**1. Introduction**

Water-cooled condensers are commonly used in vapor compression refrigeration for industrial applications due to their high rate of heat transfer [1], simple configuration and the relatively low cost of manufacturability compared to other types of condensers [2]. On the other hand, population growth, and the exponential increase in energy consumption throughout the world keep stressing freshwater resources [3]. Typical components used in refrigeration systems such as compressors, evaporators, condensers, and refrigerants are constantly iterating to provide more energy efficient solutions [4] in order to minimize the environmental impact due to toxic molecules in refrigerants and reduce the production of residual heat [5]. Unfortunately, the steps imposed by regulatory agencies in United States and

Europe sometimes lead to production ready solutions that have not been thoroughly tested for industrial applications. Perhaps, one common example is the race in banning HFC refrigerants for compressed vapor refrigeration cycles [6]. Ideally, the components in the refrigeration system can remain intact by changing refrigerants, but this fails to be the case for most systems since the oil in the compressor and even the compressor specifications need to be tailored to the new refrigerant [7].

**1.1 Numerical analysis of turbulent phase-transition in the condensation**

*Numerical Analysis of a Water-Cooled Condenser at Startup Conditions for Refrigeration…*

Multi-phase flow refers to the flow of a mixture of phases or species such as gases in liquids or liquids in gases of different densities [23] where the liquids, and gases are considered distinct phases. There are different mathematical characterizations targeted to study multi-phase flows. For instance, for dispersed flows, one phase consists of discrete, noncontinuous elements (such as bubbles) and the second phase is considered as a continuum. This approach is widely accepted for the analysis and characterization of oil and refrigerant relationships in vapor compressed cycles, given that at certain conditions, oil can scape the compressor and affect the system performance due to the variations in the thermal properties of the

In bubbly flows or other types of applications where dispersed multiphase flows are applicable, the properties of the inhomogeneous mixture are defined relative to the continuous phase [25]. The mathematical manipulation for such flows can happen under a Lagrangian representation for the dispersed phase [26], and an Eulerian reference for the continuous phase. For the continuous phase, the material properties are defined at every point within a control volume [27], whereas in a separated flow under the Euler–Euler approach the phases are continuous but

This research focuses on the incompressible volume of fluid model where the

*T* � *Tsat*

*Tsat* � *T*

for a condensation process. In the study of phase-transition of refrigerants, the saturation temperature is found based on the operating conditions of the system [29]. In this study, the inlet and outlet temperatures and pressures were measured

From a modeling perspective, the saturating temperature is a dominant factor in the prediction of the evaporating and condensing process. Therefore, the measured temperatures, pressures and the saturation temperature were loaded in the simulation as dynamics boundary conditions to drive the phase-transition process given

In order to find the quality of the mixture the volume fraction is defined as:

<sup>þ</sup> *<sup>α</sup><sup>v</sup> <sup>X</sup>*<sup>~</sup>

where the sum of volume occupied by the phases is 100%. Furthermore, the microscopic dynamics of the phase-transition process of refrigerants in heat exchangers and condensers can be studied by considering both the vapor and liquid as continuous and interpenetrating fluids under the Eulerian frame of reference [30]. Even though this approach is computationally expensive given that the governing equations for each phase are solved together with the momentum equation, the mass diffusion can be monitored by a straightforward calculation. For this

*α<sup>l</sup> X*~

case, the microscopic behavior of the phases can be monitored by:

*Tsat* , *<sup>T</sup>* <sup>&</sup>gt;*Tsat* (1)

*Tsat* , *<sup>T</sup>* <sup>&</sup>lt;*Tsat* (2)

<sup>¼</sup> <sup>1</sup> (3)

*m*\_ *<sup>v</sup>* ¼ �*m*\_ *<sup>l</sup>* ¼ *ςαlρ<sup>l</sup>*

*m*\_ *<sup>l</sup>* ¼ �*m*\_ *<sup>v</sup>* ¼ *ςαvρ<sup>v</sup>*

**process of refrigerant flow**

*DOI: http://dx.doi.org/10.5772/intechopen.97203*

mixture induced by the oil [24].

divided by a single contact surface [28].

mass transfer between phases is given by:

for evaporation and

experimentally to compute *Tsat:*

the dynamic value of *Tsat*.

**11**

Virtual experimentation using numerical simulations offer great insights at the micro and macroscopic level to support design and research activities of heat exchangers, condensers and evaporators [8] given that experimental studies can reach elevated costs and access to sensorial points to capture significant physical details are difficult to incorporate in pressurized systems [9, 10]. In fact, the analysis of startup condition for physical components in thermodynamic cycles is particularly challenging given the small-time scales and the large variations detected in the variables of interest [11]. This alone calls for special attention in the sampling rate and physical location of feedback sensors given that dynamic and unstable conditions can be reached in a thermodynamic cycle by unpredicted changes in loads or variations in energetic states, and false positive readings can be measured depending on the flow characteristics through the system.

Concomitantly, the design and fabrication of condensers and heat exchangers require the knowledge and understanding of the physical and chemical phenomenon and other factors such as the properties of the working fluids or multi-phase flows [12], their regimes and states, and the geometrical characteristics of the system [13]. But rigorous experimentation in thermodynamic systems can be particularly costly because environmental chambers are often needed to obtain reproducible results [14]. Evidently, the lack of accessibility to an environmental chamber means that the ambient temperature is a random variable and the uncertainty of the experimental results can increase significantly [15] since the thermodynamic states of the thermodynamic cycle tend to fluctuate as a function of the heat rejected and the heat absorbed to and from the environment [16].

A less rigorous alternative to this approach is to perform a design of experiments at ambient conditions and execute the test multiple times to assess the error and response variations [17]. Unfortunately, this route can also lead to an expensive and time-consuming solution on top of developing variable startup conditions that can affect the performance of the system. Consequently, Numerical simulations and theoretical analysis of thermodynamic cycles should help alleviate the cost of materials, manufacturing, and redundant testing.

Heat and time-dependent multi-phase computational solutions targeting problems with complicated geometries that cannot be simplified by axisymmetric conditions or reduction of dimensions tend to be challenging to develop, and the results are always suspicious if no experimental validation is provided. Therefore, a balance between experiments and simulations seems to be the ideal recipe to obtain costeffective solutions with solid scientific ground.

In the last few decades, significant efforts have been focused on developing more rigorous models that account for turbulent fluctuations on mufti-phase flows [18–20] evidencing the complicated nature of such problems even for simple geometries [21] such as tubes and channels [22]. However, no three-dimensional studies have been reported on the CFD multi-phase modeling of R404a condensation in a medium temperature water-cooled condenser at startup conditions. This research aims to provide a study of the unsteady condensing and evaporating characteristics of R404a in a water-cooled condenser by modeling the raising temperature and pressure in the system induced by the compressed vapor entering the condenser based on experimental data.

*Numerical Analysis of a Water-Cooled Condenser at Startup Conditions for Refrigeration… DOI: http://dx.doi.org/10.5772/intechopen.97203*

## **1.1 Numerical analysis of turbulent phase-transition in the condensation process of refrigerant flow**

Multi-phase flow refers to the flow of a mixture of phases or species such as gases in liquids or liquids in gases of different densities [23] where the liquids, and gases are considered distinct phases. There are different mathematical characterizations targeted to study multi-phase flows. For instance, for dispersed flows, one phase consists of discrete, noncontinuous elements (such as bubbles) and the second phase is considered as a continuum. This approach is widely accepted for the analysis and characterization of oil and refrigerant relationships in vapor compressed cycles, given that at certain conditions, oil can scape the compressor and affect the system performance due to the variations in the thermal properties of the mixture induced by the oil [24].

In bubbly flows or other types of applications where dispersed multiphase flows are applicable, the properties of the inhomogeneous mixture are defined relative to the continuous phase [25]. The mathematical manipulation for such flows can happen under a Lagrangian representation for the dispersed phase [26], and an Eulerian reference for the continuous phase. For the continuous phase, the material properties are defined at every point within a control volume [27], whereas in a separated flow under the Euler–Euler approach the phases are continuous but divided by a single contact surface [28].

This research focuses on the incompressible volume of fluid model where the mass transfer between phases is given by:

$$
\dot{m}\_v = -\dot{m}\_l = \xi a\_l \rho\_l \left[ \frac{T - T\_{sat}}{T\_{sat}} \right], T > T\_{sat} \tag{1}
$$

for evaporation and

Europe sometimes lead to production ready solutions that have not been

*Heat Transfer - Design, Experimentation and Applications*

refrigerant [7].

thoroughly tested for industrial applications. Perhaps, one common example is the race in banning HFC refrigerants for compressed vapor refrigeration cycles [6]. Ideally, the components in the refrigeration system can remain intact by changing refrigerants, but this fails to be the case for most systems since the oil in the compressor and even the compressor specifications need to be tailored to the new

Virtual experimentation using numerical simulations offer great insights at the

Concomitantly, the design and fabrication of condensers and heat exchangers require the knowledge and understanding of the physical and chemical phenomenon and other factors such as the properties of the working fluids or multi-phase flows [12], their regimes and states, and the geometrical characteristics of the system [13]. But rigorous experimentation in thermodynamic systems can be particularly costly because environmental chambers are often needed to obtain reproducible results [14]. Evidently, the lack of accessibility to an environmental chamber means that the ambient temperature is a random variable and the uncertainty of the experimental results can increase significantly [15] since the thermodynamic states of the thermodynamic cycle tend to fluctuate as a function of the

A less rigorous alternative to this approach is to perform a design of experiments at ambient conditions and execute the test multiple times to assess the error and response variations [17]. Unfortunately, this route can also lead to an expensive and time-consuming solution on top of developing variable startup conditions that can affect the performance of the system. Consequently, Numerical simulations and theoretical analysis of thermodynamic cycles should help alleviate the cost of mate-

Heat and time-dependent multi-phase computational solutions targeting problems with complicated geometries that cannot be simplified by axisymmetric conditions or reduction of dimensions tend to be challenging to develop, and the results are always suspicious if no experimental validation is provided. Therefore, a balance between experiments and simulations seems to be the ideal recipe to obtain cost-

In the last few decades, significant efforts have been focused on developing more rigorous models that account for turbulent fluctuations on mufti-phase flows [18–20] evidencing the complicated nature of such problems even for simple geometries [21] such as tubes and channels [22]. However, no three-dimensional studies have been reported on the CFD multi-phase modeling of R404a condensation in a medium temperature water-cooled condenser at startup conditions. This research aims to provide a study of the unsteady condensing and evaporating characteristics of R404a in a water-cooled condenser by modeling the raising temperature and pressure in the system induced by the compressed vapor entering the

heat rejected and the heat absorbed to and from the environment [16].

micro and macroscopic level to support design and research activities of heat exchangers, condensers and evaporators [8] given that experimental studies can reach elevated costs and access to sensorial points to capture significant physical details are difficult to incorporate in pressurized systems [9, 10]. In fact, the analysis of startup condition for physical components in thermodynamic cycles is particularly challenging given the small-time scales and the large variations detected in the variables of interest [11]. This alone calls for special attention in the sampling rate and physical location of feedback sensors given that dynamic and unstable conditions can be reached in a thermodynamic cycle by unpredicted changes in loads or variations in energetic states, and false positive readings can be measured

depending on the flow characteristics through the system.

rials, manufacturing, and redundant testing.

effective solutions with solid scientific ground.

condenser based on experimental data.

**10**

$$
\dot{m}\_l = -\dot{m}\_v = \xi a\_v \rho\_v \left[ \frac{T\_{sat} - T}{T\_{sat}} \right], T < T\_{sat} \tag{2}
$$

for a condensation process. In the study of phase-transition of refrigerants, the saturation temperature is found based on the operating conditions of the system [29]. In this study, the inlet and outlet temperatures and pressures were measured experimentally to compute *Tsat:*

From a modeling perspective, the saturating temperature is a dominant factor in the prediction of the evaporating and condensing process. Therefore, the measured temperatures, pressures and the saturation temperature were loaded in the simulation as dynamics boundary conditions to drive the phase-transition process given the dynamic value of *Tsat*.

In order to find the quality of the mixture the volume fraction is defined as:

$$a\_l(\tilde{X}) + a\_v(\tilde{X}) = \mathbf{1} \tag{3}$$

where the sum of volume occupied by the phases is 100%. Furthermore, the microscopic dynamics of the phase-transition process of refrigerants in heat exchangers and condensers can be studied by considering both the vapor and liquid as continuous and interpenetrating fluids under the Eulerian frame of reference [30]. Even though this approach is computationally expensive given that the governing equations for each phase are solved together with the momentum equation, the mass diffusion can be monitored by a straightforward calculation. For this case, the microscopic behavior of the phases can be monitored by:

*Heat Transfer - Design, Experimentation and Applications*

$$\frac{\partial a\_l}{\partial t} + \nabla \cdot \left(\overrightarrow{u} a\_l\right) = \frac{\dot{m}\_l}{\rho\_l} = \mathbb{S}\_{\text{mass}}\tag{4}$$

*<sup>h</sup>* <sup>¼</sup> *<sup>α</sup>lρlhl* <sup>þ</sup> *<sup>α</sup>vρvhv αlρ<sup>l</sup>* þ *αvρ<sup>v</sup>*

*Numerical Analysis of a Water-Cooled Condenser at Startup Conditions for Refrigeration…*

Since the energetic state of a refrigerant far from its critical point can only exist for stable conditions at a single pressure and temperature pair [31], it is crucial to properly identify the coupled operating pressures and temperatures to obtain the saturated temperature of the refrigerant. For this reason, an experimental setup was designed and constructed so that the inlet and outlet conditions of the water and the refrigerant under transient conditions can be detected and used as dynamic bound-

The water-cooled condenser was fabricated using copper tubing. The dimensions for the line of water, refrigerant line and copper wall separation are shown in **Table 1**. To enhance the heat transfer, thermal insulation (Polyethylene foam) was placed around the water copper jacket and the rest of the tubbing connecting the

**Figure 1** shows the configuration adopted to characterize the condensing details of R404a. The figure shows the standard cycle corresponding to a vapor compression cycle including the compressor (Copeland ZB15-KCE), the water-cooled condenser, the evaporator, and the thermostatic expansion valve (Danfoss T2). The temperature and pressure of the vapor and liquid refrigerant were measured at points (1) and (2) by attaching thermocouples to the refrigeration line and connecting pressure transducers to measure the pressure drop of the refrigerant across the helix. The water inlet and outlet temperatures are monitored (3) and (4) in a non-invasive fashion. The test methodology consisted of 6 consecutive runs for 4.75 minutes each in order to stabilize the system and reach thermal equilibrium given that an environmental chamber was not used for this study. A flow meter (5) and pressure regulator are located at the water inlet to measure the flow rate and sustain the water pressure. **Table 2** shows the magnitude of the variables monitored to control the steady

**Parameter Dimension** *D*<sup>Ω</sup><sup>1</sup> 0*:*0254 ½ � *m D*<sup>Ω</sup>2�*in* 0*:*0127 ½ � *m D*<sup>Ω</sup>2�*out* 0*:*0147 ½ � *m D*<sup>Ω</sup><sup>3</sup> 0*:*0127½ � *m* Pitch 0*:*031½ � *m DHLX* 0*:*213 ½ � *m Larc* 3*:*05½ � *m As*�Ω<sup>1</sup> <sup>0</sup>*:*<sup>3847</sup> *<sup>m</sup>*<sup>2</sup> ½ � *As*�Ω2�*out* <sup>0</sup>*:*<sup>2127</sup> *<sup>m</sup>*<sup>2</sup> ½ � *As*�Ω<sup>3</sup> <sup>0</sup>*:*<sup>1834</sup> *<sup>m</sup>*<sup>2</sup> ½ �

**2. Experimental procedure**

*DOI: http://dx.doi.org/10.5772/intechopen.97203*

ary conditions for the numerical simulation.

components in the refrigeration system.

performance of the system.

*Parameters and dimension of the water-cooled condenser.*

**Table 1.**

**13**

*hl* ¼ *Cp*,*l*ð Þ *T* � *To* , *hl* ¼ *Cp*,*v*ð Þ *T* � *To* , (15)

*Keff* ¼ *αlKl* þ *αvKv:* (16)

(14)

and

$$\frac{\partial a\_v}{\partial t} + \nabla \cdot \left(\overrightarrow{u} a\_v\right) = -\frac{\dot{m}\_v}{\rho\_v} = -\mathbb{S}\_{\text{mass}}\tag{5}$$

for which *ρ<sup>l</sup>* and *ρ<sup>v</sup>* are the densities of the liquid and vapor phases. Then. the mixture density and mixture viscosity are:

$$
\rho\_m = \rho\_l + \rho\_v \tag{6}
$$

and

$$
\mu\_{\rm m} = \mu\_l + \mu\_v. \tag{7}
$$

For each phase, the momentum conservation is given by:

$$\frac{\partial}{\partial t} \left( a\_v \rho\_v \stackrel{\smile}{u}\_v \right) + \nabla \bullet \left( a\_v \rho\_v \stackrel{\smile}{u}\_v \bullet \stackrel{\smile}{u}\_v \right) = -a\_v \nabla \mathbf{p} + \nabla \bullet \stackrel{\smile}{\bar{\tau}}\_v + \mathsf{\mu}\_v \tag{8}$$

and

$$\frac{\partial}{\partial t} \left( a\_l \rho\_l \overrightarrow{u}\_l \right) + \nabla \bullet \left( a\_l \rho\_l \overrightarrow{u}\_l \bullet \overrightarrow{u}\_l \right) = -a\_l \nabla \mathbf{p} + \nabla \bullet \overleftarrow{\overline{\mathbf{r}}}\_l + \varphi\_l \tag{9}$$

where *ψ<sup>v</sup>* and *ψ<sup>l</sup>* are the momentum sources and the stress tensor is given by:

$$\bar{\bar{\tau}}\_i = a\_i \mu\_i \left( \nabla \bar{u}\_i + \nabla \bar{u}\_i^{\ \ \ \bar{T}} \right) + a\_i \left( \lambda\_i - \frac{3}{2} \mu\_i \right) \nabla \bullet \bar{\bar{u}}\_i \stackrel{\ \text{e}}{\ I} \tag{10}$$

given that *λ<sup>i</sup>* and *μ<sup>i</sup>* are the shear and bulk viscosities of the phase *i:* Then, the two equation *κ* � *ε* turbulent model for multi-phase flow is:

$$\frac{\partial}{\partial t}(a\_v \rho\_v \kappa) + \nabla \cdot \left(a\_v \rho\_v \kappa \overline{u}\_v\right) = \frac{\partial}{\partial \mathbf{x}\_j} \left[a\_v \left(\mu + \frac{\mu\_t}{\sigma\_\varepsilon}\right) \frac{\partial \kappa}{\partial \mathbf{x}\_j}\right] - a\_v \rho\_v \varepsilon + a\_v \mathbf{G}\_k + \mathbf{S}\_k \tag{11}$$

for the turbulent kinetic energy *κ* and

$$\frac{\partial}{\partial t}(a\_v \rho\_v \varepsilon) + \nabla \cdot \left(a\_v \rho\_v \varepsilon \overline{u}\_v\right) = \frac{\partial}{\partial x\_j} \left[a\_v \left(\mu + \frac{\mu\_t}{\sigma\_k}\right) \frac{\partial \varepsilon}{\partial \mathbf{x}\_j}\right] - a\_v \mathbf{C}\_{1x} \frac{\varepsilon}{\kappa} \mathbf{G}\_k - a\_v \mathbf{C}\_{2x} \rho\_v \frac{\varepsilon^2}{\kappa} \mathbf{G}\_k + \mathbf{S}\_{\varepsilon} \tag{12}$$

for turbulent dissipation *ε* where *μ<sup>t</sup>* ¼ *Cμρ<sup>v</sup> κ*2 *<sup>ε</sup>* and *C<sup>μ</sup>* ¼ 0*:*99*:* The thermal energy in the process is conserved and computed for each phase by:

$$\frac{\partial}{\partial t} \sum\_{i} \left( a\_i \overrightarrow{u\_i} (\rho\_i E\_i + P) \right) = \nabla \bullet \left( K\_f \nabla T \right) \tag{13}$$

Where the energy is *<sup>E</sup>* <sup>¼</sup> *hi* � *<sup>P</sup> ρi* þ *u \* i* 2 <sup>2</sup> and the enthalpy and effective thermal conductivity are:

*Numerical Analysis of a Water-Cooled Condenser at Startup Conditions for Refrigeration… DOI: http://dx.doi.org/10.5772/intechopen.97203*

$$h = \frac{a l \rho\_l h\_l + a\_v \rho\_v h\_v}{a\_l \rho\_l + a\_v \rho\_v} \tag{14}$$

$$h\_l = \mathbb{C}\_{p,l}(T - T\_o), \\ h\_l = \mathbb{C}\_{p,v}(T - T\_o), \tag{15}$$

$$K\_{\rm eff} = aqK\_l + a\_vK\_v.\tag{16}$$

## **2. Experimental procedure**

*∂αl ∂t*

*Heat Transfer - Design, Experimentation and Applications*

*∂α<sup>v</sup> ∂t*

mixture density and mixture viscosity are:

*∂ <sup>∂</sup><sup>t</sup> <sup>α</sup>vρvu \* v* � �

> *∂ <sup>∂</sup><sup>t</sup> <sup>α</sup>lρlu \* l* � �

> > *τ* ¼

*<sup>∂</sup><sup>t</sup> <sup>α</sup>vρ<sup>v</sup>* ð Þþ *<sup>κ</sup>* ∇ ∙ *<sup>α</sup>vρvκ<sup>u</sup>*

*<sup>∂</sup><sup>t</sup> <sup>α</sup>vρ<sup>v</sup>* ð Þþ *<sup>ε</sup>* ∇ ∙ *<sup>α</sup>vρvε<sup>u</sup>*

conductivity are:

**12**

*<sup>i</sup>* ¼ *αiμ<sup>i</sup>* ∇*u*

*\* v* � �

for the turbulent kinetic energy *κ* and

*\* v* � �

for turbulent dissipation *ε* where *μ<sup>t</sup>* ¼ *Cμρ<sup>v</sup>*

*∂ ∂t* X *i*

Where the energy is *<sup>E</sup>* <sup>¼</sup> *hi* � *<sup>P</sup>*

and

and

and

*∂*

*∂*

þ ∇ � *u* !*α<sup>l</sup>* � �

þ ∇ � *u* !*α<sup>v</sup>* � �

For each phase, the momentum conservation is given by:

þ ∇ ∙ *αvρvu*

þ ∇ ∙ *αlρlu*

*\* <sup>i</sup>* þ ∇*u \* i*

two equation *κ* � *ε* turbulent model for multi-phase flow is:

¼ *∂ ∂x <sup>j</sup>*

¼ *∂ ∂x <sup>j</sup>*

> *αiu \**

> > *ρi* þ *u \* i* 2

*<sup>T</sup>* � �

*\* <sup>v</sup>* ∙ *u \* v*

*\* <sup>l</sup>* ∙ *u \* l*

� �

where *ψ<sup>v</sup>* and *ψ<sup>l</sup>* are the momentum sources and the stress tensor is given by:

given that *λ<sup>i</sup>* and *μ<sup>i</sup>* are the shear and bulk viscosities of the phase *i:* Then, the

*<sup>α</sup><sup>v</sup> <sup>μ</sup>* <sup>þ</sup> *<sup>μ</sup><sup>t</sup> σε* � � *∂κ*

� �

*<sup>α</sup><sup>v</sup> <sup>μ</sup>* <sup>þ</sup> *<sup>μ</sup><sup>t</sup> σk* � � *∂ε*

*<sup>i</sup>*ð Þ *ρiEi* þ *P* � �

� �

<sup>þ</sup> *<sup>α</sup><sup>i</sup> <sup>λ</sup><sup>i</sup>* � <sup>3</sup>

� �

<sup>¼</sup> *<sup>m</sup>*\_ *<sup>l</sup> ρl*

¼ � *<sup>m</sup>*\_ *<sup>v</sup> ρv*

for which *ρ<sup>l</sup>* and *ρ<sup>v</sup>* are the densities of the liquid and vapor phases. Then. the

¼ *Smass* (4)

¼ �*Smass* (5)

*ρ<sup>m</sup>* ¼ *ρ<sup>l</sup>* þ *ρ<sup>v</sup>* (6)

*μ*<sup>m</sup> ¼ *μ<sup>l</sup>* þ *μv:* (7)

¼

¼

∇ ∙ *u \* i I* ¼

*<sup>v</sup>* þ *ψ<sup>v</sup>* (8)

*<sup>l</sup>* þ *ψ<sup>l</sup>* (9)

� *αvρvε* þ *αvGk* þ *Sk* (11)

*Gk* � *αvC*2*ερ<sup>v</sup>*

<sup>¼</sup> ∇ ∙ *<sup>K</sup> <sup>f</sup>*∇*<sup>T</sup>* � � (13)

<sup>2</sup> and the enthalpy and effective thermal

*ε*2 *κ*

*Gk* þ *S<sup>ε</sup>*

(12)

(10)

¼ �*αv*∇p þ ∇ ∙ *τ*

¼ �*αl*∇p þ ∇ ∙ *τ*

2 *μi* � �

*∂x <sup>j</sup>*

� *αv*C1*<sup>ε</sup>*

*<sup>ε</sup>* and *C<sup>μ</sup>* ¼ 0*:*99*:*

*ε κ*

*∂x <sup>j</sup>*

*κ*2

The thermal energy in the process is conserved and computed for each phase by:

Since the energetic state of a refrigerant far from its critical point can only exist for stable conditions at a single pressure and temperature pair [31], it is crucial to properly identify the coupled operating pressures and temperatures to obtain the saturated temperature of the refrigerant. For this reason, an experimental setup was designed and constructed so that the inlet and outlet conditions of the water and the refrigerant under transient conditions can be detected and used as dynamic boundary conditions for the numerical simulation.

The water-cooled condenser was fabricated using copper tubing. The dimensions for the line of water, refrigerant line and copper wall separation are shown in **Table 1**. To enhance the heat transfer, thermal insulation (Polyethylene foam) was placed around the water copper jacket and the rest of the tubbing connecting the components in the refrigeration system.

**Figure 1** shows the configuration adopted to characterize the condensing details of R404a. The figure shows the standard cycle corresponding to a vapor compression cycle including the compressor (Copeland ZB15-KCE), the water-cooled condenser, the evaporator, and the thermostatic expansion valve (Danfoss T2). The temperature and pressure of the vapor and liquid refrigerant were measured at points (1) and (2) by attaching thermocouples to the refrigeration line and connecting pressure transducers to measure the pressure drop of the refrigerant across the helix. The water inlet and outlet temperatures are monitored (3) and (4) in a non-invasive fashion.

The test methodology consisted of 6 consecutive runs for 4.75 minutes each in order to stabilize the system and reach thermal equilibrium given that an environmental chamber was not used for this study. A flow meter (5) and pressure regulator are located at the water inlet to measure the flow rate and sustain the water pressure.


**Table 2** shows the magnitude of the variables monitored to control the steady performance of the system.

**Table 1.** *Parameters and dimension of the water-cooled condenser.*

#### **Figure 1.**

*Schematic representation of the refrigeration system depicting the testing points measuring the inlet and outlet temperature and pressure of the refrigerant at (1) and (2), as well as the water temperature at the inlet and outlet at (3) and (4).*

> for the vapor refrigerant pressure was reached around 1200 ms after initialization. In order to characterize the startup conditions, the first 2000 ms of the average between the different experiments corresponding to each variable displayed in the **Figure 2**

**Variable Instrument Accuracy** *P* Transducer (PX-309) 0*:*25%Full Scale *T* J-Type Thermocouple �2*:*2°C *m*\_ *<sup>H</sup>*2*<sup>O</sup>* 2321FG 2*:*0%Full Scale

*Numerical Analysis of a Water-Cooled Condenser at Startup Conditions for Refrigeration…*

*DOI: http://dx.doi.org/10.5772/intechopen.97203*

A time-dependent numerical model in three-dimension was developed to simulate the phase-transition and heat transfer of R404a in a water-cooled condenser. The geometry accounts for two fluid regions as well as one solid domain (copper) that separates both flows and provides the thermal mechanism for heat transfer. The computational domain (Ω<sup>1</sup> ∪ Ω<sup>2</sup> ∪ Ω3Þ contains three distant regions belonging

b. Solid copper region for physical division of water and refrigerant ð Þ Ω<sup>2</sup> .

The properties of the materials and working fluids are show in **Table 4**. The temperature dependent material properties were programmed in Fluent using

were programed in ANSYS Fluent as dynamic boundary conditions.

*Experimental data obtained experimentally and computed saturation temperature of R404a.*

**3. Computational domain and boundary conditions**

to the space *<sup>X</sup>*<sup>~</sup> ! *<sup>R</sup>*<sup>3</sup> assigned as follows:

c. Fluid region for refrigerant R404a ð Þ Ω<sup>3</sup> .

a. Fluid region for water ð Þ Ω<sup>1</sup> .

**Table 3.** *Instrumentation.*

**Figure 2.**

**15**

**Table 3** shows the sensors and instruments used for the experimental study as well as the accuracy reported by the manufacturers. The sampling rate was fixed to 100 ms using LabView 18 software and the corresponding hardware with the data acquisition system to gather the temperatures and pressures values of both water and refrigerant.

The water and refrigerant temperature at the inlet and outlet of the condenser are reported in **Figure 2** with the corresponding variation to document the test repeatability. The figure also shows the measured refrigerant pressure and the computed liquid saturation temperature using Coolproops 6.4.1 [32].

The experimental data demonstrated that the system reached maximum operating pressure close to 300 ms after starting the compressor, and a steady-state condition


**Table 2.** *Operational parameters of the refrigeration system.* *Numerical Analysis of a Water-Cooled Condenser at Startup Conditions for Refrigeration… DOI: http://dx.doi.org/10.5772/intechopen.97203*


**Table 3.**

*Instrumentation.*

#### **Figure 2.**

**Table 3** shows the sensors and instruments used for the experimental study as well as the accuracy reported by the manufacturers. The sampling rate was fixed to 100 ms using LabView 18 software and the corresponding hardware with the data acquisition system to gather the temperatures and pressures values of both water

*Schematic representation of the refrigeration system depicting the testing points measuring the inlet and outlet temperature and pressure of the refrigerant at (1) and (2), as well as the water temperature at the inlet and*

*Heat Transfer - Design, Experimentation and Applications*

The water and refrigerant temperature at the inlet and outlet of the condenser are reported in **Figure 2** with the corresponding variation to document the test repeatability. The figure also shows the measured refrigerant pressure and the

The experimental data demonstrated that the system reached maximum operating pressure close to 300 ms after starting the compressor, and a steady-state condition

> *s* h i

**Variable Magnitude** Super-heat 25 � 2*:*5 °½ � *C* Sub-cool 18 � 2*:*5 °½ � *C T*<sup>∞</sup> 22 � 0*:*9 °½ � *C m*\_ *<sup>R</sup>*404*<sup>a</sup>* 0*:*398 *kg*

computed liquid saturation temperature using Coolproops 6.4.1 [32].

and refrigerant.

**Table 2.**

**14**

*Operational parameters of the refrigeration system.*

*outlet at (3) and (4).*

**Figure 1.**

*Experimental data obtained experimentally and computed saturation temperature of R404a.*

for the vapor refrigerant pressure was reached around 1200 ms after initialization. In order to characterize the startup conditions, the first 2000 ms of the average between the different experiments corresponding to each variable displayed in the **Figure 2** were programed in ANSYS Fluent as dynamic boundary conditions.

#### **3. Computational domain and boundary conditions**

A time-dependent numerical model in three-dimension was developed to simulate the phase-transition and heat transfer of R404a in a water-cooled condenser. The geometry accounts for two fluid regions as well as one solid domain (copper) that separates both flows and provides the thermal mechanism for heat transfer. The computational domain (Ω<sup>1</sup> ∪ Ω<sup>2</sup> ∪ Ω3Þ contains three distant regions belonging to the space *<sup>X</sup>*<sup>~</sup> ! *<sup>R</sup>*<sup>3</sup> assigned as follows:


The properties of the materials and working fluids are show in **Table 4**. The temperature dependent material properties were programmed in Fluent using


Model validation and verification against experimental data is an important aspect of any numerical solution. For turbulent multi-phase flows, the model validation for the phase-transition process is particularly important because the solution of the volume fraction equation depends on the saturation temperature [40]. However, the model validation and identification of the saturation temperature can be challenging if the geometry is complex enough to obstruct the path of light for particle image velocimetry and particle image thermometry or block the access of probes for electric tomography techniques [41]. Unfortunately, the phase-transition process in the water-cooled condenser complies with the restrictions mentioned above because the refrigerant phase-transition takes place in a region where standard field experimental techniques offer limited information due to the water and copper jacket around the refrigerant line. Therefore, in order to develop a model that resembles reality, the saturation temperature has been programmed as a boundary condition based on the

*Numerical Analysis of a Water-Cooled Condenser at Startup Conditions for Refrigeration…*

The inlet boundary conditions for water and refrigerant are set to the mean mass flows. The flow rate of water measured experimentally going into the system ranges

The inlet and outlet time dependent temperature, pressures, and saturation temperature are loaded as user functions in Fluent from the experimental values shown in **Figure 2**. A no slip velocity condition was assigned to the boundary walls

� � and a thermal insulation condition was assigned on the wall between the water and the environment. The outlet quality was set to 100% liquid given that the actual system was designed and fabricated with the charge and specifications to

*PG*�*in*�*R*404*<sup>a</sup>* From experiments (see **Figure 2**) *PG*�*out*�*R*404*<sup>a</sup>* From experiments (see **Figure 2**) *Tin*�*R*404*<sup>a</sup>* From experiments (see **Figure 2**) *Tout*�*R*404*<sup>a</sup>* From experiments (see **Figure 2**)

*Tin*�*H*2*<sup>O</sup>* From experiments (see **Figure 2**) *Tout*�*H*2*<sup>O</sup>* From experiments (see **Figure 2**)

*TSat* From experiments (see **Figure 2**)

*<sup>s</sup>* and the inlet refrigerant mass flow corresponds to the compressor

*s* h i

*s* h i

0

inlet and outlet temperatures and pressures measured experimentally.

mass flow provided by the manufacturer at the operating conditions.

*m*\_ *in*�*R***404***<sup>a</sup>* **0***:***398** *kg*

*xin*�*R*404*<sup>a</sup>* 0 *xout*�*R*404*<sup>a</sup>* 1 *m*\_ *in*�*H*2*<sup>O</sup>* 0*:*26 *kg*

*Pout*�*H*2*<sup>O</sup>* 0½ � *Pa*

*<sup>∂</sup><sup>n</sup>* <sup>0</sup> �*Q<sup>∂</sup>Ω*2�*in* ¼ *Q<sup>∂</sup>Ω*<sup>3</sup> 12*:*7½ � *kW Q<sup>∂</sup>Ω*2�*in* ¼ �*Q<sup>∂</sup>Ω*<sup>1</sup> 12*:*7½ � *kW*

hold a constant sub-cool temperature after the condenser.

**3.1 Boundary conditions**

*DOI: http://dx.doi.org/10.5772/intechopen.97203*

from 0*:*21 to 0*:*3 *kg*

*u \* <sup>∂</sup>Ω<sup>i</sup>* ¼ 0

> *u \* <sup>∂</sup>Ω*<sup>1</sup> ¼ *u \* <sup>∂</sup>Ω*2�*in* ¼ *u \* <sup>∂</sup>Ω*2�*out* ¼ *u \* ∂Ω*<sup>3</sup>

**17**

*<sup>∂</sup>T∂Ω*3�<sup>∞</sup>

#### **Table 4.**

*Physical properties of the water, copper, and refrigerant regions.*

transient data tables and user defined routines. A schematic representation of the domains describing the computational domain is shown in **Figure 3**. The figure shows the inlet and outlet faces assigned for the water and refrigerant flows. The 3D geometry was modeled in SpaceClaim from the real dimensions and the numerical solution was obtained using Ansys Fluent 19.2. The contacting surfaces were discretized with conformal elements and the computational grid was created using tetrahedral objects with a maximum Skewness of 0.74. The mesh contains 36040897 nodes and 119573669 elements with a mean size of 3.12e-2[m].

The residual target (RMS) for the momentum and energy equations were set to 1*e* � 3 and 1*e* � 5 respectively. The time step was fixed to 1*e* � 6 for a total simulation time of 2 seconds.

#### **Figure 3.**

*Three-dimensional computational domain specifying the fluid and solid regions considered for the numerical simulation.*

*Numerical Analysis of a Water-Cooled Condenser at Startup Conditions for Refrigeration… DOI: http://dx.doi.org/10.5772/intechopen.97203*

Model validation and verification against experimental data is an important aspect of any numerical solution. For turbulent multi-phase flows, the model validation for the phase-transition process is particularly important because the solution of the volume fraction equation depends on the saturation temperature [40]. However, the model validation and identification of the saturation temperature can be challenging if the geometry is complex enough to obstruct the path of light for particle image velocimetry and particle image thermometry or block the access of probes for electric tomography techniques [41]. Unfortunately, the phase-transition process in the water-cooled condenser complies with the restrictions mentioned above because the refrigerant phase-transition takes place in a region where standard field experimental techniques offer limited information due to the water and copper jacket around the refrigerant line. Therefore, in order to develop a model that resembles reality, the saturation temperature has been programmed as a boundary condition based on the inlet and outlet temperatures and pressures measured experimentally.

#### **3.1 Boundary conditions**

transient data tables and user defined routines. A schematic representation of the domains describing the computational domain is shown in **Figure 3**. The figure shows the inlet and outlet faces assigned for the water and refrigerant flows. The 3D geometry was modeled in SpaceClaim from the real dimensions and the numerical solution was obtained using Ansys Fluent 19.2. The contacting surfaces were discretized with conformal elements and the computational grid was created using

� � 7.52 [37]

� � 18*:*6 [33] 97.6 [37]

*Tcr*�*R***404***<sup>a</sup>* ½ � *K* 345*:*25 [39] *To*�*R***404***<sup>a</sup>* ½ � *K* 227*:*15 [39]

**Water R404a vapor R404a liquid Copper**

65.24 [34] *ρ<sup>l</sup>*�*R*404*<sup>a</sup>*ð Þ *T* [34] 8978 [35]

[35]

� � 0*:*6 [33] 0.015 [34] 0.063 [34] 387*:*6 [35]

h i 4182 [36] 1221.4 [37] 1542.3 [34] 381

<sup>2</sup>*:*4432x10�2T�6*:*1536[38] *<sup>μ</sup><sup>v</sup>*�*R*404*<sup>a</sup>*ð Þ *<sup>T</sup>* [36] *<sup>μ</sup><sup>l</sup>*�*R*404*<sup>a</sup>*ð Þ *<sup>T</sup>* [36]

The residual target (RMS) for the momentum and energy equations were set to 1*e* � 3 and 1*e* � 5 respectively. The time step was fixed to 1*e* � 6 for a total simula-

*Three-dimensional computational domain specifying the fluid and solid regions considered for the numerical*

tetrahedral objects with a maximum Skewness of 0.74. The mesh contains 36040897 nodes and 119573669 elements with a mean size of 3.12e-2[m].

**Property unit Substance/Material**

*Heat Transfer - Design, Experimentation and Applications*

h i <sup>799</sup>*:*<sup>71</sup> <sup>þ</sup> <sup>1</sup>*:*6040T � <sup>3</sup>*:*161x10�<sup>3</sup>*T*<sup>2</sup> [33]

tion time of 2 seconds.

**Figure 3.**

*simulation.*

**16**

*K <sup>W</sup>*

*ρ kg*

*cp <sup>J</sup>*

*μ kg*

*ξ<sup>l</sup> mN*

*M <sup>g</sup>*

**Table 4.**

*mK*

*m*<sup>3</sup>

*kg K*

*m s*

*m*

*mol*

h i <sup>997</sup>*:*<sup>2</sup>

*Physical properties of the water, copper, and refrigerant regions.*

The inlet boundary conditions for water and refrigerant are set to the mean mass flows. The flow rate of water measured experimentally going into the system ranges from 0*:*21 to 0*:*3 *kg <sup>s</sup>* and the inlet refrigerant mass flow corresponds to the compressor mass flow provided by the manufacturer at the operating conditions.

The inlet and outlet time dependent temperature, pressures, and saturation temperature are loaded as user functions in Fluent from the experimental values shown in **Figure 2**. A no slip velocity condition was assigned to the boundary walls *u \* <sup>∂</sup>Ω<sup>i</sup>* ¼ 0 � � and a thermal insulation condition was assigned on the wall between the water and the environment. The outlet quality was set to 100% liquid given that the actual system was designed and fabricated with the charge and specifications to hold a constant sub-cool temperature after the condenser.

