**2. 1-D engine simulation**

1-D simulation tools are based on the solution of the inviscid form of the conservation laws of mass, momentum and energy (Euler equations). The equations are actually written in a 'generalized' form, in which ad-hoc terms are added, in order to properly simulate the friction and heat-exchange effects at the pipe walls. Furthermore, they are written in a quasi 1-D approach, as the variations of any dependent variable in a direction orthogonal to the flow direction are neglected, and at the same time the changes in the flow cross-section along the pipe axis are accounted for.

In the last two decades, several commercial 1-D CFD tools have specifically been developed for engine flow simulation: among others, GT-Power (Gamma Technologies), Wave (Ricardo), Boost (AVL), and AMESim (LSM). Among the different classes of computational models, such tools are often a good compromise between accuracy, the required CPU time, and completeness of the engine system that can be analyzed.

Numerical Simulation Techniques for the

the following subsection.

Unburned-gas region:

non-predictive or predictive.

Cylinder content:

Prediction of Fluid-Dynamics, Combustion and Performance in IC Engines Fuelled by CNG 261

high-pressure phase, flow leakages from the combustion chamber are usually neglected, which means that the trapped-air mass *mcyl* is considered constant. The charge thermodynamic state can be calculated, prior to the start of combustion, by solving the First Law of Thermodynamics, under the assumption of a constant mass and considering a

It should be noted that a suitable correlation for the heat transfer between the charge and the cylinder walls is needed (Catania et al., 2001; Heywood, 1988): this point will be discussed in

After the onset of combustion, four variables are required, whenever the two-zone approach is followed, to define the charge state, at each time step: pressure (p), unburned and burned-

Although the exact set of equations which is actually implemented can be different from one distributed code to another, a general framework exists. The required variables are calculated by implementing a suitable form of the energy conservation equation for the unburned zone and for the whole cylinder content, of the conservation of the instantaneous

The formulation of the energy conservation law is common to both simulation and

The conservation of the chamber volume can be used to derive an equation that links the

The enthalpy of the burned and unburned gases is determined in Eqs. (4-5) for each chemical species, by means of polynomial functions of the gas temperature. JANAF tables can be used for this purpose (Baratta et al., 2006; Catania et al., 2003, 2004). The unburnedgas enthalpy includes the contribution of the fuel chemical energy which is released during combustion. The equation set is closed by introducing a 'combustion model', that allows xb in Eqs. (4-6) to be defined. Combustion modelling is a fundamental feature of engine simulation codes. Its primary objective is to predict, or to specify, the rate of heat release (that is, the rate at which the chemical energy of a fuel is converted into thermal energy of burned gases) and hence the in-cylinder pressure evolution. Basically, the combustion model can be

A non-predictive combustion model simply imposes a burn rate as a function of the crank angle. The prescribed burn rate will be followed, regardless of the conditions inside the

1 *u bcyl bucylb b cylu cylb b dQ dQ V dp i i m dx x m di m x di* (5)

*b uu b bb*

*x RT xRT*

diagnostic models, and can be written in the following form (Catania et al., 2003):

pressure at a given crank angle to Tu, Tb, and xb (Baratta et al., 2006):

p 1 *cyl*

*cyl*

*m*

*V*

gas temperature (Tu and Tb, respectively), and burned-mass fraction ( *b b*

cylinder volume, and of a so-called 'combustion model'.

*cyl cyl cyl dQ pdV m dU* (3)

*u u bc* 1 *yl u dQ V dp x m di* (4)

(6)

*b*

*x*

*tot b u m m*

).

*m mm*

uniform temperature distribution inside the chamber (single-zone approach):

1-D codes are designed to simulate the unsteady flow throughout the whole engine system, as well as throughout the whole engine cycle. The essential processes of the complete engine system are described by means of mathematical equations in such a way that the physical states, such as pressures, temperatures and mass flows, can be calculated in all the computational volumes and at all the instants. These codes allow the calculation of any engine-relevant cycle-averaged parameter which is useful for the assessment of the engine performance: torque, power, indicated work, volumetric efficiency, fuel consumption, and so on. Engine-oriented 1-D codes have increasingly been used in order to support the engine design phase (Winterbone & Pearson, 1990; Blair, 1999). Their application usually starts from the calibration of an engine model in a 'baseline' configuration, on the basis of experimental data. Then, the predictive model is used to estimate the impact of a different engine configuration on the performance, the efficiency and the emission levels: among others, the inlet and exhaust pipes length and diameter, the turbocharger characteristics, the valve actuation and timing, and the combustion-management strategies, can be modified (Badami et al., 2002; Baratta et al., 2010; Galindo et al., 2004; Vitek et al., 2006). 1-D codes are often used to provide time-dependent boundary conditions for three-dimensional incylinder turbulent-flow simulations.

The quasi 1-D approach is adopted in the engine intake and exhaust systems, which can be considered as assemblies of pipe elements. Other engine components are modelled by means of the zero-dimensional approach, usually combined with ad-hoc lumped parameter models or performance maps. Cylinders, injectors, valves, compressors and turbines are simulated in this way, and their behaviour is properly coupled to that of the 1-D computational domain.

A brief overview of the main engine-components modelling approaches is provided hereafter. Then, the main issues concerning the model tuning procedure are discussed.

#### **2.1 Cylinders**

For the mathematical description of the physical processes that occur within cylinders, it is worth distinguishing between the gas exchange and the high-pressure phase. Only during the gas exchange, do mass flows occur between the cylinder and the connected pipes and manifolds through the valves. Cylinders are usually zero-dimensional parts in which a uniform pressure is assumed. The temperature is considered uniform in the gas exchange phase and in the high-pressure cycle prior to the start of combustion, whereas a two-zone (burnedunburned) methodology is followed after the start of combustion and prior to the opening of the exhaust valve (see, for example, Gamma Technologies, 2009). Sometimes a multizone approach is followed, in order to accurately describe the burned-gas temperature distribution and the pollutant formation mechanisms (Baratta et al., 2006, 2008; Onorati et al., 2003). When one or more valves are open, the cylinder-content evolution is governed by the continuity equation and the First Law of Thermodynamics:

$$dm\_{cyl} = \left(\dot{m}\_{in} - \dot{m}\_{out}\right)dt\tag{1}$$

$$-dQ + pdV\_{cyl} = d\left(m\_{cyl}lI\_{cyl}\right) + \left(\dot{m}\_{out}\dot{i}\_{cyl} - \dot{m}\_{in}\dot{i}\_{in}\right)dt\tag{2}$$

in which the symbols U and i denote the internal energy and the enthalpy, respectively, *Q* is the heat transfer to the walls, and *Vcyl* is the instantaneous chamber volume. During the high-pressure phase, flow leakages from the combustion chamber are usually neglected, which means that the trapped-air mass *mcyl* is considered constant. The charge thermodynamic state can be calculated, prior to the start of combustion, by solving the First Law of Thermodynamics, under the assumption of a constant mass and considering a uniform temperature distribution inside the chamber (single-zone approach):

$$-dQ + pdV\_{cyl} = m\_{cyl}d\mathcal{LI}\_{cyl} \tag{3}$$

It should be noted that a suitable correlation for the heat transfer between the charge and the cylinder walls is needed (Catania et al., 2001; Heywood, 1988): this point will be discussed in the following subsection.

After the onset of combustion, four variables are required, whenever the two-zone approach is followed, to define the charge state, at each time step: pressure (p), unburned and burned-

gas temperature (Tu and Tb, respectively), and burned-mass fraction ( *b b b tot b u m m x m mm* ).

Although the exact set of equations which is actually implemented can be different from one distributed code to another, a general framework exists. The required variables are calculated by implementing a suitable form of the energy conservation equation for the unburned zone and for the whole cylinder content, of the conservation of the instantaneous cylinder volume, and of a so-called 'combustion model'.

The formulation of the energy conservation law is common to both simulation and diagnostic models, and can be written in the following form (Catania et al., 2003): Unburned-gas region:

$$-d\mathbb{Q}\_u + V\_u d\boldsymbol{p} = \left(\mathbf{1} - \mathbf{x}\_b\right) m\_{cyl} d\mathbf{i}\_u \tag{4}$$

Cylinder content:

260 Computational Simulations and Applications

1-D codes are designed to simulate the unsteady flow throughout the whole engine system, as well as throughout the whole engine cycle. The essential processes of the complete engine system are described by means of mathematical equations in such a way that the physical states, such as pressures, temperatures and mass flows, can be calculated in all the computational volumes and at all the instants. These codes allow the calculation of any engine-relevant cycle-averaged parameter which is useful for the assessment of the engine performance: torque, power, indicated work, volumetric efficiency, fuel consumption, and so on. Engine-oriented 1-D codes have increasingly been used in order to support the engine design phase (Winterbone & Pearson, 1990; Blair, 1999). Their application usually starts from the calibration of an engine model in a 'baseline' configuration, on the basis of experimental data. Then, the predictive model is used to estimate the impact of a different engine configuration on the performance, the efficiency and the emission levels: among others, the inlet and exhaust pipes length and diameter, the turbocharger characteristics, the valve actuation and timing, and the combustion-management strategies, can be modified (Badami et al., 2002; Baratta et al., 2010; Galindo et al., 2004; Vitek et al., 2006). 1-D codes are often used to provide time-dependent boundary conditions for three-dimensional in-

The quasi 1-D approach is adopted in the engine intake and exhaust systems, which can be considered as assemblies of pipe elements. Other engine components are modelled by means of the zero-dimensional approach, usually combined with ad-hoc lumped parameter models or performance maps. Cylinders, injectors, valves, compressors and turbines are simulated in this way, and their behaviour is properly coupled to that of the 1-D

A brief overview of the main engine-components modelling approaches is provided hereafter. Then, the main issues concerning the model tuning procedure are discussed.

For the mathematical description of the physical processes that occur within cylinders, it is worth distinguishing between the gas exchange and the high-pressure phase. Only during the gas exchange, do mass flows occur between the cylinder and the connected pipes and manifolds through the valves. Cylinders are usually zero-dimensional parts in which a uniform pressure is assumed. The temperature is considered uniform in the gas exchange phase and in the high-pressure cycle prior to the start of combustion, whereas a two-zone (burnedunburned) methodology is followed after the start of combustion and prior to the opening of the exhaust valve (see, for example, Gamma Technologies, 2009). Sometimes a multizone approach is followed, in order to accurately describe the burned-gas temperature distribution and the pollutant formation mechanisms (Baratta et al., 2006, 2008; Onorati et al., 2003). When one or more valves are open, the cylinder-content evolution is governed by the

in which the symbols U and i denote the internal energy and the enthalpy, respectively, *Q* is the heat transfer to the walls, and *Vcyl* is the instantaneous chamber volume. During the

*dm m m dt cyl in out* (1)

*dQ pdV d m U m i m i dt cyl cyl cyl out cyl in in* (2)

continuity equation and the First Law of Thermodynamics:

cylinder turbulent-flow simulations.

computational domain.

**2.1 Cylinders** 

$$-\left(dQ\_u + dQ\_b\right) + V\_{cyl}d\mathbf{p} = \left(i\_b - i\_u\right)m\_{cyl}d\mathbf{x}\_b + \left(1 - \mathbf{x}\_b\right)m\_{cyl}d\mathbf{i}\_u + m\_{cyl}\mathbf{x}\_b d\mathbf{i}\_b\tag{5}$$

The conservation of the chamber volume can be used to derive an equation that links the pressure at a given crank angle to Tu, Tb, and xb (Baratta et al., 2006):

$$\mathbf{p} = \frac{m\_{cyl}}{V\_{cyl}} \left[ \left( \mathbf{1} - \mathbf{x}\_b \right) R\_u T\_u + \mathbf{x}\_b R\_b T\_b \right] \tag{6}$$

The enthalpy of the burned and unburned gases is determined in Eqs. (4-5) for each chemical species, by means of polynomial functions of the gas temperature. JANAF tables can be used for this purpose (Baratta et al., 2006; Catania et al., 2003, 2004). The unburnedgas enthalpy includes the contribution of the fuel chemical energy which is released during combustion. The equation set is closed by introducing a 'combustion model', that allows xb in Eqs. (4-6) to be defined. Combustion modelling is a fundamental feature of engine simulation codes. Its primary objective is to predict, or to specify, the rate of heat release (that is, the rate at which the chemical energy of a fuel is converted into thermal energy of burned gases) and hence the in-cylinder pressure evolution. Basically, the combustion model can be non-predictive or predictive.

A non-predictive combustion model simply imposes a burn rate as a function of the crank angle. The prescribed burn rate will be followed, regardless of the conditions inside the

Numerical Simulation Techniques for the

included in the engine model.

law was proposed in (Catania et al., 2001):

that has to be calibrated.

available in the market.

**2.3 Turbochargers** 

Prediction of Fluid-Dynamics, Combustion and Performance in IC Engines Fuelled by CNG 263

H2, and on an energy balance of the whole cylinder charge, from the start to the end of combustion. When the correlation is employed for predictive indicated-cycle calculations, the heat transfer coefficient can be set on the basis of experience previously acquired on similar engines, or can be calibrated at a few engine working points with the support of experimental tests, combined with diagnostic analysis. Lookup tables for c0 can then be

A different approach can be followed if a predictive combustion model is applied, as will be detailed in the 'Predictive 0-D combustion models' section of this chapter. Since such a combustion model needs the support of a zero-dimensional in-cylinder fluid flow and turbulence submodels, the same flow model is sometimes used to estimate an equivalent fluid velocity and, hence, the convective heat transfer coefficient (see, for example, Gamma

Although most of engine 1-D simulation codes determine the instantaneous heat flux through Eq. (7), many research works (Alkidas, 1980; Catania et al., 2001; Enomoto & Furuhama, 1989) have pointed out a phase lag and an attenuation of the heat flux calculated using the conventional convection law, with respect to the measured heat-flux distributions vs. crank angle. For this reason, in order to take the unsteadiness of the gas-wall temperature difference into account, the following unsteady formulation for Newton's convection

*p*

where: B is the bore diameter, Sp the mean piston speed, and K a dimensionless coefficient

The turbocharger sub-model is a critical part of the overall model of a turbocharged engine. The approach followed in most 1-D simulation tools is to include turbocharger performance data in the form of lookup tables (Gamma Technologies, 2009), which are processed by the software in order to obtain the final interpolated maps. The interpolation procedure can be either fully automatic or partially controlled by the user. However, the final map quality is dependent to a great extent on the amount and quality of the available experimental data,

The detailed turbocharger modelling technique which is followed by the GT-Power code is described hereafter. The approach is similar to those followed by the other codes that are

GT-Power handles measured compressor and turbine performance tables in SAE format, in which the data are organized as several "speed lines" according to standards J922 and J1826. The data for each speed line consist of mass flow rate, pressure ratio and thermodynamic efficiency triplets. As an example, Fig. 1 shows the raw turbine map data for a turbocharger which is installed on a 7.8 litre CNG engine (Baratta et al., 2010), in terms of reduced mass flow (graph on the left) and efficiency (graph on the right) versus pressure ratio for different speed lines. Quantities on abscissa and vertical axis have been normalized to their maximum value. Each coloured line refers to a different reduced speed nred. In GT-Power, the performance tables are pre-processed so as to create internal maps that define the

*<sup>w</sup>*

(9)

Technologies, 2009; Hountalas & Pariotis, 2001; Morel & Keribar, 1985).

*w*

*<sup>B</sup> dT T Q hA T T K S dt*

which are usually measured in a flow rig under steady-state conditions.

cylinder. With reference to SI engines, the Wiebe function allows the almost S-shape of experimentally observed burn rates to be reproduced (Heywood, 1988). The Wiebe function is completely straightforward to apply, but on the other hand, it does not contain any description of the various physical phenomena, such as the in-cylinder turbulence level or flame-turbulence interaction. Hence, such an approach should only be followed when the purpose of the engine simulation model is to investigate the effect of a variable that virtually does not influence the burn rate. The accuracy of the Wiebe-function approach can be enhanced by including ad-hoc lookup tables in the model for the Wiebe parameters. This procedure has successfully been followed by many researchers (see, for example, Baratta et al., 2010; Lefebvre & Guilain, 2005). In (Baratta et al., 2010), a large number of experiments were carried out on an engine test rig under steady-state operating conditions at different engine speed (N) and brake mean effective pressure (bmep) values. A heat-release analysis was then carried out with the specific tools embedded in GT-Power, and the obtained parameters were organized in lookup tables as functions of N and bmep.

An alternative approach, which was pioneered in (Blizzard & Keck, 1974), is to use predictive combustion models. These models consist of phenomenological correlations for the turbulent burning speed, and are based on physical principles, so that they can account for any changes in the in-cylinder flow, combustion chamber geometry, mixture properties and thermodynamic state, spark timing, and so on. The topic of predictive combustion models will be dealth with in a dedicated section of this chapter.

#### **2.2 In-cylinder heat transfer**

In a zero-dimensional first-law analysis of the indicated cycle in an IC engine (Eqs. 1-6), the heat transfer term has to be estimated. This is usually done on an instantaneous, spatially average basis, using Newton's law:

$$\frac{dQ}{dt} = h \cdot A \cdot \left(T - T\_w\right) \tag{7}$$

where *h* is the convective heat-transfer coefficient, *A* is the gas-wall contact area, *T* is the gas temperature, *Tw* is the wall temperature. The Woschni correlation (Sihling & Woschni, 1979; Woschni, 1967) is by far the most frequently applied relation for this purpose. The Woschni correlation defines a spatially-averaged convective coefficient:

$$\ln\left[\frac{W}{m^2K}\right] = c\_0 \cdot D\left[m\right]^{-0.2} p\left[bar\right]^{0.8} T\left[K\right]^{-0.55} w\left[\frac{m}{s}\right]^{0.8} \tag{8}$$

where, in the original Woschni's paper, c0=130, and w is an average gas velocity, which was assumed to be made up of a term proportional to the mean piston speed, and another proportional to the difference between the instantaneous pressure and the instantaneous motored pressure (at the same crank angle).

As far as the c0 coefficient is concerned, there is evidence in the literature that a fine tuning is needed if accurate results are desired (Baratta et al., 2005; Catania et al., 2003; Guezennec & Hamada, 1999). Tuning can be performed when the Woschni correlation is applied to estimate the heat transfer in a diagnostic tool, in which the experimental in-cylinder pressure trace is analyzed and the heat-release law is calculated. For example, a method for calibrating the heat transfer coefficient was proposed and assessed in (Catania et al., 2003), based on the measurement of the exhaust emissions, with specific reference to HC, CO, and H2, and on an energy balance of the whole cylinder charge, from the start to the end of combustion. When the correlation is employed for predictive indicated-cycle calculations, the heat transfer coefficient can be set on the basis of experience previously acquired on similar engines, or can be calibrated at a few engine working points with the support of experimental tests, combined with diagnostic analysis. Lookup tables for c0 can then be included in the engine model.

A different approach can be followed if a predictive combustion model is applied, as will be detailed in the 'Predictive 0-D combustion models' section of this chapter. Since such a combustion model needs the support of a zero-dimensional in-cylinder fluid flow and turbulence submodels, the same flow model is sometimes used to estimate an equivalent fluid velocity and, hence, the convective heat transfer coefficient (see, for example, Gamma Technologies, 2009; Hountalas & Pariotis, 2001; Morel & Keribar, 1985).

Although most of engine 1-D simulation codes determine the instantaneous heat flux through Eq. (7), many research works (Alkidas, 1980; Catania et al., 2001; Enomoto & Furuhama, 1989) have pointed out a phase lag and an attenuation of the heat flux calculated using the conventional convection law, with respect to the measured heat-flux distributions vs. crank angle. For this reason, in order to take the unsteadiness of the gas-wall temperature difference into account, the following unsteady formulation for Newton's convection law was proposed in (Catania et al., 2001):

$$Q = h \cdot A \cdot \left[ T - T\_w + K \frac{B}{S\_p} \frac{d\left(T - T\_w\right)}{dt} \right] \tag{9}$$

where: B is the bore diameter, Sp the mean piston speed, and K a dimensionless coefficient that has to be calibrated.

## **2.3 Turbochargers**

262 Computational Simulations and Applications

cylinder. With reference to SI engines, the Wiebe function allows the almost S-shape of experimentally observed burn rates to be reproduced (Heywood, 1988). The Wiebe function is completely straightforward to apply, but on the other hand, it does not contain any description of the various physical phenomena, such as the in-cylinder turbulence level or flame-turbulence interaction. Hence, such an approach should only be followed when the purpose of the engine simulation model is to investigate the effect of a variable that virtually does not influence the burn rate. The accuracy of the Wiebe-function approach can be enhanced by including ad-hoc lookup tables in the model for the Wiebe parameters. This procedure has successfully been followed by many researchers (see, for example, Baratta et al., 2010; Lefebvre & Guilain, 2005). In (Baratta et al., 2010), a large number of experiments were carried out on an engine test rig under steady-state operating conditions at different engine speed (N) and brake mean effective pressure (bmep) values. A heat-release analysis was then carried out with the specific tools embedded in GT-Power, and the obtained

An alternative approach, which was pioneered in (Blizzard & Keck, 1974), is to use predictive combustion models. These models consist of phenomenological correlations for the turbulent burning speed, and are based on physical principles, so that they can account for any changes in the in-cylinder flow, combustion chamber geometry, mixture properties and thermodynamic state, spark timing, and so on. The topic of predictive combustion

In a zero-dimensional first-law analysis of the indicated cycle in an IC engine (Eqs. 1-6), the heat transfer term has to be estimated. This is usually done on an instantaneous, spatially

*dQ hA T T*

where *h* is the convective heat-transfer coefficient, *A* is the gas-wall contact area, *T* is the gas temperature, *Tw* is the wall temperature. The Woschni correlation (Sihling & Woschni, 1979; Woschni, 1967) is by far the most frequently applied relation for this purpose. The Woschni

where, in the original Woschni's paper, c0=130, and w is an average gas velocity, which was assumed to be made up of a term proportional to the mean piston speed, and another proportional to the difference between the instantaneous pressure and the instantaneous

As far as the c0 coefficient is concerned, there is evidence in the literature that a fine tuning is needed if accurate results are desired (Baratta et al., 2005; Catania et al., 2003; Guezennec & Hamada, 1999). Tuning can be performed when the Woschni correlation is applied to estimate the heat transfer in a diagnostic tool, in which the experimental in-cylinder pressure trace is analyzed and the heat-release law is calculated. For example, a method for calibrating the heat transfer coefficient was proposed and assessed in (Catania et al., 2003), based on the measurement of the exhaust emissions, with specific reference to HC, CO, and

*W m h c D m p bar T K w m K <sup>s</sup>*

0.2 0.8 0.55

(8)

*<sup>w</sup>*

*dt* (7)

0.8

parameters were organized in lookup tables as functions of N and bmep.

models will be dealth with in a dedicated section of this chapter.

correlation defines a spatially-averaged convective coefficient:

2 0

motored pressure (at the same crank angle).

**2.2 In-cylinder heat transfer** 

average basis, using Newton's law:

The turbocharger sub-model is a critical part of the overall model of a turbocharged engine. The approach followed in most 1-D simulation tools is to include turbocharger performance data in the form of lookup tables (Gamma Technologies, 2009), which are processed by the software in order to obtain the final interpolated maps. The interpolation procedure can be either fully automatic or partially controlled by the user. However, the final map quality is dependent to a great extent on the amount and quality of the available experimental data, which are usually measured in a flow rig under steady-state conditions.

The detailed turbocharger modelling technique which is followed by the GT-Power code is described hereafter. The approach is similar to those followed by the other codes that are available in the market.

GT-Power handles measured compressor and turbine performance tables in SAE format, in which the data are organized as several "speed lines" according to standards J922 and J1826. The data for each speed line consist of mass flow rate, pressure ratio and thermodynamic efficiency triplets. As an example, Fig. 1 shows the raw turbine map data for a turbocharger which is installed on a 7.8 litre CNG engine (Baratta et al., 2010), in terms of reduced mass flow (graph on the left) and efficiency (graph on the right) versus pressure ratio for different speed lines. Quantities on abscissa and vertical axis have been normalized to their maximum value. Each coloured line refers to a different reduced speed nred. In GT-Power, the performance tables are pre-processed so as to create internal maps that define the

Numerical Simulation Techniques for the

**Turbine reduced speed 1157 1727 2100 2324 2673**

turbocharger (compressor, turbine and shaft) inertia.

**0 0.5 1 1.5 2 Normalized BSR [-]**

> **407 915**

> > **nred**

**0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Normalized pressure ratio [-]**

**2.4 Performance of compressors and turbines** 

(a) (b)

(c) (d)

extrapolated range of reduced speed and PR (Baratta et al., 2010).

Fig. 2. Turbine performance maps. (a), (b) mass flow and efficiency fit versus data as functions of BSR; (c), (d) final turbine mass flow and efficiency maps, including the

The potential need to adjust the mass-flow or the efficiency multipliers has long been known (Baratta et al., 2010; Gamma Technologies, 2009; Westin & Ångström, 2003; Westin et al.,

As far as the compressor is concerned, differences in installation may influence the compressor surge-line shape, as surge depends on the compressor inlet and delivery arrangements (Baines, 2005). The position of the surge line will therefore vary from the gas

**1424 1932**

gases, T0

**0**

**0**

**0.25**

**No mr alized**

2004).

**mass-flow rate [-]**

**0.5**

**0.75**

**1**

**0.3**

**Mass-f ol w rat oi [-]**

**0.6**

**0.9**

**1.2**

Prediction of Fluid-Dynamics, Combustion and Performance in IC Engines Fuelled by CNG 265

where *mair* is the mass flow rate through the compressor, *mexh* is the mass flow rate of the exhaust gases through the turbine, cp is the specific heat at a constant pressure of the air, is the ratio of the specific heats of the air, ' is the ratio of the specific heats of the exhaust

across the compressor, and ηcmp and ηtrb are the efficiencies of the compressor and the turbine, respectively. Finally, shaft is the shaft rotational speed, and ITC denotes the whole

in,cmp is the total gas temperature at the compressor inlet, PRcmp is the pressure ratio

**0**

**3458 3966**

**0**

**0.25**

**Normalized**

**efficiency [-]**

**0.5**

**0.75**

**1**

**4475 4983**

**0.3**

**Efficiency rat oi [-]**

**Turbine reduced speed**

**2441 2949** **0.6**

**0.9**

**1.2**

**0 0.5 1 1.5 2 Normalized BSR [-]**

**0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Normalized pressure ratio [-]**

**Turbine reduced speed 1157 1727 2100 2324 2673**

> **5492 6000**

performance of the turbine and compressor over a wide range of operating conditions. The topic of turbine table pre-processing is described hereafter, as it is generally accepted that turbine data quality is the most critical point in turbocharged engine simulation (Baratta et al., 2010; Westin & Ångström, 2003; Westin et al., 2004; Winkler & Ångström, 2007). Turbine data pre-processing uses the well-known characteristics of turbines regarding efficiency, reduced mass flow rates and blade speed ratio (BSR). Namely, for a fixed-geometry turbine, the efficiency and reduced mass flow rate should lie on specific trend lines when plotted against *BSR U C <sup>S</sup>* , provided each quantity is normalized to its value at the maximum efficiency point on the actual speed line. U is the rotor blade tip speed and CS is the gas velocity that would be achieved by an isentropic expansion across the turbine stage. The application of the GT-Power approach to the turbocharger data in Fig. 1 is shown in Fig. 2a,b. The agreement between the experimental data and the fit curves in Fig. 2a,b highlights the accuracy of the procedure for a wide range of BSR values. Figures 2c,d show the complete extent of the mass flow and efficiency maps, which are obtained on the basis of the fit curves, including the extrapolated ranges of nred and PR. These plots are a graphical representation of the maps used internally by the code for the turbocharger simulation.

Fig. 1. Raw turbine performance maps. Each quantity is normalized to a specific value (Baratta et al., 2010).

The turbocharger maps are lumped-parameter models which are fluid-dynamically coupled to the surrounding 1-D pipe elements. For a given pressure ratio (imposed by the pipes at the compressor and turbine boundaries), and for a given shaft speed, which is the same for both the compressor and the turbine, the maps provide a value of the mass-flow rate and the efficiency. Such values can be adjusted by means of a mass-flow and an efficiency multiplier (MFM and EM, respectively), and are then used in the calculations. The mass-flow rate is imposed as a boundary condition in the adjacent pipes, and the PR and the efficiency are used to compute the instantaneous turbine and compressor power. The unbalance between these powers determines the change in the shaft speed in the actual time step, according to the following equation:

$$\frac{1}{\eta\_{\text{sh}\text{ft}}} \left( \dot{m}\_{\text{exl}} \eta\_{\text{trb}} c\_p \, ^\circ T\_{\dot{m},\text{trb}}^0 \cdot \left( \mathbf{1} - \text{PR} \, ^{1-\gamma} \overset{\text{J}'}{\longleftrightarrow} \right) - \dot{m}\_{\text{air}} \frac{1}{\eta\_{\text{cmp}}} c\_p T\_{\dot{m},\text{exp}}^0 \left( \text{PR}\_{\text{cmp}} \overset{\text{J}'}{\longleftrightarrow} - \mathbf{1} \right) \right) = I\_{\text{TC}} \frac{d\phi\_{\text{sh}\text{ft}}}{dt} \tag{10}$$

performance of the turbine and compressor over a wide range of operating conditions. The topic of turbine table pre-processing is described hereafter, as it is generally accepted that turbine data quality is the most critical point in turbocharged engine simulation (Baratta et al., 2010; Westin & Ångström, 2003; Westin et al., 2004; Winkler & Ångström, 2007). Turbine data pre-processing uses the well-known characteristics of turbines regarding efficiency, reduced mass flow rates and blade speed ratio (BSR). Namely, for a fixed-geometry turbine, the efficiency and reduced mass flow rate should lie on specific trend lines when plotted against *BSR U C <sup>S</sup>* , provided each quantity is normalized to its value at the maximum efficiency point on the actual speed line. U is the rotor blade tip speed and CS is the gas velocity that would be achieved by an isentropic expansion across the turbine stage. The application of the GT-Power approach to the turbocharger data in Fig. 1 is shown in Fig. 2a,b. The agreement between the experimental data and the fit curves in Fig. 2a,b highlights the accuracy of the procedure for a wide range of BSR values. Figures 2c,d show the complete extent of the mass flow and efficiency maps, which are obtained on the basis of the fit curves, including the extrapolated ranges of nred and PR. These plots are a graphical representation of the maps used internally by the code for the turbocharger simulation.

> **Turbine reduced speed 1157 2100 2673 3480**

> > **0**

1 ' 1

(10)

 

> 

1 1 ' 1 <sup>1</sup> *shaft exh trb p in trb air p in cmp cmp TC*

 

*m c T PR m c T PR I*

 

**0.25**

**No mr alized eff ci ei ncy [-]**

Fig. 1. Raw turbine performance maps. Each quantity is normalized to a specific value

0 0 ' , ,

*shaft cmp*

The turbocharger maps are lumped-parameter models which are fluid-dynamically coupled to the surrounding 1-D pipe elements. For a given pressure ratio (imposed by the pipes at the compressor and turbine boundaries), and for a given shaft speed, which is the same for both the compressor and the turbine, the maps provide a value of the mass-flow rate and the efficiency. Such values can be adjusted by means of a mass-flow and an efficiency multiplier (MFM and EM, respectively), and are then used in the calculations. The mass-flow rate is imposed as a boundary condition in the adjacent pipes, and the PR and the efficiency are used to compute the instantaneous turbine and compressor power. The unbalance between these powers determines the change in the shaft speed in the actual time step, according to

**0.5**

**0.75**

**1**

**0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Normalized pressure ratio [-]**

**nred**

*d*

*dt*

**0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Normalized pressure ratio [-]**

**nred**

**0**

(Baratta et al., 2010).

the following equation:

**0.25**

**No mr alized mass-f ol w rate [-]**

**0.5**

**0.75**

**1**

where *mair* is the mass flow rate through the compressor, *mexh* is the mass flow rate of the exhaust gases through the turbine, cp is the specific heat at a constant pressure of the air, is the ratio of the specific heats of the air, ' is the ratio of the specific heats of the exhaust gases, T0 in,cmp is the total gas temperature at the compressor inlet, PRcmp is the pressure ratio across the compressor, and ηcmp and ηtrb are the efficiencies of the compressor and the turbine, respectively. Finally, shaft is the shaft rotational speed, and ITC denotes the whole turbocharger (compressor, turbine and shaft) inertia.

Fig. 2. Turbine performance maps. (a), (b) mass flow and efficiency fit versus data as functions of BSR; (c), (d) final turbine mass flow and efficiency maps, including the extrapolated range of reduced speed and PR (Baratta et al., 2010).

#### **2.4 Performance of compressors and turbines**

The potential need to adjust the mass-flow or the efficiency multipliers has long been known (Baratta et al., 2010; Gamma Technologies, 2009; Westin & Ångström, 2003; Westin et al., 2004).

As far as the compressor is concerned, differences in installation may influence the compressor surge-line shape, as surge depends on the compressor inlet and delivery arrangements (Baines, 2005). The position of the surge line will therefore vary from the gas

Numerical Simulation Techniques for the

in Eq. (10).

the calculations.

**2.5 Engine-model tuning procedure** 

turbine efficiency' (Baines, 2005; Watson & Janota, 1982).

**0.5**

**1**

**trb,apparent**

**trb,steady**

**1.5**

**2**

Prediction of Fluid-Dynamics, Combustion and Performance in IC Engines Fuelled by CNG 267

turbine efficiency under pulse-flow conditions, but rather that the overall efficiency of the whole exhaust system is different. This has recently been referred to as 'apparent pulse

The necessity of adjusting the turbine efficiency for each operation point would mean that is practically impossible to build a fully predictive 1-D model for a turbocharged engine. However, the problem can be overcome by organizing the turbine efficiency multipliers, obtained in the calibrated points, in a suitable form. For example, in (Baratta et al., 2010), the calibration of the turbine efficiency was carried out over a wide range of engine speeds and loads, with reference to a Heavy-Duty turbocharged CNG engine, and the obtained efficiency multiplier resulted to have a well defined trend when plotted against the turbine expansion ratio, as shown in Fig. 4. Such a trend is in agreement with the findings of (Watson & Janota, 1982), as well as with those of (Westin & Ångström, 2003), who calculated a multiplier value of 1.42 at partial load (i.e., low turbine expansion ratio) and of 0.69 at full load, for a 4-cylinder 2 litre gasoline-fuelled SI engine. ηtrb,apparent in Fig. 4 corresponds to ηtrb

> **0.5 0.6 0.7 0.8 0.9 1 cycle-averaged PR [-]**

Fig. 4. Ratio of apparent turbine efficiency under pulsating flow conditions to steady-state flow efficiency. Cycle-averaged PR is normalized to a specific value (Baratta et al., 2010).

The turbine efficiency multiplier data, organized as in Fig. 4, can be very useful to allow the model to make reliable predictions of the turbine behaviour outside the calibration points. Furthermore, they are even more important if a transient simulation has to be performed. For example, (Baratta et al., 2010) considered the simulation of engine load transients at fixed speed, and almost the whole curve reported in Fig. 4 was used by the software during

Finally, it is worth stressing that heat losses from the turbine are usually neglected in the simulations. (Westin et al., 2004) proposed an approach, based on experimental heat-transfer measurements, to account for the heat transferred from the turbine to the surroundings. In this way, the magnitude of the correction needed for the turbine efficiency decreased.

It is generally accepted that 1D models need a careful calibration procedure in order to obtain accurate results (Baratta et al., 2010; Gamma Technologies, 2009; Westin & Ångström, 2003), especially for turbocharged engine applications. In fact, due to their combined onedimensional and zero-dimensional nature, these models are characterized by a simplified

stand to the engine, and from one engine installation to another. Fortunately, these variations are quite small in many cases. Due to the limited extent of the pulsating flow, which is usually observed at the compressor side, it has been found that the compressor averaging point can be predicted with good accuracy without having to adjust the compressor map. Both the compressor speed and pressure ratio usually fit well the measured values (Westin & Ångström, 2003).

Fig. 3. Simulated compressor and turbine operating points for the maximum torque operation point of a TC 7.8 litre CNG engine. Steady-state engine operating conditions, N = 0.55 Nmax.

Conversely, the power from the turbine often has to be adjusted for each single operating conditions for many reasons (Westin et al., 2004):


Figure 3 shows the simulated compressor and turbine operating points for the maximum torque operation point of a TC 7.8 litre CNG engine (Baratta et al., 2010), under steady-state engine operating conditions. The black lines show the excursion of the compressor and turbine working point on the map during the engine cycle (two lines are plotted for the turbine, which is of the twin-entry type). The empty circles denote 'average' points, which are given by the time-average of the mass-flow rate and pressure ratio. The different extent of the pulsating flow at the compressor and at the turbine side is apparent.

As regards the turbine, the EM factor actually accounts for two processes (Baines, 2005): the fraction of the exhaust-gas energy that is available at the turbine inlet, which depends on the engine exhaust-pipes arrangements, and the efficiency with which the turbine converts this energy into shaft work. The correction does not, therefore, necessarily mean higher or lower

stand to the engine, and from one engine installation to another. Fortunately, these variations are quite small in many cases. Due to the limited extent of the pulsating flow, which is usually observed at the compressor side, it has been found that the compressor averaging point can be predicted with good accuracy without having to adjust the compressor map. Both the compressor speed and pressure ratio usually fit well the

Fig. 3. Simulated compressor and turbine operating points for the maximum torque operation point of a TC 7.8 litre CNG engine. Steady-state engine operating conditions,

Conversely, the power from the turbine often has to be adjusted for each single operating




Figure 3 shows the simulated compressor and turbine operating points for the maximum torque operation point of a TC 7.8 litre CNG engine (Baratta et al., 2010), under steady-state engine operating conditions. The black lines show the excursion of the compressor and turbine working point on the map during the engine cycle (two lines are plotted for the turbine, which is of the twin-entry type). The empty circles denote 'average' points, which are given by the time-average of the mass-flow rate and pressure ratio. The different extent

As regards the turbine, the EM factor actually accounts for two processes (Baines, 2005): the fraction of the exhaust-gas energy that is available at the turbine inlet, which depends on the engine exhaust-pipes arrangements, and the efficiency with which the turbine converts this energy into shaft work. The correction does not, therefore, necessarily mean higher or lower

of the pulsating flow at the compressor and at the turbine side is apparent.

measured values (Westin & Ångström, 2003).

conditions for many reasons (Westin et al., 2004):

extrapolation may be a source of error;

is usually extrapolated;

used when measuring the maps.

N = 0.55 Nmax.

turbine efficiency under pulse-flow conditions, but rather that the overall efficiency of the whole exhaust system is different. This has recently been referred to as 'apparent pulse turbine efficiency' (Baines, 2005; Watson & Janota, 1982).

The necessity of adjusting the turbine efficiency for each operation point would mean that is practically impossible to build a fully predictive 1-D model for a turbocharged engine. However, the problem can be overcome by organizing the turbine efficiency multipliers, obtained in the calibrated points, in a suitable form. For example, in (Baratta et al., 2010), the calibration of the turbine efficiency was carried out over a wide range of engine speeds and loads, with reference to a Heavy-Duty turbocharged CNG engine, and the obtained efficiency multiplier resulted to have a well defined trend when plotted against the turbine expansion ratio, as shown in Fig. 4. Such a trend is in agreement with the findings of (Watson & Janota, 1982), as well as with those of (Westin & Ångström, 2003), who calculated a multiplier value of 1.42 at partial load (i.e., low turbine expansion ratio) and of 0.69 at full load, for a 4-cylinder 2 litre gasoline-fuelled SI engine. ηtrb,apparent in Fig. 4 corresponds to ηtrb in Eq. (10).

Fig. 4. Ratio of apparent turbine efficiency under pulsating flow conditions to steady-state flow efficiency. Cycle-averaged PR is normalized to a specific value (Baratta et al., 2010).

The turbine efficiency multiplier data, organized as in Fig. 4, can be very useful to allow the model to make reliable predictions of the turbine behaviour outside the calibration points. Furthermore, they are even more important if a transient simulation has to be performed. For example, (Baratta et al., 2010) considered the simulation of engine load transients at fixed speed, and almost the whole curve reported in Fig. 4 was used by the software during the calculations.

Finally, it is worth stressing that heat losses from the turbine are usually neglected in the simulations. (Westin et al., 2004) proposed an approach, based on experimental heat-transfer measurements, to account for the heat transferred from the turbine to the surroundings. In this way, the magnitude of the correction needed for the turbine efficiency decreased.

## **2.5 Engine-model tuning procedure**

It is generally accepted that 1D models need a careful calibration procedure in order to obtain accurate results (Baratta et al., 2010; Gamma Technologies, 2009; Westin & Ångström, 2003), especially for turbocharged engine applications. In fact, due to their combined onedimensional and zero-dimensional nature, these models are characterized by a simplified

Numerical Simulation Techniques for the

**2.5.2 Turbocharged engines** 

engine.

in (Baratta et al., 2005; Catania et al., 2003).

**2.6 Steady-state engine-model tuning example** 

from which Fig. 5 is taken. The engine features are reported in Table 1.

HR profile. However, the alternative a) is preferable.

organized in lookup tables and then included in the engine model.

Prediction of Fluid-Dynamics, Combustion and Performance in IC Engines Fuelled by CNG 269

b. If the heat release has been determined previously and is directly imposed, the heat transfer can only be calibrated on the basis of the match between the experimental and numerical in-cylinder pressure. However, in this case, such a calibration is also affected by an additional uncertainty, due to the calculation of the gas thermodynamic properties with different sub-models. In some applications, it may be acceptable to keep the standard C0 coefficient, and to match the cylinder pressure by slightly shifting the

Once the heat transfer model has been calibrated at all the engine working points which have been investigated experimentally, the related heat-transfer multiplier values can be

The calibration procedure is more complex in the case of turbocharged engines, in which the compressor, the engine and the turbine are fluid-dynamically coupled. For turbocharged engine applications, it is not advisable to tune the entire model, consisting of the engine and the turbocharger, from the beginning. In fact, slight inaccuracies that are usually present before model tuning can make the compressor operation point (and, hence, the boost level) deviate to a great extent from the real one. In this case, it is very difficult to isolate the root cause of a performance problem (Baratta et al., 2010; Gamma Technologies, 2009; Westin & Ångström, 2003). For this reason, an engine model without the turbocharger should be built first. The intercooler outlet and the turbine inlet should be replaced by two environments in which pressure, temperature and fluid composition are properly set on the basis of measured data, and the model should be calibrated, as in the case of a naturally-aspirated

The procedure outlined above allows the 1-D model of a turbocharged engine to obtain a rather high degree of predictability, not only in a qualitative sense, but also from a quantitative point of view. It was followed almost exactly in this way in (Baratta et al, 2010),

As can be seen, the engine model is generally well calibrated in all the tested cases. With reference to the whole intake system, and the portion of the exhaust ports within the cylinder head, the wall temperatures at the fluid side were set to specific values, which were selected on the basis of the outcomes of the experimental tests. The wall temperature was evaluated taking account of the gas-wall heat transfer for the pipes downstream from the exhaust ports and the external temperature was set equal to the value in the cell cabinet. The intake and exhaust ports were modelled as straight pipes, and heat-transfer multipliers were thus introduced to account for the bends, roughness, the additional surface area and turbulence caused by the valves and stems (Gamma Technologies, 2009). There was no need to set heat-transfer multipliers elsewhere in the intake system or to add friction multipliers to the model because the pressures and temperatures in the engine manifolds and ports were well reproduced (Fig. 5a,c,d). The agreement between the simulated and experimental values of PFP (peak firing pressure, Fig. 5e) and engine brake torque (Fig. 5f) demonstrate the accuracy of the combustion and engine friction sub-models, respectively. The above

determines LHVM on the basis of an energy balance, that is similar to the one proposed

description of many physical phenomena, such as: wall friction and heat transfer, concentrated losses, flow through the valves, fuel injection, and so on. Thus, they are generally not able to describe the engine fluid-dynamics accurately, unless semi-empirical input data are provided by means of the model calibration, which is usually carried out by adjusting specific model coefficients so as to accurately reproduce the experimental measurements taken at selected steady-state operating conditions.

In order to calibrate the flow losses in the intake and exhaust pipelines of a SI engine, points at wide-open throttle are more significant, due to the very high mass-flow rate. However, part-load data should also be acquired, in view of using the model for predictive purposes over a wide range of operating conditions. In general, a 1-D model will unlikely be fully predictive (i.e., quantitative) outside the calibration region, though its results may still be significant as trends. If an engine is in the early stages of design, the experimental database may be incomplete, but measurements from other engines with common or similar components may still be useful.
