work done in [10], where models and control techniques are developed to enable waste heat recovery for a Euro VI heavy duty diesel engine. By following an alternating optimization approach, system and control design is separated. A general optimization framework is defined that deals with the impact of component size on overall fuel consumption, system costs and system mass. A new, scalable WHR system model is proposed to support this optimization methodology. It is noted that the optimization is performed using a stand-alone WHR system, since it is seen from our research that this does not affect the optimality of the results, compared to using the complete powertrain model.

This work is organized as follows. The studied engine with WHR system and the general WHR optimization problem are introduced in Sections 2 and 3, respectively. Section 4 presents the scalable WHR system model. In the proposed alternating optimization approach, optimal component sizing and control design are split. Section 5 introduces the sizing optimization problem, which is followed to determine optimal scaling factors for evaporators and expander using the developed, scalable WHR model. For a switching MPC controller, the optimally sized WHR system performance is validated over the hot start World Harmonized Transient Cycle (WHTC) in Section 6. Finally, the main conclusions are summarized in Section 7.

## 2. System description

To meet these challenging targets for trucks, besides vehicle and logistic measures, increase of the powertrain efficiency is an important research area. In modern diesel engines, around 25% of the fuel energy is converted into heat and is wasted with the exhaust gases into the environment. Extracting this energy and converting it into useful propulsion energy will potentially

The Organic Rankine Cycle (ORC) seems a promising waste heat recovery (WHR) technology for heavy-duty applications [1, 2]. For future implementation, further optimization of the costbenefit ratio is crucial. More precisely, optimal sizing of the WHR system is necessary to maximize the WHR power output and fuel economy of the vehicle. However, this is challenging, since there are many factors that affect the optimality of WHR system size, including: driving conditions, system constraints, and the control strategy. In [3], it is shown that dynamic operating conditions play an important role for optimization of WHR systems, especially in truck applications. A huge gap was observed between predictions based on steady-state and dynamic conditions. Similar results are found in [4]: performance evaluation in steady-state operating points derived by driving cycle reduction tends to overestimate the fuel gain induced by the WHR system. In addition, the coupling between system and control design

In the literature, publications dedicated to topology design and architecture, control and integration with the powertrain system can be found for ORC-based WHR systems in automotive applications. The studied physics-based models [5–9] are based on stock component models, which are already available commercially. The size of the components is chosen based on the packaging requirements and cost. In summary, models with scalable components and

In this study, a new methodology is presented for optimal component sizing of WHR systems in the presence of highly dynamic engine conditions. The main goal is to minimize overall powertrain fuel consumption, while meeting safety constraints. This study is an extension of the work done in [10], where models and control techniques are developed to enable waste heat recovery for a Euro VI heavy duty diesel engine. By following an alternating optimization approach, system and control design is separated. A general optimization framework is defined that deals with the impact of component size on overall fuel consumption, system costs and system mass. A new, scalable WHR system model is proposed to support this optimization methodology. It is noted that the optimization is performed using a stand-alone WHR system, since it is seen from our research that this does not affect the optimality of the

This work is organized as follows. The studied engine with WHR system and the general WHR optimization problem are introduced in Sections 2 and 3, respectively. Section 4 presents the scalable WHR system model. In the proposed alternating optimization approach, optimal component sizing and control design are split. Section 5 introduces the sizing optimization problem, which is followed to determine optimal scaling factors for evaporators and expander using the developed, scalable WHR model. For a switching MPC controller, the optimally sized WHR system performance is validated over the hot start World Harmonized Transient

Cycle (WHTC) in Section 6. Finally, the main conclusions are summarized in Section 7.

lead to significant reductions in fuel consumption.

80 Organic Rankine Cycle Technology for Heat Recovery

has to be dealt with.

component sizing approaches are lacking.

results, compared to using the complete powertrain model.

Figure 1 shows the studied system, which is based on a 13 liter, 6 cylinder Euro-VI heavy-duty diesel engine. This engine is equipped with common rail fuel injection, a high-pressure exhaust gas recirculation (EGR) system, variable turbocharger geometry (VTG) and an aftertreatment system. This aftertreatment system consists of a diesel oxidation catalyst (DOC), a diesel particulate filter (DPF) and a selective catalytic reduction (SCR) system with ammonia oxidation catalyst (AMOX).

A waste heat recovery system is installed that recovers heat from the EGR line as well as the line downstream of the aftertreatment system using an EGR and Exhaust Gas (EXH) evaporator, respectively. The working principle of this WHR system is based on an Organic Rankine Cycle (ORC). The working fluid is ethanol. It is pumped from the open reservoir, which is at ambient pressure, through the evaporators by two electrically driven pumps. In the evaporators, heat is extracted from the exhaust gases and is used to vaporize the ethanol. This vapor expands in the two-piston expander and generates mechanical power. Note that the expander is mechanically coupled to the engine crankshaft. The expander is said to operate safely if vapor state is maintained before the expander, that is, the working fluid must be in superheated state. The presence of droplets can damage the expander. After expansion, the working fluid is cooled in the condenser. The resulting liquid working fluid flows back to the reservoir, where it is stored at atmospheric pressure. For WHR system control, both pumps are used. A throttle valve ut at the expander inlet is also available to accommodate gear shifting. When the driver's requested power is less than the net power delivered by the WHR system, Preq ≤ Pwhr,

Figure 1. Scheme of the complete powertrain with WHR system [11].

this valve is closed to avoid unwanted torque responses. In this study, this valve is maintained at fully opened position, since we focus on realizing maximum power output. The system pressure is limited to 60 bar by a pressure relief valve. The EGR valve ug<sup>1</sup> is controlled by the engine control unit (ECU), whereas the exhaust gas bypass valve ug<sup>2</sup> is controlled, such that the condenser cooling capacity is not exceeded.

In previous work [10], an electrified WHR system is also studied. This WHR system is equipped with a battery for energy storage, and the expander is coupled to a generator instead of the engine crankshaft. However, to demonstrate the potential of the WHR component sizing methodology, the configuration shown in Figure 1 is chosen. This configuration is more attractive for short-term application due to its relatively low system costs and complexity.

## 3. Optimization problem

#### 3.1. General problem definition

The high-level objective of this study is to minimize fuel consumption of the overall powertrain by optimal sizing and control of WHR system components over a transient drive cycle, while guaranteeing safe operation. In other words, optimal component scaling factors (λi) in combination with optimal speed settings for both pumps (ωp<sup>1</sup> and ωp2) have to be determined:

$$\underset{\omega\_{p1\cdot},\omega\_{p2\cdot},\lambda\_i}{\text{minimize}} \quad \int\_0^{t\_f} \dot{m}\_{fuel}(t)dt \tag{1}$$

As this study focuses on maximizing the WHR system performance, the fuel consumption in Eq. (2) can be reduced by lowering the engine torque τe. This is done by maximizing the net WHR power output Pwhr, Eq. (3)–(4). The external inputs to the WHR system are the EGR and exhaust gas flows from the engine and aftertreatment system, which are also a function of

Figure 2. Scheme of the dynamic model for the studied engine-WHR system. WHR-related components are indicated by

ðtf 0

λmin

Tout

Pwhrð Þt dt

<sup>i</sup> ≤ λ<sup>i</sup> ≤ λmax

egrð Þ<sup>t</sup> <sup>≥</sup> <sup>120</sup><sup>∘</sup>

Tf <sup>1</sup>, <sup>2</sup>ð Þ<sup>t</sup> <sup>≤</sup> <sup>270</sup><sup>∘</sup> <sup>C</sup>

<sup>p</sup> <sup>≤</sup> <sup>ω</sup>p1,p2ð Þ<sup>t</sup> <sup>≤</sup> <sup>ω</sup>max

C

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p

<sup>i</sup> ; f g i ¼ 1…n

χfð Þt ≥ 1 (5)

In conclusion, a combined design and control optimization problem is formulated:

minimize <sup>ω</sup>p1, <sup>ω</sup>p2, <sup>λ</sup><sup>i</sup>

subject to : ωmin

τe, Ne, EGR and VTG positions.

with optimization variables:

Problem 1

red blocks.

where tf is the duration of drive cycle. The fuel mass flow is a function of engine torque τe, engine speed Ne and EGR valve and VTG positions:

$$
\dot{m}\_{fuel} = f(\tau\_\text{e}, \text{N}\_\text{e}, \text{EGR\%}, \text{VTG\%}) \tag{2}
$$

The dynamic model of the engine with WHR system is shown in Figure 2. This scheme illustrates the components and their interaction. Ambient temperature and pressure (Tamb and patm), the requested engine speed Nd and the torque τ<sup>d</sup> associated with the drive cycle are the external model inputs (in green). The variables to be optimized, that is, control inputs ωp1,<sup>2</sup> and scaling parameters λi, are indicated in blue.

To meet the torque request τd, the required engine torque is given by:

$$
\tau\_e = \tau\_d - \tau\_{whr} \tag{3}
$$

with the torque τwhr provided by the WHR system:

$$
\tau\_{wlrr} = \frac{P\_{wlrr}}{\omega\_{\varepsilon}} = \frac{P\_{exp} - P\_{p1} - P\_{p2}}{\omega\_{\varepsilon}} \tag{4}
$$

Optimal Sizing of Waste Heat Recovery Systems for Dynamic Engine Conditions http://dx.doi.org/10.5772/intechopen.78590 83

Figure 2. Scheme of the dynamic model for the studied engine-WHR system. WHR-related components are indicated by red blocks.

As this study focuses on maximizing the WHR system performance, the fuel consumption in Eq. (2) can be reduced by lowering the engine torque τe. This is done by maximizing the net WHR power output Pwhr, Eq. (3)–(4). The external inputs to the WHR system are the EGR and exhaust gas flows from the engine and aftertreatment system, which are also a function of τe, Ne, EGR and VTG positions.

In conclusion, a combined design and control optimization problem is formulated:

#### Problem 1

this valve is closed to avoid unwanted torque responses. In this study, this valve is maintained at fully opened position, since we focus on realizing maximum power output. The system pressure is limited to 60 bar by a pressure relief valve. The EGR valve ug<sup>1</sup> is controlled by the engine control unit (ECU), whereas the exhaust gas bypass valve ug<sup>2</sup> is controlled, such that the

In previous work [10], an electrified WHR system is also studied. This WHR system is equipped with a battery for energy storage, and the expander is coupled to a generator instead of the engine crankshaft. However, to demonstrate the potential of the WHR component sizing methodology, the configuration shown in Figure 1 is chosen. This configuration is more attractive for short-term application due to its relatively low system costs and complexity.

The high-level objective of this study is to minimize fuel consumption of the overall powertrain by optimal sizing and control of WHR system components over a transient drive cycle, while guaranteeing safe operation. In other words, optimal component scaling factors (λi) in combina-

> ðtf 0

where tf is the duration of drive cycle. The fuel mass flow is a function of engine torque τe,

The dynamic model of the engine with WHR system is shown in Figure 2. This scheme illustrates the components and their interaction. Ambient temperature and pressure (Tamb and patm), the requested engine speed Nd and the torque τ<sup>d</sup> associated with the drive cycle are the external model inputs (in green). The variables to be optimized, that is, control inputs ωp1,<sup>2</sup> and

> <sup>¼</sup> Pexp � Pp<sup>1</sup> � Pp<sup>2</sup> ωe

m\_ fuelð Þt dt (1)

m\_ fuel ¼ fð Þ τe; Ne; EGR%; VTG% (2)

τ<sup>e</sup> ¼ τ<sup>d</sup> � τwhr (3)

(4)

tion with optimal speed settings for both pumps (ωp<sup>1</sup> and ωp2) have to be determined:

minimize <sup>ω</sup>p1, <sup>ω</sup>p2, <sup>λ</sup><sup>i</sup>

To meet the torque request τd, the required engine torque is given by:

<sup>τ</sup>whr <sup>¼</sup> Pwhr ωe

condenser cooling capacity is not exceeded.

82 Organic Rankine Cycle Technology for Heat Recovery

3. Optimization problem

3.1. General problem definition

engine speed Ne and EGR valve and VTG positions:

scaling parameters λi, are indicated in blue.

with the torque τwhr provided by the WHR system:

$$\begin{array}{ll}\text{minimize}\_{\omega\_{\mathbb{P}^1}\circ\omega\_{\mathbb{P}^2}\boldsymbol{A}\_i} \stackrel{\text{f}\_f}{\underset{p}{\operatorname{P}}} \mathbf{P}\_{\text{whr}}(t)\mathbf{d}\mathbf{t} \\\\ \text{subject to} : \qquad \boldsymbol{a}\_p^{\min} \le \boldsymbol{a}\_{p1, p2}(t) \le \boldsymbol{a}\_p^{\max} \\\\ \boldsymbol{\lambda}\_i^{\min} \le \boldsymbol{\lambda}\_i \le \boldsymbol{\lambda}\_i^{\max} \quad ; \quad \{i = 1...n\} \\\\ \boldsymbol{T}\_{\text{cgr}}^{\text{out}}(t) \ge 120^\circ \,\mathsf{C} \\\\ \boldsymbol{T}\_{f1,2}(t) \le 270^\circ \,\mathsf{C} \\\\ \boldsymbol{\chi}\_f(t) \ge 1 \end{array} \tag{5}$$

with optimization variables:


This optimization problem is subject to the following constraints:


$$\chi\_f = \frac{h\_f - h\_l \left(p\_f\right)}{h\_v \left(p\_f\right) - h\_l \left(p\_f\right)}\tag{6}$$

size might not be functional for a different size, due to the changing heat exchanger system dynamics. When using a nested framework, for every evaluation of plant design, multiple MPCs must be obtained covering the WHR operating area. Moreover, high tuning effort is

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Due to the high complexity of the optimization problem, the alternating optimization method is selected in this study. The main reasons are as follows: applicability to other WHR systems topologies and possibility to sequentially run the controller and plant optimization, which

The sizing optimization requires significant controller tuning effort for different plant sizes. Therefore, a size independent feed forward controller is necessary to significantly reduce the tuning effort and thus the computational complexity of the optimization problem. Even though a feed forward controller does not give the full performance, it is still representative for solving sizing problems. Moreover, in Section 6,

The low-level pump controllers have to guarantee that the working fluid at the expander inlet is at superheated state: χ<sup>f</sup> ≥ 1. Both pumps control the mass flow of the working flow through the evaporators and by that the heat transfer between the exhaust gas and the working fluid. The discussed MPC strategy needs relatively high tuning effort when the WHR system has to

Considering these issues, a feed forward (FF) pump controller is introduced, which is independent of the plant size. It is based on the measured EGR and exhaust gas heat flows from the engine, measured temperature of the working fluid at the evaporator inlet, and the working fluid system pressure. For stationary conditions, the amount of heat that needs to be transferred from the exhaust gas to the working fluid is determined from the energy balance:

<sup>Q</sup>\_ <sup>g</sup> � <sup>Q</sup>\_ g,loss <sup>¼</sup> <sup>Q</sup>\_

where Q\_ <sup>g</sup> is the heat flow from the exhaust gas, Q\_ <sup>g</sup>,loss are the heat transfer losses and Q\_ <sup>f</sup> is the heat flow toward the working fluid. From this equation, the required working fluid mass flow

> <sup>g</sup> � <sup>Q</sup>\_ g,loss

h ref f out � hf in

estimated enthalpy of the working fluid corresponding to a post-evaporator temperature of

C above the saturation temperature. The feed forward pump controller realizes this

<sup>m</sup>\_ <sup>f</sup> <sup>¼</sup> <sup>Q</sup>\_

where hfin is the actual enthalpy of the working fluid at the evaporator inlet and href

<sup>f</sup> (7)

(8)

fout is the

we will show that using such a controller produces results with acceptable validation properties.

required to implement a switching MPC strategy to obtain good disturbance rejection.

reduces the instantaneous computational burden.

3.3. Feedforward pump control

can be determined, using:

required working fluid flow.

10<sup>∘</sup>

be simulated on a grid of design points.

Remark 1.

where hl pf and hv pf denote the specific saturated liquid and vapor enthalpy, respectively, as a function of system pressure pf . To avoid damage by droplets, this fraction should be larger than 1 at the expander inlet.

Note that maximizing the WHR system power output by optimizing component sizes can lead to an increase in the needed cooling power in the condenser. However, in this work, we assume that this cooling capacity is always available (ideal condenser).

#### 3.2. Optimization methodologies

The problem stated above is nonconvex and highly nonlinear where both control and design parameters are optimization variables. For combined plant and control design problems, three approaches can be distinguished [12]:


The WHR system shown in Figure 1 is controlled by a switching model predictive control (MPC) strategy. With an alternating optimization architecture, an MPC tuned for one system size might not be functional for a different size, due to the changing heat exchanger system dynamics. When using a nested framework, for every evaluation of plant design, multiple MPCs must be obtained covering the WHR operating area. Moreover, high tuning effort is required to implement a switching MPC strategy to obtain good disturbance rejection.

Due to the high complexity of the optimization problem, the alternating optimization method is selected in this study. The main reasons are as follows: applicability to other WHR systems topologies and possibility to sequentially run the controller and plant optimization, which reduces the instantaneous computational burden.

#### Remark 1.

• Pump speeds ωp1ð Þt and ωp2ð Þt , which control the mass flow rate of the working fluid

• Design variables λi: these time-independent scaling factors are applied to vary the size of different components of WHR system, where n is the number of components to be scaled.

> hf � hl pf

as a function of system pressure pf . To avoid damage by droplets, this fraction should be larger

Note that maximizing the WHR system power output by optimizing component sizes can lead to an increase in the needed cooling power in the condenser. However, in this work, we

The problem stated above is nonconvex and highly nonlinear where both control and design parameters are optimization variables. For combined plant and control design problems, three

• Alternating plant and control design: the plant is optimized first, which is then followed by an optimal control design. Subsequently, this process is repeated until the coupled

• Nested optimization: the control design is nested within the plant design, that is, for each evaluation of the plant, the controller design is optimized. Often, nested optimization

• Simultaneous optimization: optimization of plant and controller design is done simulta-

The WHR system shown in Figure 1 is controlled by a switching model predictive control (MPC) strategy. With an alternating optimization architecture, an MPC tuned for one system

architectures are also called bi-level, referring to the two design layers;

� hl pf

hv pf 

• Ethanol temperature should always be less than 270<sup>∘</sup> C to avoid degradation;

χ<sup>f</sup> ¼

• χfð Þt is the vapor fraction of the working fluid, which is given by:

assume that this cooling capacity is always available (ideal condenser).

<sup>p</sup> are the minimum and maximum pump speeds to limit the mass flow rate of

egrð Þ<sup>t</sup> at the EGR evaporator outlet should be more than 120<sup>∘</sup>

denote the specific saturated liquid and vapor enthalpy, respectively,

(6)

C

required to extract heat energy from both the evaporators;

This optimization problem is subject to the following constraints:

• ωmin

where hl pf

than 1 at the expander inlet.

3.2. Optimization methodologies

approaches can be distinguished [12]:

neously, that is, solving Eq. (5) all-in-one.

variables converge;

<sup>p</sup> and ωmax

working fluid in the WHR system;

84 Organic Rankine Cycle Technology for Heat Recovery

• Exhaust gas temperature Tout

to prevent condensation;

and hv pf  The sizing optimization requires significant controller tuning effort for different plant sizes. Therefore, a size independent feed forward controller is necessary to significantly reduce the tuning effort and thus the computational complexity of the optimization problem. Even though a feed forward controller does not give the full performance, it is still representative for solving sizing problems. Moreover, in Section 6, we will show that using such a controller produces results with acceptable validation properties.

## 3.3. Feedforward pump control

The low-level pump controllers have to guarantee that the working fluid at the expander inlet is at superheated state: χ<sup>f</sup> ≥ 1. Both pumps control the mass flow of the working flow through the evaporators and by that the heat transfer between the exhaust gas and the working fluid. The discussed MPC strategy needs relatively high tuning effort when the WHR system has to be simulated on a grid of design points.

Considering these issues, a feed forward (FF) pump controller is introduced, which is independent of the plant size. It is based on the measured EGR and exhaust gas heat flows from the engine, measured temperature of the working fluid at the evaporator inlet, and the working fluid system pressure. For stationary conditions, the amount of heat that needs to be transferred from the exhaust gas to the working fluid is determined from the energy balance:

$$
\dot{\mathcal{Q}}\_{\mathcal{g}} - \dot{\mathcal{Q}}\_{\mathcal{g},\text{loss}} = \dot{\mathcal{Q}}\_{\mathcal{f}} \tag{7}
$$

where Q\_ <sup>g</sup> is the heat flow from the exhaust gas, Q\_ <sup>g</sup>,loss are the heat transfer losses and Q\_ <sup>f</sup> is the heat flow toward the working fluid. From this equation, the required working fluid mass flow can be determined, using:

$$
\dot{m}\_f = \frac{\dot{Q}\_g - \dot{Q}\_{g,loss}}{h\_{f\_{out}}^{\text{ref}} - h\_{f\_{in}}} \tag{8}
$$

where hfin is the actual enthalpy of the working fluid at the evaporator inlet and href fout is the estimated enthalpy of the working fluid corresponding to a post-evaporator temperature of 10<sup>∘</sup> C above the saturation temperature. The feed forward pump controller realizes this required working fluid flow.

## 4. Scalable WHR system model

In this section, the Waste Heat Recovery model from [13] is made scalable for component size. For each component, the physical parameters that have the biggest impact on the WHR power output are identified to scale the overall size of these components. The WHR system model is described using a component-based approach. The pumps and expander are map-based components. The remaining components, that is, evaporators, condenser, valves, and pressure volumes, are based on conservation of mass and energy principles.

Wnet,ideal ¼ W<sup>12</sup> þ W<sup>23</sup> þ W<sup>45</sup> þ W<sup>56</sup> (10)

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V<sup>κ</sup>�<sup>1</sup> 2

(11)

87

(12)

Using the ideal gas law, work delivered for different sub processes in the cycle are given by [14]:

ð Þ Vhead <sup>þ</sup> Vd <sup>κ</sup>�<sup>1</sup> � <sup>1</sup>

ð Þ Vhead <sup>κ</sup>�<sup>1</sup> � <sup>1</sup>

The physical parameter that is affecting the power output of the expander is its volume, as indicated by Eq. (11). Thus, applying the same scaling factor to Vhead and Vd, will change the overall dimensions of the expander. By applying the scaling factor to these volumes, it is assumed that the bore-to-stroke ratio of the cylinder is not changed. Hence, new volumes are defined:

head ¼ λexp � Vhead

<sup>d</sup> ¼ λexp � Vd

To keep the valve timings of the expander same as the original system, the same scaling factor,

Figure 3. p-V diagram of the expansion process (V<sup>2</sup> ¼ VIC: intake valve closing volume; V<sup>5</sup> ¼ VEC: exhaust valve closing

!

!

V<sup>κ</sup>�<sup>1</sup> 5

W<sup>12</sup> ¼ p � ð Þ V<sup>2</sup> � Vhead

2 ð Þ <sup>1</sup> � <sup>κ</sup> � <sup>1</sup>

W<sup>45</sup> ¼ patm � ð Þ V<sup>5</sup> � Vhead � Vd

5 ð Þ <sup>1</sup> � <sup>κ</sup> � <sup>1</sup>

V∗

V∗

<sup>W</sup><sup>23</sup> <sup>¼</sup> pV<sup>κ</sup>

<sup>W</sup><sup>56</sup> <sup>¼</sup> patmV<sup>κ</sup>

where κ is the adiabatic index, and patm is the atmospheric pressure.

λexp is applied to V2 and V5.

volume; Vhead: clearance volume; Vd: displacement volume).

The following assumptions are made in the model:


#### 4.1. Pumps

There are two identical pumps in the WHR system to pump the working fluid from the reservoir to the EGR and exhaust gas evaporators. Pumping power Pp1,<sup>2</sup> is directly proportional to the displacement volume and rotational speed of the pump. Thus, it can be inferred that a smaller pump can rotate at higher rotational speeds to meet the demands of mass flow rates of working fluid, while maintaining the same pressure difference without necessarily affecting the power output. Therefore, any variation in their displacement volume would not affect the required working fluid mass flow rate for the same operation cycle. Hence, sizing of the pumps is not considered here.

#### 4.2. Expander

The expansion process in the two-piston expander is illustrated in Figure 3. This cycle consists of two isobaric strokes (1!2 and 4!5), two isentropic stokes (2!3 and 5!6) and two isenthalpic mass transfers at the end of the strokes (3!4 and 6!1).

The expander power is ideally calculated by multiplying net work done in the cycle with the expander speed, given by

$$P\_{exp,ideal} = \mathcal{W}\_{net,ideal} \cdot \frac{\mathcal{N}\_{exp}}{60} \tag{9}$$

where

$$W\_{net,ideal} = W\_{12} + W\_{23} + W\_{45} + W\_{56} \tag{10}$$

Using the ideal gas law, work delivered for different sub processes in the cycle are given by [14]:

$$\begin{aligned} W\_{12} &= p \cdot (V\_2 - V\_{\text{head}})\\ W\_{23} &= \frac{pV\_2^{\kappa}}{(1-\kappa)} \cdot \left(\frac{1}{(V\_{\text{head}} + V\_d)^{\kappa-1}} - \frac{1}{V\_2^{\kappa-1}}\right) \\ W\_{45} &= p\_{\text{atm}} \cdot (V\_5 - V\_{\text{head}} - V\_d) \\ W\_{56} &= \frac{p\_{\text{atm}}V\_5^{\kappa}}{(1-\kappa)} \cdot \left(\frac{1}{(V\_{\text{head}})^{\kappa-1}} - \frac{1}{V\_5^{\kappa-1}}\right) \end{aligned} \tag{11}$$

where κ is the adiabatic index, and patm is the atmospheric pressure.

4. Scalable WHR system model

86 Organic Rankine Cycle Technology for Heat Recovery

In this section, the Waste Heat Recovery model from [13] is made scalable for component size. For each component, the physical parameters that have the biggest impact on the WHR power output are identified to scale the overall size of these components. The WHR system model is described using a component-based approach. The pumps and expander are map-based components. The remaining components, that is, evaporators, condenser, valves, and pressure

• Change in exhaust gas density as a function of temperature and pressure is neglected;

• Pressure dynamics in the heat exchangers are not considered because of small time scales

• Temperature along the transverse direction is considered to be uniform for both exhaust

• Condenser model is ideal, such that the reservoir provides the working fluid at an ambi-

There are two identical pumps in the WHR system to pump the working fluid from the reservoir to the EGR and exhaust gas evaporators. Pumping power Pp1,<sup>2</sup> is directly proportional to the displacement volume and rotational speed of the pump. Thus, it can be inferred that a smaller pump can rotate at higher rotational speeds to meet the demands of mass flow rates of working fluid, while maintaining the same pressure difference without necessarily affecting the power output. Therefore, any variation in their displacement volume would not affect the required working fluid mass flow rate for the same operation cycle. Hence, sizing of

The expansion process in the two-piston expander is illustrated in Figure 3. This cycle consists of two isobaric strokes (1!2 and 4!5), two isentropic stokes (2!3 and 5!6) and two

The expander power is ideally calculated by multiplying net work done in the cycle with the

Nexp

Pexp,ideal ¼ Wnet,ideal �

isenthalpic mass transfers at the end of the strokes (3!4 and 6!1).

C. Hence, condenser sizing is not considered

<sup>60</sup> (9)

volumes, are based on conservation of mass and energy principles.

• Transport delays and pressure drops along the pipes are neglected;

The following assumptions are made in the model:

compared to temperature phenomena;

ent pressure of 1 bar and temperature of 65<sup>∘</sup>

gas and working fluid;

the pumps is not considered here.

expander speed, given by

in this study.

4.1. Pumps

4.2. Expander

where

The physical parameter that is affecting the power output of the expander is its volume, as indicated by Eq. (11). Thus, applying the same scaling factor to Vhead and Vd, will change the overall dimensions of the expander. By applying the scaling factor to these volumes, it is assumed that the bore-to-stroke ratio of the cylinder is not changed. Hence, new volumes are defined:

$$\begin{aligned} V\_{head}^\* &= \lambda\_{exp} \cdot V\_{head} \\ V\_d^\* &= \lambda\_{exp} \cdot V\_d \end{aligned} \tag{12}$$

To keep the valve timings of the expander same as the original system, the same scaling factor, λexp is applied to V2 and V5.

Figure 3. p-V diagram of the expansion process (V<sup>2</sup> ¼ VIC: intake valve closing volume; V<sup>5</sup> ¼ VEC: exhaust valve closing volume; Vhead: clearance volume; Vd: displacement volume).

$$\begin{aligned} V\_2^\* &= \lambda\_{exp} \cdot V\_2\\ V\_5^\* &= \lambda\_{exp} \cdot V\_5 \end{aligned} \tag{13}$$

Scaling factors λl, λ<sup>w</sup> and λ<sup>h</sup> are applied to length l, width w and height h of the evaporators:

lnew ¼ λ<sup>l</sup> � l wnew ¼ λ<sup>w</sup> � w hnew ¼ λ<sup>h</sup> � h

Consequently, the following model parameters are affected. The number of plates inside the

Note that number of plates should be a discrete number, that is, np,new ∈ N. But in this study, it

In addition, the surface area available for the working fluid to extract the heat energy from

This also impacts the surface area available for the exhaust gas to transmit its heat to the

where Sg,fins is the surface area of fins at exhaust gas side. The surface area of the wall is linear

Accordingly, the Reynolds number for the working fluid and gas side is affected:

is varied continuously with the scaling factors, as it does not affect the end results.

np,new ¼ λ<sup>h</sup> � np (16)

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Sf ¼ 2 � np,new � wnew � lnew (17)

Sg ¼ Sf þ Sg,fins (18)

Sw ¼ lnew � wnew (19)

Ai,new ¼ wnew � hnew f g i ¼ fluid; gas (20)

evaporator will vary, when its height is changed,

Figure 5. Exhaust gas recirculation heat exchanger modular design.

exhaust gases through the wall or plates is affected:

working fluid through wall or plates, which is given by:

dependent on evaporator length and width:

Finally, the flow cross-sectional area, Ai is given by,

(15)

89

The ideal physics-based model of the expander deviates from the measurements because the model simulates an ideal cycle, and a number of adverse effects are not taken into account, for example, drag in the outlet, formation of droplets, Van der Waals interactions and volumetric efficiency. Hence, a steady state physics-based model of the expander was estimated in [14] based on the measurement data. This data were obtained during steady-state dynamometer testing for different values of expander speed Nexp and system pressure pf [10]. Results for different expander sizes are provided by the expander manufacturer. It suggests that the nominal power output increases linearly with increase in displacement volume. This is due to the modular design of the expanders. Therefore, for this study, the losses Ploss are considered equal for different expander sizes (λexp ), so Figure 4 is used:

$$P\_{whr} = P\_{whr,ideal} \cdot \left[1 - P\_{loss}\left(N\_{exp}, p\_f\right)\right] \tag{14}$$

#### 4.3. Evaporators

The evaporator model [15] is based on the conservation principles of mass and energy. To scale the evaporators size, the scaling factor needs to be applied on the volume of the evaporator. And the volume of evaporator can be varied by changing either length or width or height of the evaporator. The general structure of the studied evaporator is shown in Figure 5.

Figure 4. Expander power losses.

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Figure 5. Exhaust gas recirculation heat exchanger modular design.

V∗

V∗

equal for different expander sizes (λexp ), so Figure 4 is used:

88 Organic Rankine Cycle Technology for Heat Recovery

4.3. Evaporators

Figure 4. Expander power losses.

<sup>2</sup> ¼ λexp � V<sup>2</sup>

(13)

(14)

<sup>5</sup> ¼ λexp � V<sup>5</sup>

The ideal physics-based model of the expander deviates from the measurements because the model simulates an ideal cycle, and a number of adverse effects are not taken into account, for example, drag in the outlet, formation of droplets, Van der Waals interactions and volumetric efficiency. Hence, a steady state physics-based model of the expander was estimated in [14] based on the measurement data. This data were obtained during steady-state dynamometer testing for different values of expander speed Nexp and system pressure pf [10]. Results for different expander sizes are provided by the expander manufacturer. It suggests that the nominal power output increases linearly with increase in displacement volume. This is due to the modular design of the expanders. Therefore, for this study, the losses Ploss are considered

Pwhr ¼ Pwhr,ideal � 1 � Ploss Nexp ; pf

The evaporator model [15] is based on the conservation principles of mass and energy. To scale the evaporators size, the scaling factor needs to be applied on the volume of the evaporator. And the volume of evaporator can be varied by changing either length or width or height of

the evaporator. The general structure of the studied evaporator is shown in Figure 5.

h i � �

Scaling factors λl, λ<sup>w</sup> and λ<sup>h</sup> are applied to length l, width w and height h of the evaporators:

$$l\_{new} = \lambda\_l \cdot l$$

$$w\_{new} = \lambda\_w \cdot w$$

$$h\_{new} = \lambda\_h \cdot h$$

Consequently, the following model parameters are affected. The number of plates inside the evaporator will vary, when its height is changed,

$$
\Lambda n\_{p,new} = \Lambda\_{\text{lt}} \cdot n\_{\text{p}} \tag{16}
$$

Note that number of plates should be a discrete number, that is, np,new ∈ N. But in this study, it is varied continuously with the scaling factors, as it does not affect the end results.

In addition, the surface area available for the working fluid to extract the heat energy from exhaust gases through the wall or plates is affected:

$$S\_f = \mathbf{2} \cdot n\_{p,new} \cdot w\_{new} \cdot l\_{new} \tag{17}$$

This also impacts the surface area available for the exhaust gas to transmit its heat to the working fluid through wall or plates, which is given by:

$$\mathcal{S}\_{\mathcal{S}} = \mathcal{S}\_{\mathcal{f}} + \mathcal{S}\_{\mathcal{g},fins} \tag{18}$$

where Sg,fins is the surface area of fins at exhaust gas side. The surface area of the wall is linear dependent on evaporator length and width:

$$S\_w = l\_{new} \cdot w\_{new} \tag{19}$$

Finally, the flow cross-sectional area, Ai is given by,

$$A\_{i,new} = w\_{new} \cdot h\_{new} \qquad \qquad \{\text{i} = \text{fluid}, \text{ gas}\} \tag{20}$$

Accordingly, the Reynolds number for the working fluid and gas side is affected:

$$Re\_i = \frac{\dot{m}\_i \cdot dh\_i}{A\_{i,new} \cdot \eta\_i} \tag{21}$$

The component sizes are optimized based on fuel consumption and investment cost criteria. In the next section, the alternating optimization method is described in detail. The optimal sizes λopt that are finally determined are input for the overall performance analysis with switching

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Optimizing the controller and plant iteratively to converge the coupled variables can be computationally too expensive. Therefore, an alternating architecture is followed for only one complete loop, see Figure 7. The controller designed for a specific WHR system will give different performance for a resized WHR system. Consequently, the feed forward controller from Section 3.3 is applied, which calculates the pumps speeds, such that χ<sup>f</sup> ≥ 1 at the outlet of both the evaporators for given engine exhaust heat flows. Although with lower performance

Model Predictive Control (MPC) strategy in Section 6.

Figure 6. Approach for optimal sizing and control of WHR systems.

5.1. Alternating system optimization

Figure 7. Optimization architecture.

where η<sup>i</sup> is the viscosity, dhi is the hydraulic diameter, that is, outer gap height of one plate and m\_ <sup>i</sup> is the mass flow rate of the working fluid and gas. The heat transfer coefficient α<sup>i</sup> for the working fluid and exhaust gas also depends on Ai,new:

$$\alpha\_{i} = \frac{\mathcal{N}u\_{i} \cdot \Lambda\_{i}}{d\hbar\_{i}} = \frac{\mathcal{N}u\_{i}}{\mathcal{Re}\_{i}} \cdot \frac{\dot{m}\_{i}\Lambda\_{i}}{A\_{i,new} \cdot \eta\_{i}} \tag{22}$$

where Λ<sup>i</sup> is the thermal conductivity of the working fluid and exhaust gas.

For varying evaporator length, there will be no change in the flow cross sectional area as well as in the exhaust gas side cross sectional area. As a result, there will be no effect on Reynolds number, Re, and the Nusselt number, Nu, which is directly proportional to Re. The surface areas available for exhaust gas and working fluid increase with increasing l and vice versa (see Eqs. (17)–(19)). These areas directly affect the working fluid temperature at the evaporator's outlet.

The cross-sectional areas Ai,new varies with width as well as with height and is inversely proportional to the heat transfer coefficients αfluid and αgas. The surface areas Sf and Sg increase with w and h and, hence, the working fluid temperature at the evaporator's outlet will behave in the same direction through equations for conservation of energy. However, Sw will stay the same with change in height, because the number of plates will change with this dimension.

With the introduced scaling factors, the evaporator size can be changed by varying its length, width or height depending on the requirements from the system, input heat flows, and type of working fluid. These three parameters have different impact on the evaporator's performance. Therefore, a sensitivity analysis has to be done to select the parameter that has the most positive impact on WHR system power output.

#### 5. WHR system size optimization

This section presents a methodology to optimize component size for WHR systems under transient driving conditions. Figure 6 gives an outline of the approach that is followed in this study. The scalable WHR system model developed in the previous section is crucial input for this approach. From a sensitivity analysis for the exhaust evaporator, scaling of the evaporator length is identified as the most promising route to maximize WHR power output. Details can be found in [16]. As a result, evaporator width and height will be set to their original system values in the sequel of this study. In summary, the following parameters are considered for optimal component sizing in order to maximize WHR power output:


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Figure 6. Approach for optimal sizing and control of WHR systems.

The component sizes are optimized based on fuel consumption and investment cost criteria. In the next section, the alternating optimization method is described in detail. The optimal sizes λopt that are finally determined are input for the overall performance analysis with switching Model Predictive Control (MPC) strategy in Section 6.

#### 5.1. Alternating system optimization

Rei <sup>¼</sup> <sup>m</sup>\_ <sup>i</sup> � dhi Ai,new � η<sup>i</sup>

where η<sup>i</sup> is the viscosity, dhi is the hydraulic diameter, that is, outer gap height of one plate and m\_ <sup>i</sup> is the mass flow rate of the working fluid and gas. The heat transfer coefficient α<sup>i</sup> for the

> <sup>¼</sup> Nui Rei

For varying evaporator length, there will be no change in the flow cross sectional area as well as in the exhaust gas side cross sectional area. As a result, there will be no effect on Reynolds number, Re, and the Nusselt number, Nu, which is directly proportional to Re. The surface areas available for exhaust gas and working fluid increase with increasing l and vice versa (see Eqs. (17)–(19)).

The cross-sectional areas Ai,new varies with width as well as with height and is inversely proportional to the heat transfer coefficients αfluid and αgas. The surface areas Sf and Sg increase with w and h and, hence, the working fluid temperature at the evaporator's outlet will behave in the same direction through equations for conservation of energy. However, Sw will stay the same with change in height, because the number of plates will change with this dimension.

With the introduced scaling factors, the evaporator size can be changed by varying its length, width or height depending on the requirements from the system, input heat flows, and type of working fluid. These three parameters have different impact on the evaporator's performance. Therefore, a sensitivity analysis has to be done to select the parameter that has the most

This section presents a methodology to optimize component size for WHR systems under transient driving conditions. Figure 6 gives an outline of the approach that is followed in this study. The scalable WHR system model developed in the previous section is crucial input for this approach. From a sensitivity analysis for the exhaust evaporator, scaling of the evaporator length is identified as the most promising route to maximize WHR power output. Details can be found in [16]. As a result, evaporator width and height will be set to their original system values in the sequel of this study. In summary, the following parameters are considered for

optimal component sizing in order to maximize WHR power output:

� <sup>m</sup>\_ <sup>i</sup>Λ<sup>i</sup> Ai,new � η<sup>i</sup>

<sup>α</sup><sup>i</sup> <sup>¼</sup> Nui � <sup>Λ</sup><sup>i</sup> dhi

where Λ<sup>i</sup> is the thermal conductivity of the working fluid and exhaust gas.

These areas directly affect the working fluid temperature at the evaporator's outlet.

working fluid and exhaust gas also depends on Ai,new:

90 Organic Rankine Cycle Technology for Heat Recovery

positive impact on WHR system power output.

• Exhaust gas evaporator length scaling λexh;

• EGR evaporator length scaling λEGR.

5. WHR system size optimization

• Expander scaling λexp ;

(21)

(22)

Optimizing the controller and plant iteratively to converge the coupled variables can be computationally too expensive. Therefore, an alternating architecture is followed for only one complete loop, see Figure 7. The controller designed for a specific WHR system will give different performance for a resized WHR system. Consequently, the feed forward controller from Section 3.3 is applied, which calculates the pumps speeds, such that χ<sup>f</sup> ≥ 1 at the outlet of both the evaporators for given engine exhaust heat flows. Although with lower performance

Figure 7. Optimization architecture.

compared to PI control or MPC, it is seen to maintain the same trend for fuel consumption with different components sizes, without affecting the optimality of WHR system components sizes.

The standalone WHR system with feed forward controller is simulated on a 3D design grid of different sizes of EGR evaporator, exhaust evaporator and expander for a hot-start WHTC. WHR system performance is strongly affected by operating conditions. Therefore, besides overall (complete cycle) performance, also optimization is performed on urban, rural and highway driving parts, which are illustrated in Figure 8. The design grid is chosen such that: (1) it captures the main trend in outputs due to component sizing and (2) costs and total system mass remain acceptable. For the scaling factors, the following grid is chosen: λEGR ¼ λexh ¼ ½ � 0:4 : 0:1 : 1:5 and λexp ¼ ½ � 0:4 : 0:1 : 2:5 .

#### 5.1.1. Objective functions

Using exhaustive search, also referred to as brute force search, the WHR system performance is determined for each point on the grid. To obtain the optimal size of the plant, the following objective functions are defined:

• Fuel consumption (FC), which is determined from Eqs. (2)–(3). For the specified design space, WHTC results are summarized in Figure 9. Note that the net fuel consumption is normalized by using engine-only (without WHR system) results. Minimal fuel consumption is found at maximum evaporator size, although the reduction in fuel consumption decreases with increasing size. For highway conditions, where engine exhaust heat flows are relatively high, fuel economy increases for increasing expander sizes. The exhaust evaporator's size has a significant impact on fuel consumption, especially in the urban

region. Due to low exhaust gas heat flows in this region, the time for the working fluid to

• Specific investment cost (SIC, in €/kJ): in this study, we focus on installation (Costlabor) and material and production cost of the components (Costcomp) corresponding a specific

Figure 9. Normalized fuel consumption for different sizes of WHR system components on different driving conditions

SIC <sup>¼</sup> Costlabor <sup>þ</sup> Costcomp Ðtv

vapor. For the evaporators and expander, cost correlations are taken from [17]:

Costevap ¼ 190 þ 310 � Aevap � λevap

where Pwhrð Þt is the instantaneous net WHR power output and tv is cumulative time in

These equations clearly show that the component costs are proportional to the scaling factors to be applied. The cost of other components, such as pumps, piping, condenser and valves, are not included in the SIC. Their sizes are assumed to be fixed in this study, which will not affect the objective function. For SIC, similar graphs are generated as for FC. From these results, it is concluded that λEGR has negligible effect on SIC, whereas λexp has the biggest impact, because of its dominant share in the total system cost. Details can

<sup>0</sup> Pwhrð Þ<sup>t</sup> dt (23)

Cost exp <sup>¼</sup> <sup>1</sup>:<sup>5</sup> � <sup>225</sup> <sup>þ</sup> <sup>170</sup> � Vexp � <sup>λ</sup>exp � � (24)

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extract heat increases with increase in length (or surface area) of evaporator.

WHR energy output:

from hot-start WHTC.

be found in [16].

Figure 8. Engine torque, engine speed and heat flows for hot start WHTC.

Optimal Sizing of Waste Heat Recovery Systems for Dynamic Engine Conditions http://dx.doi.org/10.5772/intechopen.78590 93

compared to PI control or MPC, it is seen to maintain the same trend for fuel consumption with different components sizes, without affecting the optimality of WHR system components sizes. The standalone WHR system with feed forward controller is simulated on a 3D design grid of different sizes of EGR evaporator, exhaust evaporator and expander for a hot-start WHTC. WHR system performance is strongly affected by operating conditions. Therefore, besides overall (complete cycle) performance, also optimization is performed on urban, rural and highway driving parts, which are illustrated in Figure 8. The design grid is chosen such that: (1) it captures the main trend in outputs due to component sizing and (2) costs and total system mass remain acceptable. For the scaling factors, the following grid is chosen: λEGR ¼

Using exhaustive search, also referred to as brute force search, the WHR system performance is determined for each point on the grid. To obtain the optimal size of the plant, the following

• Fuel consumption (FC), which is determined from Eqs. (2)–(3). For the specified design space, WHTC results are summarized in Figure 9. Note that the net fuel consumption is normalized by using engine-only (without WHR system) results. Minimal fuel consumption is found at maximum evaporator size, although the reduction in fuel consumption decreases with increasing size. For highway conditions, where engine exhaust heat flows are relatively high, fuel economy increases for increasing expander sizes. The exhaust evaporator's size has a significant impact on fuel consumption, especially in the urban

λexh ¼ ½ � 0:4 : 0:1 : 1:5 and λexp ¼ ½ � 0:4 : 0:1 : 2:5 .

92 Organic Rankine Cycle Technology for Heat Recovery

Figure 8. Engine torque, engine speed and heat flows for hot start WHTC.

5.1.1. Objective functions

objective functions are defined:

Figure 9. Normalized fuel consumption for different sizes of WHR system components on different driving conditions from hot-start WHTC.

region. Due to low exhaust gas heat flows in this region, the time for the working fluid to extract heat increases with increase in length (or surface area) of evaporator.

• Specific investment cost (SIC, in €/kJ): in this study, we focus on installation (Costlabor) and material and production cost of the components (Costcomp) corresponding a specific WHR energy output:

$$SIC = \frac{\text{Cost}\_{\text{labor}} + \text{Cost}\_{\text{comp}}}{\int\_0^{t\_v} P\_{\text{ubir}}(t)dt} \tag{23}$$

where Pwhrð Þt is the instantaneous net WHR power output and tv is cumulative time in vapor. For the evaporators and expander, cost correlations are taken from [17]:

$$\begin{aligned} \text{Cost}\_{\text{evap}} &= 190 + 310 \cdot \text{A}\_{\text{evap}} \cdot \lambda\_{\text{evap}} \\ \text{Cost}\_{\text{exp}} &= 1.5 \cdot \left( 225 + 170 \cdot \text{V}\_{\text{exp}} \cdot \lambda\_{\text{exp}} \right) \end{aligned} \tag{24}$$

These equations clearly show that the component costs are proportional to the scaling factors to be applied. The cost of other components, such as pumps, piping, condenser and valves, are not included in the SIC. Their sizes are assumed to be fixed in this study, which will not affect the objective function. For SIC, similar graphs are generated as for FC. From these results, it is concluded that λEGR has negligible effect on SIC, whereas λexp has the biggest impact, because of its dominant share in the total system cost. Details can be found in [16].

#### 5.1.2. Sizing optimization problem

Having defined the objective functions for FC and SIC, the optimization problem boils down to:

$$\min\_{\lambda\_{\text{exh}\_{\theta}}, \lambda\_{\text{EGR}\_{\theta}}, \lambda\_{\text{exp}}} J \tag{25}$$

subject to,

$$m\_{\rm erg}(\lambda\_{EGR}) + m\_{\rm exh}(\lambda\_{\rm exh}) + m\_{\rm exp}\left(\lambda\_{\rm exp}\right) \le M\_{\rm tot}^{\rm max} \tag{26}$$

where the multi-objective function J is given by:

$$J = \begin{cases} \int\_0^{t\_f} \dot{m}\_{fuel} dt \\\\ \text{SIC} \end{cases} \tag{27}$$

increasing λexh. Hence, Mmax

Figure 11. Optimal components sizes for Mmax

components is much more beneficial in terms of energy recovery.

tot plays a bigger role in sizing because increasing the size of other

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Apart from highway driving conditions, the optimal scaling of EGR evaporator is found to be bigger than the original one. During highway driving, the amount of heat that needs to be extracted from the exhaust gases is high, which leads to higher ethanol flows. The results

tot ¼ 210kg and for different objective functions.

Figure 10. Optimal component sizes to realize minimal fuel consumption for different mass constraints.

Note that mass of the WHR system is directly proportional to the components sizes and directly affects the overall load carrying capacity of a truck. Therefore, a limit, Mmax tot , is defined on the component mass associated with sizing.

#### 5.1.3. Sizing optimization for different system mass

As a next step to solve Eqs. (25)–(27), optimal λ setting is determined for different mass constraints Mmax tot . This is done using the lambda sweep plots for FC as well as SIC, similar to Figure 9. For each objective function, the best λEGR, λexh and λexp combination is determined, which gives lowest FC or SIC while meeting a varying Mmax tot . Figure 10 shows an example of results for using the FC objective function. The resulting scaling parameters are given for four different operating conditions associated with the hot WHTC. For the overall WHTC, the corresponding fuel consumption is shown in the lower plot. Similar plots are made for SIC.

#### 5.1.4. Best WHR sizing per objective function

Final step in the optimization approach is to select Mmax tot . For the purpose of benchmarking, the optimal component sizes associates with the two different optimization criteria are compared for a mass constraint equal to the original mass of the system: Mmax tot = 210 kg, which is indicated in the plots of Figure 10 by the blue vertical lines. The results of this final step are summarized in Figure 11.

The results clearly indicate that different operating conditions and different optimization criteria lead to different component sizing. However, optimal exhaust evaporator size is smaller (i.e., λexh < 1) than its original size for all the driving conditions and both FC and SIC optimization. The exhaust evaporator has the biggest mass of the three scaled components. Although longer exhaust evaporator have better performance, the increment reduces with Optimal Sizing of Waste Heat Recovery Systems for Dynamic Engine Conditions http://dx.doi.org/10.5772/intechopen.78590 95

Figure 10. Optimal component sizes to realize minimal fuel consumption for different mass constraints.

5.1.2. Sizing optimization problem

94 Organic Rankine Cycle Technology for Heat Recovery

where the multi-objective function J is given by:

on the component mass associated with sizing.

5.1.3. Sizing optimization for different system mass

5.1.4. Best WHR sizing per objective function

which gives lowest FC or SIC while meeting a varying Mmax

Final step in the optimization approach is to select Mmax

a mass constraint equal to the original mass of the system: Mmax

to:

subject to,

constraints Mmax

Figure 11.

Having defined the objective functions for FC and SIC, the optimization problem boils down

min <sup>λ</sup>exh, <sup>λ</sup>EGR, <sup>λ</sup>exp

> Ðtf <sup>0</sup> m\_ fueldt

8 >><

>>:

SIC

Note that mass of the WHR system is directly proportional to the components sizes and

As a next step to solve Eqs. (25)–(27), optimal λ setting is determined for different mass

Figure 9. For each objective function, the best λEGR, λexh and λexp combination is determined,

results for using the FC objective function. The resulting scaling parameters are given for four different operating conditions associated with the hot WHTC. For the overall WHTC, the corresponding fuel consumption is shown in the lower plot. Similar plots are made for SIC.

optimal component sizes associates with the two different optimization criteria are compared for

the plots of Figure 10 by the blue vertical lines. The results of this final step are summarized in

The results clearly indicate that different operating conditions and different optimization criteria lead to different component sizing. However, optimal exhaust evaporator size is smaller (i.e., λexh < 1) than its original size for all the driving conditions and both FC and SIC optimization. The exhaust evaporator has the biggest mass of the three scaled components. Although longer exhaust evaporator have better performance, the increment reduces with

tot . This is done using the lambda sweep plots for FC as well as SIC, similar to

megrð Þþ λEGR mexhð Þþ λexh mexp λexp

J ¼

directly affects the overall load carrying capacity of a truck. Therefore, a limit, Mmax

J (25)

tot (26)

tot . Figure 10 shows an example of

tot . For the purpose of benchmarking, the

tot = 210 kg, which is indicated in

(27)

tot , is defined

� � ≤ Mmax

increasing λexh. Hence, Mmax tot plays a bigger role in sizing because increasing the size of other components is much more beneficial in terms of energy recovery.

Apart from highway driving conditions, the optimal scaling of EGR evaporator is found to be bigger than the original one. During highway driving, the amount of heat that needs to be extracted from the exhaust gases is high, which leads to higher ethanol flows. The results

Figure 11. Optimal components sizes for Mmax tot ¼ 210kg and for different objective functions.

indicate that the original evaporator is over dimensioned for this condition. For urban and rural conditions, where exhaust heat flows are low, the ethanol flow needs to be low to extract the maximum amount of heat. However, when mass flows reach the lower boundary condition and no vapor is generated, increased evaporator length would provide more surface area and hence more time for the working fluid to extract heat. This effect is confirmed for the EGR evaporator with bigger optimal sizes for urban and rural regions. As these regions play an important role in the overall cycle result, it is expected that similar λEGR is found for the overall cycle.

Considering the real time system dynamics of WHR system, the controller sampling time is chosen to be Ts ¼ 0:4 seconds. The prediction and control horizon are Ny ¼ 50 and Nu ¼ 4 time

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The proposed switching MPC strategy is validated on the highly dynamic, hot start WHTC. Disturbances from the engine, that is, engine speed and EGR and exhaust gas heat flows, are inputs for the simulation. The objective of the controller is to maintain vapor state. However, due to the highly dynamic disturbances and limitations of the control input, it is challenging to achieve this target for all the time. To avoid damage, the expander is bypassed using the

Figure 12 shows the vapor fraction after EGR and EXH evaporators, and the mixing junction for the original and optimized system. Vapor fraction is not meeting the reference (indicated by dashed line) between 200 and 400 s, due to the low heat flows in the urban region. However, the controller shows improved overall performance in terms of disturbance rejection, where the controller specifications, χ<sup>f</sup> ,mix ≥ 1, are met with short periods of time reaching at 0.9

Figure 12. Comparison of vapor fraction after the EGR and EXH evaporators, mixing junction for MPC strategy between

original and optimally sized system (with vapor fraction according to Eq. (6)).

steps, respectively, for all the three linear models.

bypass valve, such that net power output: Pwhr ¼ 0.

6.1. Controller performance validation

(around 800 and 1200 s).

The optimal expander scaling is found to be bigger than the original one for all driving conditions. This especially holds for FC optimization. For highway conditions, λexp is twice the original one due, in order to exploit the high heat flows. The expander has the biggest impact on WHR system performance. With mass comparable to other components, this leaves room for increasing λexp .

Finally, these results also indicate that optimal sizing of a single component strongly depends on the performance of all components. Interaction between evaporators and expander as well as the total mass constraint play an important role.

#### 5.2. Selected optimal scaling of WHR components

In order to make a final decision on optimal component scaling, a trade off has to be made between the optimization criteria. Therefore, the impact on FC and SIC are analyzed for both criteria. Focus is on the overall cycle result, since this is assumed to be representative for realworld performance. As expected, fuel consumption can be reduced by 0.85% compared to the originally sized system (and 2.78% compared to engine-only mode) in case of FC minimization. In case of SIC minimization, compared to the original system, there is no FC reduction, but system costs are reduced by 25%. The SIC of the FC optimal system is 60 €/kJ higher than that for the SIC minimal case.

Comparison of both cases learns that the additional system costs associated with the FC minimum case, requires an additional 1 month truck operation for return on investment. Therefore, the final optimal components scaling for the WHR system are based on the values for FC minimization:

$$
\lambda\_{\text{exh},opt} = 0.63 \qquad \lambda\_{\text{EGR},opt} = 1.47 \qquad \lambda\_{\text{exp}},opt = 1.50 \tag{28}
$$

These values will be used in the sequel of this study.

## 6. Simulation results

In this section, the switching MPC strategy from [18] is applied to the standalone WHR system with optimal component sizes. A comparison is made with the original WHR system. The MPC strategy is first evaluated on a simple stepwise cycle data from a real Euro VI heavy-duty diesel engine and then on a hot-start World Harmonized Transient Cycle (WHTC) [16]. Considering the real time system dynamics of WHR system, the controller sampling time is chosen to be Ts ¼ 0:4 seconds. The prediction and control horizon are Ny ¼ 50 and Nu ¼ 4 time steps, respectively, for all the three linear models.

#### 6.1. Controller performance validation

indicate that the original evaporator is over dimensioned for this condition. For urban and rural conditions, where exhaust heat flows are low, the ethanol flow needs to be low to extract the maximum amount of heat. However, when mass flows reach the lower boundary condition and no vapor is generated, increased evaporator length would provide more surface area and hence more time for the working fluid to extract heat. This effect is confirmed for the EGR evaporator with bigger optimal sizes for urban and rural regions. As these regions play an important role in

The optimal expander scaling is found to be bigger than the original one for all driving conditions. This especially holds for FC optimization. For highway conditions, λexp is twice the original one due, in order to exploit the high heat flows. The expander has the biggest impact on WHR system performance. With mass comparable to other components, this leaves

Finally, these results also indicate that optimal sizing of a single component strongly depends on the performance of all components. Interaction between evaporators and expander as well

In order to make a final decision on optimal component scaling, a trade off has to be made between the optimization criteria. Therefore, the impact on FC and SIC are analyzed for both criteria. Focus is on the overall cycle result, since this is assumed to be representative for realworld performance. As expected, fuel consumption can be reduced by 0.85% compared to the originally sized system (and 2.78% compared to engine-only mode) in case of FC minimization. In case of SIC minimization, compared to the original system, there is no FC reduction, but system costs are reduced by 25%. The SIC of the FC optimal system is 60 €/kJ higher than

Comparison of both cases learns that the additional system costs associated with the FC minimum case, requires an additional 1 month truck operation for return on investment. Therefore, the final optimal components scaling for the WHR system are based on the values

In this section, the switching MPC strategy from [18] is applied to the standalone WHR system with optimal component sizes. A comparison is made with the original WHR system. The MPC strategy is first evaluated on a simple stepwise cycle data from a real Euro VI heavy-duty diesel engine and then on a hot-start World Harmonized Transient Cycle (WHTC) [16].

λexh, opt ¼ 0:63 λEGR, opt ¼ 1:47 λexp , opt ¼ 1:50 (28)

the overall cycle result, it is expected that similar λEGR is found for the overall cycle.

room for increasing λexp .

96 Organic Rankine Cycle Technology for Heat Recovery

that for the SIC minimal case.

for FC minimization:

6. Simulation results

as the total mass constraint play an important role.

5.2. Selected optimal scaling of WHR components

These values will be used in the sequel of this study.

The proposed switching MPC strategy is validated on the highly dynamic, hot start WHTC. Disturbances from the engine, that is, engine speed and EGR and exhaust gas heat flows, are inputs for the simulation. The objective of the controller is to maintain vapor state. However, due to the highly dynamic disturbances and limitations of the control input, it is challenging to achieve this target for all the time. To avoid damage, the expander is bypassed using the bypass valve, such that net power output: Pwhr ¼ 0.

Figure 12 shows the vapor fraction after EGR and EXH evaporators, and the mixing junction for the original and optimized system. Vapor fraction is not meeting the reference (indicated by dashed line) between 200 and 400 s, due to the low heat flows in the urban region. However, the controller shows improved overall performance in terms of disturbance rejection, where the controller specifications, χ<sup>f</sup> ,mix ≥ 1, are met with short periods of time reaching at 0.9 (around 800 and 1200 s).

Figure 12. Comparison of vapor fraction after the EGR and EXH evaporators, mixing junction for MPC strategy between original and optimally sized system (with vapor fraction according to Eq. (6)).

case a switching MPC strategy (λ<sup>i</sup> ¼ 1 MPC ð Þ) is applied. The optimally sized WHR system with feed forward control strategy (λ<sup>i</sup> ¼ optimal FF ð Þ) reduces fuel consumption by 2.78%. Using a switching MPC strategy (λ<sup>i</sup> ¼ optimal MPC ð Þ) gives a fuel consumption reduction of 3.82% as compared to the engine only mode. In summary, by optimizing the size of WHR system components, an additional 1.08% reduction in fuel consumption can be achieved

Optimal Sizing of Waste Heat Recovery Systems for Dynamic Engine Conditions

http://dx.doi.org/10.5772/intechopen.78590

99

A methodology for optimal components sizing is presented for waste heat recovery systems operated during dynamic engine conditions. Optimality was defined in terms of minimizing the fuel consumption of the overall powertrain system. The main challenge in developing this methodology is the coupling between system design and control parameters. Focus is on Euro-VI heavy-duty engines with a mechanically coupled WHR system. Based on this work, the

• An existing WHR system model [13] is extended with a detailed expander model and is made scalable for component size. Expander volume as well as evaporator length, width

• Sensitivity analysis shows that length is the most promising route to optimize power

• An alternating optimization architecture is presented, which uses the standalone, scalable WHR system model. This methodology combines an constrained optimization problem based on fuel consumption, system costs and system mass considerations with a feed

• This methodology is successfully followed for optimal design and control of WHR system for transient driving conditions while satisfying safe operation. The components scaled in this study are EGR and exhaust gas evaporator, and expander. Different optimal component sizes are found for city, urban, rural and overall hot-start WHTC

• By implementing a switching model predictive control (MPC) strategy on the optimally sized WHR system, time in vapor state is identical, while the net fuel consumption, as

compared to the originally sized WHR system, is reduced by:

forward pump controller in order to isolate system design from control design;

compared to the original WHR system using the methodology given in this study.

7. Conclusions

following conclusions are drawn:

and height can be varied;

output for evaporators;

driving conditions;

• Urban: 0.30%. • Rural: 1.46%.

• Highway: 1.61%.

• Overall hot-start WHTC: 1.08%.

Figure 13. Performance indices in terms of recovered thermal energy (left) and time in vapor (right) compared with original system.

The main objective of MPC tuning is to keep the vapor fraction of working fluid after both the evaporators' outlets close to reference data with good disturbance rejection properties. Due to different system dynamics, the values of the weighting matrices WΔ<sup>u</sup> and Wy vary from the original to the optimally sized system. Hence, the performance of the two controllers, that is, MPC for original system and optimally sized system, is quantified in terms of net thermal energy recovered and total time in vapor state, tv for different parts of the WHTC. Figure 13 illustrates that the optimally sized system outperforms the original system in terms of recovered thermal energy for all the driving conditions. Note that the recovered energy is almost doubled when complete cycle is considered. This is due to the increased expander size leading to more power output. In terms of time in vapor, both systems behave similarly, with slightly increased tv for the optimal system over the full WHTC.

#### 6.2. Powertrain performance validation

The net fuel consumption results for the studied cases are compared with the engine only mode in Figure 14. The original sized WHR system gives a 1.94% reduction in fuel consumption using the feed forward controller (λ<sup>i</sup> ¼ 1 FF ð Þ). An additional 0.8% reduction is found in

Figure 14. Fuel consumption for different driving conditions from hot-start WHTC.

case a switching MPC strategy (λ<sup>i</sup> ¼ 1 MPC ð Þ) is applied. The optimally sized WHR system with feed forward control strategy (λ<sup>i</sup> ¼ optimal FF ð Þ) reduces fuel consumption by 2.78%. Using a switching MPC strategy (λ<sup>i</sup> ¼ optimal MPC ð Þ) gives a fuel consumption reduction of 3.82% as compared to the engine only mode. In summary, by optimizing the size of WHR system components, an additional 1.08% reduction in fuel consumption can be achieved compared to the original WHR system using the methodology given in this study.

## 7. Conclusions

The main objective of MPC tuning is to keep the vapor fraction of working fluid after both the evaporators' outlets close to reference data with good disturbance rejection properties. Due to different system dynamics, the values of the weighting matrices WΔ<sup>u</sup> and Wy vary from the original to the optimally sized system. Hence, the performance of the two controllers, that is, MPC for original system and optimally sized system, is quantified in terms of net thermal energy recovered and total time in vapor state, tv for different parts of the WHTC. Figure 13 illustrates that the optimally sized system outperforms the original system in terms of recovered thermal energy for all the driving conditions. Note that the recovered energy is almost doubled when complete cycle is considered. This is due to the increased expander size leading to more power output. In terms of time in vapor, both systems behave similarly, with slightly

Figure 13. Performance indices in terms of recovered thermal energy (left) and time in vapor (right) compared with

The net fuel consumption results for the studied cases are compared with the engine only mode in Figure 14. The original sized WHR system gives a 1.94% reduction in fuel consumption using the feed forward controller (λ<sup>i</sup> ¼ 1 FF ð Þ). An additional 0.8% reduction is found in

increased tv for the optimal system over the full WHTC.

Figure 14. Fuel consumption for different driving conditions from hot-start WHTC.

6.2. Powertrain performance validation

98 Organic Rankine Cycle Technology for Heat Recovery

original system.

A methodology for optimal components sizing is presented for waste heat recovery systems operated during dynamic engine conditions. Optimality was defined in terms of minimizing the fuel consumption of the overall powertrain system. The main challenge in developing this methodology is the coupling between system design and control parameters. Focus is on Euro-VI heavy-duty engines with a mechanically coupled WHR system. Based on this work, the following conclusions are drawn:

	- Overall hot-start WHTC: 1.08%.
	- Urban: 0.30%.
	- Rural: 1.46%.
	- Highway: 1.61%.

## Author details

Emanuel Feru1,2, Srajan Goyal2,3 and Frank Willems1,2\*

\*Address all correspondence to: frank.willems@tno.nl


## References

[1] Park T, Teng H, Hunter GL, van der Velde B, Klaver J. A rankine cycle system for recovering waste heat from hd diesel engines-experimental results, Technical report. SAE Technical Paper. 2011-01-1337. 2011

[10] Feru EE. Auto-calibration for efficient diesel engines with a waste heat recovery system.

Optimal Sizing of Waste Heat Recovery Systems for Dynamic Engine Conditions

http://dx.doi.org/10.5772/intechopen.78590

101

[11] Feru E, Willems F, de Jager B, Steinxbuch M. Modeling and control of a parallel waste heat recovery system for Euro-VI heavy-duty diesel engines. Energies. 2014;7(10):6571-6592

[12] Silvas E, Hofman T, Murgovski N, Etman LFP., Steinbuch M. Review of optimization strategies for system-level design in hybrid electric vehicles. In: IEEE Transactions on

[13] Feru E, Kupper F, Rojer C, Seykens X, Scappin F, Willems F, Smits J, De Jager B, Steinbuch M. Experimental validation of a dynamic waste heat recovery system model for control

[14] Oom M. Identification and validation of an expander model for automotive waste heat recovery systems, Technical report. Eindhoven University of Technology; 2014

[15] Feru E, de Jager B, Willems F, Steinbuch M. Two-phase plate-fin heat exchanger modeling for waste heat recovery systems in diesel engines. Applied Energy. 2014;133:183-196 [16] Goyal S. Optimal sizing of waste heat recovery system for dynamic engine conditions,

[17] Quoilin S, Declaye S, Tchanche BF, Lemort V. Thermo-economic optimization of waste heat recovery organic rankine cycles. Applied Thermal Engineering. 2011;31(14):2885-2893 [18] Feru E, Willems F, de Jager B, Steinbuch M. Model predictive control of a waste heat recovery system for automotive diesel engines. In: System Theory, Control and Comput-

Vehicular Technology. Jan 2017;66(1):57-70. DOI: 10.1109/TVT.2016.2547897

purposes, Technical report. SAE Technical Paper; 2013-01-1647. 2013

Master thesis CST 2016.137. Eindhoven University of Technology; 2016

ing (ICSTCC), 2014 18th International Conference. IEEE; 2014. pp. 658-663

Ph.D. thesis, Eindhoven University of Technology; 2015


[10] Feru EE. Auto-calibration for efficient diesel engines with a waste heat recovery system. Ph.D. thesis, Eindhoven University of Technology; 2015

Author details

References

Emanuel Feru1,2, Srajan Goyal2,3 and Frank Willems1,2\*

\*Address all correspondence to: frank.willems@tno.nl

2 Eindhoven University of Technology, Eindhoven, The Netherlands

tomorrow. MTZ Worldwide eMagazine. 2011;72(4):52-56

Technical report. Eindhoven University of Technology; 2016

systems. Applied Energy. 2013;105:293-303

[1] Park T, Teng H, Hunter GL, van der Velde B, Klaver J. A rankine cycle system for recovering waste heat from hd diesel engines-experimental results, Technical report. SAE

[2] Bredel DE, Nickl IJ, Bartosch D-IS. Waste heat recovery in drive systems of today and

[3] Grelet V. Rankine cycle based waste heat recovery system applied to heavy duty vehicles: Topological optimization and model based control. Ph.D. thesis, Université de Liège,

[4] Goyal S. Optimal sizing of waste heat recovery system for HD truck: Steady state analysis,

[5] Horst TA, Rottengruber H-S, Seifert M, Ringler J. Dynamic heat exchanger model for performance prediction and control system design of automotive waste heat recovery

[6] Horst TA, Tegethoff W, Eilts P, Koehler J. Prediction of dynamic rankine cycle waste heat recovery performance and fuel saving potential in passenger car applications considering interactions with vehicles energy management. Energy Conversion and Management.

[7] Lecompte S, Huisseune H, van den Broek M, De Schampheleire S, De Paepe M. Part load based thermo-economic optimization of the organic rankine cycle (orc) applied to a com-

[8] Seher D, Lengenfelder T, Gerhardt J, Eisenmenger N, Hackner M, Krinn I. Waste heat recovery for commercial vehicles with a rankine process. In: 21st Aachen Colloquium on

[9] Quoilin S, Aumann R, Grill A, Schuster A, Lemort V, Spliethoff H. Dynamic modeling and optimal control strategy of waste heat recovery organic rankine cycles. Applied Energy.

bined heat and power (chp) system. Applied Energy. 2013;111:871-881

Automobile and Engine Technology, Aachen, Germany. Oct, 2012. pp. 7-9

1 TNO Automotive, Helmond, The Netherlands

Technical Paper. 2011-01-1337. 2011

3 FlandersMake, Lommel, Belgium

100 Organic Rankine Cycle Technology for Heat Recovery

Liège, Belgique; 2016

2014;78:438-451

2011;88(6):2183-2190


**Chapter 6**

**Provisional chapter**

**Dynamic Modeling of ORC Power Plants**

**Dynamic Modeling of ORC Power Plants**

DOI: 10.5772/intechopen.78390

This chapter presents dynamic modeling approaches suitable for organic Rankine cycle (ORC) power plants. Dynamic models are necessary for the better understanding of the plants' behavior during transient operation, such as start-up, shutdown, and during rapid load changes. The estimation of plant operating parameters during transient operation is crucial for monitoring and control of the plant so that the system state variables do not exceed the pre-defined operating range. One example is the proportion of liquid and vapor phase in the condenser and evaporator that must be kept within acceptable ranges to avoid stalling or temperature shocks during transient conditions. Using dynamic models enables plant operators to predict changes in power output as a function of the plant's boundary conditions such as temperature of the heat source and ambient conditions, so that they can respond to the expected heat and power demand accordingly. The aim of the chapter is to investigate and review the methodologies applicable for dynamic

**Keywords:** dynamic modeling, transient conditions, simulation, time constants, ORC,

The mathematical modeling of the dynamic systems and analysis of their dynamic characteristics is essential for developing the control and monitoring systems. A dynamic model is able to trace the variation of the system operating parameters in all operating conditions and consequently detect the critical points and outranges. Generally, the dynamic behavior of a system including mechanical, electrical, fluid, thermal, and so on can be described by a set of

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Mohsen Assadi and Yaser Mollaei Barzi

Mohsen Assadi and Yaser Mollaei Barzi

http://dx.doi.org/10.5772/intechopen.78390

simulation of ORC power plants.

thermal power plant

**1.1. Basics of dynamic modeling**

**1. Introduction**

**Abstract**

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

#### **Dynamic Modeling of ORC Power Plants Dynamic Modeling of ORC Power Plants**

#### Mohsen Assadi and Yaser Mollaei Barzi Mohsen Assadi and Yaser Mollaei Barzi

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.78390

#### **Abstract**

This chapter presents dynamic modeling approaches suitable for organic Rankine cycle (ORC) power plants. Dynamic models are necessary for the better understanding of the plants' behavior during transient operation, such as start-up, shutdown, and during rapid load changes. The estimation of plant operating parameters during transient operation is crucial for monitoring and control of the plant so that the system state variables do not exceed the pre-defined operating range. One example is the proportion of liquid and vapor phase in the condenser and evaporator that must be kept within acceptable ranges to avoid stalling or temperature shocks during transient conditions. Using dynamic models enables plant operators to predict changes in power output as a function of the plant's boundary conditions such as temperature of the heat source and ambient conditions, so that they can respond to the expected heat and power demand accordingly. The aim of the chapter is to investigate and review the methodologies applicable for dynamic simulation of ORC power plants.

DOI: 10.5772/intechopen.78390

**Keywords:** dynamic modeling, transient conditions, simulation, time constants, ORC, thermal power plant

## **1. Introduction**

#### **1.1. Basics of dynamic modeling**

The mathematical modeling of the dynamic systems and analysis of their dynamic characteristics is essential for developing the control and monitoring systems. A dynamic model is able to trace the variation of the system operating parameters in all operating conditions and consequently detect the critical points and outranges. Generally, the dynamic behavior of a system including mechanical, electrical, fluid, thermal, and so on can be described by a set of

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

transient differential equations (ODE or PDE) which originates from the governing physical principals and inherent physical characteristics.

performance is also the foundation for developing control systems during the early design stage of an ORC power plant. In an ORC dynamic operation analysis, the following factors

Dynamic Modeling of ORC Power Plants http://dx.doi.org/10.5772/intechopen.78390 105

• the time response of the ORC components (including turbine, pump, heat exchangers, etc.) and identification of the slowest responding component to an input parameter change; • the total system response time, overshoots, and identification of limitations and outranges;

• an unexpected slow or sharp transient in response to change in one or multiple physical

Much of the recent research on ORC systems focused on finding the ideal working fluids and developing turbines and heat exchangers that can provide the highest efficiency for the given power plant layout and the nominal steady-state operational conditions. A wide range of literature is available dealing with the steady-state operation of ORC systems for geothermal

A thorough exposition on the dynamic modeling of ORCs is given in a two-part series by Paliano and Putten [7] and [8]. They give insight into the requirements for dynamic model development and validation of Rankine cycle systems and present a simulation of a 600 kWe biomass-fired steam power plant. They use a self-developed dynamic cycle analysis library using an object-oriented, general simulation software (http://www.mathworks.com). The developed models are designed for observing transients around the steady state and do not cope well with unusual circumstances, such as sudden large drops in the temperature of the

The dynamic modeling of the organic Rankine cycle (ORC) was also carried out by Wei et al. [9] targeting ORC system control and diagnostic. They tested two different modeling approaches for this purpose, focusing on computational time, simulation accuracy, and complexity. The first approach was based on the moving boundary numerical method and the second one was performed using the general discretization technique. The code was developed in Modelica and simulated by the Dymola module. After comparison and evaluation of the two approaches, they suggested the moving boundary approach as the most suitable ones

Sohel et al. [6] published their study on the dynamic modeling of a 5.4 MW binary cycle unit of a geothermal power plant. Pentane was used as the ORC motive fluid and it is powered by separated brine from the geothermal fluid. The results of simulation were compared to the plant performance data and the prediction capability of the model at steady and transient

operational conditions was proved with reasonably good accuracy.

are of interest to be investigated and identified [5].

• recognition of the start-up and shut-down operation mode;

variables like thermal input, power output, and so on;

power plants, while dynamic models and studies are not so common [6].

• the part-load capability of the system.

**1.3. State of the art (literature review)**

heating fluid or start-up and shutdown.

for control design applications.

The basic concepts that have to be known in dynamic modeling include system inertia, initial condition, input stimulus variable, and time constant.

The *inertia of a system* is defined by its tendency to remain unchanged or its resistivity against the variation. Obviously, the system's dynamic response depends on its inherent inertia and also the input stimulus which causes the system to break through its initial steady-state condition. To simulate and predict a system's dynamic response, all parameters and properties of the system which affect system inertia have to be known and considered. In mathematics and particularly in dynamic systems, an *initial condition* is the value of an evolving variable at some specific point in time (typically denoted as t = 0). Generally, initial conditions are needed in order to be able to trace the changes in the system's variables in time. Initial conditions affect the value of dynamic variables (state variables) at any time in the future [1].

In dynamic modeling, it is assumed that the system's initial state is disturbed due to an external excitation or load change which forces the system to respond dynamically. This input excitation pulse is called *input stimulus variable*. The input stimulus can be an impulse function, a step function, a linear function, a sinusoidal function or any other type of timedependent function.

Moreover, *time constant* is defined as a time which represents the speed with which a particular system can respond to change, typically equal to the time taken for a specified parameter to vary conventionally by a factor of 1–1/*e* (approximately 0.6321). Actually, it is a criterion that enables us to evaluate the response speed and inertia of the system and also to compare the response time of different systems to each other. Physically, a smaller time constant means a quicker system response. For example, time constants are a feature of the lumped system analysis (lumped capacity analysis method) for thermal systems, used when objects cool or warm uniformly under the influence of convective cooling or heating [2]. This concept is also used in other dynamic systems including mechanical vibration and damping, electrical circuits, electronic systems, fluid and hydraulic systems, thermodynamic systems, chemical and electrochemical processes, and so on [3].

In this chapter, we are going to focus on thermal power plants' dynamic behavior modeling and specialize it for ORC power plants.

### **1.2. Theory of thermal power systems and organic Rankine cycles' dynamic operation**

In the development of thermal power plants, a good estimation/prediction of the plant behavior under design and/or during operation is highly desired [4]. Thermal power systems and especially organic Rankine cycles (ORCs) have complex starting and shut-down mechanisms and normally undergo fluctuations in operating conditions during their service period. Therefore, their dynamic behavior has to be identified to ensure the secure and continuous operation of the system when facing fluctuations and perturbations. The dynamic plant performance is also the foundation for developing control systems during the early design stage of an ORC power plant. In an ORC dynamic operation analysis, the following factors are of interest to be investigated and identified [5].


transient differential equations (ODE or PDE) which originates from the governing physical

The basic concepts that have to be known in dynamic modeling include system inertia, initial

The *inertia of a system* is defined by its tendency to remain unchanged or its resistivity against the variation. Obviously, the system's dynamic response depends on its inherent inertia and also the input stimulus which causes the system to break through its initial steady-state condition. To simulate and predict a system's dynamic response, all parameters and properties of the system which affect system inertia have to be known and considered. In mathematics and particularly in dynamic systems, an *initial condition* is the value of an evolving variable at some specific point in time (typically denoted as t = 0). Generally, initial conditions are needed in order to be able to trace the changes in the system's variables in time. Initial conditions

In dynamic modeling, it is assumed that the system's initial state is disturbed due to an external excitation or load change which forces the system to respond dynamically. This input excitation pulse is called *input stimulus variable*. The input stimulus can be an impulse function, a step function, a linear function, a sinusoidal function or any other type of time-

Moreover, *time constant* is defined as a time which represents the speed with which a particular system can respond to change, typically equal to the time taken for a specified parameter to vary conventionally by a factor of 1–1/*e* (approximately 0.6321). Actually, it is a criterion that enables us to evaluate the response speed and inertia of the system and also to compare the response time of different systems to each other. Physically, a smaller time constant means a quicker system response. For example, time constants are a feature of the lumped system analysis (lumped capacity analysis method) for thermal systems, used when objects cool or warm uniformly under the influence of convective cooling or heating [2]. This concept is also used in other dynamic systems including mechanical vibration and damping, electrical circuits, electronic systems, fluid and hydraulic systems, thermodynamic systems, chemical and

In this chapter, we are going to focus on thermal power plants' dynamic behavior modeling

In the development of thermal power plants, a good estimation/prediction of the plant behavior under design and/or during operation is highly desired [4]. Thermal power systems and especially organic Rankine cycles (ORCs) have complex starting and shut-down mechanisms and normally undergo fluctuations in operating conditions during their service period. Therefore, their dynamic behavior has to be identified to ensure the secure and continuous operation of the system when facing fluctuations and perturbations. The dynamic plant

**1.2. Theory of thermal power systems and organic Rankine cycles' dynamic** 

affect the value of dynamic variables (state variables) at any time in the future [1].

principals and inherent physical characteristics.

104 Organic Rankine Cycle Technology for Heat Recovery

dependent function.

**operation**

electrochemical processes, and so on [3].

and specialize it for ORC power plants.

condition, input stimulus variable, and time constant.

#### **1.3. State of the art (literature review)**

Much of the recent research on ORC systems focused on finding the ideal working fluids and developing turbines and heat exchangers that can provide the highest efficiency for the given power plant layout and the nominal steady-state operational conditions. A wide range of literature is available dealing with the steady-state operation of ORC systems for geothermal power plants, while dynamic models and studies are not so common [6].

A thorough exposition on the dynamic modeling of ORCs is given in a two-part series by Paliano and Putten [7] and [8]. They give insight into the requirements for dynamic model development and validation of Rankine cycle systems and present a simulation of a 600 kWe biomass-fired steam power plant. They use a self-developed dynamic cycle analysis library using an object-oriented, general simulation software (http://www.mathworks.com). The developed models are designed for observing transients around the steady state and do not cope well with unusual circumstances, such as sudden large drops in the temperature of the heating fluid or start-up and shutdown.

The dynamic modeling of the organic Rankine cycle (ORC) was also carried out by Wei et al. [9] targeting ORC system control and diagnostic. They tested two different modeling approaches for this purpose, focusing on computational time, simulation accuracy, and complexity. The first approach was based on the moving boundary numerical method and the second one was performed using the general discretization technique. The code was developed in Modelica and simulated by the Dymola module. After comparison and evaluation of the two approaches, they suggested the moving boundary approach as the most suitable ones for control design applications.

Sohel et al. [6] published their study on the dynamic modeling of a 5.4 MW binary cycle unit of a geothermal power plant. Pentane was used as the ORC motive fluid and it is powered by separated brine from the geothermal fluid. The results of simulation were compared to the plant performance data and the prediction capability of the model at steady and transient operational conditions was proved with reasonably good accuracy.

An ORC dynamic modeling package was presented by Casella et al. [10] for the system design and prediction of the off-design conditions. They validated their results with Triogen ORC system data [11]. The system standard module included Triogen turbo-generator, turbo pump, condenser, and recuperator, while the evaporator could be designed and customized for available energy sources. For evaporator heat exchanger modeling purpose, they used one-dimensional heat transfer equations and considered a standard geometry with some simplifying correlations.

input heat load, were assessed using the dynamic model with reference to a sample heat load

Dynamic Modeling of ORC Power Plants http://dx.doi.org/10.5772/intechopen.78390 107

Furthermore, Xu et al. [17] developed a dynamic organic Rankine cycle waste heat recovery model (ORC-WHR) using Simulink and an engine model for heavy-duty diesel applications. Their physics-based ORC-WHR system model, constructed in GT-POWER software platform, included parallel evaporators, flow control valves, a turbine expander, a reservoir, pumps, compressible volumes, and junctions. Experimental data for the ORC-WHR component models were identified and collected over a wide range of steady-state and transient operational conditions. The data were collected from an ORC-WHR system on a 13 L heavy-duty diesel engine. The model was supposed to serve as a virtual plant for offline simulations to explore the potential of fuel savings and emission reduction for different driving cycles of the heavy-

The reviewed papers presented here illuminate different modeling methodologies and strategies with various levels of accuracy and computational time/cost (based on the system application and modeling purpose). In addition, it is expected that a comprehensive dynamic model enables a full-range analysis of a system's transient response to variation of input parameters, that is, minimum (near-zero) to maximum possible input thermal load. The function, representing the input variations, should be flexible enough to enable the users to study

It is also advantageous to be able to switch these inputs and outputs around for improved flexibility. In addition, adaptation of the model to closed loop control systems should be con-

In this chapter, a general framework is devised to provide a flexible dynamic modeling approach adaptable to different ORC system applications and different dynamic modeling purposes based on the reviewed modeling attempts and reported results. The modeling framework incorporates step-by-step dynamic modeling methodology for both component and system levels. Technical aspects as well as assumptions and required considerations for ORC dynamic modeling are described. Besides, component assembling approaches to build dynamic models of the whole ORC system are discussed and key aspects and related noticeable remarks are highlighted. Moreover, the potential applicable software tools as well as developed computer codes and data libraries customized for transient modeling of ORC power plants are reviewed,

To build a comprehensive and meanwhile enough fast dynamic model of an ORC power system, the intelligent selection of component models with proper input/output parameters as well as appropriate simplifying assumptions is crucial. The ORC systems are generally utilized for the very vast range of heat recovery applications for each of which the specific type of components might be used with different operating characteristics and conditions. For example, various types and sizes of heat exchangers, expanders, pumps, valves, and so on are used for the ORCs depending on the scale of thermal power input, working fluid, secondary

profile of the hot water source and at different timescales.

duty trucks and provide guidelines for the experimental studies.

**2. Dynamic modeling of ORC at the component level**

the effects on the power output as the function of time.

sidered too.

evaluated, and described.

Desideri et al. [12] developed a dynamic model of the ORC system, validated both in steadystate and transient conditions via experimental data using a 10 kWe waste heat recovery (WHR) ORC system with a screw expander. They used an open-source Modelica library, ThermoCycle, developed by the Energy Systems Research Unit at the University of Liege. The commercial program Dymola (Dynamic Modeling Laboratory) was used to perform all the simulations. They implemented a liquid receiver model after the condenser to incorporate the accumulated liquid in the tank based on the phase equilibrium assumption. Moreover, effects of the noncondensable gases were incorporated in their model using the gas mixture theory.

Eventually, they demonstrated that the ThermoCycle library can reliably be used for the modeling of such thermodynamic systems, allowing, for instance, the implementation and simulation of various control strategies.

Ziviani et al. [13] discussed the challenges involved in ORC modeling for low-grade thermal energy recovery. They studied and reviewed various software packages, to identify the most applicable and suitable ones for ORC system modeling. Their recommended package list included Matlab/Simulink, EES, Phyton, Modelica, AMESim, and Cycle-Tempo.

In another relevant study, Grelet et al. [14] presented a method to model heat exchangers used in waste heat recovery Rankine-based systems in heavy-duty trucks using the water ethanol mixture and recovering heat from the exhaust gas recirculation (EGR) system. The model predicted both the heat transfer and physical properties of the working fluid such as temperature and density after the heat exchange process. The authors claim that the model presents an advantage of being low in terms of computational needs and is suitable for control software integration. Grelet et al. [15] published also another paper investigating the transient performance of a waste heat recovery Rankine cycle-based system for a heavy-duty truck and compared it to the steady-state study. Simple thermodynamic simulations are carried out assuming certain conditions for the comparison of several working fluids. Fluid choice and concept optimization are conducted, taking into account integration constraints (heat rejection, packaging, etc.). The study exposes the importance of the modeling phase when designing Rankine cycle-based heat recovery systems (HRSs) and yields a better understanding when it comes to the integration of a Rankine cycle in a truck.

Marchionni et al. [16] presented a modeling approach to analyze and design waste heat to power conversion units based on an ORC. They implemented the model in the commercial software platform GT-SUITE. Sub-models were developed and calibrated for the components like plate heat exchangers and multistage centrifugal pumps using performance data of industrial map data at design and off-design conditions. The pump and turbine speed were optimized at different operating conditions of the evaporator to maximize the net power output. Furthermore, the effects of thermal inertial of the evaporator, in response to transient input heat load, were assessed using the dynamic model with reference to a sample heat load profile of the hot water source and at different timescales.

An ORC dynamic modeling package was presented by Casella et al. [10] for the system design and prediction of the off-design conditions. They validated their results with Triogen ORC system data [11]. The system standard module included Triogen turbo-generator, turbo pump, condenser, and recuperator, while the evaporator could be designed and customized for available energy sources. For evaporator heat exchanger modeling purpose, they used one-dimensional heat transfer equations and considered a standard geometry with some sim-

Desideri et al. [12] developed a dynamic model of the ORC system, validated both in steadystate and transient conditions via experimental data using a 10 kWe waste heat recovery (WHR) ORC system with a screw expander. They used an open-source Modelica library, ThermoCycle, developed by the Energy Systems Research Unit at the University of Liege. The commercial program Dymola (Dynamic Modeling Laboratory) was used to perform all the simulations. They implemented a liquid receiver model after the condenser to incorporate the accumulated liquid in the tank based on the phase equilibrium assumption. Moreover, effects of the non-

Eventually, they demonstrated that the ThermoCycle library can reliably be used for the modeling of such thermodynamic systems, allowing, for instance, the implementation and

Ziviani et al. [13] discussed the challenges involved in ORC modeling for low-grade thermal energy recovery. They studied and reviewed various software packages, to identify the most applicable and suitable ones for ORC system modeling. Their recommended package list

In another relevant study, Grelet et al. [14] presented a method to model heat exchangers used in waste heat recovery Rankine-based systems in heavy-duty trucks using the water ethanol mixture and recovering heat from the exhaust gas recirculation (EGR) system. The model predicted both the heat transfer and physical properties of the working fluid such as temperature and density after the heat exchange process. The authors claim that the model presents an advantage of being low in terms of computational needs and is suitable for control software integration. Grelet et al. [15] published also another paper investigating the transient performance of a waste heat recovery Rankine cycle-based system for a heavy-duty truck and compared it to the steady-state study. Simple thermodynamic simulations are carried out assuming certain conditions for the comparison of several working fluids. Fluid choice and concept optimization are conducted, taking into account integration constraints (heat rejection, packaging, etc.). The study exposes the importance of the modeling phase when designing Rankine cycle-based heat recovery systems (HRSs) and yields a better understand-

Marchionni et al. [16] presented a modeling approach to analyze and design waste heat to power conversion units based on an ORC. They implemented the model in the commercial software platform GT-SUITE. Sub-models were developed and calibrated for the components like plate heat exchangers and multistage centrifugal pumps using performance data of industrial map data at design and off-design conditions. The pump and turbine speed were optimized at different operating conditions of the evaporator to maximize the net power output. Furthermore, the effects of thermal inertial of the evaporator, in response to transient

condensable gases were incorporated in their model using the gas mixture theory.

included Matlab/Simulink, EES, Phyton, Modelica, AMESim, and Cycle-Tempo.

ing when it comes to the integration of a Rankine cycle in a truck.

plifying correlations.

106 Organic Rankine Cycle Technology for Heat Recovery

simulation of various control strategies.

Furthermore, Xu et al. [17] developed a dynamic organic Rankine cycle waste heat recovery model (ORC-WHR) using Simulink and an engine model for heavy-duty diesel applications. Their physics-based ORC-WHR system model, constructed in GT-POWER software platform, included parallel evaporators, flow control valves, a turbine expander, a reservoir, pumps, compressible volumes, and junctions. Experimental data for the ORC-WHR component models were identified and collected over a wide range of steady-state and transient operational conditions. The data were collected from an ORC-WHR system on a 13 L heavy-duty diesel engine. The model was supposed to serve as a virtual plant for offline simulations to explore the potential of fuel savings and emission reduction for different driving cycles of the heavyduty trucks and provide guidelines for the experimental studies.

The reviewed papers presented here illuminate different modeling methodologies and strategies with various levels of accuracy and computational time/cost (based on the system application and modeling purpose). In addition, it is expected that a comprehensive dynamic model enables a full-range analysis of a system's transient response to variation of input parameters, that is, minimum (near-zero) to maximum possible input thermal load. The function, representing the input variations, should be flexible enough to enable the users to study the effects on the power output as the function of time.

It is also advantageous to be able to switch these inputs and outputs around for improved flexibility. In addition, adaptation of the model to closed loop control systems should be considered too.

In this chapter, a general framework is devised to provide a flexible dynamic modeling approach adaptable to different ORC system applications and different dynamic modeling purposes based on the reviewed modeling attempts and reported results. The modeling framework incorporates step-by-step dynamic modeling methodology for both component and system levels. Technical aspects as well as assumptions and required considerations for ORC dynamic modeling are described. Besides, component assembling approaches to build dynamic models of the whole ORC system are discussed and key aspects and related noticeable remarks are highlighted. Moreover, the potential applicable software tools as well as developed computer codes and data libraries customized for transient modeling of ORC power plants are reviewed, evaluated, and described.

## **2. Dynamic modeling of ORC at the component level**

To build a comprehensive and meanwhile enough fast dynamic model of an ORC power system, the intelligent selection of component models with proper input/output parameters as well as appropriate simplifying assumptions is crucial. The ORC systems are generally utilized for the very vast range of heat recovery applications for each of which the specific type of components might be used with different operating characteristics and conditions. For example, various types and sizes of heat exchangers, expanders, pumps, valves, and so on are used for the ORCs depending on the scale of thermal power input, working fluid, secondary transfer fluid, and the specific operating conditions. Based on the ORC system application and its specific operating conditions, a proper model with reasonable simplifying assumptions has to be considered for component modeling. In this section, we will discuss modeling methodology and analogy of the ORC components, trying to clarify general aspects of the mathematic formulation and simulation details. In some cases, we need to specialize the models for a particular component or specific assumptions requiring further modeling details.

Generally, the heat exchanger as a power plant component is simulated using one-dimensional heat and mass transfer equations because of the acceptable accuracy of one-dimensional models and limitation in computational time especially for the dynamic models and control applications. One-dimensional consideration leads to the following assumptions which nor-

• The pressure drop is considered in some models but omitted in others. It depends on the

• Mass accumulation is considered for the fluids (even though it is neglected in some devel-

• The heat exchanger could be assumed either with or without phase change depending on

• One-dimensional mass and energy equations are considered and the equations are solved numerically along the heat exchanger. For more simple modeling, lumped thermal capacitance can also be assumed for both the metal pipe and the fluids; hence, just one thermal

• The external pipe is assumed to be ideally insulated from the environment; hence, heat

• Axial heat conduction in working fluid, wall, and exhaust gas is not considered (even

Heat exchanger modeling tools are generally based on the finite difference method, applying the energy conservation and mass conservation equations in a differential form. The

each of length ∆x, that are the places where the conservation equations are applied. For each discrete volume three nodes can be defined in the radial direction: one referring to the state of the transfer fluid in the annulus (indexed by tf), one to the state of the metal constituting the metal pipe (indexed by p), and one referring to the organic fluid within the internal pipe

The system inputs are characterized by the parameters representing the two fluids at the heat exchanger inlet. Particularly their temperature, pressure, and mass flow rate must be known, and the fluid pressures are introduced since many properties depend also upon pressure. The output generated by the system can be any of the state variables but of particular interest; in the view of linking the heat exchanger to other components in a complex network, the state of the fluids leaving the exchanger must be provided, as the temperature of the two fluids. Due to the counter-flow design this temperature will be the one calculated at the node with index

longitudinal lumped volumes,

Dynamic Modeling of ORC Power Plants http://dx.doi.org/10.5772/intechopen.78390 109

• The wall and fluid temperature in the radial direction is internally uniform.

though in some modeling attempts, it is taken into account).

straight pipe in a typical heat exchanger design is split into nx

1 for the fluid flowing in the annulus, as shown in **Figure 3** [18].

(indexed by f), according to the scheme of **Figure 2**.

• Energy accumulation is considered in both metal pipe and the two working fluids.

importance of the pressure loss in a specific modeling strategy.

mally are applied:

oped models for simplicity).

the actual case under study.

losses are neglected.

node needs to be defined with such assumptions.

#### **2.1. Heat exchanger (evaporator, condenser, etc.)**

In the ORC waste heat recovery systems, the heat exchangers are generally used either as evaporators or as condensers. Evaporators absorb heat from the heat source and release it to the working fluid while the condensers reject heat from the working fluid to cooling water. Since the evaporators and condensers are crucial components when determining the overall dynamic behavior of the ORCs, the heat exchanger model should be characterized by sufficient flexibility to allow simple generalization of the design.

Different types of heat exchangers might be used in the ORC systems including plate/compact heat exchangers, tubular co-flow/counter-flow heat exchangers, shell and tube heat exchangers, and so on. The detailed heat and mass transfer equations are slightly different for different types of heat exchangers due to their configuration and geometry, but the principles are the same for all these heat exchanger types. Here, we will present the modeling methodology and general equations used.

For the modeling purpose, the heat exchangers are normally represented as a straight pipe, despite the fact that different and more complex designs are usually adopted in order to enhance the heat exchanged and to reduce the overall dimensions of the system (see a schematic sample configuration in **Figure 1**) [18]. The assumption of a straight pipe, however, simplifies the resulting dynamic problem to a great extent and is commonly adopted when the heat exchanger dynamic modeling is considered [9, 19].

**Figure 1.** An example of a compact heat exchanger development into a unidirectional pipe [18].

Generally, the heat exchanger as a power plant component is simulated using one-dimensional heat and mass transfer equations because of the acceptable accuracy of one-dimensional models and limitation in computational time especially for the dynamic models and control applications. One-dimensional consideration leads to the following assumptions which normally are applied:

transfer fluid, and the specific operating conditions. Based on the ORC system application and its specific operating conditions, a proper model with reasonable simplifying assumptions has to be considered for component modeling. In this section, we will discuss modeling methodology and analogy of the ORC components, trying to clarify general aspects of the mathematic formulation and simulation details. In some cases, we need to specialize the models for a particular component or specific assumptions requiring further modeling details.

In the ORC waste heat recovery systems, the heat exchangers are generally used either as evaporators or as condensers. Evaporators absorb heat from the heat source and release it to the working fluid while the condensers reject heat from the working fluid to cooling water. Since the evaporators and condensers are crucial components when determining the overall dynamic behavior of the ORCs, the heat exchanger model should be characterized by suf-

Different types of heat exchangers might be used in the ORC systems including plate/compact heat exchangers, tubular co-flow/counter-flow heat exchangers, shell and tube heat exchangers, and so on. The detailed heat and mass transfer equations are slightly different for different types of heat exchangers due to their configuration and geometry, but the principles are the same for all these heat exchanger types. Here, we will present the modeling methodology

For the modeling purpose, the heat exchangers are normally represented as a straight pipe, despite the fact that different and more complex designs are usually adopted in order to enhance the heat exchanged and to reduce the overall dimensions of the system (see a schematic sample configuration in **Figure 1**) [18]. The assumption of a straight pipe, however, simplifies the resulting dynamic problem to a great extent and is commonly adopted when

**2.1. Heat exchanger (evaporator, condenser, etc.)**

108 Organic Rankine Cycle Technology for Heat Recovery

and general equations used.

ficient flexibility to allow simple generalization of the design.

the heat exchanger dynamic modeling is considered [9, 19].

**Figure 1.** An example of a compact heat exchanger development into a unidirectional pipe [18].


Heat exchanger modeling tools are generally based on the finite difference method, applying the energy conservation and mass conservation equations in a differential form. The straight pipe in a typical heat exchanger design is split into nx longitudinal lumped volumes, each of length ∆x, that are the places where the conservation equations are applied. For each discrete volume three nodes can be defined in the radial direction: one referring to the state of the transfer fluid in the annulus (indexed by tf), one to the state of the metal constituting the metal pipe (indexed by p), and one referring to the organic fluid within the internal pipe (indexed by f), according to the scheme of **Figure 2**.

The system inputs are characterized by the parameters representing the two fluids at the heat exchanger inlet. Particularly their temperature, pressure, and mass flow rate must be known, and the fluid pressures are introduced since many properties depend also upon pressure. The output generated by the system can be any of the state variables but of particular interest; in the view of linking the heat exchanger to other components in a complex network, the state of the fluids leaving the exchanger must be provided, as the temperature of the two fluids. Due to the counter-flow design this temperature will be the one calculated at the node with index 1 for the fluid flowing in the annulus, as shown in **Figure 3** [18].

Here, the rotational speed and the pressure ratio are input variables, while mass flow rate and efficiency (from which power and torque can be derived) are outputs; however, the input/output variables could be changed or replaced depending on specific application requirements or design/optimization strategies [17]. The turbine can be integrated with an electric generator or it can also be mechanically connected to an engine crank shaft through a transmission, as in [21]. Due to the choked flow status at high expansion ratios 10–30, turbine expander mass flow rate can be written as a linear function of turbine inlet pressure as shown in Eq. (1) [17].

*hout*,*turb* = *hin*,*turb* − *ηis*,*turb*(*hin*,*turb* − *hout*,*is*,*turb*) (2)

*ηis*,*turb* = *map*( *Nturb*, *pin*,*turb* /*pout*,*turb*, *Tin*,*turb*) (3)

*hout*,*is*,*turb* = *map*( *Sout*,*turb*, *pout*,*turb*) (4)

*Sout*,*turb* = *Sin*,*turb* (5)

*Sis*,*turb* = *map*( *hin*,*turb*, *pin*,*turb*) (6)

The turbine efficiency map has to be provided by the turbine manufacturer. Outlet temperature, Tout,tur, is calculated from outlet enthalpy and outlet pressure using a thermodynamic table

*Tout*,*turb* = *map*( *hout*,*turb*, *pout*,*turb*) (7)

*turb* = *aturb pin*,*turb* + *bturb* (1)

Dynamic Modeling of ORC Power Plants http://dx.doi.org/10.5772/intechopen.78390 111

*m*̇

of the working fluid.

**Figure 4.** Block diagram of the turbine/expander model.

The outlet enthalpy is calculated by isentropic efficiency as follows:

**Figure 2.** Discretization assumed for typical tubular counter-flow heat exchanger with phase change and main heat fluxes involved [18].

**Figure 3.** The heat exchanger block.

Subscribes f1 and f<sup>2</sup> refer to fluid 1 (in the inner pipe) and fluid 2 (in the annulus), respectively, and subscribe p relates to the pipe body. Once the system has been fully defined, the heat and mass transfer coefficients and correlations must be introduced to calculate the actual thermal fluxes.

An interesting study conducted on this topic is by García-Vallardes et al. [20], in which the thermal and fluid dynamic behavior of a tubular heat exchanger (could be applied as evaporator or condenser) are simulated numerically. Continuity, momentum and energy conservation equations were applied for the internal and annulus tubes to accurately predict the heat and mass transfer inside the heat exchanger. Energy conservation equations have in fact been applied to the external tube and insulation, hence dropping the hypothesis of the ideally insulated system. However, such detailed simulation of the heat exchanger is not useful for the modeling of dynamic ORC systems, since one needs to compromise between expected accuracy and computational time and cost.

#### **2.2. Expander**

The expander turbine is simulated generally as a component based upon steady-state characteristic curves. Inputs/outputs of the system are shown in **Figure 4**.

Here, the rotational speed and the pressure ratio are input variables, while mass flow rate and efficiency (from which power and torque can be derived) are outputs; however, the input/output variables could be changed or replaced depending on specific application requirements or design/optimization strategies [17]. The turbine can be integrated with an electric generator or it can also be mechanically connected to an engine crank shaft through a transmission, as in [21]. Due to the choked flow status at high expansion ratios 10–30, turbine expander mass flow rate can be written as a linear function of turbine inlet pressure as shown in Eq. (1) [17].

$$
\dot{m}\_{\text{turb}} = a\_{\text{turb}} p\_{\text{in,turb}} + b\_{\text{turb}} \tag{1}
$$

The outlet enthalpy is calculated by isentropic efficiency as follows:

$$h\_{out,tuvb} = h\_{in,tuvb} - \eta\_{is,tuvb} (h\_{in,tuvb} - h\_{out,is,tuvb}) \tag{2}$$

$$\eta\_{is, turb} = \max\{ \left( \mathbf{N}\_{uub'}, p\_{iu, nub'} / p\_{out, nub'}, T\_{in, nub} \right) \tag{3}$$

$$h\_{out,is,turb} = \text{map}\left(\mathbb{S}\_{out,turb'}, p\_{out,ub}\right) \tag{4}$$

$$\mathcal{S}\_{out,turb} = \mathcal{S}\_{in,turb} \tag{5}$$

$$S\_{is,taub} = \text{map}\left(h\_{i\text{u},taub'}, p\_{i\text{u},taub}\right) \tag{6}$$

The turbine efficiency map has to be provided by the turbine manufacturer. Outlet temperature, Tout,tur, is calculated from outlet enthalpy and outlet pressure using a thermodynamic table of the working fluid.

$$T\_{out, turb} = \text{map}\left(h\_{out, turb'}, p\_{out, turb}\right) \tag{7}$$

**Figure 4.** Block diagram of the turbine/expander model.

Subscribes f1

fluxes involved [18].

110 Organic Rankine Cycle Technology for Heat Recovery

**2.2. Expander**

and f<sup>2</sup>

**Figure 3.** The heat exchanger block.

accuracy and computational time and cost.

refer to fluid 1 (in the inner pipe) and fluid 2 (in the annulus), respectively, and

subscribe p relates to the pipe body. Once the system has been fully defined, the heat and mass transfer coefficients and correlations must be introduced to calculate the actual thermal fluxes.

**Figure 2.** Discretization assumed for typical tubular counter-flow heat exchanger with phase change and main heat

An interesting study conducted on this topic is by García-Vallardes et al. [20], in which the thermal and fluid dynamic behavior of a tubular heat exchanger (could be applied as evaporator or condenser) are simulated numerically. Continuity, momentum and energy conservation equations were applied for the internal and annulus tubes to accurately predict the heat and mass transfer inside the heat exchanger. Energy conservation equations have in fact been applied to the external tube and insulation, hence dropping the hypothesis of the ideally insulated system. However, such detailed simulation of the heat exchanger is not useful for the modeling of dynamic ORC systems, since one needs to compromise between expected

The expander turbine is simulated generally as a component based upon steady-state charac-

teristic curves. Inputs/outputs of the system are shown in **Figure 4**.

Turbine boundary conditions are pressure and enthalpy at the inlet and pressure at outlet. In addition, the inlet and outlet are adiabatic. The heat transfer between turbine outer surface and ambient is considered based on the turbine isentropic efficiency map.

#### **2.3. Pump**

The pumps of the ORC system have to maintain both pressure and working fluid mass flow. The HP pump is considered here to be a positive displacement type, whereas the feed pump is an inline roller cell pump. Due to the dominance of the HP pump, only the HP pump model is formulated here. The pump mass flow rate is interpolated using the map (Eq. (8)) provided by the ORC system manufacturer [22]. Pump power consumption and outlet temperature are calculated by Eq. (9) and (10).

$$
\dot{m}\_{pump} = \text{map}\left(\text{N}\_{pump}\right) \tag{8}
$$

*Hres* <sup>=</sup> \_\_*<sup>V</sup>*

different based on the thermodynamic state of the fluid.

Here, *V*<sup>0</sup>

environment.

pressure ratio [23]:

Here, γ =

*<sup>m</sup>*̇ <sup>=</sup> *<sup>O</sup> Cd <sup>A</sup>*<sup>0</sup> <sup>√</sup>

Cp \_\_\_ Cv *<sup>m</sup>*̇ <sup>=</sup> *<sup>O</sup> Cd <sup>A</sup>*<sup>0</sup> (

**2.5. Valve**

*V*0

is the entire reservoir volume and V is instant volume of the working fluid.

Then, *Hres* represents the ratio of the reservoir's fluid level to the reservoir's total height. Reservoir boundary conditions are mass flow rate and enthalpy at the inlet and mass flow rate at the outlet. The reservoir is assumed to be adiabatic, that is, no heat loss to the

The proportional valves or distribution/control valves are commonly used in ORC heat recovery units to enhance the flexibility and controllability of the system. Depending on the fluid state when flowing over the valve, the flow might be either incompressible or compressible. The valve located after the pump operates normally with incompressible fluid flow, while the working fluid passes through a valve before the expander, is usually super-heated vapor and shows compressible behavior. Hence, the mathematical model defined for the valves is

When the working fluid is in liquid state and thus incompressible, the outlet temperature is assumed to be equal to the inlet temperature due to the small temperature change across the incompressible valves. The necessary boundary condition for the incompressible flow valve is mass flow rate from the pump at the inlet. The valves are assumed adiabatic, that is, no heat loss to the environment. Therefore, a simple mass conservation equation, describing the relation between the valve opening ratio and the mass flow passing through the valve, can be used. Then the valve opening ratio has to be given as an input parameter. Besides, the valve's pressure loss (if found to be considerable) can be calculated by the formulation provided by the manufacturer as a function of mass flow rate. The turbine inlet valve and turbine bypass valve both experience vapor phase flow. They can be modeled based on the compressible flow status: subsonic flow or supersonic flow depending on inlet/outlet

> \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ <sup>2</sup>*<sup>γ</sup>* \_\_\_

> > \_\_\_\_\_\_ *<sup>γ</sup> pin <sup>ρ</sup>in if* <sup>0</sup> <sup>≤</sup> *<sup>p</sup>*

valve and no heat loss consideration (hin <sup>=</sup> hout), the outlet temperature is calculated as [8]:

*Tout* = *f*(*pout*, *hout*) (15)

] *if* (

\_\_\_*out pin* ≤ ( \_\_\_2 *γ* + 1)

is heat capacity ratio. With the isentropic assumption of the process across the

\_\_\_2 *γ* + 1) *γ* \_\_\_\_\_ (*γ*−1) ≤ *p* \_\_\_*out pin*

*γ* \_\_\_\_\_ (*γ*−1) ≤ 1 (*Subsonic*)

(*Supersonic*) (14)

*p* \_\_\_*out pin* ) \_\_2 *γ* − ( *p* \_\_\_*out pin* ) *γ*+1 \_\_\_ *γ*

*<sup>γ</sup>* <sup>−</sup> <sup>1</sup> *pin ρin*[(

*γ*+1 \_\_\_\_\_ 2(*γ*−1) √

\_\_\_2 *γ* + 1) (13)

113

Dynamic Modeling of ORC Power Plants http://dx.doi.org/10.5772/intechopen.78390

$$P\_{pump} = \frac{\dot{m}\_{pump}}{\rho} \frac{(p\_{out,pump} - p\_{in,pump})}{\eta\_{is,pump}} \tag{9}$$

$$T\_{out,pump} = \left. T\_{in,pump} + \frac{\left(1 - \eta\_{i,pump}\right)P\_{pump}}{\dot{m}\_{pump}C\_{p,pump}} \right. \tag{10}$$

where ρ is the working fluid density upstream of the pump, pin,pump, pout,pump are upstream and downstream pressures, respectively, Cp,pump is the upstream specific heat capacity of the working fluid, and ηis,pump is isentropic efficiency and is expressed as a function of pump mass flow rate and the rotational speed, which can be drawn from the pump map data [22].

#### **2.4. Reservoir**

The reservoir in an ORC system works as a buffer storage for the working fluid in order to supply fluid or accumulate it as the ORC system experiences transients. When the ORC system starts, the working fluid level is low in the reservoir because the entire circuit is full of liquid. When the system warms up, part of the ORC system is occupied by vaporized working fluid and the working fluid level in the reservoir increases compared to the cold condition. To calculate the working fluid level as well as the mean temperature, both mass balance and energy balance are applied in the reservoir. The mass balance can be described by Eq. (11) and the energy balance is given typically by Eq. (12). The reservoir working fluid level can be obtained by Eq. (13) [17].

$$\frac{d\,m\_f}{dt} = \dot{m}\_{f,in} - \dot{m}\_{f,out} \tag{11}$$

$$\frac{d(mh)}{dt} = \dot{m}\_{ln}h\_{in} - \dot{m}\_{out}h\_{out} \tag{12}$$

$$H\_{\rm res} = \frac{V}{V\_o} \tag{13}$$

Here, *V*<sup>0</sup> is the entire reservoir volume and V is instant volume of the working fluid. Then, *Hres* represents the ratio of the reservoir's fluid level to the reservoir's total height. Reservoir boundary conditions are mass flow rate and enthalpy at the inlet and mass flow rate at the outlet. The reservoir is assumed to be adiabatic, that is, no heat loss to the environment.

#### **2.5. Valve**

Turbine boundary conditions are pressure and enthalpy at the inlet and pressure at outlet. In addition, the inlet and outlet are adiabatic. The heat transfer between turbine outer surface

The pumps of the ORC system have to maintain both pressure and working fluid mass flow. The HP pump is considered here to be a positive displacement type, whereas the feed pump is an inline roller cell pump. Due to the dominance of the HP pump, only the HP pump model is formulated here. The pump mass flow rate is interpolated using the map (Eq. (8)) provided by the ORC system manufacturer [22]. Pump power consumption and outlet temperature are

*ρ*

(*pout*,*pump* − *pin*,*pump*) \_\_\_\_\_\_\_\_\_\_\_\_\_ *<sup>η</sup>is*,*pump*

> *m*̇ *pump Cp*,*pump*

where ρ is the working fluid density upstream of the pump, pin,pump, pout,pump are upstream and downstream pressures, respectively, Cp,pump is the upstream specific heat capacity of the working fluid, and ηis,pump is isentropic efficiency and is expressed as a function of pump mass flow

The reservoir in an ORC system works as a buffer storage for the working fluid in order to supply fluid or accumulate it as the ORC system experiences transients. When the ORC system starts, the working fluid level is low in the reservoir because the entire circuit is full of liquid. When the system warms up, part of the ORC system is occupied by vaporized working fluid and the working fluid level in the reservoir increases compared to the cold condition. To calculate the working fluid level as well as the mean temperature, both mass balance and energy balance are applied in the reservoir. The mass balance can be described by Eq. (11) and the energy balance is given typically by Eq. (12). The reservoir working fluid level can be

*dt* <sup>=</sup> *<sup>m</sup>*̇

*dt* <sup>=</sup> *<sup>m</sup>*̇

*<sup>f</sup>*,*in* − *m*̇

*in hin* − *m*̇

*<sup>f</sup>*,*out* (11)

*out hout* (12)

rate and the rotational speed, which can be drawn from the pump map data [22].

\_\_\_\_\_\_\_\_\_\_\_\_

*pump* = *map*( *Npump*) (8)

(9)

(10)

and ambient is considered based on the turbine isentropic efficiency map.

**2.3. Pump**

**2.4. Reservoir**

obtained by Eq. (13) [17].

*<sup>d</sup> mf* \_\_\_\_

*<sup>d</sup>*(*mh*) \_\_\_\_\_

calculated by Eq. (9) and (10).

*m*̇

112 Organic Rankine Cycle Technology for Heat Recovery

*Ppump* <sup>=</sup> *<sup>m</sup>*̇ \_\_\_\_\_ *pump*

*Tout*,*pump* <sup>=</sup> *Tin*,*pump* <sup>+</sup> (<sup>1</sup> <sup>−</sup> *<sup>η</sup>is*,*pump*) *Ppump*

The proportional valves or distribution/control valves are commonly used in ORC heat recovery units to enhance the flexibility and controllability of the system. Depending on the fluid state when flowing over the valve, the flow might be either incompressible or compressible. The valve located after the pump operates normally with incompressible fluid flow, while the working fluid passes through a valve before the expander, is usually super-heated vapor and shows compressible behavior. Hence, the mathematical model defined for the valves is different based on the thermodynamic state of the fluid.

When the working fluid is in liquid state and thus incompressible, the outlet temperature is assumed to be equal to the inlet temperature due to the small temperature change across the incompressible valves. The necessary boundary condition for the incompressible flow valve is mass flow rate from the pump at the inlet. The valves are assumed adiabatic, that is, no heat loss to the environment. Therefore, a simple mass conservation equation, describing the relation between the valve opening ratio and the mass flow passing through the valve, can be used. Then the valve opening ratio has to be given as an input parameter. Besides, the valve's pressure loss (if found to be considerable) can be calculated by the formulation provided by the manufacturer as a function of mass flow rate. The turbine inlet valve and turbine bypass valve both experience vapor phase flow. They can be modeled based on the compressible flow status: subsonic flow or supersonic flow depending on inlet/outlet pressure ratio [23]:

$$\dot{m} = O\,\mathcal{C}\_d A\_0 \sqrt{\frac{2\gamma}{\gamma - 1} p\_{in} \rho\_{in} \left[ \left( \frac{p\_{out}}{p\_{in}} \right)^{\frac{2}{\gamma}} - \left( \frac{p\_{out}}{p\_{in}} \right)^{\frac{\gamma + 1}{\gamma}} \right]} \quad \text{if } \left( \frac{2}{\gamma + 1} \right)^{\frac{\gamma}{(\gamma - 1)}} \le \frac{p\_{out}}{p\_{in}} \le 1 \text{ (Subosonic)}$$

$$\dot{m} = O\,\mathcal{C}\_d A\_0 \left( \frac{2}{\gamma + 1} \right)^{\frac{\gamma + 1}{2(\gamma - 1)}} \sqrt[4]{\gamma} \, p\_{in} \rho\_{in} \text{ if } 0 \le \frac{p\_{out}}{p\_{in}} \le \left( \frac{2}{\gamma + 1} \right)^{\frac{\gamma}{(\gamma - 1)}} \text{ (Supersonic)}\tag{14}$$

Here, γ = Cp \_\_\_ Cv is heat capacity ratio. With the isentropic assumption of the process across the valve and no heat loss consideration (hin <sup>=</sup> hout), the outlet temperature is calculated as [8]:

$$T\_{out} = f(p\_{out}, h\_{out}) \tag{15}$$

The boundary conditions necessary for these valves are pressure and enthalpy at the inlet and pressure at the outlet.

#### **2.6. Pipes and junctions**

#### *2.6.1. Pipes*

The pressure and heat loss through the pipes containing the liquid state are normally negligible compared with other components. If in a certain case their contribution is found to be considerable, they could be mathematically modeled using the general fluid mechanics principles using pipe-flow pressure loss and heat transfer equations. However, the pipe flow after the evaporators and upstream of the turbine valves are considered as compressible volumes, which has to be taken into account, especially for their dynamic inertia applied to the system [24]. Three equations are utilized in this volume: mass balance, energy balance, and the ideal gas law [25]. Three parameters can be calculated by solving these three equations: working fluid's mass inside the volume, working fluid's mean temperature, and mean pressure inside the volume [8].

$$
\mu \frac{dm}{dt} + m \gets\_v \frac{dT}{dt} = \dot{H}\_{in} - \dot{H}\_{out} \tag{16}
$$

**3. System-level dynamic modeling**

transient conditions;

inserted in the simulation models;

adding new fixed common state variables.

**3.2. Initialization of the system simulation model**

in the initial condition list definition [9].

**3.1. Integration of the component dynamic models**

Once dynamic models of every individual component are ready and evaluated with known input state variables and calculated outputs, the components are interconnected to build a thermodynamic model of the whole thermal power system. Before interconnecting the individual component models to each other, the following important issues have to be reviewed:

Dynamic Modeling of ORC Power Plants http://dx.doi.org/10.5772/intechopen.78390 115

• ensuring the validity and accuracy of the component models for both steady-state and

• creating and fully parameterizing the ORC components, the boundary sources, and sinks. Besides, the operating range and limitations for all components have to specified and

• defining appropriate known and unknown variables for the system, based on the design or optimization requirements and strategy. More detailed aspects of the system variable

• omitting the unnecessary fixed common variables of the individual component models or

After above-listed considerations and the preparation of required data, the ORC components will be connected properly to establish the system model. Connecting the component models means uniting the common variables of a specific component to its neighboring components

Apparently, the initialization of closed-loop dynamic models is a difficult task which should be carefully approached and planned. To initialize the dynamic model, the initial conditions have to be defined appropriately. At some point during the initialization process, one must thoroughly plan the thermodynamic cycle as a steady-state problem to find appropriate states for the initialization of the problem [5]. Initial state points can be set as parameters calculated by a steady-state model in which the analysis is expected to begin in a time domain. Initialization problems require starting arrays for all components, which can also be stored as parameters in the test bench level. Diagnostic and summary variables should also be included

The ORC dynamic model developers must prepare an input/output variable list considering the aspects mentioned in Section 3.1, where all fixed model inputs based on the real-test

so that the set of components create a closed loop by linking them to each other.

**3.3. Input and output parameters and identification of the constraints**

definition that need to be considered are presented in Section 3.3.

$$\frac{RT}{V}\frac{dm}{dt} + \frac{p}{T}\frac{dT}{dt} - \frac{dp}{dt} = 0\tag{17}$$

where u represents specific internal energy, cv represents specific heat capacity, Ḣ in and Ḣ out represent inlet and outlet enthalpy flow rate, R represents ideal gas constant, and V represents vapor volume. Boundary conditions of the compressible vapor volume are mass flow rate and enthalpy at the inlet and mass flow rate at the outlet. Meanwhile, the inlet, outlet, and outer surfaces are all assumed to be adiabatic.

#### *2.6.2. Junctions*

Pressure loss in the pipe junctions is negligible. Besides, the junctions are assumed to be adiabatic with no heat loss to the environment. Similar to the reservoir, junctions are modeled by mass balance and energy balance via Eq. (18) and (19), respectively [8].

$$
\dot{m}\_{\text{mix}} = \dot{m}\_1 + \dot{m}\_2 \tag{18}
$$

$$
\dot{m}\_{\text{mix}} h\_{\text{mix}} = \dot{m}\_1 h\_1 + \dot{m}\_2 h\_2 \tag{19}
$$

The junction boundary conditions are mass flow rate and enthalpy at the inlet and the outlet which are considered to be adiabatic.

## **3. System-level dynamic modeling**

The boundary conditions necessary for these valves are pressure and enthalpy at the inlet and

The pressure and heat loss through the pipes containing the liquid state are normally negligible compared with other components. If in a certain case their contribution is found to be considerable, they could be mathematically modeled using the general fluid mechanics principles using pipe-flow pressure loss and heat transfer equations. However, the pipe flow after the evaporators and upstream of the turbine valves are considered as compressible volumes, which has to be taken into account, especially for their dynamic inertia applied to the system [24]. Three equations are utilized in this volume: mass balance, energy balance, and the ideal gas law [25]. Three parameters can be calculated by solving these three equations: working fluid's mass inside the volume, working fluid's mean temperature, and mean pressure inside the volume [8].

*dt* <sup>+</sup> *<sup>m</sup> Cv*

*V* \_\_\_ *dm dt* <sup>+</sup> *<sup>p</sup>*\_\_ *T* \_\_\_ *dT dt* <sup>−</sup> *dp*\_\_\_

mass balance and energy balance via Eq. (18) and (19), respectively [8].

\_\_\_ *dT dt* <sup>=</sup> *<sup>H</sup>*̇

represent inlet and outlet enthalpy flow rate, R represents ideal gas constant, and V represents vapor volume. Boundary conditions of the compressible vapor volume are mass flow rate and enthalpy at the inlet and mass flow rate at the outlet. Meanwhile, the inlet, outlet, and outer

Pressure loss in the pipe junctions is negligible. Besides, the junctions are assumed to be adiabatic with no heat loss to the environment. Similar to the reservoir, junctions are modeled by

*mix* = *m*̇

The junction boundary conditions are mass flow rate and enthalpy at the inlet and the outlet

*mix hmix* = *m*̇

<sup>1</sup> + *m*̇

<sup>1</sup> *h*<sup>1</sup> + *m*̇

*in* <sup>−</sup> *<sup>H</sup>*̇

*out* (16)

in and Ḣ

out

*dt* <sup>=</sup> <sup>0</sup> (17)

<sup>2</sup> (18)

<sup>2</sup> *h*<sup>2</sup> (19)

represents specific heat capacity, Ḣ

pressure at the outlet.

114 Organic Rankine Cycle Technology for Heat Recovery

**2.6. Pipes and junctions**

*u* \_\_\_ *dm*

*RT*\_\_\_

surfaces are all assumed to be adiabatic.

*m*̇

*m*̇

which are considered to be adiabatic.

*2.6.2. Junctions*

where u represents specific internal energy, cv

*2.6.1. Pipes*

## **3.1. Integration of the component dynamic models**

Once dynamic models of every individual component are ready and evaluated with known input state variables and calculated outputs, the components are interconnected to build a thermodynamic model of the whole thermal power system. Before interconnecting the individual component models to each other, the following important issues have to be reviewed:


After above-listed considerations and the preparation of required data, the ORC components will be connected properly to establish the system model. Connecting the component models means uniting the common variables of a specific component to its neighboring components so that the set of components create a closed loop by linking them to each other.

#### **3.2. Initialization of the system simulation model**

Apparently, the initialization of closed-loop dynamic models is a difficult task which should be carefully approached and planned. To initialize the dynamic model, the initial conditions have to be defined appropriately. At some point during the initialization process, one must thoroughly plan the thermodynamic cycle as a steady-state problem to find appropriate states for the initialization of the problem [5]. Initial state points can be set as parameters calculated by a steady-state model in which the analysis is expected to begin in a time domain. Initialization problems require starting arrays for all components, which can also be stored as parameters in the test bench level. Diagnostic and summary variables should also be included in the initial condition list definition [9].

#### **3.3. Input and output parameters and identification of the constraints**

The ORC dynamic model developers must prepare an input/output variable list considering the aspects mentioned in Section 3.1, where all fixed model inputs based on the real-test condition are presented. The model outputs which are to be calculated as a result of the simulation need to be fixed too. Then the variation of the outputs as a function of the time step can be studied and investigated. Besides, different post-processing activities can be considered, using the simulation results.

*3.4.4. Subsystem interaction*

*3.5.1. Matlab/Simulink*

has to be considered and incorporated in the simulation.

In ORC-based heat recovery systems, the operation of the plant that generates heat might be influenced by the integration of the ORC. For such systems, the impact on lateral subsystems

Dynamic Modeling of ORC Power Plants http://dx.doi.org/10.5772/intechopen.78390 117

For example, in an ORC heat recovery system for a heavy-duty truck (experimented and simulated by Grelet et al. [15] and also Xu et al. [17]), the ORC system shares the cooling system of the vehicle and therefore the charge air cooling capacity can be lower, which has a negative impact on the engine performance. Another example is the use of exhaust gas recirculation (EGR) as the heat source in a heat recovery system designed for heavy-duty trucks. This leads to a trade-off between EGR cooling and ORC performance, which could impact negatively the engine emissions. Several other interactions such as the exhaust back pressure or the weight penalty could also be cited. In such heat recovery systems (HRSs), the performance, and thereby the fuel economy, will be dependent on all the aspects mentioned above. It is therefore critical to model the complete system and its surrounding environment in order to optimize the whole integrated setup. It helps to select the best design using simulation and

After reviewing the modeling methodologies of ORC systems, an analysis has been conducted in this section, in order to determine available commercial software that might have been employed as tools for implementing the modeling processes. Other computer-based models within the field of the energy conversion system, available in the open literature, have also been surveyed. The analysis has brought to identify some software that may appear to be proper for the scope. Software that have been used for power cycle modeling purposes are Matlab/Simulink, AMESim, Trnsys, Modelica (OpenModelica, Dymola, Wolfram System Modeler, and MapleSim are all based on Modelica), GateCycle, EES, Phyton, Cycle-Tempo, and GT-SUITE. It should be noted that the analysis of commercial software reported here is neither complete nor exhaustive but is limited to those packages that have been found by the authors to be applicable for dynamic, thermodynamic, and energy modeling purposes. These software have been utilized in order to provide a deeper understanding of their characteristics and a brief description is presented here. Some of these software like GateCycle and Trnsys, while appropriate for some applications, turned out to be improper for the scope of the ORC dynamic analysis, and therefore will not be discussed here. Matlab/Simulink, AMESim, and Modelica feature some common characteristics that make them more suitable for the development of customized dynamic component models of energy systems, for both control purposes

thereby reduce the number of experimental tests needed to be carried out [15].

and optimization. Therefore, they will be further discussed briefly here [18].

Matlab is a high-performance language for technical modeling and computation; the name Matlab stands for matrix laboratory. The Matlab language is a high-level matrix/array language with controls flow statements, functions, data structures, input/output, and objectoriented programming features. Matlab/Simulink is a general purpose software package

**3.5. Survey of available codes for modeling power plant systems**

It has to be kept in mind that the number of unknown variables of the whole system has to be equal to the number of equations so that the differential sets of equations are closed. Otherwise, the equations are not solved or won't have unique results. When the component models are integrated to build the thermal power system, the number of unknown variables for each component will be different from the case when the component models were simulated individually. It is usually helpful if components are connected one by one and simulated step by step to ensure the correct connectivity and the number of input/output variables.

Moreover, the output variable trends are strongly dependent on the constraints forced to the simulation model. Obviously, the output trends will follow the real plant's output when the system constraints imposed during simulation are the same as for the real plant [26].

#### **3.4. Key aspects of ORC power systems to be considered for the analysis**

#### *3.4.1. Working fluid*

There are several aspects to be taken into account when using a working fluid for a specific application. The aspects that have to be considered include fluid deterioration, environmental aspects, as well as boiling, condensation, and freezing temperatures that decide the operating ranges. The above limitations have to be incorporated in the simulation tool.

#### *3.4.2. Heat sources*

The heat sources have different grades of quality (temperature levels) and quantity (amount of thermal energy). The dynamic model has to take into account the possible range of operating temperatures and the amount of thermal energy of the heat sources. If the number of heat sources is larger than one, additional complexity and more challenges for the design of the system (fluid, expansion machine, control, etc.) will arise. Generally, variation in heat source parameters is a common input to the stimulation of the ORC systems, which leads to a dynamic response.

#### *3.4.3. Heat sink*

For a specific ORC application, the heat sink available is usually an independent or commonly used cooling package including radiators containing a coolant, which is cooled by means of cooling fans or an air-cooling module. The integration of a heat recovery system model into the cooling module results in more conclusive and realistic results, which eventually limit the amount of heat that can be converted into useful work. In addition, thermal and mass inertia of the heat sink (cooling module) may affect dynamic behavior and time response of the whole system. Therefore, a complete system analysis including the cooling package is necessary to find the optimal way of recovering the heat from a heat source and to design a reliable control and monitoring system.

#### *3.4.4. Subsystem interaction*

condition are presented. The model outputs which are to be calculated as a result of the simulation need to be fixed too. Then the variation of the outputs as a function of the time step can be studied and investigated. Besides, different post-processing activities can be considered,

It has to be kept in mind that the number of unknown variables of the whole system has to be equal to the number of equations so that the differential sets of equations are closed. Otherwise, the equations are not solved or won't have unique results. When the component models are integrated to build the thermal power system, the number of unknown variables for each component will be different from the case when the component models were simulated individually. It is usually helpful if components are connected one by one and simulated step by step to ensure the correct connectivity and the number of input/output variables.

Moreover, the output variable trends are strongly dependent on the constraints forced to the simulation model. Obviously, the output trends will follow the real plant's output when the

There are several aspects to be taken into account when using a working fluid for a specific application. The aspects that have to be considered include fluid deterioration, environmental aspects, as well as boiling, condensation, and freezing temperatures that decide the operating

The heat sources have different grades of quality (temperature levels) and quantity (amount of thermal energy). The dynamic model has to take into account the possible range of operating temperatures and the amount of thermal energy of the heat sources. If the number of heat sources is larger than one, additional complexity and more challenges for the design of the system (fluid, expansion machine, control, etc.) will arise. Generally, variation in heat source parameters is a common input to the stimulation of the ORC systems, which leads to

For a specific ORC application, the heat sink available is usually an independent or commonly used cooling package including radiators containing a coolant, which is cooled by means of cooling fans or an air-cooling module. The integration of a heat recovery system model into the cooling module results in more conclusive and realistic results, which eventually limit the amount of heat that can be converted into useful work. In addition, thermal and mass inertia of the heat sink (cooling module) may affect dynamic behavior and time response of the whole system. Therefore, a complete system analysis including the cooling package is necessary to find the optimal way of recovering the heat from a heat source and to design a

system constraints imposed during simulation are the same as for the real plant [26].

**3.4. Key aspects of ORC power systems to be considered for the analysis**

ranges. The above limitations have to be incorporated in the simulation tool.

using the simulation results.

116 Organic Rankine Cycle Technology for Heat Recovery

*3.4.1. Working fluid*

*3.4.2. Heat sources*

a dynamic response.

reliable control and monitoring system.

*3.4.3. Heat sink*

In ORC-based heat recovery systems, the operation of the plant that generates heat might be influenced by the integration of the ORC. For such systems, the impact on lateral subsystems has to be considered and incorporated in the simulation.

For example, in an ORC heat recovery system for a heavy-duty truck (experimented and simulated by Grelet et al. [15] and also Xu et al. [17]), the ORC system shares the cooling system of the vehicle and therefore the charge air cooling capacity can be lower, which has a negative impact on the engine performance. Another example is the use of exhaust gas recirculation (EGR) as the heat source in a heat recovery system designed for heavy-duty trucks. This leads to a trade-off between EGR cooling and ORC performance, which could impact negatively the engine emissions. Several other interactions such as the exhaust back pressure or the weight penalty could also be cited. In such heat recovery systems (HRSs), the performance, and thereby the fuel economy, will be dependent on all the aspects mentioned above. It is therefore critical to model the complete system and its surrounding environment in order to optimize the whole integrated setup. It helps to select the best design using simulation and thereby reduce the number of experimental tests needed to be carried out [15].

#### **3.5. Survey of available codes for modeling power plant systems**

After reviewing the modeling methodologies of ORC systems, an analysis has been conducted in this section, in order to determine available commercial software that might have been employed as tools for implementing the modeling processes. Other computer-based models within the field of the energy conversion system, available in the open literature, have also been surveyed. The analysis has brought to identify some software that may appear to be proper for the scope. Software that have been used for power cycle modeling purposes are Matlab/Simulink, AMESim, Trnsys, Modelica (OpenModelica, Dymola, Wolfram System Modeler, and MapleSim are all based on Modelica), GateCycle, EES, Phyton, Cycle-Tempo, and GT-SUITE. It should be noted that the analysis of commercial software reported here is neither complete nor exhaustive but is limited to those packages that have been found by the authors to be applicable for dynamic, thermodynamic, and energy modeling purposes. These software have been utilized in order to provide a deeper understanding of their characteristics and a brief description is presented here. Some of these software like GateCycle and Trnsys, while appropriate for some applications, turned out to be improper for the scope of the ORC dynamic analysis, and therefore will not be discussed here. Matlab/Simulink, AMESim, and Modelica feature some common characteristics that make them more suitable for the development of customized dynamic component models of energy systems, for both control purposes and optimization. Therefore, they will be further discussed briefly here [18].

#### *3.5.1. Matlab/Simulink*

Matlab is a high-performance language for technical modeling and computation; the name Matlab stands for matrix laboratory. The Matlab language is a high-level matrix/array language with controls flow statements, functions, data structures, input/output, and objectoriented programming features. Matlab/Simulink is a general purpose software package suitable for dynamic systems, which is well known among the control community as it offers excellent performance qualities for designing regulation algorithms. It makes the tool an ideal candidate for process and control engineers, working with the same software package. The environment provided by Matlab software facilitates a general overview of all computations step by step, that can be used for a wide range of applications including simulation, data acquisition, data analysis, and visualization as well as scientific and engineering graphics.

The system modeling is carried out in four steps [18]:

nent is chosen.

*3.5.3. Modelica*

control layout.

• Sketch mode: The stage in which different components are linked.

• Run mode: The stage in which the simulation is executed.

• Sub-model mode: The stage in which the physical sub-model associated with each compo-

Modelica language is designed basically for the modeling of multi-component systems to provide an environment in which a virtual system can be built, similar to what is implemented by engineers in real system development. As an example, standard components like compressor, turbine, and heat exchanger can be selected based on the manufacturers' catalogs with related technical interfaces and specifications [27]. For this purpose, some manufacturer's catalogs are proposed to be used with Modelica standard libraries. If a particular subsystem or component doesn't exist in

Mathematical component models are generally described by differential, algebraic, and discrete equations in Modelica. Hence, the solution method of the describing equations doesn't need to be specified by the users. The software decides the algorithm, the computational methodology,

on the free Modelica library ThermoFluid are presented. The library development is carried out in an Airbus Deutschland research project and is focused on obtaining a library for

lyzed (**Figure 5**). The developed model can be used for optimization of specific heat exchangers and evaluation of optimum system configuration as well as for optimization of system

The literature survey concerning non-commercial models of inter-connectable components of energy system networks resulted in very few examples, which has led to the conclusion that this field still lacks a complete and exhaustive review work. The models proposed are mainly developed for specific applications and often are limited concerning scalability, flexibility, or generality. Examples of custom libraries of components for dynamic modeling and analysis

In [29, 30] a modular code for dynamic simulation of a single-shaft gas turbine is presented. The code, called CAMEL, is a modular object-oriented process simulator, for energy

refrigeration systems based

Dynamic Modeling of ORC Power Plants http://dx.doi.org/10.5772/intechopen.78390 119

refrigeration cycle has been ana-

) as the

• Parameter mode: The stage in which the parameters for each sub-model are chosen.

the software library, it can be built by the user based on software standardized interfaces.

or strategy to be used to solve the equations of a particular system and its components.

detailed numerical investigation of refrigeration systems with carbon dioxide (CO<sup>2</sup>

In [28], the results of development of a Modelica library for CO<sup>2</sup>

refrigerant. Using the developed component library a CO<sup>2</sup>

*3.5.4. Customized tools for simulation of energy systems*

of complex energy systems can be found in [29–31].

For the dynamic modeling purpose, Simulink provides a graphical user interface (GUI) for building models as block diagrams, using click-and-drag mouse operations. Because Matlab and Simulink are integrated, one can simulate, analyze, and revise models in either environment at any point. Application of Matlab language code and its integration with the Simulink environment, in order to create the desired models of components considered in the analysis of energy systems, depend on the equations used, the methodology applied, and the input/ output parameters, which will be discussed in the next sections [18].

#### *3.5.2. AMESim*

AMESim is an advanced modeling environment for performing simulations of engineering systems. The main features and applications of this tool are:


The software has the typical feature of an icon-based program and engineering systems can be built by adding symbols or icons to a drawing area. AMESim therefore enables the users to build complex multi-domain system models through an interactive graphical interface. The resulting sketch is easy to understand and offers a logical representation of the system model under investigation. When the sketch is complete, simulation of the system proceeds in the following stages:


The system modeling is carried out in four steps [18]:


#### *3.5.3. Modelica*

suitable for dynamic systems, which is well known among the control community as it offers excellent performance qualities for designing regulation algorithms. It makes the tool an ideal candidate for process and control engineers, working with the same software package. The environment provided by Matlab software facilitates a general overview of all computations step by step, that can be used for a wide range of applications including simulation, data acquisition, data analysis, and visualization as well as scientific and engineering graphics.

For the dynamic modeling purpose, Simulink provides a graphical user interface (GUI) for building models as block diagrams, using click-and-drag mouse operations. Because Matlab and Simulink are integrated, one can simulate, analyze, and revise models in either environment at any point. Application of Matlab language code and its integration with the Simulink environment, in order to create the desired models of components considered in the analysis of energy systems, depend on the equations used, the methodology applied, and the input/

AMESim is an advanced modeling environment for performing simulations of engineering

• performance evaluation of intelligent systems from the early stage of development until

• the optimization of interactions between subsystems of a multi-mechanism system like

• overall product quality and performance improvement through exploration of critical

• enhancing the product development process using novel design features and applying

The software has the typical feature of an icon-based program and engineering systems can be built by adding symbols or icons to a drawing area. AMESim therefore enables the users to build complex multi-domain system models through an interactive graphical interface. The resulting sketch is easy to understand and offers a logical representation of the system model under investigation. When the sketch is complete, simulation of the system proceeds in the

• Graphical representation of the components is associated with the mathematical models.

• Graphical representation of the results is prepared and post-processing is performed to

electric/electronic, mechanical, hydraulic, pneumatic, and thermal systems;

output parameters, which will be discussed in the next sections [18].

systems. The main features and applications of this tool are:

on-site application of the system;

118 Organic Rankine Cycle Technology for Heat Recovery

functions and design update;

• The component parameters are defined.

customize the results' visualization.

proper algorithms.

following stages:

• The system is simulated.

*3.5.2. AMESim*

Modelica language is designed basically for the modeling of multi-component systems to provide an environment in which a virtual system can be built, similar to what is implemented by engineers in real system development. As an example, standard components like compressor, turbine, and heat exchanger can be selected based on the manufacturers' catalogs with related technical interfaces and specifications [27]. For this purpose, some manufacturer's catalogs are proposed to be used with Modelica standard libraries. If a particular subsystem or component doesn't exist in the software library, it can be built by the user based on software standardized interfaces.

Mathematical component models are generally described by differential, algebraic, and discrete equations in Modelica. Hence, the solution method of the describing equations doesn't need to be specified by the users. The software decides the algorithm, the computational methodology, or strategy to be used to solve the equations of a particular system and its components.

In [28], the results of development of a Modelica library for CO<sup>2</sup> refrigeration systems based on the free Modelica library ThermoFluid are presented. The library development is carried out in an Airbus Deutschland research project and is focused on obtaining a library for detailed numerical investigation of refrigeration systems with carbon dioxide (CO<sup>2</sup> ) as the refrigerant. Using the developed component library a CO<sup>2</sup> refrigeration cycle has been analyzed (**Figure 5**). The developed model can be used for optimization of specific heat exchangers and evaluation of optimum system configuration as well as for optimization of system control layout.

#### *3.5.4. Customized tools for simulation of energy systems*

The literature survey concerning non-commercial models of inter-connectable components of energy system networks resulted in very few examples, which has led to the conclusion that this field still lacks a complete and exhaustive review work. The models proposed are mainly developed for specific applications and often are limited concerning scalability, flexibility, or generality. Examples of custom libraries of components for dynamic modeling and analysis of complex energy systems can be found in [29–31].

In [29, 30] a modular code for dynamic simulation of a single-shaft gas turbine is presented. The code, called CAMEL, is a modular object-oriented process simulator, for energy

significant modeling techniques are applied in order to generate components applicable to

Dynamic Modeling of ORC Power Plants http://dx.doi.org/10.5772/intechopen.78390 121

Dynamic models are necessary for the better understanding of the ORC plants' behavior during transient operation, such as start-up, shutdown, and during rapid load changes. The estimation of plant operating parameters during transient operation is crucial for monitoring and control of the plant so that the system state variables do not exceed the pre-defined operating ranges. Using dynamic models enables plant operators to predict changes in power output as a function of the plant's boundary conditions such as temperature of the heat source and ambient conditions, so that they can respond to the expected heat and power demand

Key elements of an ORC dynamic model are firstly the proper transient configuration of the component's sub-models and secondly the assembly of individual sub-models to build the whole system model. Thermal and mass inertia of the components (component body and

Arrangement of the input/output variables and the system constraints play an important role in receiving reliable results. The fixed input state variables and constraints of the model have

For the dynamic modeling of an ORC system the initial conditions have to be defined and applied appropriately to the model for simulation initialization. All system variables have to be pre-defined as an array at the starting time based on the assumed initial state conditions. Obviously, the initial conditions have to be set up based on the purpose of the dynamic analysis: start-up, shut-down, system response to an input, or any other operating modes. For many cases, the initial conditions can be generated as a result of a steady-state simulation

For transient modeling of ORC plants, one can either use suitable commercial software or open source codes for formulation and parameter selection flexibility. Some ready-made data libraries for system components as well as material properties have been developed and cus-

In sum, the following general steps are defined and proposed based on ORC power plants'

**1.** specifying the modeling assumptions for every single component as well as the whole

**2.** validation of the component models, to guarantee validity and accuracy for both steady-

containing fluid) are two decisive factors for the system's response time.

to be coincident with the real plant fixed and controlled variables.

with the initial operating condition setup of the system.

dynamic modeling framework:

state and transient conditions;

tomized for the transient modeling of thermal power systems.

system according to the purpose of the analysis and application;

**3.** parameterizing the ORC components and the boundary sources and sinks;

any kind of micro-turbine-based energy conversion system.

**4. Conclusion**

accordingly.

**Figure 5.** Modelica object diagram of a CO<sup>2</sup> cooling cycle [28].

conversion system (with specific reference to micro-turbines), and the modeling method is a black-box approach. Each component of the system under analysis can be assembled in an engineering process scheme where the connections between two elements represent either mechanical power coupling or a working fluid stream. The code is devoted to energy system design and is based on C++. For each separate component, a proper set of first-order (linear/ non-linear) algebraic or differential equations are cast and all the block equations pertaining to the different blocks are assembled together and solved in matrix form, once assigned proper boundary conditions and parameters. Equations are integrated in time according to a fourth-order Runge-Kutta method. The code is used for both steady-state off-design and dynamic operating conditions.

In another original code [31] called TRANSEO, transient and dynamic simulation of microgas turbine-based systems is presented. The code is a model-based software developed in the Simulink platform The library features some advanced components such as heat exchangers, which are modeled according to finite volume approach. Many of the blocks have been validated with reference to a commercial recuperated micro-turbine. From the models realized, some advance-cycle configurations have been proposed and analyzed: for example, externally fired micro-turbine cycles, closed Brayton cycles for space applications, and hybrid micro-turbine fuel cell systems. The library indeed provides some advanced components, and significant modeling techniques are applied in order to generate components applicable to any kind of micro-turbine-based energy conversion system.

## **4. Conclusion**

conversion system (with specific reference to micro-turbines), and the modeling method is a black-box approach. Each component of the system under analysis can be assembled in an engineering process scheme where the connections between two elements represent either mechanical power coupling or a working fluid stream. The code is devoted to energy system design and is based on C++. For each separate component, a proper set of first-order (linear/ non-linear) algebraic or differential equations are cast and all the block equations pertaining to the different blocks are assembled together and solved in matrix form, once assigned proper boundary conditions and parameters. Equations are integrated in time according to a fourth-order Runge-Kutta method. The code is used for both steady-state off-design and

cooling cycle [28].

In another original code [31] called TRANSEO, transient and dynamic simulation of microgas turbine-based systems is presented. The code is a model-based software developed in the Simulink platform The library features some advanced components such as heat exchangers, which are modeled according to finite volume approach. Many of the blocks have been validated with reference to a commercial recuperated micro-turbine. From the models realized, some advance-cycle configurations have been proposed and analyzed: for example, externally fired micro-turbine cycles, closed Brayton cycles for space applications, and hybrid micro-turbine fuel cell systems. The library indeed provides some advanced components, and

dynamic operating conditions.

**Figure 5.** Modelica object diagram of a CO<sup>2</sup>

120 Organic Rankine Cycle Technology for Heat Recovery

Dynamic models are necessary for the better understanding of the ORC plants' behavior during transient operation, such as start-up, shutdown, and during rapid load changes. The estimation of plant operating parameters during transient operation is crucial for monitoring and control of the plant so that the system state variables do not exceed the pre-defined operating ranges. Using dynamic models enables plant operators to predict changes in power output as a function of the plant's boundary conditions such as temperature of the heat source and ambient conditions, so that they can respond to the expected heat and power demand accordingly.

Key elements of an ORC dynamic model are firstly the proper transient configuration of the component's sub-models and secondly the assembly of individual sub-models to build the whole system model. Thermal and mass inertia of the components (component body and containing fluid) are two decisive factors for the system's response time.

Arrangement of the input/output variables and the system constraints play an important role in receiving reliable results. The fixed input state variables and constraints of the model have to be coincident with the real plant fixed and controlled variables.

For the dynamic modeling of an ORC system the initial conditions have to be defined and applied appropriately to the model for simulation initialization. All system variables have to be pre-defined as an array at the starting time based on the assumed initial state conditions. Obviously, the initial conditions have to be set up based on the purpose of the dynamic analysis: start-up, shut-down, system response to an input, or any other operating modes. For many cases, the initial conditions can be generated as a result of a steady-state simulation with the initial operating condition setup of the system.

For transient modeling of ORC plants, one can either use suitable commercial software or open source codes for formulation and parameter selection flexibility. Some ready-made data libraries for system components as well as material properties have been developed and customized for the transient modeling of thermal power systems.

In sum, the following general steps are defined and proposed based on ORC power plants' dynamic modeling framework:


**4.** defining the operating ranges and limitations for all components and introducing them to individual component models;

[5] Twomey BL. Dynamic simulation and experimental validation of an organic Rankine cycle model [PhD thesis]. University of Queensland, School of Mechanical and Mining

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[8] van Putten H, Colonna Paliano P. Dynamic modeling of steam power cycles: Part II—Simulation of a small simple Rankine cycle system. Applied Thermal Engineering.

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[10] Casella F, Mathijssen T, Colonna di Paliano P, Buijtenen J. Dynamic modeling of organic Rankine cycle power systems. Journal of Engineering for Gas Turbines and Power.

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## **Author details**

Mohsen Assadi1 \* and Yaser Mollaei Barzi<sup>2</sup>

\*Address all correspondence to: mohsen.assadi@uis.no

1 Department of Energy and Petroleum Engineering, University of Stavanger, Stavanger, Norway

2 Department of Mechanical Engineering, Islamic Azad University, Kaeshan Branch, Kashan, Iran

## **References**


[5] Twomey BL. Dynamic simulation and experimental validation of an organic Rankine cycle model [PhD thesis]. University of Queensland, School of Mechanical and Mining Engineering; 2015

**4.** defining the operating ranges and limitations for all components and introducing them to

**5.** defining appropriate known and unknown (input/output) variables for the system, based on the design and analysis requirements and strategies. This may lead to omitting unnecessary fixed variables of the individual component models or adding new fixed common

**7.** compiling, executing and diagnosis of the system model, first for steady-state conditions;

1 Department of Energy and Petroleum Engineering, University of Stavanger, Stavanger,

[1] William J. Baumol, Economic Dynamics: An Introduction, 3rd edition, London: Collier-

[2] North GR. Lessons from energy balance models, In: Schlesinger ME. (Eds.), Physically-Based Modeling and Simulation of Climate and Climatic Change, NATO ASI Series (Series C: Mathematical and Physical Sciences), Vol. 243. Springer, Dordrecht, pp. 627-651,

[3] Mollayi Barzi Y, Ghassemi M, Hamedi MH. A 2D transient numerical model combining heat/mass transport effects in a tubular solid oxide fuel cell. Journal of Power Sources.

[4] Franco A, Villani M. Optimal design of binary cycle power plants for water-dominated,

medium-temperature geothermal fields. Geothermics. 2009;**38**(4):379-391

2 Department of Mechanical Engineering, Islamic Azad University, Kaeshan Branch,

**6.** interconnecting the ORC components properly to build the whole system model;

**10.** customizing the dynamic model for a particular purpose or application.

individual component models;

122 Organic Rankine Cycle Technology for Heat Recovery

**8.** initial condition definition and data preparation;

**9.** running the transient model, diagnosis and validation;

\* and Yaser Mollaei Barzi<sup>2</sup>

\*Address all correspondence to: mohsen.assadi@uis.no

Macmillan. pp. 160, 1970. ISBN: 0-02-306660-1

1988. ISBN 90-277-2789-9

2009;**192**:200-207

state variables;

**Author details**

Mohsen Assadi1

Norway

Kashan, Iran

**References**


[19] Bestrin R, Vermeulen AG. Mathematical modeling and analysis of vapour compression system. International Report. Eindhoven, Netherlands: University of Technology; August 2003

**Section 3**

**Applications**


**Section 3**
