CFD Based Design for Ejector Cooling System Using HFOS (1234Ze(E) and 1234Yf)

Article CFD Based Design for Ejector Cooling System Using HFOS (1234ze(E) and 1234yf)

Anas F A Elbarghthi 1,*, Saleh Mohamed 2, Van Vu Nguyen 1 and Vaclav Dvorak 1

1 Department of Applied Mechanics, Faculty of Mechanical Engineering, Technical University of Liberec, Studentská 1402/2, 46117 Liberec, Czech Republic; [email protected] (V.V.N.); [email protected] (V.D.) 2 Department of Mechanical and Materials Engineering, Masdar Institute, Khalifa University of Science and Technology, Abu Dhabi, UAE; [email protected] * Correspondence: [email protected]

Received: 18 February 2020; Accepted: 14 March 2020; Published: 18 March 2020

Abstract: The field of computational fluid dynamics has been rekindled by recent researchers to unleash this powerful tool to predict the ejector design, as well as to analyse and improve its performance. In this paper, CFD simulation was conducted to model a 2-D axisymmetric supersonic ejector using NIST real gas model integrated in ANSYS Fluent to probe the physical insight and consistent with accurate solutions. HFOs (1234ze(E) and 1234yf) were used as working fluids for their promising alternatives, low global warming potential (GWP), and adhering to EU Council regulations. The impact of different operating conditions, performance maps, and the Pareto frontier performance approach were investigated. The expansion ratio of both refrigerants has been accomplished in linear relationship using their critical compression ratio within 0.30% accuracy. The results show that ± R1234yf achieved reasonably better overall performance than R1234ze(E). Generally, by increasing the primary flow inlet saturation temperature and pressure, the entrainment ratio will be lower, and this allows for a higher critical operating back pressure. Moreover, it was found out that increasing the degree of superheat for inlet primary flow by 25 K improved the entrainment ratio by almost 20.70% for R1234yf. Conversely, increasing the degree of superheat to the inlet secondary flow has a relativity negative impact on the performance. The maximum overall ejector efficiency reached was 0.372 and 0.364 for R1234yf and R1234ze(E) respectively. Comparing the results using ideal gas model, the ejector entrainment ratio was overestimated up to 50.26% for R1234yf and 25.66% for R1234ze(E) higher than using real gas model.

Keywords: CFD; R1234yf; R1234ze(E); ejector cooling system; ejector eﬃciency; real gas model

1. Introduction Refrigeration is identiﬁed as an indispensable method that is widely used in many applications, including food storage, providing thermal comfort, and in the health care industry to preserve pharmaceuticals and medicines. The conventional vapor-compression refrigeration systems are mainly driven by electricity and are usually characterized by high energy consumption [1]. It was observed by the International Energy Agency in 2018 that the demand for air-conditioners worldwide is predicted to soar, resulting in an increase in the number of air-conditioners from 1.6 billion units today to 5.6 billion units by mid-century [2]. Therefore, there is a growing concern that the amount of electricity needed to power them will overload the electrical grids. Even though the need to reduce the cost associated with high energy consumption of conventional refrigerators has resulted in many developments in refrigeration systems such as more energy eﬃcient compressors, there is a limit to which this can be achieved. In addition, there is an increase in global-warming emissions caused by refrigeration

Energies 2020, 13, 1408; doi:10.3390/en13061408 www.mdpi.com/journal/energies Energies 2020, 13, 1408 2 of 19 systems relying on fossil fuels and the use of harmful substances such as chlorofluorocarbons (CFCs) as refrigerants. In fact, the emissions from these systems also contribute to ozone depletion which is most likely to increase the demand for air-conditioning, especially for thermal comfort [2]. Compared with conventional systems, ejector refrigeration systems (ERS) are more attractive, especially as we become more energy conscious. ERS come with advantages such as simple mode of function, lack of moving parts in construction, low cost, long lifespan, in addition to simplicity of installation and maintenance. This refrigeration system utilizes an ejector, generator and a liquid pump in place of the compressor which is electricity driven [3]. For a low-grade heat source, the liquid pump may consume up to 1% of the supplied heat to the ejector system. Compared to other conventional systems of the same refrigerating capacity, the ejector system may consume only one fifth of electricity consumed by the other systems [4,5]. Coefficient of performance (COP) is one of the main parameters for measuring ejector efficiency. The cooling systems of the refrigeration system may be analyzed from the COP. There exists a healthy relationship between the COP and the entrainment ratio in ejector cooling systems such that systems with high COP have high entrainment ratios, which provide high cooling capacity. Generally, the efficiency of ejector cooling system is usually not high. This is due to the complex nature of fluid flow in the ejector system and thus makes it difficult to attain a high COP. In addition, conditions such as turbulent mixing of two streams, shock waves and supersonic flow also affect the COP negatively; otherwise, ejector refrigerator is more sustainable and a good competitor to many types of refrigeration systems [6]. The advantages of using ERS have resulted in many researchers trying to exploit different techniques to enhance ejector performance. An example of such technique is the computational fluid dynamics (CFD). Over the years, CFD has shown very promising potential of predicting experimental results and assisting in the design of tools to improve the operation of ejectors [7]. Despite this, most numerical models of ejector systems have been limited to ideal gas, and as such fluid flow at subcritical condition of real gas where vapor coexist with liquid in two-phase flow are not considered [8]. Also, CFD results have shown that using the ideal gas model the entrainment ratio turns to be lower than when the real gas. An underestimated value of 20%–40% of the ideal gas model has been reported [9]. In this paper, the baseline ejector model was simulated using the real gas model because the properties of HFOs deviate significantly from the ideal gas law, especially at higher pressures. For example, air could be treated as an ideal gas, because the deviation between the ideal gas and real gas of this fluid is not large [10]. Moreover, the efficiency of the ejector was calculated in both cases too. It should be noted that this ejector was designed to apply the drop-in methodology where the same ejector can be used for both HFOs (1234ze(E) and 1234yf) working at the same required operating temperatures. The comprehensive CFD simulation was performed based on the NIST real gas model in order to increase the accuracy and consistency of the results, and this was used to model and design 2-D axisymmetric ejectors. Most researches applied hydrofluorocarbons while HFOs (1234ze(E) and 1234yf) are used in this paper as working fluid based on the regulation of the European Parliament and the EU Council No.517/2014 [11]. The CFD analysis covered the working conditions of R1234ze(E) and R1234yf at saturation points which has not been presented in ejector often. Furthermore, the effect of superheat degrees at the primary and the secondary flow, which was negligible in most of the research papers, ideal gas computational, performance map, and the efficiency of the ejector were also studied. The work from Mohamed et al. [12] was pertinent to this paper based on the CFD design of the ejector under real gas modelling in spite despite the use of a different solver and turbulent model.

2. Ejector Refrigeration Cycle The ejector refrigeration cycle system operates on a similar principle as the Carnot cycle. However, for the ejector refrigeration cycle, supersonic ejector provides an alternative method for the required compression. Therefore, the mechanical compressor in Carnot cycle is replaced with components Energies 2020, 13, 1408 3 of 19 such as ejector, liquid pump, and heat generator. The working fluid for this system is divided into two; primary and secondary flow. The primary fluid enters a converging-diverging ejector nozzle where it expands, generates a very low pressure and subsequently accommodates a supersonic flow at the exit [13]. Due to a local pressure drop and tangential force that develop at the edge of the primary flow, the secondary fluid is sucked into the ejector mixing chamber and entrained with higher velocity. In the mixing chamber, part of the energy from primary flow in the form of kinetic energy is transmitted to secondary stream and another part converted into pressure energy. The rest of the energy from both streams is dissipated as heat due to friction and mixing. Afterwards, a normal shock wave is experienced followed by a moderate back pressure in the condenser, causing sudden pressure to increase and deceleration to subsonic flow. The compressed stream then enters the diffuser with intermediate pressure between the motive fluid featured by the primary pressure and the secondary pressure of the entrained flow with deceleration to convert its kinetic energy back into potential energy. The resulting mixed stream leaves to the condenser to reject the heat and condense to liquid. Part of the working fluid then pumped to the generator as the primary stream and the rest goes to the evaporator through the expansion valve where the heat load will be absorbed from the cooling space or products. In the refrigeration cycles, the performance of the ejector can be analyzed by several parameters. The energy efficiency of the cycle can be quantified by assessing the COP. It is defined as the ratio between the cooling capacities at the evaporator to the gross energy input to the cycle. The ratio between the secondary flow mass flow rate and the primary flow mass flow rate has another important evaluation parameter called entrainment ratio (ω). This is because the entrainment ratio indicates the operational mode of the ejector. For the duration of the critical mode (on design) of operation, both the primary and the secondary flow are choked upon reaching the maximum value, and it remain constant with a low range of back pressure. However, only the primary flow is choked at the sub-critical mode (off design), resulting in a change in the mass flow rate ratio with respect to back pressure. In the case of back flow mode, a reverse flow at the secondary flow is observed and the entrainment ratio declines to lower than zero. In addition, the compression ratio parameter (CR) (also called pressure lift) is a key indicator for the pumping power because it points out how effectively the pressure of the suction secondary stream can be increased and thus measure the cycle operative range. CR is defined as the ratio of the static pressure between diffuser exit flow and secondary flow. Another important dimensionless parameter is the expansion ratio ER defined as the ratio between the primary pressure to secondary pressure. Regarding the ejector efficiency itself (ηejector), it can be defined by ASHRAE as the ratio between the actual recovered compression energy and the available theoretical energy in the primary stream [14,15].

3. Numerical Model Descriptions In the analytical approach such as the 1-D model, many assumptions needed to be considered such as the friction coeﬃcients related to the mixing losses and isentropic eﬃciency, hypothetical throat inside the constant area, and the location of the shock waves. CFD does not require these assumptions or any correction factors from empirical results to accurate the model.

3.1. Ejector Design The ejector remains the critical part that influences the ERS overall performance. Therefore, the geometry has to be sensibly determined. The simulated ejector was designed based on the study proposal of 30 KW ejector refrigeration system test stand at technical university of Liberec considering the guidelines obtained from Huang et al. 1999 [16] and preceding literatures to meet the system operational conditions, heat exchangers calculations and selecting of the working fluid. In addition, the geometry is designed to encounter the optimum working condition for both HFOs (1234ze(E) and 1234yf) refrigerants. These refrigerants are promising alternatives to fluorocarbons with low GWP and generally low flammability. Most importantly, they have a positively sloped saturation vapor curve where its entropy decreases along the upper limit curve known as the dry-expansion. In other words, Energies 2020, 13, x FOR PEER REVIEW 3 of 20

of the entrained flow with deceleration to convert its kinetic energy back into potential energy. The resulting mixed stream leaves to the condenser to reject the heat and condense to liquid. Part of the working fluid then pumped to the generator as the primary stream and the rest goes to the evaporator through the expansion valve where the heat load will be absorbed from the cooling space or products. In the refrigeration cycles, the performance of the ejector can be analyzed by several parameters. The energy efficiency of the cycle can be quantified by assessing the COP. It is defined as the ratio between the cooling capacities at the evaporator to the gross energy input to the cycle. The ratio between the secondary flow mass flow rate and the primary flow mass flow rate has another important evaluation parameter called entrainment ratio (ω). This is because the entrainment ratio indicates the operational mode of the ejector. For the duration of the critical mode (on design) of operation, both the primary and the secondary flow are choked upon reaching the maximum value, and it remain constant with a low range of back pressure. However, only the primary flow is choked at the sub-critical mode (off design), resulting in a change in the mass flow rate ratio with respect to back pressure. In the case of back flow mode, a reverse flow at the secondary flow is observed and the entrainment ratio declines to lower than zero. In addition, the compression ratio parameter (CR) (also called pressure lift) is a key indicator for the pumping power because it points out how effectively the pressure of the suction secondary stream can be increased and thus measure the cycle operative range. CR is defined as the ratio of the static pressure between diffuser exit flow and secondary flow. Another important dimensionless parameter is the expansion ratio ER defined as the ratio between the primary pressure to secondary pressure. Regarding the ejector efficiency itself (ηejector), it can be defined by ASHRAE as the ratio between the actual recovered compression energy and the available theoretical energy in the primary stream [14,15].

3. Numerical Model Descriptions In the analytical approach such as the 1-D model, many assumptions needed to be considered such as the friction coefficients related to the mixing losses and isentropic efficiency, hypothetical throat inside the constant area, and the location of the shock waves. CFD does not require these assumptions or any correction factors from empirical results to accurate the model.

3.1. Ejector Design The ejector remains the critical part that influences the ERS overall performance. Therefore, the geometry has to be sensibly determined. The simulated ejector was designed based on the study proposal of 30KW ejector refrigeration system test stand at technical university of Liberec considering the guidelines obtained from Huang et al. 1999 [16] and preceding literatures to meet the system operational conditions, heat exchangers calculations and selecting of the working fluid. In addition, the geometry is designed to encounter Energiesthe optimum2020, 13, working 1408 condition for both HFOs (1234ze(E) and 1234yf) refrigerants. These refrigerants4 ofare 19 promising alternatives to fluorocarbons with low GWP and generally low flammability. Most importantly, they have a positively sloped saturation vapor curve where its entropy decreases along the upper limit curve theknown expansion as the dry-expansion. process of the In ﬂuid other at words, saturated the expans vaporion will process end of in the the fluid superheated at saturated vapor vapor ﬂow will regionend in whichthe superheated is useful tovapor avoid flow condensation region which within is useful the to ejectoravoid condensation [17,18]. within the ejector [17,18]. TheThe general schematic schematic drawing drawing of the of ejector the ejector simulated simulated in this paper in this is papershown in is Figure shown 1. in In Figureorder to1. Inreduce order the to reducecomplexity the and complexity time-consu andmption time-consumption due to real gas duenon-linearity to real gas, an non-linearity, axisymmetric antwo-dimensional axisymmetric two-dimensionalejector model was ejector used. In model contrast, was the used. results In contrast,of axisymmetric the results and ofthree-dimensio axisymmetricnal and simulation three-dimensional are similar simulation[19]. are similar [19].

3.2. CFD Implementation In this paper, the simulation was performed with real gas modelling approach using National

Institute of Standards and Technology (NIST) fluid database (REFPROP v9.1) integrated in Figure 1. Schematic diagram of the ejector geometries as the base model. commercial Ansys Fluent R18.1 package [20]. In this respect, the governing equations are discretized 3.2.using CFD a control Implementation volume technique. The calculated axisymmetric space domain was divided as the final structured mesh into 274,241.00 and 270,182.00 number of elements for R1234yf and R1234ze(E) In this paper, the simulation was performed with real gas modelling approach using National respectively. The reason for that difference is to account for y+ which in all cases was less than 5 as Institute of Standards and Technology (NIST) fluid database (REFPROP v9.1) integrated in commercial well as to capture the relevant phenomena and probe the physical insight that occur close to the wall. Ansys Fluent R18.1 package [20]. In this respect, the governing equations are discretized using a control The domain was quadrilateral meshing structural as shown in Figure 2, provides higher volume technique. The calculated axisymmetric space domain was divided as the final structured orthogonality and good quality mesh to obtain fast and stable convergence using the real gas model. mesh into 274,241.00 and 270,182.00 number of elements for R1234yf and R1234ze(E) respectively. To ensure gaining accurate numerical results, mesh sensitivity analysis was performed with four- The reason for that difference is to account for y+ which in all cases was less than 5 as well as to capture and 15-times finer mesh on both working fluids as shown in Table 1. The analysis was conducted for the relevant phenomena and probe the physical insight that occur close to the wall. the entrainment ratio (ω), primary and secondary mass flow rates (ṁp and ṁs), and the exit The domain was quadrilateral meshing structural as shown in Figure2, provides higher temperatures Tc. This indicated how the number of the mesh can affect the numerical results orthogonality and good quality mesh to obtain fast and stable convergence using the real gas depending on further mesh density. It is shown from the table that the results are stable and there is model. To ensure gaining accurate numerical results, mesh sensitivity analysis was performed with no significant change with any further increase in the number of elements. Therefore, to perform the four- and 15-times finer mesh on both working fluids as shown in Table1. The analysis was conducted computation with less cost and time-consuming using NIST real gas non-linear model, case number for the entrainment ratio (ω), primary and secondary mass flow rates (m˙ p and m˙ s), and the exit 1 was selected to perform the numerical model analysis. temperatures Tc. This indicated how the number of the mesh can affect the numerical results depending The k-ω SST turbulence model has been approved to be the most suitable for ejector calculation on further mesh density. It is shown from the table that the results are stable and there is no significant because of higher accuracy than another renormalization group RNG-based k-ε. In addition, it also change with any further increase in the number of elements. Therefore, to perform the computation shows better performances in term of stream mixing inside the ejector. Consequently, it has been with less cost and time-consuming using NIST real gas non-linear model, case number 1 was selected selected as the turbulence model [1,3,21–24]. to perform the numerical model analysis.

Figure 2. Mesh of the ﬂow region. Figure 2. Mesh of the flow region.

The simulation was performed under pressure-based coupled solver and the flow was set based on steady-state. For complex flows, it may be ideal to use the second-order upwind discretization since it leads to obtain good results in case of tetrahedral and quad/hex meshes [25]. Real gas models are usually characterized by complex equations, and therefore the solution seems to converge at a much longer time than ideal gas. Hence, to ensure convergence at a shorter time, the flow courant number was started from 1 and the under-relaxation factors values set at 0.1 with increasing values of superheat degrees for both inlet flow streams to higher than 30 K, and then after an adequate number of iterations, these parameters can be adjusted gradually to accelerate the convergence depending on the solution stability. It is easier to converge in the single-choke condition hence it is recommended to start within non-critical condition and then step by step increase the back-flow pressure to reach the critical condition. Most of the simulation converged to the residues up to 10–8 which is very difficult to reach if the density-based solver where used.

Energies 2020, 13, x; doi: FOR PEER REVIEW www.mdpi.com/journal/energies Energies 2020, 13, 1408 5 of 19

Table 1. Mesh sensitivity results.

Working Fluid Case Mesh [Cells] m˙ s [kg/s] m˙ p [kg/s] ω [-] Tc [K] R1234ze(E) 1 270,182 0.0516 0.0924 0.5585 308.9 R1234ze(E) 2 1,074,146 0.0518 0.0919 0.5639 308.8 R1234ze(E) 3 4,196,330 0.0519 0.0917 0.5665 308.9 R1234yf 1 274,241 0.0791 0.1230 0.6427 298.6 R1234yf 2 1,076,795 0.0794 0.1224 0.6489 298.5 R1234yf 3 4,198,463 0.0796 0.1224 0.6500 298.5

Primary ﬂow Temperature 70 ◦C, secondary ﬂow Temperature 6 ◦C. Degree of superheat 0K, outlet pressure 400 kPa.

The k-ω SST turbulence model has been approved to be the most suitable for ejector calculation because of higher accuracy than another renormalization group RNG-based k-ε. In addition, it also shows better performances in term of stream mixing inside the ejector. Consequently, it has been selected as the turbulence model [1,3,21–24]. The simulation was performed under pressure-based coupled solver and the flow was set based on steady-state. For complex flows, it may be ideal to use the second-order upwind discretization since it leads to obtain good results in case of tetrahedral and quad/hex meshes [25]. Real gas models are usually characterized by complex equations, and therefore the solution seems to converge at a much longer time than ideal gas. Hence, to ensure convergence at a shorter time, the flow courant number was started from 1 and the under-relaxation factors values set at 0.1 with increasing values of superheat degrees for both inlet flow streams to higher than 30 K, and then after an adequate number of iterations, these parameters can be adjusted gradually to accelerate the convergence depending on the solution stability. It is easier to converge in the single-choke condition hence it is recommended to start within non-critical condition and then step by step increase the back-flow pressure to reach the 8 critical condition. Most of the simulation converged to the residues up to 10− which is very difficult to reach if the density-based solver where used.

3.3. Boundary Conditions The boundary conditions specify the dependent variables on the boundaries of the model to control the solution of the PDE. Basically, the simulated ejector is a passive device where the flow is confined and derived by its unique geometry. The boundary conditions were associated with two inlets linked with the motive flow from the generator and suction flow from the evaporator and one outlet-mixed flow which passed to the condenser. The walls are considered adiabatic. In this simulation, both refrigerant inlet conditions are set at saturated vapor. The primary flow stream temperatures Tp were tested at 87, 80, and 70 ◦C while the secondary flow stream temperatures Ts were at 6, 10, and 14 ◦C. Both flow streams were taken as the corresponding saturation pressure at their temperatures. Two pressure inlets were selected for the motive as the primary flow and the suction as the secondary flow entering the ejector and one outlet pressure for the mixed stream discharged to the condenser.

4. Numerical Validation At the beginning of this work, the best available validation found was the experimental result from Huang et al. using 30 different cases at different ejector area ratios and similar operation conditions using results achieved at critical mode [16]. The reason for using Ref. 16 for validation is that the experimental data under various configurations and a wide range of operating conditions were clearly presented. The values of the entrainment ratio and critical back pressure were even specified by numbers. As well as the signature geometries were clearly mentioned and validated in the literature. The best turbulent model which can predict more precise results becomes the main challenge. Table2 summarizes the test conditions along with the experimental and numerical entrainment ratio (ω), CFD primary and secondary mass flow rates (m˙ p and m˙ s), exit temperatures Tc, the error between the CFD model and the experimental data, as well as the number of mesh cells examined. The numerical work Energies 2020, 13, x FOR PEER REVIEW 3 of 19 Energies 2020, 13, 1408 6 of 19 Table 2. Verification of the CFD results with Huang et al. experimental results. wasHuang performed et al. 1999 under (E k-xperimental)ω SST turbulence [16] model using a pressure-basedPresent Work ( solver,Numerical) and the inlet flow Pp Ps Pc ω ω Error ṁp ṁs Tc Cells streamsEjector are set to be at saturated vapor. The numerical simulation was observed to converge when the residues[kPa] of all governing[kPa] [kPa] equations [- fall] below[-] 1 10%8 . The present[kg/s] calculated[kg/s] numerical[°C] modelNo. × − wasAA able to538.20 predict the39.97 experimental 128.13 0.2246 entrainment 0.2393 ration 6.56 within 0.0119414% error 0.00286 as seen in340.35 Figure 3, while211,900 ± MohamedAA 465.68 el at. show 39.97 a similar 114.22 comparison 0.2880 with0.2685 his CFD–6.79 work using0.01038 density-based 0.00279 solver335.04 and 211,900 RNG k-εAAturbulence 604.79 model 47.26 but with144.26 result 0.2350 error within0.256420%. 9.10 0.01336 0.00343 343.76 211,900 AA 604.79 39.97 142.39 0.1859 0.1896± 2.02 0.01336 0.00253 346.14 211,900 AA 538.20Table 47.26 2. Verification 130.72of the0.2946 CFD results0.2943 with – Huang0.11 et0.01194 al. experimental 0.00351 results. 338.88 211,900 AA Huang465.68 et al.47.26 1999 (Experimental)116.19 0.3398 [16] 0.3577 5.27 Present0.01038 Work (Numerical)0.00371 332.74 211,900 P P P ω ω Error m˙ m˙ T Cells AG Ejector604.79 p 47.26 s 127.28 c 0.3503 0.3175 –9.37 0.013345p 0.00424s c 340.83 210,100 [kPa] [kPa] [kPa] [-] [-] % [kg/s] [kg/s] [◦C] No. AG AA538.20 538.20 47.26 39.97 116.19 128.13 0.4034 0.2246 0.37690.2393 –6.56 6.56 0.0119210.01194 0.002860.00449340.35 335.54211,900 210,100 AG AA465.68 465.68 47.26 39.97 102.59 114.22 0.4790 0.2880 0.49380.2685 3.086.79 0.0103660.01038 0.002790.00512335.04 328.35211,900 210,100 − AG AA400.74 604.79 47.26 47.26 91.59 144.26 0.6132 0.2350 0.60590.2564 –1.18 9.10 0.0089680.01336 0.003430.00543343.76 322.19211,900 210,100 AA 604.79 39.97 142.39 0.1859 0.1896 2.02 0.01336 0.00253 346.14 211,900 AC AA604.79 538.20 39.97 47.26 117.38 130.72 0.2814 0.2946 0.26710.2943 –5.090.11 0.0133620.01194 0.003510.00357338.88 341.92211,900 237,600 − AC AA538.20 465.68 39.97 47.26 107.72 116.19 0.3488 0.3398 0.30050.3577 –13.85 5.27 0.0119360.01038 0.003710.00359332.74 337.23211,900 237,600 AG 604.79 47.26 127.28 0.3503 0.3175 9.37 0.013345 0.00424 340.83 210,100 AC 465.68 39.97 95.94 0.4241 0.3872 –8.71− 0.010379 0.00402 330.27 237,600 AG 538.20 47.26 116.19 0.4034 0.3769 6.56 0.011921 0.00449 335.54 210,100 − AC AG400.74 465.68 39.97 47.26 84.262 102.59 0.4889 0.4790 0.53040.4938 8.48 3.08 0.0103660.00898 0.005120.00476328.35 322.50210,100 237,600 AD AG604.79 400.74 39.97 47.26 106.98 91.59 0.3457 0.6132 0.30560.6059 –11.601.18 0.0133560.008968 0.005430.00408322.19 339.96210,100 235,200 − AC 604.79 39.97 117.38 0.2814 0.2671 5.09 0.013362 0.00357 341.92 237,600 AD 465.68 39.97 87.70 0.5387 0.4770 –11.45− 0.010375 0.00495 327.24 235,200 AC 538.20 39.97 107.72 0.3488 0.3005 13.85 0.011936 0.00359 337.23 237,600 − AD AC400.74 465.68 39.97 39.97 76.834 95.94 0.6227 0.4241 0.65670.3872 5.458.71 0.0089750.010379 0.004020.00589330.27 319.27237,600 235,200 − AD AC604.79 400.74 47.26 39.97 110.36 84.262 0.4541 0.4889 0.42760.5304 –5.85 8.48 0.0133560.00898 0.004760.00571322.50 336.43237,600 235,200 AD 604.79 39.97 106.98 0.3457 0.3056 11.60 0.013356 0.00408 339.96 235,200 AD 538.20 47.26 101.16 0.5422 0.5198 –−4.13 0.011931 0.0062 330.727 235,200 AD 465.68 39.97 87.70 0.5387 0.4770 11.45 0.010375 0.00495 327.24 235,200 − AD AD465.68 400.74 47.26 39.97 90.60 76.834 0.6350 0.6227 0.66240.6567 4.31 5.45 0.0103750.008975 0.005890.00687319.27 323.88235,200 235,200 AD AD400.74 604.79 47.26 47.26 80.629 110.36 0.7412 0.4541 0.82310.4276 11.055.85 0.0089750.013356 0.005710.00739336.43 317.66235,200 235,200 − AD 538.20 47.26 101.16 0.5422 0.5198 4.13 0.011931 0.0062 330.727 235,200 EG 604.79 39.97 137.36 0.2043 0.2251 10.18− 0.015341 0.00345 344.27 196,860 AD 465.68 47.26 90.60 0.6350 0.6624 4.31 0.010375 0.00687 323.88 235,200 EC AD604.79 400.74 39.97 47.26 177.70 80.629 0.2273 0.7412 0.25080.8231 10.35 11.05 0.0153390.008975 0.007390.00385317.66 342.85235,200 195,829 EC EG604.79 604.79 47.26 39.97 129.85 137.36 0.3040 0.2043 0.29760.2251 –2.12 10.18 0.0153390.015341 0.003450.00456344.27 341.64196,860 195,829 ED EC604.79 604.79 39.97 39.97 120.61 177.70 0.2902 0.2273 0.25120.2508 –13.45 10.35 0.0152290.015339 0.003850.00383342.85 342.63195,829 240,400 EC 604.79 47.26 129.85 0.3040 0.2976 2.12 0.015339 0.00456 341.64 195,829 − EE ED604.79 604.79 39.97 39.97 109.23 120.61 0.3505 0.2902 0.35800.2512 2.1513.45 0.0152290.015229 0.003830.00545342.63 337.89240,400 236,800 − EE EE604.79 604.79 47.26 39.97 109.23 109.23 0.4048 0.3505 0.44770.3580 10.59 2.15 0.0152290.015229 0.005450.00682337.89 335.65236,800 236,800 EF EE604.79 604.79 39.97 47.26 104.77 109.23 0.3937 0.4048 0.36350.4477 –7.68 10.59 0.0151480.015229 0.006820.00551335.65 337.55236,800 233,600 EF 604.79 39.97 104.77 0.3937 0.3635 7.68 0.015148 0.00551 337.55 233,600 − EF EF604.79 604.79 47.26 47.26 105.13 105.13 0.4989 0.4989 0.50440.5044 1.11 1.11 0.0151480.015148 0.007640.00764333.76 333.76233,600 233,600 EH EH604.79 604.79 39.97 39.97 98.70 98.70 0.4377 0.4377 0.42720.4272 –2.402.40 0.0152630.015263 0.006520.00652335.03 335.03242,300 242,300 −

Figure 3. CFD model validation with experimental result Ref. [16] and comparing result from Ref. [12]. Figure 3. CFD model validation with experimental result Ref. [16] and comparing result from Ref. [12].

Energies 2020, 13, x FOR PEER REVIEW 4 of 20

Figure 3. CFD model validation with experimental result Ref. [16] and comparing result from Ref. Energies[12].2020 , 13, 1408 7 of 19

5. Comparison of Real and Ideal Gas Flow Results 5. Comparison of Real and Ideal Gas Flow Results The entrainment ratio results of the ejector in the case of working by ideal gas have been obtained in orderThe to entrainment evaluate the ratio difference resultsof between the ejector ideal in an thed casethe used of working NIST real by idealgas model. gas have The been approach obtained of indefining order tothe evaluate physical the properties difference of the between ideal gas ideal mo anddel is the an used important NIST realconsideration. gas model. For The that approach reason, ofthe defining physical the properties physical of properties the ideal ofgas the model ideal gaswere model specified is an based important on the consideration. primary flow For[26,27]. that reason,Therefore, the viscosity, physical properties specific heat, of the and ideal thermal gas model conductivity were specified were treated based as on constants the primary throughout flow [26, 27the]. Therefore,calculation viscosity, domain and specific depending heat, and on thermal the operating conductivity conditions were in treated each case, as constants except the throughout density was the calculationmodelled using domain the andideal depending gas law. on the operating conditions in each case, except the density was modelledThe results using theshow ideal that gas the law. performance of the ejector was overestimated using ideal gas model as illustratedThe results in Figure show that 4. For the example, performance the entr of theainment ejector ratio was for overestimated R1234yf in ideal using gas ideal model gas at model Tp = 70 as illustrated°C and Ts = in 6 Figure °C was4. 16.78% For example, higher the than entrainment using real ratio gas model. for R1234yf This inratio ideal increased gas model to at50.26%Tp = when70 ◦C andTp = T87s =°C.6 ◦ComparingC was 16.78% to R1234ze(E) higher than at using the same real gasprevious model. working This ratio conditions, increased ω toof 50.26%the ideal when gas Tmodelp = 87 is◦ C.aboutComparing 11.40% higher to R1234ze(E) than that at of the real same gas model previous at T workingp = 70 °C, conditions, but as the inletω of primary the ideal flow gas modelsaturation is about temperature 11.40% higher increased than to that 87 of°C, real the gas difference modelat becomes Tp = 70 25.66%.◦C, but asResearchers the inlet primary assumed flow in saturationmany reviews temperature that simulations increased using to 87 the◦C, ideal the digasfference model becomes are able 25.66%.to predict Researchers sufficient assumedresults but, in manyironically, reviews the comparison that simulations shows using how it the diverges ideal gas from model the actual are able real to gas predict model su results.fficient results but, ironically, the comparison shows how it diverges from the actual real gas model results.

1 1 Tp =70°C / real gas Tp =70°C / real gas 0.9 Tp =70°C / ideal gas 0.9 Tp =70°C / ideal gas Tp = 80°C / real gas Tp = 80°C / real gas 0.8 0.8 Tp =80°C / ideal gas Tp =80°C / ideal gas 0.7 Tp =87°C / real gas 0.7 Tp =87°C / real gas Tp =87°C / ideal gas Tp =87°C / ideal gas 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 Entrainment Ratio Entrainment 0.2 Ratio Entrainment 0.2 0.1 0.1 0 0 350 450 550 650 750 850 950 350 450 550 650 750 850 950 Back pressure, [kPa] Back pressure, [kPa] (a) (b)

Figure 4. EjectorEjector CFD results with real andand idealideal gasgas modelmodelvs vsentrainment entrainment ratio ratio at at T Ts s==6°C.6 ◦C. ( (aa)) R1234yf. R1234yf. (b) R1234ze(E). 6. CFD Analysis of the Ejector 6. CFD Analysis of the Ejector 6.1. Effect of Operation Conditions 6.1. Effect of Operation Conditions The primary and the secondary flow inlet to the ejector were examined under their saturation The primary and the secondary flow inlet to the ejector were examined under their saturation conditions. Three different primary temperatures (70, 80, and 87 ◦C) and entrained temperatures (6, 10, conditions. Three different primary temperatures (70, 80, and 87 °C) and entrained temperatures (6, and 14 ◦C) were selected based on the working range of the designed ejector for both refrigerants. The10, and details 14 °C) of thewere ejector selected performance based on the were working considered range by of investigatingthe designed ejector the characteristic for both refrigerants. curves for theThe ejectordetails criticalof the ejector and subcritical performance modes were because consider theed ejector by investigating performance the is characteristic assessed in terms curves of thefor energythe ejector recovered critical and by the subcritical secondary modes flow because with respect the ejector to the performance energy available is assessed in the in primary terms of flow. the Figureenergy5 recovered represent by the the e ff ectsecondary of the primary flow with flow resp asect the to desired the energy amount available of energy in the to accelerateprimary flow. and suckFigure the 5 secondaryrepresent the flow effect by convertingof the primary the pressureflow as the energy desired of the amount primary of energy flow into to kineticaccelerate energy and whilesuck the mixing. secondary Therefore, flow theby entrainmentconverting the ratio pressure was predicted energy overof the the primary working flow range into of kinetic back pressure. energy Thewhile dashed mixing. lines Therefore, represent the that entrainment the predicted ratio data fitwas the predicted performance over curves the working while the range markers of showback thepressure. numerical The results.dashed lines represent that the predicted data fit the performance curves while the markersIt can show be the seen numerical from Figure results.5 that increasing the primary flow temperature caused a lower entrainment ratio and produced a higher critical back pressure. This is associated to the increase of the primary mass flow rate and serves to enlarge the expansion angle, causing a reduction of the annular effective area and increasing the resulting momentum of the mixed stream due to the higher Energies 2020, 13, x FOR PEER REVIEW 5 of 19 ejector will operate at higher critical pressure. In addition, when the primary or secondary saturated flow temperatures is fixed, then the compression ratio will increase with increasing expansion ratio (ER), causing a lower entrainment ratio, and vice versa. R1234yf represent higher entrainment ratio than R1234ze(E). At Tp = 70 °C and Ts = 14 °C the ejector works at the highest entrainment ratio. R1234yf recorded ω = 0.9158 where R1234ze(E) has ω = 0.8435. Decreasing the secondary temperatures to 10 °C and 6 °C also decrease ω by (14.72%, 17.71%) for R1234yf and (16.94%, 20.28%) for R1234ze(E) which is a decrease of about 13% back pressure. In other word, decreasing Ts at a fixed Tp will decrease the entrainment ratio because the secondary mass flow rate, s, is decreasing whereas the primary mass flow rate, p, is fixed. Moreover, the difference in ω between the refrigerants will be decreasing in case of increasing the ṁ ṁ fixed Tp. For example, at Tp = 70 °C the difference decreases by 8.57%, 11.47% and15.60% in case of Ts = 14 °C, 10 °C, and 6 °C respectively. When Tp = 87 °C, the difference in ω between the working fluids decreases to 4.91%. These differences are not varying that much in the case of increasing Tp at the fixing Ts, as represented in Figure 5. The operating back pressure was affected by the inlet operating temperatures. With increasing both inlet saturated flow temperatures or even by increasing one of them, the critical mode for the Energies 2020, 13, 1408 8 of 19 ejector working with two refrigerants will increase. The on design working mode range is relatively higher in case of using R1234yf. Comparatively, it was found that at fixed Ts, the value of the critical velocityback pressure of the P entrainedc-cri increased stream by 100 attained. kPa when Therefore, Tp increased the shockfrom 70 waves to 80 move°C or from downstream, 80 to 87 °C and, while the ejectorPc-cri for will R1234ze(E) operate atincreased higher criticalby 75 kPa pressure. at similar In addition, conditions. when the primary or secondary saturated flowIn temperatures general, R1234yf is fixed, has then in the the region compression of 23.50% ratio higher will critical increase back with pressure increasing than expansionR1234ze(E) ratio and (ER),higher causing ejector a working lower entrainment back pressure ratio, range. and vice versa.

1 1 Ts =6°C/R1234yf Tp =70°CR1234yf 0.9 Ts =10°C/R1234yf 0.9 Tp =80°C/R1234yf Ts =14°C/R1234yf 0.8 0.8 Tp =87°C/R1234yf Ts =6°C/R1234ze(E) Tp =70°C/R1234ze(E) 0.7 Ts = 10°C/R1234ze(E) 0.7 Tp = 80°C/R1234ze(E) Ts = 14°C/R1234ze(E) 0.6 0.6 Tp = 87°C/R1234ze(E) 0.5 0.5 0.4 0.4 0.3 0.3 Entrainment RatioEntrainment 0.2 RatioEntrainment 0.2 0.1 0.1 0 0 350 450 550 650 750 850 950 1050 350 450 550 650 750 850 950 1050 Back pressure, [kPa] Back pressure, [kPa] (a) (b)

1 1 Ts =6°C/R1234yf Ts =10°C/R1234yf Tp =70°CR1234yf 0.9 Ts =14°C/R1234yf Ts =6°C/R1234ze(E) 0.9 Tp =80°C/R1234yf Ts = 10°C/R1234ze(E) Ts = 14°C/R1234ze(E) 0.8 0.8 Tp =87°C/R1234yf Tp =70°C/R1234ze(E) 0.7 0.7 Tp = 80°C/R1234ze(E) 0.6 0.6 Tp = 87°C/R1234ze(E) 0.5 0.5 0.4 0.4 0.3 0.3 Entrainment RatioEntrainment Entrainment RatioEntrainment 0.2 0.2 0.1 0.1 0 0 350 450 550 650 750 850 950 1050 350 450 550 650 750 850 950 1050 Energies 2020, 13, x FOR PEER REVIEW 6 of 19 Back pressure, [kPa] Back pressure, [kPa] (c) (d)

1 1 Ts =6°C/R1234yf Tp =70°CR1234yf 0.9 Ts =10°C/R1234yf 0.9 Tp =80°C/R1234yf

0.8 Ts =14°C/R1234yf 0.8 Tp =87°C/R1234yf Ts =6°C/R1234ze(E) Tp =70°C/R1234ze(E) 0.7 0.7 Tp = 80°C/R1234ze(E) Ts = 10°C/R1234ze(E) Tp = 87°C/R1234ze(E) 0.6 Ts = 14°C/R1234ze(E) 0.6 0.5 0.5 0.4 0.4 0.3 0.3 Entrainment RatioEntrainment Entrainment RatioEntrainment 0.2 0.2 0.1 0.1 0 0 350 450 550 650 750 850 950 1050 350 450 550 650 750 850 950 1050 Back pressure, [kPa] Back pressure, [kPa]

(e) (f)

FigureFigure 5.5. CFD Entrainment ratio vs back pressure for the ejector at didifferentﬀerent primaryprimary andand secondarysecondary

ﬂowflow temperaturestemperatures when (a)T) Tp == 70°C.70 ◦C. (b ()b T)Ts =s =6°C.6 ◦ (C.c) (Tcp)T = p80°C.= 80 (◦dC.) T (sd =)T 10°C.s = 10 (e)◦ C.Tp (=e )T87°C.p = (87f) T◦sC. = (14°C.f)Ts = 14 ◦C.

(a)

Energies 2020, 13, 1408 9 of 19

R1234yf represent higher entrainment ratio than R1234ze(E). At Tp = 70 ◦C and Ts = 14 ◦C the ejector works at the highest entrainment ratio. R1234yf recorded ω = 0.9158 where R1234ze(E) has ω = 0.8435. Decreasing the secondary temperatures to 10 ◦C and 6 ◦C also decrease ω by (14.72%, 17.71%) for R1234yf and (16.94%, 20.28%) for R1234ze(E) which is a decrease of about 13% back pressure. In other word, decreasing Ts at a fixed Tp will decrease the entrainment ratio because the secondary mass flow rate, m˙ s, is decreasing whereas the primary mass flow rate, m˙ p, is fixed. Moreover, the difference in ω between the refrigerants will be decreasing in case of increasing the fixed Tp. For example, at Tp = 70 ◦C the difference decreases by 8.57%, 11.47% and15.60% in case of Ts = 14 ◦C, 10 ◦C, and 6 ◦C respectively. When Tp = 87 ◦C, the difference in ω between the working fluids decreases to 4.91%. These differences are not varying that much in the case of increasing Tp at the fixing Ts, as represented in Figure5. The operating back pressure was affected by the inlet operating temperatures. With increasing both inlet saturated flow temperatures or even by increasing one of them, the critical mode for the ejector working with two refrigerants will increase. The on design working mode range is relatively higher in case of using R1234yf. Comparatively, it was found that at fixed Ts, the value of the critical back pressure Pc-cri increased by 100 kPa when Tp increased from 70 to 80 ◦C or from 80 to 87 ◦C, while Pc-cri for R1234ze(E) increased by 75 kPa at similar conditions. In general, R1234yf has in the region of 23.50% higher critical back pressure than R1234ze(E) and higher ejector working back pressure range. The maximum ejector efficiency at minimum energy cost should be considered when ejector cooling system is designed. This is linked with the energy required at the generator to increase the primary flow temperature to a certain limit where the ejection ratio reaches the maximum, nevertheless any extra energy added to the generator will have no significant effect and will be wasted. This analysis needs to be study at specific secondary and back pressure from the working fluid conditions to avoid testing the optimum case with all parameters. Figure6 illustrates the contours of Mach number at different primary temperatures Tp inside ejector baseline for R1234ze(E) at Ts = 10 ◦C, Pc = 560 kPa and R1234yf at Ts = 10 ◦C, Pc = 730 kPa. Both refrigerants were represented at same Tp = 70, 80, 87 ◦C from top to bottom. It can be seen that increasing Tp, i.e., Pp at Tp saturation, will increase the oblique shock waves intensity and shift them upstream to the diffuser part. Furthermore, operating at higher Pp results in double-choking condition (critical mode) because the amount of energy that drives the entrained flow is enough to accelerate it to the choking state (sonic speed) achieving the peak value of the secondary mass flow rate and lift the flow to that particular back pressure. In addition, the size of the jet core is increased with higher Pp and, as a result, this has inversely proportional relation with the effective area (hypothetical throat) [28]. Consequently, it can be seen that the strong normal shock waves occur close to the diffuser at high Tp which is an indicator that the ejector is working in double-choking mode of operation but away from the critical point. On the other hand, when Tp is fixed and Ts is increased, then higher entrained flow energy and less amount of primary flow is required to accelerate the flow. At that point the m˙ s will be increasing and hence the entrainment ratio. For this reason, it is recommended to work at higher secondary flow (saturation) temperatures. The primary nozzle operates in the under-expanded regime in all cases and the jet converged toward the ejector center when increasing Tp. It can be observed that the flow patterns are almost similar with slightly less intense shock waves for R1234yf. Figure7 illustrates the contours of Mach number for both working fluids at di fferent back pressure. The top contours of the Mach number for both refrigerants represent the results at critical region where both primary and secondary flow are choked, and the entrainment ratio remains constant. The primary flow leaves the primary nozzle at supersonic velocity and the shock train can be observed along the centerline through the fluctuation of the static pressure before the mixing. A separation layer takes place between the primary and the secondary flow because of the velocity difference in between so that the entrained flow velocity will increase until the mixing take place at the constant throat area. The velocity become subsonic and the oblique shock waves take place due to the static pressure increase. Energies 2020, 13, x FOR PEER REVIEW 6 of 19

1 1 Ts =6°C/R1234yf Tp =70°CR1234yf 0.9 Ts =10°C/R1234yf 0.9 Tp =80°C/R1234yf 0.8 Ts =14°C/R1234yf 0.8 Tp =87°C/R1234yf Ts =6°C/R1234ze(E) Tp =70°C/R1234ze(E) 0.7 0.7 Ts = 10°C/R1234ze(E) Tp = 80°C/R1234ze(E) Tp = 87°C/R1234ze(E) 0.6 Ts = 14°C/R1234ze(E) 0.6 0.5 0.5 0.4 0.4 0.3 0.3 Entrainment Ratio Entrainment Entrainment Ratio Entrainment 0.2 0.2 0.1 0.1 0 0 350 450 550 650 750 850 950 1050 350 450 550 650 750 850 950 1050 Back pressure, [kPa] Back pressure, [kPa]

(e) (f)

Figure 5. CFD Entrainment ratio vs back pressure for the ejector at different primary and secondary

flow temperatures when (a) Tp = 70°C. (b) Ts = 6°C. (c) Tp = 80°C. (d) Ts = 10°C. (e) Tp = 87°C. (f) Ts = 14°C.

The maximum ejector efficiency at minimum energy cost should be considered when ejector cooling system is designed. This is linked with the energy required at the generator to increase the primary flow temperature to a certain limit where the ejection ratio reaches the maximum, nevertheless any extra energy added to the generator will have no significant effect and will be wasted. This analysis needs to be study at specific secondary and back pressure from the working fluid conditions to avoid testing the optimum case with all parameters. Figure 6 illustrates the contours of Mach number at different primary temperatures Tp inside ejector baseline for R1234ze(E) Energies 2020, 13, x FOR PEER REVIEW 7 of 19 at Ts = 10 °C, Pc = 560 kPa and R1234yf at Ts = 10 °C, Pc = 730 kPa. Both refrigerants were represented at same Tp = 70, 80, 87 °C from top to bottom. It can be seen that increasing Tp, i.e., Pp at Tp saturation, will increase the oblique shock waves intensity and shift them upstream to the diffuser part. Furthermore, operating at higher Pp results in double-choking condition (critical mode) because the amount of energy that drives the entrained flow is enough to accelerate it to the choking state (sonic speed) achieving the peak value of the secondary mass flow rate and lift the flow to that particular back pressure. In addition, the size of the jet core is increased with higher Pp and, as a result, this has inversely proportional relation with the effective area (hypothetical throat) [28]. Consequently, it can be seen that the strong normal shock waves occur close to the diffuser at high Tp which is an indicator that the ejector is working in double-choking mode of operation but away from the critical point. On the other hand, when Tp is fixed and Ts is increased,(b) then higher entrained flow energy and less amount of primary flow is required to accelerate the flow. At that point the ṁs will be increasing and henceFigure the entrainment 6. Mach number ratio. contours For this inside reason, ejector it baselineis recommended given Tp = 70, to 80,work 87°C at respectively higher secondary from top flow (saturation)to bottom temperatures. for: (a) R1234ze(E) The atprimary Ts = 10°C, nozzle Pc = 560 oper kPa.ates (b) R1234yfin the under-expanded at Ts = 10°C, Pc = 730 regime kPa. in all cases Energiesand the2020 jet, 13converged, 1408 toward the ejector center when increasing Tp. It can be observed that the10 flow of 19 patternsFigure are 7almost illustrates similar the with contours slightly of less Mach intense numb shocker for waves both for working R1234yf. fluids at different back pressure. The top contours of the Mach number for both refrigerants represent the results at critical region where both primary and secondary flow are choked, and the entrainment ratio remains constant. The primary flow leaves the primary nozzle at supersonic velocity and the shock train can be observed along the centerline through the fluctuation of the static pressure before the mixing. A separation layer takes place between the primary and the secondary flow because of the velocity difference in between so that the entrained flow velocity will increase until the mixing take place at the constant throat area. The velocity become subsonic and the oblique shock waves take place due to the static pressure increase. When the back pressure is increased to the critical value, the region of the subcritical mode starts, and that point called the critical back pressure where the Mach number contours represent at the Energies 2020, 13, x FOR PEER REVIEW 7 of 19 middle contours in the figure. After that point, furt(hera) increase in back pressure will cause a sharp decrease in the entrainment ratio till it reaches zero and a single choking appeared only for the primary flow as represented in the bottom contours. Afterwards, an additional increase in the back pressure will lead to the presence of reverse flow. Moreover, it can be observed that increasing the back pressure will move the position of the shock waves towards the back of the primary nozzle direction and eliminate the existence of the shock waves when reaching the critical back pressure, as noticed in operating at back pressure of 613kPa in case of R1234ze(E) and 801 kPa for R1234yf under the inlet condition of Tp = 80 °C, Ts = 10 °C. Regardless of the higher range of critical region for R1234yf, the contours of the Mach number and the shock waves look similar. Additional increase in the back pressure after the critical point will decrease the axial velocity of the mixed flow and move(b) the oblique shock waves to the primary nozzle exit, where it disturbs the primary jet core to the limit when the primary flow could not expand, Figure 6. Mach number contours inside ejector baseline given T = 70, 80, 87 C respectively from top forcingFigure it to 6. flow Mach reversibly number contours to the entrained inside ejector flow baseline entrance. given Tpp = 70, 80, 87°C◦ respectively from top to bottom for (a) R1234ze(E) at T = 10 C, P = 560 kPa. (b) R1234yf at T = 10 C, P = 730 kPa. to bottom for: (a) R1234ze(E) at Ts s = 10°C,◦ Pcc = 560 kPa. (b) R1234yf at Ts =s 10°C,◦ Pc = c730 kPa.

Figure 7 illustrates the contours of Mach number for both working fluids at different back pressure. The top contours of the Mach number for both refrigerants represent the results at critical region where both primary and secondary flow are choked, and the entrainment ratio remains constant. The primary flow leaves the primary nozzle at supersonic velocity and the shock train can be observed along the centerline through the fluctuation of the static pressure before the mixing. A separation layer takes place between the primary and the secondary flow because of the velocity difference in between so that the entrained flow velocity will increase until the mixing take place at the constant throat area. The velocity become subsonic and the oblique shock waves take place due

Energies 2020, 13, x FOR PEER REVIEW 8 of 19 to the static pressure increase. (a) When the back pressure is increased to the critical value, the region of the subcritical mode starts, and that point called the critical back pressure where the Mach number contours represent at the middle contours in the figure. After that point, further increase in back pressure will cause a sharp decrease in the entrainment ratio till it reaches zero and a single choking appeared only for the primary flow as represented in the bottom contours. Afterwards, an additional increase in the back pressure will lead to the presence of reverse flow. Moreover, it can be observed that increasing the back pressure will move the position of the shock waves towards the back of the primary nozzle direction and eliminate the existence of the shock waves when reaching the critical back pressure, as noticed in operating at back pressure of 613kPa in case of R1234ze(E) and 801 kPa for R1234yf(b) under the inlet condition of Tp = 80 °C, Ts = 10 °C. Regardless of the higher range of critical region for R1234yf, the contours of the Mach number and theFigure shock 7. Mach waves number look similar.contours Additionalwith different diﬀerent increase back pressurepressure in the insideinsideback pressure ejectorejector baselinebaseline after the givengiven critical TTpp == 80 point °C,◦C, will a b decreaseTs = 10°C 10the◦ Caxial for: for: ( avelocity () )R1234ze(E) R1234ze(E) of the at at mixedP Pc c== 600,600, flow 613, 613, and 645 645 movekPa kPa respectively respectively the oblique from from shock top top wavesto to bottom. to the ( b)) primary R1234yf atnozzle P = 780, 801, 840 kPa, respectively from top to bottom. exit, Pwherec = 780, it801, disturbs 840 kPa, the respectively primary fromjet core top toto bottom. the limit when the primary flow could not expand, forcing it to flow reversibly to the entrained flow entrance. 6.2. EffectWhen of theSuperheat. back pressure is increased to the critical value, the region of the subcritical mode starts, and that point called the critical back pressure where the Mach number contours represent at the middleIn general, contours the in main the ﬁgure. sources After of superheat that point, affect furthering the increase ejector in operation back pressure can be will divided cause into a sharp two parts. The first part is due to the internal superheat created by flow irreversibility as a result of the existence of normal shock waves and friction during stream mixing. Another source comes from superheating the inlet primary and/or secondary flow. The global superheat effect then will be a combination of these effects depending on the flow characteristics at inlet constant section determined by the Mach number. The input stream with superheat affects the performance of the system differently. Slightly superheating the refrigerant at the inlet may ensure that the formation of droplets inside the ejector is prevented. Formation of droplets is caused by internal condensation after the working fluids in the primary and secondary nozzles are expanded. This should be prevented because it seriously affects the gas dy(namica) process and the performance of the ejector [16,29]. In addition, blockage of the effective area arises, and this may lead to bumping of the ejector wall which will cause periodically oscillating, unsteady flow, and thus the ejector operation becomes unstable [30,31]. However, the degree of superheat excess will have a negative impact on the system overall performance because of the energy being wasted. The main observations from the results obtained in case of primary flow superheated are shown in Figure 8. The results reveal that, at fixed inlet saturated pressure at Tp = 80 °C and Ts = 6 °C, increasing the degree of superheat in the inlet primary flow will significantly increase the entrainment ratio and thus the ejector performance. For R1234yf, ω increased by 6.31% when the primary flow temperature is superheated with 5 K. Moreover, ω extended 20.70% higher when the degree of superheating reached 25 K, and after which ω is barely improved by the excessive superheat. For example, for the last 5 K added to reach 25 K of superheat, ω increased only by 2.43% compared with 6.31% increasing of ω at the first 5 K of superheat added. R1234ze(E) has the same influence of increasing ω with increasing the degree of superheat in the primary flow but around half the values compared to R1234yf. For example, ω is increased by just 11.48% at 25 K degree of superheat. The condition of increasing superheat coincides with slight travel of critical pressure point towards higher back pressure range. The previous result of increasing the superheat degrees in the primary flow contrasts with the secondary flow superheating which has negative impact on the performance while maintaining fixed conditions at the primary inlet flow, as illustrated in Figure 9. It can be seen that 5 K of secondary flow superheat decreased ω by 1.30% and 1.16% for R1234yf and R1234ze(E), respectively. Further, ω continued declining by around 1.17% for each 5K degree of superheat added. This effect is very small compared to the primary flow superheat and explaining why it is negligible in most of the research papers, for example, that of Chen et al. [32].

Energies 2020, 13, 1408 11 of 19 decrease in the entrainment ratio till it reaches zero and a single choking appeared only for the primary flow as represented in the bottom contours. Afterwards, an additional increase in the back pressure will lead to the presence of reverse flow. Moreover, it can be observed that increasing the back pressure will move the position of the shock waves towards the back of the primary nozzle direction and eliminate the existence of the shock waves when reaching the critical back pressure, as noticed in operating at back pressure of 613 kPa in case of R1234ze(E) and 801 kPa for R1234yf under the inlet condition of Tp = 80 ◦C, Ts = 10 ◦C. Regardless of the higher range of critical region for R1234yf, the contours of the Mach number and the shock waves look similar. Additional increase in the back pressure after the critical point will decrease the axial velocity of the mixed flow and move the oblique shock waves to the primary nozzle exit, where it disturbs the primary jet core to the limit when the primary flow could not expand, forcing it to flow reversibly to the entrained flow entrance.

6.2. Effect of Superheat In general, the main sources of superheat affecting the ejector operation can be divided into two parts. The first part is due to the internal superheat created by flow irreversibility as a result of the existence of normal shock waves and friction during stream mixing. Another source comes from superheating the inlet primary and/or secondary flow. The global superheat effect then will be a combination of these effects depending on the flow characteristics at inlet constant section determined by the Mach number. The input stream with superheat affects the performance of the system differently. Slightly superheating the refrigerant at the inlet may ensure that the formation of droplets inside the ejector is prevented. Formation of droplets is caused by internal condensation after the working fluids in the primary and secondary nozzles are expanded. This should be prevented because it seriously affects the gas dynamic process and the performance of the ejector [16,29]. In addition, blockage of the effective area arises, and this may lead to bumping of the ejector wall which will cause periodically oscillating, unsteady flow, and thus the ejector operation becomes unstable [30,31]. However, the degree of superheat excess will have a negative impact on the system overall performance because of the energy being wasted. The main observations from the results obtained in case of primary flow superheated are shown in Figure8. The results reveal that, at fixed inlet saturated pressure at Tp = 80 ◦C and Ts = 6 ◦C, increasing the degree of superheat in the inlet primary flow will significantly increase the entrainment ratio and thus the ejector performance. For R1234yf, ω increased by 6.31% when the primary flow temperature is superheated with 5 K. Moreover, ω extended 20.70% higher when the degree of superheating reached 25 K, and after which ω is barely improved by the excessive superheat. For example, for the last 5 K added to reach 25 K of superheat, ω increased only by 2.43% compared with 6.31% increasing of ω at the first 5 K of superheat added. R1234ze(E) has the same influence of increasing ω with increasing the degree of superheat in the primary flow but around half the values compared to R1234yf. For example, ω is increased by just 11.48% at 25 K degree of superheat. The condition of increasing superheat coincides with slight travel of critical pressure point towards higher back pressure range. The previous result of increasing the superheat degrees in the primary flow contrasts with the secondary flow superheating which has negative impact on the performance while maintaining fixed conditions at the primary inlet flow, as illustrated in Figure9. It can be seen that 5 K of secondary flow superheat decreased ω by 1.30% and 1.16% for R1234yf and R1234ze(E), respectively. Further, ω continued declining by around 1.17% for each 5 K degree of superheat added. This effect is very small compared to the primary flow superheat and explaining why it is negligible in most of the research papers, for example, that of Chen et al. [32]. Energies 2020, 13, x FOR PEER REVIEW 9 of 20

EnergiesThe 2020 previous, 13, x FOR result PEER REVIEW of increasing the superheat degrees in the primary flow contrasts with9 of the 20 secondary flow superheating which has negative impact on the performance while maintaining fixed conditionsThe previous at the primary result of inlet increasing flow, as the illustrated superheat in degrees Figure 9.in Itthe can primary be seen flow that contrasts 5 K of secondary with the secondaryflow superheat flow superheatingdecreased ω bywhich 1.30% has and negative 1.16% impact for R1234yf on the and performance R1234ze(E), while respectively. maintaining Further, fixed conditionsω continued at decliningthe primary by inletaround flow, 1.17% as illustrated for each 5K in degreeFigure of9. Itsuperheat can be seen added. that This5 K ofeffect secondary is very flowsmall superheat compared decreased to the primary ω by 1.30% flow superheatand 1.16% andfor R1234yfexplaining and why R1234ze(E), it is negligible respectively. in most Further, of the ωresearch continued papers, declining for example, by around that 1.17%of Chen for et each al. [32]. 5K degree of superheat added. This effect is very small compared to the primary flow superheat and explaining why it is negligible in most of the Energiesresearch2020 papers,, 13, 1408 for example, that of Chen et al. [32]. 12 of 19 0.55 0.45

0.5 0.4 0.55 0.45 0.45 0.5 0.35 0.4 0.4 0.45 0.3 0.35 0.35 0.4 0.3 0.25 0.35 0.3 0.25 Tp_superheat =0K 0.2 Tp_superheat =0K 0.3 0.2 Tp_superheat =5K 0.25 Tp_superheat =5K Entrainment Ratio Entrainment Tp_superheat =10K Ratio Entrainment 0.15 Tp_superheat =10K 0.25 Tp_superheat =0K 0.15 Tp_superheatTp_superheat =0K=15K 0.2 Tp_superheat =15K Tp_superheat =5K 0.2 Tp_superheatTp_superheat =5K=20K 0.1 Tp_superheat =20K Entrainment Ratio Entrainment 0.1 Ratio Entrainment Tp_superheat =10K Tp_superheatTp_superheat =10K=25K 0.15 Tp_superheat =25K 0.15 0.05 Tp_superheat =15K 0.05 Tp_superheat =15K 0.1 745 755Tp_superheat 765 =20K 775 785 795 805 0.1 575Tp_superheat 585 =20K 595 605 615 Tp_superheat =25K Tp_superheat =25K 0.05 Back pressure, [kPa] 0.05 Back pressure, [kPa] 745 755 765 775 785 795 805 575 585 595 605 615 (a) (b) Back pressure, [kPa] Back pressure, [kPa]

Figure 8. CFD Entrainment ratio(a) vs back pressure for the ejector with (b superheated) primary flow at Ts = 6 °C and Tp = 80 °C (a) R1234yf. (b) R1234ze(E). Figure 8. CFDCFD Entrainment Entrainment ratio ratio vs vs back back pressure pressure for for the the ejector ejector with with superheated superheated primary primary flow ﬂow at atTs T= s6= °C6 ◦andC and Tp = T 80p = °C80 (◦aC() R1234yf.a) R1234yf. (b) R1234ze(E). (b) R1234ze(E).

0.45 0.4

0.4 0.35 0.45 0.4 0.35 0.3 0.4 0.35 0.3 0.35 0.25 0.3 0.25 0.3 Ts_superheat =0K 0.2 Ts_superheat =0K 0.25 0.2 Ts_superheat =5K Ts_superheat =5K 0.25 Ts_superheat =10K 0.15 Ts_superheat =10K 0.15 Entrainment Ratio Entrainment Ts_superheat =0K Entrainment Ratio Entrainment Ts_superheat =0K 0.2 Ts_superheat =15K Ts_superheat =15K 0.2 Ts_superheat =5K Ts_superheat =5K 0.1 Ts_superheat =20K 0.1 Ts_superheat =20K Ts_superheat =10K 0.15 Ts_superheat =10K 0.15 Ts_superheat =25K Ts_superheat =25K Entrainment Ratio Entrainment Entrainment Ratio Entrainment 0.05 Ts_superheat =15K 0.05 Ts_superheat =15K 0.1 0.1 745 755Ts_superheat 765 =20K 775 785 795 805 575Ts_superheat 585 =20K 595 605 615 Ts_superheat =25K Ts_superheat =25K 0.05 Back pressure, [kPa] 0.05 Back pressure, [kPa] 745 755 765 775 785 795 805 575 585 595 605 615 . Back pressure,(a) [kPa] (bBack) pressure, [kPa] .

FigureFigure 9.9. CFD Entrainment(a ) ratio vs back pressure forfor the the ejectorejector with with superheatedsuperheated (b) secondarysecondary ﬂowflow atat

TTss = 66 °C◦C and and T Tpp == 8080 °C◦C( (a)a R1234yf.) R1234yf. (b) (b R1234ze(E).) R1234ze(E). Figure 9. CFD Entrainment ratio vs back pressure for the ejector with superheated secondary flow at 6.3. Ejector Performance Mapping 6.3. EjectorTs = 6 °C Performance and Tp = 80 °CMapping (a) R1234yf. (b) R1234ze(E). To limit the number of the numerical simulations required to analyze ejector performance that To limit the number of the numerical simulations required to analyze ejector performance that relies6.3. Ejector on di ffPerformanceerent inlet andMapping outlet operation conditions, characteristic curves are generally proposed relies on different inlet and outlet operation conditions, characteristic curves are generally proposed in terms of these variables which can provide a useful and universal aid to the practical design. in termsTo limit of these the numbervariables of which the numerical can provide simulation a usefuls andrequired universal to analyze aid to ejectorthe practical performance design. thatThe The analysis yields a critical system design map from which a system design can be simply studied. reliesanalysis on yieldsdifferent a critical inlet and system outlet design operation map conditions,from which characteristic a system design curves can arebe simplygenerally studied. proposed The The map can be plotted for the ejector using data from simulations or experiments including ω and inmap terms can ofbe theseplotted variables for the ejectorwhich usingcan provide data from a useful simulations and universal or experiments aid to the including practical ω design. and critical The critical back pressure [13,33,34]. A complete performance map expressed by ejector entrainment ratio analysisback pressure yields a[13,33,34]. critical system A complete design mapperforma from ncewhich map a system expressed design by can ejector be simply entrainment studied. ratio The varyingmap can with be plotted the critical for the back ejector pressure using for data a range from ofsimulations primary and or experiments secondary flow including temperatures ω and critical under saturationback pressure conditions [13,33,34]. for both A complete working fluidsperforma is reportednce map in Figureexpressed 10. by ejector entrainment ratio

Energies 2020, 13, x FOR PEER REVIEW 10 of 20

varying with the critical back pressure for a range of primary and secondary flow temperatures under saturation conditions for both working fluids is reported in Figure 10. Energies 2020, 13, 1408 13 of 19

Tp=70°C 0.9 Tp=14°C 0.8 Tp=10°C 0.7 Tp=80°C

0.6 Tp=6°C

Tp=87°C 0.5 Tp=70°C

0.4 Tp=14°C T =80°C p T =10°C Entrainment Ratio Entrainment 0.3 p T =6°C 0.2 Tp=87°C p

0.1 R1234ze(E) R1234yf 0 450 550 650 750 850 950 Back pressure, [kPa]

Figure 10. Performance map of the ejector based on CFD data. Figure 10. Performance map of the ejector based on CFD data. 6.4. Pareto Frontier Solution Curve 6.4. Pareto Frontier Solution Curve A Pareto frontier performance curve predicts the critical back pressure at which the critical workingA Pareto mode offrontier the ejector performance ends [12]. curve Alternatively, predicts it the can critical demonstrate back thepressure boundaries at which of the the baseline’s critical limit,working where mode the of variation the ejector of the ends working [12]. Alternativ design parametersely, it can is demonstrate practical and the can boundaries be consider of as the an optimumbaseline’s solution. limit, where Figure the 11 variation shows theof the Pareto working frontier design performance parameters curve is practical for all operation and can casesbe consider of the ejectoras an optimum based on solution. CFD results Figure drawn 11 shows on the the criticalPareto frontier points. performance It can be seen curve that R1234ze(E)for all operation performs cases muchof the better, ejector unlike based as on seen CFD in aresult previouss drawn comparison on the becausecritical ofpoints. the higher It can entrainment be seen that ratio R1234ze(E) achieved forperforms a given much compression better, unlike ratio. as In seen this in nondimensional a previous comparison comparison, because R1234ze(E) of the higher is working entrainment under higherratio achieved compression for a ratio given since compression the secondary ratio. flow In pressurethis nondimensional at the saturation comparison, condition isR1234ze(E) much lower is relativeworking to under R1234yf. higher Generally, compression operating ratio at high since condenser the secondary temperature flow (highpressure back pressure)at the saturation requires highcondition compression is much ratio lower to pressurizerelative to theR1234yf. mixed Ge streamnerally, to theoperating increased at condenserhigh condenser pressure temperature and thus causing(high back low pressure) entrainment requires ratio. high It can compression be concluded ratio that to by pressurize using the Paretothe mixed frontier stream performance to the increased curve, thecondenser critical entrainmentpressure and ratio thusω causingcri can below predicted entrainmen for botht ratio. refrigerants It can be concluded by the help that of their by using pressure the liftPareto ratio frontier in this ejectorperformance and specify curve, the the working critical modeentrainment using polynomialratio ωcri can relations be predicted (1) and for (2) withboth refrigerants7.11% and by2.26% the help accuracy of their for pressure R1234yf andlift ratio R1234ze(E), in this ejector respectively. and specify Nevertheless, the working at any mode equivalent using ± ± expansionpolynomial ratio relations under any(1) and operation (2) with condition ±7.11% the and performance ±2.26% accuracy characteristics for R1234yf follow and the R1234ze(E), same trend. Forrespectively. example, forNevertheless, R1234yf at Tatp =any80 ◦equivalentC, Ts = 6 ◦ C,ex ERpansion= 6.54 ratio and Tunderp = 87 any◦C, Toperations =10 ◦C, ERcondition= 6.63, thethe diperformancefference in critical characteristics value of compressionfollow the same ratio trend. is 1%. For Moreover, example, R1234ze(E)for R1234yf has at Tp0.77% = 80 °C, diff Terences = 6 °C, at ± ± TERp = = 806.54◦C, and Ts =Tp6 =◦ C,87 ER°C,= T7.47,s =10°C, and ER Tp == 6.63,87 ◦ C,the T sdifference= 10 ◦C, ERin =critical7.54. value of compression ratio is ±1%. Moreover, R1234ze(E) has ±0.77% difference at Tp = 80 °C, Ts = 6 °C, ER = 7.47, and Tp = 87 °C, Ts = 10 °C, ER = 7.54. ω = 0.2166CR3 0.5345CR2 1.1788CR + 3.1368 (1) cri_R1234y f − − = 0.2166 − 0.5345 − 1.1788 + 3.1368 ω_ = 0.1121CR3 + 1.1586CR2 3.9764CR + 4.6712(1) (2) cri_ R1234ze(E) − − The expansion_ ratio () (ER) = of −0.1121 both refrigerants + 1.1586 has been − accomplished 3.9764 + 4.6712 in linear relationship(2) using their critical compression ratio within 0.30% accuracy. These correlations are concluded in The expansion ratio (ER) of both refrigerants± has been accomplished in linear relationship using Equations (3) and (4). By using these relations, the ejector expansion ratio can be easily achieved with their critical compression ratio within ±0.30% accuracy. These correlations are concluded in equations the help of the critical compression ratio and simplified the techniques to calculate the entrainment (3) and (4). By using these relations, the ejector expansion ratio can be easily achieved with the help ratio at any operation condition. This approach could save computational time and cost for predicting of the critical compression ratio and simplified the techniques to calculate the entrainment ratio at the ejector performance. any operation condition. This approach could save computational time and cost for predicting the ER = 4.7991CR 3.0028 (3) ejector performance. R1234y f cri − ERR1234ze(E) = 4.7757CRcri 2.9626 (4) = 4.7991 −− 3.0028 (3)

Energies 2020, 13, 1408 14 of 19 Energies 2020, 13, x FOR PEER REVIEW 11 of 19

1 R1234yf Pareto Frontier 0.9 performance curve 0.8 R1234ze(E) Pareto Frontier performance curve 0.7

0.6

0.5 Entrainment Ratio Entrainment 0.4

0.3

0.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 Compression Ratio Figure 11. ParetoPareto Frontier performance curve for all oper operationation cases of the ejector based on CFD data. 6.5. Ejector Efficiency 6.5. Ejector Efficiency The ejector efficiency was first introduced by Köhler et al. [35]. The great advantage of this The ejector efficiency was first introduced by Köhler et al. [35]. The great advantage of this represented efficiency is that it can be calculated by using only the external parameters which are easy represented efficiency is that it can be calculated by using only the external parameters which are to measure. The same expression for the total ejector efficiency was presented by Elbel et al. deriving easy to measure. The same expression for the total ejector efficiency was presented by Elbel et al. by different approach as shown in Equation (5) [36]. This formula was used in many other literatures, deriving by different approach as shown in Equation (5) [36]. This formula was used in many other as in [37–39]. It was defined as the ratio of the amount of the recovered ejector expansion work rate literatures, as in [37–39]. It was defined as the ratio of the amount of the recovered ejector expansion with maximum possible expansion work rate recovery potential. It can also describe the effectiveness work rate with maximum possible expansion work rate recovery potential. It can also describe the of the ejector as the ratio of actual work recovered to the maximum available work recovery. effectiveness of the ejector as the ratio of actual work recovered to the maximum available work recovery. hs,is hs ηejector = ω − (5) hp hp,is ℎ,− −ℎ η =ω (5) ℎ −ℎ where hs,is and hp,is are referred to specific enthalpy for an, assumed isentropic state from the inlet primary and secondary conditions to the ejector outlet pressure. hs and hp are the specific enthalpy for where hs,is and hp,is are referred to specific enthalpy for an assumed isentropic state from the inlet the inlet primary and secondary conditions. primary and secondary conditions to the ejector outlet pressure. hs and hp are the specific enthalpy Moreover, Dvorak et al. proposed the ejector efficiency based on the relation between the specific for the inlet primary and secondary conditions. compression work acquired by the secondary stream and the specific work exerted by the primary Moreover, Dvorak et al. proposed the ejector efficiency based on the relation between the specific flow as Equation (6) [40]. This formula has been used in many researches [41,42]. The only problem in compression work acquired by the secondary stream and the specific work exerted by the primary Dvorak formula is the adiabatic exponent which needs to be constant and represents the ideal gas flow. flow as Equation (6) [40]. This formula has been used in many researches [41,42]. The only problem Therefore, Equation (5) is used in this work to analyze the efficiency for the ejector model. in Dvorak formula is the adiabatic exponent which needs to be constant and represents the ideal gas flow. Therefore, Equation (5) is used in this work to analyzek the1/k efficiency for the ejector model. 1 (Ps/Pc) − η = ω − (6) ejector 1−( ⁄)k 1/k⁄ (Pp/Pc) − 1 η =ω ⁄ − (6) ⁄ −1 In Figure 12 the ejector efficiency based on the numerical results were presented for different workingIn Figure conditions. 12 the The ejector markers efficiency on the based figure showon the the numerical CFD obtained results results were while presented as the for lines different predict theworking efficiency conditions. that fit theseThe markers results. on The the same figure trends show were the revealed CFD obtained for both results refrigerants’ while as effi theciencies. lines Inpredict addition, the efficiency the characteristic that fit th curveese results. of the ejectorThe same efficiency trends ends were at revealed which the for critical both refrigerants’ flow occurs. Aefficiencies. further reduction In addition, in the the back characteristic pressure at curve critical of mode the ejector will not efficiency lead to anends increase at which in thethe entrainmentcritical flow ratiooccurs. through A further the ejectorreduction and in will the only back decline pressure the at effi criticalciency mode until zero.will not It can lead be to seen an thatincrease R1234ze(E) in the hasentrainment higher e ffiratiociency through compared the ejector to R1234yf and will under only the decline same entrainmentthe efficiency ratio until while zero. R1234yfIt can be could seen providethat R1234ze(E) higher ejector has higher efficiency effici atency critical compared point. Theto R1234yf maximum under effi ciencythe same reached entrainment at the critical ratio while point wereR1234yf 0.372 could and provide 0.364 for higher R1234yf ejecto andrR1234ze(E) efficiency at respectively. critical point. Furthermore, The maximum at fixed efficiency Ts, the ejectorreached has at highthe critical efficiency point when were it 0.372 works and under 0.364 low for TR1234yfp. On the and other R1234ze(E) hand, at respectively. subcritical mode Furthermore, condition at where fixed theTs, the back ejector pressure has high increases, efficiency the e ffiwhenciency it works decreases under which low T isp as. On a resultthe other of the hand, decreasing at subcritical of the mode mass entrainmentcondition where ratio the at these back operationpressure conditions.increases, the Comparing efficiency the decreases results in which the case is ofas usinga result Dvorak’s of the decreasing of the mass entrainment ratio at these operation conditions. Comparing the results in the case of using Dvorak’s proposal as an ideal efficiency of the gas flow, the efficiency of the ejector will

Energies 2020, 13, x FOR PEER REVIEW 12 of 20 condition where the back pressure increases, the efficiency decreases which is as a result of the decreasing of the mass entrainment ratio at these operation conditions. Comparing the results in the Energiescase of2020 using, 13, 1408Dvorak’s proposal as an ideal efficiency of the gas flow, the efficiency of the ejector15 ofwill 19 have the same change trends, with lower values up to 16% in the case of R1234yf and 5.36% for proposalR1234ze(E). as an ideal efficiency of the gas flow, the efficiency of the ejector will have the same change trends, with lower values up to 16% in the case of R1234yf and 5.36% for R1234ze(E).

0.5 Ts =6°C/Tp =87°C /R1234yf Ts =6°C/Tp =87°C /R1234ze(E) 0.45 Ts =6°C/Tp =80°C /R1234yf Ts =6°C/Tp =80°C /R1234ze(E) 0.4 Ts =6°C/Tp =70°C /R1234yf Ts =6°C/Tp =70°C /R1234ze(E) 0.35 0.3 0.25 0.2 0.15 Ejector efficiency 0.1 0.05 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Entrainment Ratio (a)

0.5 Ts =10°C/Tp =87°C /R1234yf Ts =10°C/Tp =87°C /R1234ze(E) 0.45 Ts =10°C/Tp =80°C /R1234yf Ts =10°C/Tp =80°C /R1234ze(E) 0.4 Ts =10°C/Tp =70°C /R1234yf Ts =10°C/Tp =70°C /R1234ze(E) 0.35 0.3 0.25 0.2 0.15 Ejector efficiency 0.1 0.05 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Entrainment Ratio

(b)

0.5 Ts =14°C/Tp =87°C /R1234yf Ts =14°C/Tp =87°C /R1234ze(E) 0.45 Ts =14°C/Tp =80°C /R1234yf Ts =14°C/Tp =80°C /R1234ze(E) 0.4 Ts =14°C/Tp =70°C /R1234yf Ts =14°C/Tp =70°C /R1234ze(E) 0.35 0.3 0.25 0.2 0.15 Ejector efficiency 0.1 0.05 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Entrainment Ratio (c)

FigureFigure 12.12.Ejector Ejector eefficiencyﬃciency vsvs thethe massmass entrainmententrainment ratioratio forforvarious various workingworking conditionsconditions basedbased onon

CFDCFD results.results. ((a)a)T Tss == 6°C.6 ◦C. (b) (b )TTs s=10°C.=10 ◦ C.(c) ( cT)Ts =s 14°C.= 14 ◦C. 7. Conclusions 7. Conclusions This paper is mainly devoted to computational fluid dynamics simulation conducted for a 2D axisymmetric ejector to present the performance over the entire operation conditions using NIST real gas model integrated in commercial ANSYS Fluent. The experimental data were used to validate Energies 2020, 13, 1408 16 of 19 how effective the model is. The comparison results have shown that the model could accurately be able to predict the experimental results with error less than 14%. The numerical analysis study was ± applied using k-ω SST turbulence model and pressure-based coupled solver. Most of the simulations converged to the residues fall below 1 10 8. HFOs (R1234ze(E) and R1234yf) were selected as the × − working fluids because of their promising alternatives to fluorocarbons with low global warming potential and flammability as well as adhering to EU Council regulations. Mesh sensitivity was performed to ensure the result stability via different number of elements. The inlet primary and the secondary flow were examined under their saturation conditions. Given the energy available in the primary flow, the ejector performance is assessed based on how much of this energy the secondary flow can recover. This was done by investigating the characteristic curves for the ejector critical and subcritical modes. It was shown that increasing the primary flow temperature caused lower entrainment ratio and produced higher critical back pressure. When the primary or secondary saturated flow temperatures are fixed then the compression ratio will increase with increasing the expansion ratio and causes lower entrainment ratio indeed. As a result, R1234yf represented higher entrainment ratio than R1234ze(E) by 4.91% to 15.60%. The contours of Mach number for both working fluids at different inlet primary pressure and different back pressure were represented. Several phenomena in the ejector were discussed, like the shock waves, effective mixing, and operational modes. In order to prevent the formation of droplet inside the ejector, adding degree of superheat in the inlet flow is important but the excess of value will have a negative impact on the system overall performance because of the energy being wasted. Therefore, the amount of superheat to be added should be carefully studied. From the performance evaluation point of view, the analysis demonstrated that the entrainment ratio can be increased up to 20.70% with 25 K superheat for R1234yf, which is almost double the percentage compared to R1234ze(E). Secondary flow superheating has a negative impact on the performance, which slightly decreases ω within 1.17% for both refrigerants for each 5 K degree of superheat added. Ejector performance map was proposed using the critical back pressure to obtain the characteristic curve and show the large critical mode which R1234yf can work in comparing to R1234ze(E). A Pareto frontier performance curve was performed. This approach could save computational time and cost for predicting the ejector performance by calculating the critical entrainment ratio using ejector pressure lift ratio. Moreover, the expansion ratio (ER) of both refrigerants was accomplished in linear correlation using their critical compression ratio. It was also shown that regardless of any operation condition, the refrigerant working at equivalent expansion ratio have similar performance characteristics curve trend. The effectiveness of the modelled ejector was determined to compare both working fluids efficiency. The maximum efficiency reached at the critical point was 0.372 and 0.364 for R1234yf and R1234ze(E) respectively. In other words, the efficiency was lower when using ideal gas flow formula. The ideal gas model has been simulated and compared with the real gas model. It was concluded that the performance of the ejector will be overestimated in the case of using the ideal gas model with maxima of 50.26% and 25.66% for R1234yf and R1234ze(E), respectively. This explains the necessity of using a real gas model in CFD and why the ideal gas model could fail to predict the performance of the ejector. In a nutshell, R1234ze(E) can achieve relatively better overall performance than R1234yf. This study was conducted to design a high-performance ejector that has been manufactured already and currently under test. The main essential parameters for energy-efficient HFOs ejector cooling systems have been investigated to estimate the suitability of the modeled ejector. However, more results and greater accuracy, for example, the effect of the NXP, pressure distribution along the ejector, and the entropy generation will be considered and validated with experiments in future work.

Author Contributions: Conceptualization, A.F.A.E. and V.V.N.; Data curation, A.F.A.E. and V.D.; Formal analysis, A.F.A.E.; Funding acquisition, A.F.A.E., V.V.N. and V.D.; Investigation, A.F.A.E. and S.M.; Methodology, A.F.A.E. and V.D.; Project administration, V.V.N.; Resources, A.F.A.E.; Software, A.F.A.E. and S.M.; Supervision, V.D.; Validation, A.F.A.E. and S.M.; Writing—original draft, A.F.A.E.; Writing—review & editing, A.F.A.E., V.D. and S.M. All authors have read and agreed to the published version of the manuscript. Energies 2020, 13, 1408 17 of 19

Funding: This publication was written at the Technical University of Liberec as part of the project 21226/2220 with the support of the Specific University Research Grant, as provided by the Ministry of Education, Youth and Sports of the Czech Republic in the year 2019. Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature

CR compression ratio parameter ER expansion ratio NXP Nozzle Exit Position 1 h specific enthalpy (kJkg− ) P Pressure (kPa) T Temperature (◦C) ω entrainment ratio (-) η efficiency (-) m˙ mass flow rate (kg/s) κ specific heat ratio, (-) Subscripts p primary flow s secondary flow c outlet mixed flow cri critical is isentropic

References

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