#### 4.1. Effect of Hot Stream Inlet Pressure

Figure 5 illustrates the cold stream liquid-phase and gas-phase convection coefficients against various cold channel mass fluxes from 0.1

$\text{}\mathrm{kg}/{\mathrm{m}}^{2}\xb7\mathrm{s}$ to 7.8

$\mathrm{kg}/{\mathrm{m}}^{2}\xb7\mathrm{s}$ at a hot stream inlet pressure of 10 MPa and a cold stream superheat temperature difference of 3 K. For all cases, the convection coefficients increase with the cold channel mass flux because of the increment in the Reynolds number. For the cold stream liquid phase, the convection coefficients increased from 41 to 262 and 270

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ for R1234yf and R1234ze(E), respectively. For the cold stream gas phase, the convection coefficients increased from 36 and 25 to 378 and 269

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ for R1234yf and R1234ze(E), respectively. The difference is more apparent for the gas-phase convection coefficients because the viscosity is ten times lower at the gas phase for both HFOs, resulting in a more apparent difference in the Reynolds number. The slope for the liquid phase is more horizontal because the viscosity ratio decreases from 1.9 to 1.2 for R1234yf and from 1.6 to 1.1 for R1234ze(E), while it is almost constant for the gas phase. Moreover, the convection coefficients of the cold stream gas-phase of R1234ze(E) are less than the liquid ones at a cold channel mass flux less than 6.8

$\mathrm{kg}/{\mathrm{m}}^{2}\xb7\mathrm{s}$ because the conductivity is relatively low in the gas phase in comparison with R1234yf. On the other hand, a less than 4% increase in the liquid phase convection coefficients and a less than 1% decrease in the gas phase convection coefficients were observed as the hot stream inlet pressure was increased from 9 MPa to 12 MPa. This can be explained by the effect of the hot stream inlet temperature on the viscosity at the surface, which decreases in the liquid phase and increases in the gas phase, according to the Martin model.

In contrast, the two-phase convection coefficient was influenced steeply by the hot stream inlet pressure.

Figure 6 demonstrates the cold stream two-phase convection coefficients versus various cold channel mass fluxes from 0.1

$\text{}\mathrm{kg}/{\mathrm{m}}^{2}\xb7\mathrm{s}$ to 7.8

$\mathrm{kg}/{\mathrm{m}}^{2}\xb7\mathrm{s}$ at hot stream inlet pressures of 9 MPa and 12 MPa and a cold stream superheat temperature difference of 3 K. The result reveals that the cold-stream two-phase convection coefficient at high pressure increases from 592

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ to 2110

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ for the R1234ze(E) and from 1181

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ to 4196

$\text{}\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ for the R1234yf. At a lower pressure, the two-phase convection coefficient showed parabolic tendencies for R1234ze(E) from 477

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ to the peak at 1334

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ and then decreased significantly to 673

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$. The two-phase convection coefficient also showed parabolic tendencies for R1234yf from 959

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ to the peak at 2857

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ and then decreased slightly to 2785

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$. As shown in

Figure 6, the convection coefficient is much higher at higher pressures due to the increased heat flux between the two streams, resulting in higher boiling numbers. For most cases, the R1234ze(E) had higher two-phase convection coefficients due to the higher bond number than for R1234yf. According to Amalfi et al.’s correlation for the macro-scale plate heat exchanger, the flow in the two-phase region is very turbulent even at a low vapour quality [

21]. This turbulence is represented by the Bond number (

$\mathrm{Bd}$) with a critical value of 4. In this study, the bond number was estimated to be 90 for R1234ze(E) and 24 for R1234yf by using Equation (18) [

21]. This difference in turbulence leads to higher convection coefficients for the R1234ze(E). The observed two-phase convection coefficients show good agreement with the results of Longo et al. [

34].

On the other hand, the parabolic tendency of the two-phase convection coefficients at 9 MPa was due to the significant decrease in the hot stream temperature and the convergence of the overall heat transfer coefficient to a constant value. The peak occurs when the overall heat transfer coefficient converges to a constant value, and the significant reduction after the peak appears when the hot stream temperature drops and gets closer to the cold stream saturation temperature, leading to a considerable decrease in the Boiling number, as shown in Equation (16). This effect of the overall heat transfer coefficient and the temperature drop on the Boiling number is illustrated in

Figure 7 for both HFOs.

Figure 7 demonstrates the boiling number with a broader range of cold channel mass fluxes. For all curves, it is clear that the boiling number decreases significantly at a particular flow flux when the temperature difference in Equation (16) approaches zero, which explains along with the overall heat transfer coefficient the parabolic tendency of the two-phase convection coefficient.

The results illustrated in

Figure 8 show how the hot stream convection coefficients change with the mean hot stream temperature and the variation in the cold channel mass flux from 0.1

$\text{}\mathrm{kg}/{\mathrm{m}}^{2}\xb7\mathrm{s}$ to 7.8

$\text{}\mathrm{kg}/{\mathrm{m}}^{2}\xb7\mathrm{s}$ at hot stream inlet pressures of 9 MPa and 12 MPa and a cold stream superheat temperature difference of 3 K. At a high pressure, the hot stream convection coefficients increased from 951 to 1009 and 998

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ for R1234yf and R1234ze(E), respectively. In addition, the temperature drops from 138 °C to 113 °C and 117 °C for R1234yf and R1234ze(E), respectively. At a lower pressure, the hot stream convection coefficients increased from 896 to 958 and 946

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ for R1234yf and R1234ze(E), respectively. In addition, the temperature drops from 107 °C to 88 °C and 84 °C for R1234yf and R1234ze(E), respectively. The results show good agreement with Zendehboudi et al. [

5]. The hot stream convection coefficients and mean temperature drops at different pressures were found to have identical differences between the hot stream inlet and outlet, even though the CO

_{2} was operating in the supercritical region. This is explained by the idea that the CO

_{2} temperature is relatively high and far from the critical value at which the thermophysical properties change linearly in this region.

Conversely, as the supercritical phase approaches the critical point, the deviation between the R1234yf and R1234ze(E) curves becomes more pronounced with the temperature drop because of the increase in the nonlinearity of the thermophysical properties. In contrast, hot stream convection coefficients have higher values with R1234ze(E) because it has a lower specific heat, resulting in a higher temperature drop.

Figure 9 illustrates the cold stream liquid-phase, two-phase, and gas-phase pressure drops against various cold channel mass fluxes from 0.1

$\text{}\mathrm{kg}/{\mathrm{m}}^{2}\xb7\mathrm{s}$ to 7.8

$\mathrm{kg}/{\mathrm{m}}^{2}\xb7\mathrm{s}$ at a hot stream inlet pressure of 11 MPa and a cold stream superheat temperature difference of 3 K. The liquid-phase pressure drop for both gases has the same tendency, with a maximum value of 0.3

$\mathrm{kPa}/\mathrm{m}$. This is because they have similar values of the Reynolds number, which is dominant in the Martin fanning friction model. In contrast, R1234yf has a higher pressure drop in the gas phase than R1234ze(E), with a value of 27

$\mathrm{kPa}/\mathrm{m}$, because of the difference in surface tension. This difference affects the Weber number as illustrated in Equation (17). For the gas phase, the maximum pressure drop equals 0.7

$\mathrm{kPa}/\mathrm{m}$ for R1234yf and 1.1

$\mathrm{kPa}/\mathrm{m}$ for R1234ze(E). The difference in pressure drop for the gas phase illustrates the deviation between R1234yf and R1234ze(E) more clearly than the liquid phase due to the difference in the Reynolds number as explained above for the convection coefficients. In contrast, the effect of the hot stream pressure on the pressure drop is negligible because the Weber and Bond numbers are functions of the cold stream temperature. According to the used model, these numbers remained constant at different hot stream pressures because an identical temperature increase in the cold fluid was considered. The vapourisation pressure drop showed good agreement with Longo et al.’s experimental study [

34] and Amalfi et al. review [

21].

On the other hand,

Figure 10 shows how the hot stream pressure drop changes with the mean hot stream temperature and a cold channel mass flux that varies from 0.1

$\text{}\mathrm{kg}/{\mathrm{m}}^{2}\xb7\mathrm{s}$ to 7.8

$\mathrm{kg}/{\mathrm{m}}^{2}\xb7\mathrm{s}$ at hot stream inlet pressures of 9 MPa and 12 MPa and a cold stream superheat temperature difference of 3 K. At a high pressure, the total hot stream pressure drop decreased from 7.44

$\mathrm{KPa}/\mathrm{m}$ to 6.46

$\text{}\mathrm{KPa}/\mathrm{m}$ and 6.14

$\mathrm{KPa}/\mathrm{m}$ for R1234yf and R1234ze(E), respectively, while at a lower pressure, it decreased from 10.27

$\text{}\mathrm{KPa}/\mathrm{m}$ to 8.75

$\text{}\mathrm{KPa}/\mathrm{m}$ and 8.33

$\mathrm{KPa}/\mathrm{m}$ for R1234yf and R1234ze(E), respectively. The pressure drops decreased with the mean hot stream temperature drop because of the decrease in the Reynolds number with the temperature at the supercritical phase. The viscosity increased with the temperature drop in the supercritical phase, unlike in the gaseous phase. On the other hand, the pressure drop increased at a lower hot stream inlet pressure because of the increase in the mass flow rate, which the used compressor model estimates.

Figure 11 demonstrates the effectiveness versus cold channel mass fluxes from 0.1 to 7.8

$\mathrm{kg}/{\mathrm{m}}^{2}\xb7\mathrm{s}$ at a hot stream inlet pressure of 10 MPa and a cold stream superheat temperature difference of 3 K. The effectiveness is 100% at cold channel mass fluxes less than 1 and 2

$\mathrm{kg}/{\mathrm{m}}^{2}\xb7\mathrm{s}$ for R1234yf and R1234ze(E), respectively. The effectiveness then decreases to 95.5% and 98.5% for R1234yf and R1234ze(E), respectively.

Moreover, the R1234yf showed lower effectiveness than the R1234ze(E) and an earlier deviation from 100% effectiveness because the specific heat of R1234yf is approximately one time higher than R1234ze(E) at each phase, which leads to higher heat capacity values and lower effectiveness [

47]. In addition, the effect of the hot stream pressure on the effectiveness is negligible because, for the investigated flow fluxes, the cold stream was dominant at the minimum heat capacity since it has a lower flow rate than the hot stream. Moreover, the hot stream convection coefficients did not change significantly with pressure because the hot stream flow flux slightly decreased with increasing pressure.

#### 4.2. Effect of Superheat

Generally, the effect of superheat was negligible on the effectiveness, the single-phase convection coefficients, and the pressure drops. In contrast, it was slightly effective on the two-phase convection coefficient. This ensures stable operation of the proposed cycle under different operating conditions.

Figure 12 demonstrates the cold stream two-phase convection coefficients versus various cold channel mass fluxes from 0.1

$\text{}\mathrm{kg}/{\mathrm{m}}^{2}\xb7\mathrm{s}$ to 16

$\mathrm{kg}/{\mathrm{m}}^{2}\xb7\mathrm{s}$ at a hot stream inlet pressures of 12 MPa and cold stream superheat temperature differences of 5 K and 20 K. The cold-stream two-phase convection coefficient at a temperature difference of 5 K increases from 591

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ to 2175

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ for the R1234ze(E) and from 1182

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ to 4518

$\text{}\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ for the R1234yf. At a temperature difference of 20 K, the two-phase convection coefficient showed parabolic tendencies for R1234ze(E) from 589

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ to the peak at 1954

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ and then decreased significantly to 820

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$. The two-phase convection coefficient also showed parabolic tendencies for the R1234yf from 1183

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ to the peak at 3904

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ and then decreased to 2710

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$. The convection coefficient decreased to about 12–15% when the superheat temperature difference increased from 5 K to 20 K. This can be explained by Longo et al. observations [

33] using IR thermography. The authors reported that the heat transfer area covered with a single-gas flow increases significantly with the superheat difference. According to these observations, lower heat fluxes will occur in the two-phase region, leading to lower Boiling numbers and a lower two-phase convection coefficient.

Figure 13 demonstrates the effectiveness versus cold channel mass fluxes from 0.1 to 15

$\mathrm{kg}/{\mathrm{m}}^{2}\xb7\mathrm{s}$ at a hot stream inlet pressure of 12 MPa and cold stream superheat temperature differences of 5 K and 20 K. The effectiveness is 100% at cold channel mass fluxes less than 1 and 2

$\mathrm{kg}/{\mathrm{m}}^{2}\xb7\mathrm{s}$ for R1234yf and R1234ze(E), respectively. The effectiveness then decreases to 91% and 95% for R1234yf and R1234ze(E), respectively. Additionally, the effectiveness at a 20 K superheating difference was slightly lower for channel mass fluxes less than 9 and 15

$\mathrm{kg}/{\mathrm{m}}^{2}\xb7\mathrm{s}$ for R1234yf and R1234ze(E), respectively. However, the effect of the cold stream superheating difference is negligible, which provides a considerable advantage for a broader range of operations for the CERC.

#### 4.3. Effect of Heat Exchanger Size

The effectiveness, convection coefficients, and pressure drops were investigated with two different sizes of plates: A and B.

Table 1 describes the geometrical specifications of each plate. The following sections illustrate the difference between using the two different plates. The number of plates for the size B PHE was determined based on an effective area identical to the size A PHE.

Figure 14 shows the cold stream two-phase convection coefficients versus various cold channel mass fluxes from 0.1

$\mathrm{kg}/{\mathrm{m}}^{2}\xb7\mathrm{s}$ to 7

$\mathrm{kg}/\xb7\mathrm{s}$ at a hot stream inlet pressure of 10 MPa, a cold stream superheat temperature difference of 3 K, and two different plate sizes: size A (marked with solid lines) and size B (marked with dashed lines). For size A, the cold-stream two-phase convection coefficient increases from 538

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ to 1696

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ for the R1234ze(E) and from 1069

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ to 3491

$\text{}\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ for the R1234yf. When using plate B, the two-phase convection coefficient showed parabolic tendencies for R1234ze(E) from 431

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ to the peak at 1386

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ and then decreased to 1099

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$. The two-phase convection coefficient also showed parabolic tendencies for R1234yf from 863

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ to the peak at 2937

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ and then decreased to 2877

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$. The cold stream two-phase convection coefficient for the size A PHE is higher than that for the size B PHE, with a maximum percentage of 50%.

The cold stream two-phase convection coefficients were approximately the same for both sizes at a low channel flow flux, and then the curves deviated when the heat flux approached the peak value. At this peak, the reduction in the temperature in Equation (16) becomes more dominant than the increment in the overall heat transfer coefficient. After that, the convection coefficient increased continuously until it reached a particular peak; then, it started to decrease. This topmost value occurred when the overall heat transfer coefficient converged to a constant value. The decrement occurred because the enthalpy of the vaporisation product by the channel mass flux shown in Equation (16) regularly increased with the flow rate. Generally, the plate B heat exchanger has a lower heat flux between the streams because it has a higher number of channels, resulting in a more distributed total heat rate.

The results illustrated in

Figure 15 show how the hot stream convection coefficients change with the mean hot stream temperature and cold channel mass fluxes from 0.1

$\text{}\mathrm{kg}/{\mathrm{m}}^{2}\xb7\mathrm{s}$ to 7

$\mathrm{kg}/{\mathrm{m}}^{2}\xb7\mathrm{s}$ at a hot stream inlet pressure of 10 MPa, a cold stream superheat temperature difference of 3 K, and two different plate sizes: size A (marked with solid lines) and size B (marked with dashed lines).

For size A, the hot stream convection coefficients increased from 917

$\text{}\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ to 972

$\text{}\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ and 968

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ for R1234yf and R1234ze(E), respectively. In addition, the temperature drops from 118 °C to 89 °C and 84 °C for R1234yf and R1234ze(E), respectively. At a lower pressure, the hot stream convection coefficients increased from 686

$\text{}\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ to 727

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ and 725

$\mathrm{W}/{\mathrm{m}}^{2}\xb7\mathrm{K}$ for R1234yf and R1234ze(E), respectively, and the temperature dropped from 118 °C to 89 °C and 84 °C for R1234yf and R1234ze(E), respectively. The two investigated sizes have identical differences in the hot stream convection coefficients and temperature drops because the CO

_{2} temperature is relatively high and far from the critical one. In addition, the peak of both HFOs is more apparent than the one illustrated in

Figure 8 because of the wider range of the y-axis. This peak represents the point at which the viscosity changes its tendency from a decrease to in increase in the supercritical region. Additionally, it was observed for the Reynolds number at the same temperature. The hot stream convection coefficients were 20% higher for size A due to the difference in the Grashof number and the Reynolds number since size A has a higher hot channel mass flux. We maintained an identical hot channel mass flux for both sizes, which was possible because the hot stream flow rate was estimated using the compressor model. Moreover, the number of plates was chosen to maintain equivalent cold channel mass fluxes for both sizes.

Figure 16 demonstrates the effectiveness versus cold channel mass fluxes from 0.1 to 7

$\mathrm{kg}/{\mathrm{m}}^{2}\xb7\mathrm{s}$ at a hot stream inlet pressure of 10 MPa, a cold stream superheat temperature difference of 3 K, and two different plate sizes: size A (marked with solid lines) and size B (marked with dashed lines). For size A, the effectiveness decreases to 96% and 99% for R1234yf and R1234ze(E), respectively, while for size B, the effectiveness decreases to 87% and 93% for R1234yf and R1234ze(E), respectively. The lower effectiveness for size B is due mainly to the lower effective plate area, leading to a lower NTU. Moreover, as explained before, the size A exchanger had higher overall heat transfer coefficients and heat fluxes.

According to the achieved results, the effectiveness is relatively high, especially at a larger plate size, leading to a higher compression ejector refrigeration cycle COP. In addition, the PHE pressure drop is strongly influenced by the cold-stream two-phase flow. However, the pressure drops are relatively low and seem to converge at a high pressure, which is crucial for estimating the mass flow rate of the compression ejector inlet in the CERC. On the other hand, the applicable flow rate range was limited only by the HFO saturation temperature in the two-phase flow region (k = 2). In this region, the limitation is due to the difference in temperature between the two streams. The flow rate must be modified to a value that guarantees that the CO_{2} temperature is higher than the HFO saturation temperature. Once a good flow range is specified, a stable and smooth variation in the convection coefficient would be observed for the three different phases, resulting in a smooth operation of the overall combined cycle. For the gas-cooler side, the relatively high temperature of the CO_{2} negates the nonlinearity in the CO_{2}’s properties, making it a suitable driving heat source for the generator in the combined cycle.