Performance of Supercritical CO 2 Power Cycle and Its Turbomachinery with the Printed Circuit Heat Exchanger with Straight and Zigzag Channels

: Since printed circuit heat exchangers (PCHE) respectively, are optimal for sCO 2 − BC and present a good bargain between cycle efﬁciency and its layout size.


Introduction
Supercritical power systems have recently gained widespread attention because they offer advantages in multiple industry sectors. Primarily, it is expected that they can significantly improve energy conversion efficiency, create new markets because of their smaller size combined with higher efficiency, and are economically more viable. The potential applications for sCO 2 -Brayton cycle in particular, are extensive because it can be used in any application that uses a Rankine cycle, including power generation. Major components, i.e., turbines and compressors. In this perspective, the current research evaluates the impact of zigzag and straight-channel PCHEs on the cycle's performance and its components. In this study, an in-house PCHE design and analysis code (PCHE-DAC) was used for the PCHE design and analysis to compute the effect of Reynolds number (Re), effectiveness ( ) and channel configurations (straight and zigzag) on the initial PCHE size and performance. Heat exchanger designs with straight and zigzag-channel geometries and other parameters, i.e., , and Re are used to investigate the effects on the turbomachinery design and overall cycle performance. An in-house Cycle simulation and analysis code (DDPC) was used to compute the cycle performance at its design point. Properties of sCO 2 have been incorporated in the code by coupling with NIST REFPROP. An optimized design based on the straight and zigzag channels has been proposed for the sCO 2 − BC. Because the performance, size, and layout of the sCO 2 − BC power cycle are extremely sensitive to the design and performance of its PCHEs; current study provides valuable data and guidelines to further enhance the performance and layout of the sCO 2 − BC.

Mathematical Model for PCHE Design and Analysis Code (PCHE-DAC)
The mathematical model adopted for PCHE-DAC in the current study is based on a discretized LMTD method used and developed by Saeed et al. [2,30,31]. A heat exchanger code was built based on this model; pressure drop and heat transfer correlation used for the current study are listed in Table 1. The number of divisions (n) used to discretize the model (Figure 1) was ensured to be sufficient to capture the steep variations in the thermophysical properties of the working fluid (sCO 2 ). The following procedure has been adopted to study the printed circuit heat exchanger.

Configuration Correlations Channel Geometry
Genelisi [32] = ( /8)( − 1000) 1 + 12.7 ( 8 ) 0.5 * (Pr PCHE design and analysis code (PCHE-DAC) was validated by utilizing a two-step validation procedure that involves both validations of the conditions at boundaries along with the validation of data at every nodal point along the PCHE's length. Validation of conditions at boundaries was carried by comparing the code boundary data with the experimental results of Ishizuka et al. [33]. On the other hand, the validation of the nodal data was conducted by comparing the temperature profiles obtained from the code with the temperature profiles extracted from the previous study's CFD results [3]. Numerical results employed for the validation were taken from the CFD model [3] that was authenticated using experimental data [33]. The validation purpose's boundary conditions are listed in Table 2, while a comparison of the PCHE-DAC data with the experimental data Ishizuka et al. [33] h = 0.210Re + 44.16 f = −2 × 10 −6 Re + 0.1023 (5,   PCHE design and analysis code (PCHE-DAC) was validated by utilizing a two-step validation procedure that involves both validations of the conditions at boundaries along with the validation of data at every nodal point along the PCHE's length. Validation of conditions at boundaries was carried by comparing the code boundary data with the experimental results of Ishizuka et al. [33]. On the other hand, the validation of the nodal data was conducted by comparing the temperature profiles obtained from the code with the temperature profiles extracted from the previous study's CFD results [3]. Numerical results employed for the validation were taken from the CFD model [3] that was authenticated using experimental data [33]. The validation purpose's boundary conditions are listed in Table 2, while a comparison of the PCHE-DAC data with the experimental data is provided in Table 3. Validation of the computed data suggests the maximum difference between the code and experimental results is around 5%. On the other hand, comparison Kim et al. [34] Saeed and Kim [35] It is assumed that the header of the heat exchanger distributes the flow to all channels uniformly. Heat losses to the surroundings are exceedingly small and can be ignored. It is also assumed that the flow and heat transfer characteristics in a unit consisting of one channel from the hot and cold side each can represent the behavior of the whole heat exchanger, as shown in Figure 1. The blue and red colors used in Figure 1 demonstrate the heat exchanger's cold and hot sides, respectively. Hot and cold fluids in their respective channels flow in the counterclockwise direction. The state of working fluids at both hot and cold side inlets is known (marked green), while the exit condition (characterized as red) is unknown. It should be noted here that the formulation is given in the section below, and Figure 2 is provided for the i th segment bounded by the side node, i.e., i th and i + 1 th node. Step 1. Estimate the values of Δ and Δ ℎ . Step 2. Using known inlet condition values, exit conditions for both hot and cold channels were computed using the effectiveness value. The working fluid's thermophysical properties were calculated as a function of temperature and pressure by linking NIST REFPROP with the MATLAB code via a subroutine. The procedure for calculating the exit condition is given in the following equations.
Step 3. Current conditions at the inlet and outlet of the heat exchanger can be used to compute the initial pressure drop and heat transfer values through each cell, as demonstrated in the following equations. Step 1. Estimate the values of ∆P cold and ∆P hot .
Step 2. Using known inlet condition values, exit conditions for both hot and cold channels were computed using the effectiveness value. The working fluid's thermophysical properties were calculated as a function of temperature and pressure by linking NIST REFPROP with the MATLAB code via a subroutine. The procedure for calculating the exit condition is given in the following equations.
Step 3. Current conditions at the inlet and outlet of the heat exchanger can be used to compute the initial pressure drop and heat transfer values through each cell, as demonstrated in the following equations. dP cold i th = ∆P cold /n (4) dP hot i th = ∆P hot /n (5) Step 4. Once quantities in the i th cell are known, the (i + 1) th cell can be computed using the following equation. Further mean values at the cell center were computed by taking an average of the i th and (i + 1) th values.
P hot i+1 th = (P) i th + dp hot i th (11) (15) Step 5. In the next step, the working fluid properties were computed based on the pressure and enthalpy's cell-centered values to calculate the friction factor and overall heat transfer coefficient, which were used to calculate new pressure drop and heat transfer values as shown in the following equations. It should be noted here that friction factor and heat transfer coefficient value were computed using correlations provided in Table 1 Step 6. The next step controls the convergence of the solution of Equation (24) until all cells are computed.
Step 7. The outer loop controls the convergence of boundary conditions, as given in the following equation.   with the validation of data at every nodal point along the PCHE's length. Validation of conditions at boundaries was carried by comparing the code boundary data with the experimental results of Ishizuka et al. [33]. On the other hand, the validation of the nodal data was conducted by comparing the temperature profiles obtained from the code with the temperature profiles extracted from the previous study's CFD results [3]. Numerical results employed for the validation were taken from the CFD model [3] that was authenticated using experimental data [33]. The validation purpose's boundary conditions are listed in Table 2, while a comparison of the PCHE-DAC data with the experimental data is provided in Table 3. Validation of the computed data suggests the maximum difference between the code and experimental results is around 5%. On the other hand, comparison of the nodal data ( Figure 3) indicate that code data is in close agreement with the CFD data.

Model for Cycle Simulation and Analysis Code (CSAC)
The current section provides a mathematical model for the design point analysis of the recompression supercritical carbon dioxide cycle( 2 − ) as shown in Figure 4. The major components of the recompression 2 − is a turbine, two compressors (a main and a recompressor), two internal heat exchangers (LTR and HTR), a primary heat exchanger or heater, and a pre-cooler as shown in Figure 4. High-pressure fluid (state 6) gets heated from the heater (state 6-7). It gets expanded in the turbine (state 7-8), and during the expansion process, shaft work ( ) is obtained. After expansion, its temperature is still considerably high, as can be seen from Figure 4b. Therefore, to recuperate the valuable heat to the high-pressure side of the cycle, it passes first through the high-temperature recuperator (HTR) (state 8-9) and then flows through the low-temperature recuperator (LTR) (state 9-state 10). It should be noted here that before entering, the pre-cooler flow is split into two streams. A fraction (x) is sent to the recompressor (state 10-10b) while the remaining fraction (1-x) passes through the pre-cooler (state 10a-1). After the pre-

Model for Cycle Simulation and Analysis Code (CSAC)
The current section provides a mathematical model for the design point analysis of the recompression supercritical carbon dioxide cycle (sCO 2 − BC) as shown in Figure 4. The major components of the recompression sCO 2 − BC is a turbine, two compressors (a main and a recompressor), two internal heat exchangers (LTR and HTR), a primary heat exchanger or heater, and a pre-cooler as shown in Figure 4. High-pressure fluid (state 6) gets heated from the heater (state 6-7). It gets expanded in the turbine (state 7-8), and during the expansion process, shaft work (W T ) is obtained. After expansion, its temperature is still considerably high, as can be seen from Figure 4b. Therefore, to recuperate the valuable heat to the high-pressure side of the cycle, it passes first through the high-temperature recuperator (HTR) (state 8-9) and then flows through the low-temperature recuperator (LTR) (state 9-state 10). It should be noted here that before entering, the pre-cooler flow is split into two streams. A fraction (x) is sent to the recompressor (state 10-10b) while the remaining fraction (1-x) passes through the pre-cooler (state 10a-1). After the pre-cooler flow gets compressed in the main-compressor (state 1-2) gets heated from the LTR (state 2-3) and then combines with the flow coming from the re-compressor. Now the flow gets heated first in HTR (state 4-6) and then from the heater again for the next cycle.  To model high-temperature and low-temperature recuperators, PCHE-DAC was used in the heat exchanger model. The heat exchanger model is flexible and able to use any channel geometry; however, zigzag and straight-channel designs were utilized in the existing work. The model was coded in the MATLAB© environment, and the flow chart To model high-temperature and low-temperature recuperators, PCHE-DAC was used in the heat exchanger model. The heat exchanger model is flexible and able to use any channel geometry; however, zigzag and straight-channel designs were utilized in the existing work. The model was coded in the MATLAB© environment, and the flow chart of the code is shown in Figure 5. To obtain the thermodynamic properties of sCO 2 REFPROP [36] was coupled with MATLAB through a function code at different states of the cycle.

Turbomachinery Models
In the literature [37], turbomachinery modeling is based on the turbine and compressor's single equation relations, using isentropic efficiencies and pressure ratio information. In the current study, isentropic efficiencies (Table 4) are estimated using the Balje chart [38]; a non-isentropic compression and expansion process has been modeled using the following relations. Equation (3) Output: Equations (4) and (8) Output

Turbomachinery Models
In the literature [37], turbomachinery modeling is based on the turbine and compressor's single equation relations, using isentropic efficiencies and pressure ratio information.
In the current study, isentropic efficiencies (Table 4) are estimated using the Balje chart [38]; a non-isentropic compression and expansion process has been modeled using the following relations. The heat exchanger models explained earlier are recuperator models. Assuming that both PCHEs are fully shielded for heat losses to surroundings, the energy conservation equation for the LTR and HTR is given by Equations (30) and (31).
where the split-mass-fraction (x) can be calculated utilizing the following equation under the assumptions of ideal mixing and splitting at corresponding values. The mixing value is modeled using Equation (33) by considering an ideal mixing.
Pressure losses across all heat exchangers are modeled using the following relation, and cycle efficiency is given by Equation (34).
Definitions of w t , w c , and w rc are given by the following equations.
The power cycle's selected boundary conditions are based on the literature review of boundaries for the recompression Brayton cycle [7] and are listed in Table 4. Cycle calculations under given conditions (Table 4) were simulated using a CSAC for different split fraction values "x". Thermodynamics state properties were obtained by coupling the MATLAB code with the REFPROP.

Heat Exchanger Optimization Based on Cycle Performance
For the PCHE optimization, four parameters were considered for the optimization process: , Re, channel configuration, and split mass fraction. The optimization method uses the genetic algorithm (GA). The design variables, including upper and lower bounds, are listed in Table 5. The GA has been frequently adopted in the literature [20,[39][40][41][42][43] to solve global maximization and minimization problems. It is based on the stochastic method and uses the principle of survival of the fittest [39]. The GA is initialized through a random population of selected size based on the design variables chosen to define the first generation. The population is tested against the defined fitness function. The population in each generation improves through an iterative process using mutation, crossover, and elite selection. A schematic of the process is shown in Figure 6. The population size for the current study uses 100 combinations of the defined variables. For the values of the crossover fraction, mutation fractions for the current problem were chosen as 0.9 and 0.01. A 1% elite of the total population was carried forward unchanged to the next generation.

Characteristics of the PCHEs
The current study was conducted to evaluate the cycle's performance and its components using zigzag and straight channels for the HTR and LTR. The research focuses mainly on discovering how operating conditions change across the different components of the cycle, i.e., turbine, compressor, and heat exchangers with zigzag and straight-channel geometries.
Design variables and upper/lower bounds (Table 2) Generate initial papulation

Characteristics of the PCHEs
The current study was conducted to evaluate the cycle's performance and its components using zigzag and straight channels for the HTR and LTR. The research focuses mainly on discovering how operating conditions change across the different components of the cycle, i.e., turbine, compressor, and heat exchangers with zigzag and straight-channel geometries. Figures 7 and 8 show the profiles of temperature, Nusselt number (Nu), Reynolds number, specific heat capacity (C p ), thermal conductivity (k), and heat transfer coefficient (h) for high-and low-temperature recuperators under the cycle conditions given in Table 5. Figure 7 shows the LTR characteristics and suggests that the Reynolds number initially increases substantially along the length of PCHE before the curve flattens. In the cold side, the Re increases along the PCHE's length. Variations in the thermal conductivity, heat transfer coefficient, and thermal and specific heat capacity are as significant as variations in the Reynolds number. Furthermore, in Figure 7, the Nusselt number increases along the heat exchanger's length on the hot side due to the increase in the Reynolds number. Figure 8 shows the characteristics of a high temperature recuperator (HTR). The HTR length is much longer than the LTR; variation in the working fluid properties along the length of the HTR is quite apparent. The temperature profiles in the heat exchanger are not linear that is quite interesting and help to avoid pinch point within the heat exchanger. The Reynolds number on the hot side increases along the heat exchanger's length; on the cold side, the Reynolds number increases initially and starts decreasing after reaching the maximum value. The heat transfer coefficient's value decreases along the heat exchanger's length on the hot side; it decreases initially and then increases toward the end of the heat exchanger. In contrast, the Nusselt number increases along the heat exchanger's length on both the hot and cold sides. It should be noted that the profiles of Reynold number, htc and Nu can be explained by the variation of the properties of carbon dioxide, based on its operation near the critical point. The variation in the specific heat capacity (Cp) and thermal conductivity (k) is shown in Figure 8. It shows that both Cp and k vary substantially along the heat exchange's length due to temperature and pressure. in the Reynolds number. Furthermore, in Figure 7, the Nusselt number increases along the heat exchanger's length on the hot side due to the increase in the Reynolds number. Figure 8 shows the characteristics of a high temperature recuperator (HTR). The HTR length is much longer than the LTR; variation in the working fluid properties along the length of the HTR is quite apparent. The temperature profiles in the heat exchanger are not linear that is quite interesting and help to avoid pinch point within the heat exchanger. The Reynolds number on the hot side increases along the heat exchanger's length; on the cold side, the Reynolds number increases initially and starts decreasing after reaching the maximum value. The heat transfer coefficient's value decreases along the heat exchanger's length on the hot side; it decreases initially and then increases toward the end of the heat exchanger. In contrast, the Nusselt number increases along the heat exchanger's length on both the hot and cold sides. It should be noted that the profiles of Reynold number, ℎ and can be explained by the variation of the properties of carbon dioxide, based on its operation near the critical point. The variation in the specific heat capacity ( ) and thermal conductivity ( ) is shown in Figure 8. It shows that both and vary substantially along the heat exchange's length due to temperature and pressure. This section presents an assessment study for PCHEs with the straight-channel and zigzag-channel configurations. Temperature profiles along the length of the PCHE with straight-channel and zigzag-channel arrangements designed for the same heat load are shown in Figure 9. It can be seen that the size of the heat exchanger computed by the heat transfer characteristics linked with that certain channel configuration. In contrast, the pressure drop is linked with the pressure coefficient and the calculated length of the channel for a certain channel configuration   This section presents an assessment study for PCHEs with the straight-channel and zigzag-channel configurations. Temperature profiles along the length of the PCHE with straight-channel and zigzag-channel arrangements designed for the same heat load are shown in Figure 9. It can be seen that the size of the heat exchanger computed by the heat exchanger design code (PCHE-DAC) is three times longer for the LTR with a straightchannel configuration than with a zigzag-channel configuration. Furthermore, Figure 9 demonstrates the pressure drop variations across the PCHE with different design values for Re, , and channel's geometry (zigzag or straight). Interestingly, the pressure drop across the PCHEs with the straight-channel is significantly higher than PCHEs with zigzagchannels even though the former's friction factor is substantially higher than the latter (2-2.5 times). This can be explained by examining the data displayed in Figures 9-12. The channel's computed length for a certain channel's configuration is greatly reliant on heat transfer characteristics linked with that certain channel configuration. In contrast, the pressure drop is linked with the pressure coefficient and the calculated length of the channel for a certain channel configuration.        The data displayed in Figure 10 reflects Nusselt number values for the zigzag-channel geometry are comprehensively enhanced compared to the corresponding values for the straight-channel configuration. The for the zigzag-channel is 2.5-3.5 times higher than the straight-channel geometry. That is why the zigzag-channel requires considerably shorter lengths to transfer similar values of the heat when ϵ is same for both configurations. Figure 13 shows that the length of the PCHEs with zigzag channels is 2-4 times less for various values of ϵ and Reynolds number. Based on the above discussion, it can be concluded that pressure losses across straight-channel geometry are dominated by longer channel lengths (3 to 4 times) rather than lower friction factor value (e.g., 2-2.5). This is the reason pressure losses in PCHEs with straight channels are higher in comparison with zigzag-channels.

Comparison of Heat Exchanger Designs with Straight and Zigzag Channels
The data displayed in Figure 10 reflects Nusselt number values for the zigzag-channel geometry are comprehensively enhanced compared to the corresponding values for the straight-channel configuration. The Nu for the zigzag-channel is 2.5-3.5 times higher than the straight-channel geometry. That is why the zigzag-channel requires considerably shorter lengths to transfer similar values of the heat when is same for both configurations. Figure 13 shows that the length of the PCHEs with zigzag channels is 2-4 times less for various values of and Reynolds number. Based on the above discussion, it can be concluded that pressure losses across straight-channel geometry are dominated by longer channel lengths (3 to 4 times) rather than lower friction factor value (e.g., 2-2.5). This is the reason pressure losses in PCHEs with straight channels are higher in comparison with zigzag-channels tions. Figure 13 shows that the length of the PCHEs with zigzag channels is 2-4 times less for various values of ϵ and Reynolds number. Based on the above discussion, it can be concluded that pressure losses across straight-channel geometry are dominated by longer channel lengths (3 to 4 times) rather than lower friction factor value (e.g., 2-2.5). This is the reason pressure losses in PCHEs with straight channels are higher in comparison with zigzag-channels.   Figure 11 demonstrates ∆P for PCHEs designed for different Re in , , and channel shapes (zigzag or straight). For the both zigzag and straight-channel configurations, PCHE's length increases with increasing Re. The increasing trend in PCHE's length with Re is understandable as it increases the mass flow rate that in turn would require more surface area if is fixed. Alternatively, increase in the design value of would increase the PCHE's length as now again it would require more heat to be transferred to bring the difference in the exit temperature of hot and cold side further close. Consequently, pressure losses across the channel being a direct function of channel's length would increase as well. Therefore, an increase in the length of the channel with the design values of the inlet Reynolds number and effectiveness of the heat exchanger is the main reason for the rise in pressure drop. However, at any fixed designed values of the inlet Reynolds number and effectiveness, the pressure drop in a straight-channel configuration is almost three times greater than in a zigzag-channel configuration. The surge in the ∆P with Re is small at lower values (Re < 40,000). By contrast, at higher values of Re (Re > 40 k), the pressure drop becomes highly sensitive to Re. Figure 12 shows the variation in the pressure drop in the cold side of the PCHE. The pressure drop increases significantly with increasing Re and for all channel designs. An increase in the pressure drop in the cold side with Re follows the same trend observed on the hot side. However, unlike the hot side of the PCHE, the pressure drop across the straight-channel geometry is less than ∆P for the straight-channel and is only slightly greater than ∆P for the zigzag channel. Figure 13 shows the heat exchanger size variation for heat exchangers with different design values for Re, , and channel configuration (zigzag or straight). It is observed in the figure that the PCHE's size decreases sharply with an increase in the Re in values for all values and both channel configurations. However, once Re exceeds 40,000, the decrease in the size of the heat exchanger with Re becomes minimal. It is evident from Figure 10 that all curves relating to various values of and both channel geometries become relatively flattered for Re > 40, 000. It can be inferred from Figures 10-13 that Reynolds numbers ranging from Re = 30, 000 to Re = 40, 000 are appropriate for designing a heat exchanger that favors both the PCHE's smaller size and lower pressure drop across it.

Cycle simulations Results
This section describes how the PCHE design is crucial to the cycle's overall performance and the design of its turbomachinery components. Performance of the sCO 2 − BC was computed using different heat exchanger designs, as described earlier. Figure 14 shows the pressure ratio trend across the main compressor for heat exchangers with varying design values for Reynolds number, effectiveness, and channel configuration (zigzag or straight). It is observed in the figure that the pressure ratio across the main compressor does not change with modifications in the design. This is due to the imposed cycle's boundary conditions dictating that the compressor's inlet pressure and cycle pressure ratio remain constant. In contrast, the pressure ratio across the recompression compressor changes substantially with an increase in the design values of , Re, and channel configuration. The pressure ratio for the recompression compressor (Pr RC ) decreases with an increase in . The slope of the Pr RC lines become steeper as the heat exchanger's effectiveness increases, dictating that the pressure ratio across the compressor declines sharply when > 0.95. In Figure 14, the Pr RC values are relatively higher for heat exchanger designs with higher inlet Reynolds number. However, recompression load is significantly higher on the recompressor for cycle layouts using PCHEs with straight-channel configurations. The load increases further if the heat exchanger designs have higher design values of and Re.  Figure 15 shows the variation in the turbine's pressure ratio profiles for heat exchangers with different design values for , , and channel geometry (zigzag or straight). The figure suggests that the pressure ratio across the turbine decreases substantially with an increase in heat exchanger effectiveness. Heat exchanger designs with higher inlet Reynolds number experienced a greater decrease in with . Comparison between zigzag and straight-channel configurations suggests that for a heat exchanger with a zigzagchannel is significantly higher than with a straight-channel configuration. Figure 13 also shows the variation in the split mass values for different heat exchanger designs. The value decreases in heat exchanger designs with higher effectiveness. There is no appreciable change in the split mass fraction with varying inlet Reynolds number or channel's shape.  Figure 15 shows the variation in the turbine's pressure ratio profiles for heat exchangers with different design values for Re, , and channel geometry (zigzag or straight). The figure suggests that the pressure ratio across the turbine decreases substantially with an increase in heat exchanger effectiveness. Heat exchanger designs with higher inlet Reynolds number experienced a greater decrease in Pr T with . Comparison between zigzag and straight-channel configurations suggests that Pr T for a heat exchanger with a zigzag-channel is significantly higher than with a straight-channel configuration. Figure 13 also shows the variation in the split mass values for different heat exchanger designs. The x value decreases in heat exchanger designs with higher effectiveness. There is no appreciable change in the split mass fraction with varying inlet Reynolds number or channel's shape.
figure suggests that the pressure ratio across the turbine decreases substantially with an increase in heat exchanger effectiveness. Heat exchanger designs with higher inlet Reynolds number experienced a greater decrease in with . Comparison between zigzag and straight-channel configurations suggests that for a heat exchanger with a zigzagchannel is significantly higher than with a straight-channel configuration. Figure 13 also shows the variation in the split mass values for different heat exchanger designs. The value decreases in heat exchanger designs with higher effectiveness. There is no appreciable change in the split mass fraction with varying inlet Reynolds number or channel's shape.

Inlet Reynolds number = 30,000
Inlet Reynolds number = 45,000  Figure 16 demonstrates that the variation in and specific work of the cycle for PCHE designs. For a PCHE design with a low inlet Reynolds number, i.e., Re = 30,000, the increases substantially with a rise in the with a zigzag-channel configuration. For straight channels, the deteriorates once ϵ > 0.97. The specific work decreases appreciably for both channel geometries as the design value of ϵ increases. For heat exchanger designs with Re = 45,000, initially increases with ϵ, then decreases after a certain value of effectiveness, ϵ ≈ 0.96 and 0.98 for PCHEs with the straight-channel and zigzag-channel configurations, respectively. Furthermore, trends for PCHEs designs with Re = 60,000 are significantly different than with Re = 30,000 and 45,000. The increases decline sharply with ϵ for heat exchanger designs with straight-channel configurations.  Figure 16 demonstrates that the variation in η cyc and specific work of the cycle for PCHE designs. For a PCHE design with a low inlet Reynolds number, i.e., Re = 30,000, the η cyc increases substantially with a rise in the with a zigzag-channel configuration. For straight channels, the η cyc deteriorates once > 0.97. The specific work decreases appreciably for both channel geometries as the design value of increases. For heat exchanger designs with Re = 45,000, η cyc initially increases with , then decreases after a certain value of effectiveness, ≈ 0.96 and 0.98 for PCHEs with the straight-channel and zigzag-channel configurations, respectively. Furthermore, η cyc trends for PCHEs designs with Re = 60,000 are significantly different than with Re = 30,000 and 45,000. The η cyc increases decline sharply with for heat exchanger designs with straight-channel configurations.
certain value of effectiveness, ϵ ≈ 0.96 and 0.98 for PCHEs with the straight-channel and zigzag-channel configurations, respectively. Furthermore, trends for PCHEs designs with Re = 60,000 are significantly different than with Re = 30,000 and 45,000. The increases decline sharply with ϵ for heat exchanger designs with straight-channel configurations. Inlet Reynolds number = 60,000 For heat exchanger design with zigzag-channel configurations, values increase slightly, with ranging from 0.8 to 0.9. For > 0.93, the value of decreases sharply with a further increase in the of the PCHE. Trends of specific work with are almost identical for all values of Re. The specific-work for heat exchanger designs with a straightchannel configuration is significantly smaller than with a zigzag-channel configuration. A similar trend is observed for PCHE designs with different values for the inlet Reynolds number. Figure 17 suggests that the main compressor power increases considerably with an increase in . This could be explained by the split mass fraction decreasing with , reflecting that the mass flow rate through the main-compressor decreases, and thus also the size of the compressor and required power to run it. In contrast, the power required to run the recompression compressor increases faster than the decrease in the main compressor power. Thus, the total ability to run the compressor increases, despite the reduction in the main compressor power, as shown in Figure 17. A substantial increase in the main compressor power is attributed to the rise in the flow rate and pressure ratio across it with an increase in with . For heat exchanger design with zigzag-channel configurations, η cyc values increase slightly, with ranging from 0.8 to 0.9. For > 0.93, the value of η cyc decreases sharply with a further increase in the of the PCHE. Trends of specific work with are almost identical for all values of Re. The specific-work for heat exchanger designs with a straight-channel configuration is significantly smaller than with a zigzag-channel configuration. A similar trend is observed for PCHE designs with different values for the inlet Reynolds number. Figure 17 suggests that the main compressor power increases considerably with an increase in . This could be explained by the split mass fraction decreasing with , reflecting that the mass flow rate through the main-compressor decreases, and thus also the size of the compressor and required power to run it. In contrast, the power required to run the recompression compressor increases faster than the decrease in the main compressor power. Thus, the total ability to run the compressor increases, despite the reduction in the main compressor power, as shown in Figure 17. A substantial increase in the main compressor power is attributed to the rise in the flow rate and pressure ratio across it with an increase in x with . of the compressor and required power to run it. In contrast, the power required to run the recompression compressor increases faster than the decrease in the main compressor power. Thus, the total ability to run the compressor increases, despite the reduction in the main compressor power, as shown in Figure 17. A substantial increase in the main compressor power is attributed to the rise in the flow rate and pressure ratio across it with an increase in with . Inlet Reynolds number = 60,000   Figure 18 reflects the changes in the total compressor power and turbine power for heat exchangers with different design values for Re, and channel's geometry (zigzag or straight). The figure suggests that the total compressor power increases while the turbine power decreases with for all values of the inlet Re, and channel's geometry (zigzag or straight). For all heat exchanger designs with different and Re, W T values are higher for PCHEs using zigzag-channel configurations. However, the computed values of W C were almost identical for both channel configurations. Figure 19 shows PCHE optimization results and the convergence history; data for the final converged solution is presented in Table 6. All converged solutions in the Pareto front are for the zigzag-channel geometry, attributed to the superior thermal characteristics associated with the zigzag-channel geometry. Minimum and maximum heat exchanger sizes were 0.07 m 3 and 0.614 m 3 , respectively, corresponding to 53% and 56% overall efficiencies of the power cycle. A 3% increase in the cycle performance is at the expense of a nine-fold increase in the heat exchanger size. Considering the fact that most of the layout size for the sCO 2 − BC comes from the heat exchanger [29], it can be rephrased that a 3% increase in the cycle performance comes at the cost of a nine-fold increase in the layout size, which considerably impacts the initial cost. The region highlighted in Figure 17 also displays the optimal points from the Pareto front that offer a good compromise between the cycle performance and layout size for the sCO 2 − BC. Figure 18 demonstrates the fluctuations in power consumed by the main compressor when the effectiveness was varied from 0.8 to 0.99 for different design values of the Re_in number (30k, 45k, and 60k) for straight and zigzag-channel configurations. straight). The figure suggests that the total compressor power increases while the turbine power decreases with for all values of the inlet , and channel's geometry (zigzag or straight). For all heat exchanger designs with different and , values are higher for PCHEs using zigzag-channel configurations. However, the computed values of were almost identical for both channel configurations.

Heat Exchanger Optimization Results
Inlet Reynolds number = 30,000 Inlet Reynolds number = 45,000 Inlet Reynolds number = 60,000

Conclusions
The current study was conducted to evaluate the effect of straight and zigzag-channel configurations on the overall performance of the 2 − and its turbomachinery. To evaluate the different designs of the printed circuit heat exchanger, an in-house code was used for the PCHE design and analysis. The PCHE code was further used as a subroutine with a cycle design point analysis code to evaluate the effect of different PCHE designs

Conclusions
The current study was conducted to evaluate the effect of straight and zigzag-channel configurations on the overall performance of the sCO 2 − BC and its turbomachinery. To evaluate the different designs of the printed circuit heat exchanger, an in-house code was used for the PCHE design and analysis. The PCHE code was further used as a subroutine with a cycle design point analysis code to evaluate the effect of different PCHE designs on the cycle's performance and its components, i.e., compressor and turbomachinery. The following conclusions were drawn from the study.

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For the same heat load, PCHEs with zigzag-channel configuration are computed to be approximately one third the size of PCHE with straight-channel configuration reasoned by the superior heat transfer characteristics associated with the zigzag channels. This in turn, reduces the pressure drop across the PCHEs with zigzagchannel in comparison with the PCHEs with straight-channel even though the friction factor for the latter is lower than the former.

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For both channel configurations, the heat exchanger size increases with an increase in the design value for effectiveness. It decreases with a decrease in the design value for the inlet Reynolds number. The pressure drops increase by increasing both and Re in both hot and cold side channels of the heat exchanger and vice versa. The pressure drop for the PCHE on the cold side is only slightly higher for straight-channel geometry than for zigzag-channel geometry. However, the heat exchanger's hot side's pressure drop was three times higher for the straight-channel geometry than for the zigzag-channel geometry. Similar results were reported for the heat exchanger's size by Saeed et al. [29]; however, they did not note the channel's geometry's effect on the component size.

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Due to the high-pressure drop in PCHEs with a straight-channel configuration, available pressure across the turbine is significantly smaller in the sCO 2 − BC than with a zigzag-channel configuration. Further load on the recompression compressor can be reduced significantly if PCHE designs with straight channels are replaced with zigzag-channels. In contrast, the main-compressor load was found to be independent of the PCHE design as inlet conditions were kept constant for the current study.

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PCHEs with a zigzag-channel configuration with design values for the inlet Reynolds number and heat exchanger effectiveness ranging from 32 k to 42 k and 0.94 > > 0.87, respectively, are optimal for the sCO 2 − BC and provide a good compromise between cycle efficiency and layout size.