Thermal–Hydraulic Performance Comparison of Printed Circuit Heat Exchangers with Identical-Size and Hybrid-Size Unit Channels

Abstract

The supercritical carbon dioxide Brayton cycle has been identified as being applicable in a wide variety of applications, and printed circuit heat exchangers (PCHEs) are widely used in these applications due to their good compactness and high thermal efficiency. A PCHE with hybrid-size unit channels has been proposed and found capable of improving the heat transfer performance, but most results were obtained at non-consistent total volume and mass flow rate. Therefore, given the space constraints of heat exchangers in supercritical CO₂ Brayton cycles, this study investigates the application of standard-size and hybrid-size unit channel configurations under different hot-to-cold fluid thermal resistance ratios while maintaining a fixed total volume and consistent total mass flow rate. The results demonstrate that the hybrid-size unit channel configuration fails to enhance heat transfer. The heat transfer rate per volume exhibits a marginal 5.2% reduction at smaller thermal resistance ratios and a drastic 28.9% degradation at larger thermal resistance ratios. The hybrid-size channel configuration significantly improves the pressure drop per unit length on the hot side, achieving maximum reductions of 80.3% and 79.7% under the two thermal resistance ratios, respectively. The enhancement magnitude on the hot side outweighs the increased pressure drop on the cold side. Simultaneously, the ratio of average heat transfer rate to total pumping power exhibits significant differences between the two channel configurations under varying thermal resistance ratios. Under scenarios with substantial thermal resistance disparities, the hybrid-size unit channel configuration achieves a maximum 356.2% improvement in the ratio compared to the identical-size unit channel configuration, whereas balanced thermal resistance ratios lead to a degradation in overall performance.

1. Introduction

The present energy crisis poses a considerable number of challenges with regard to industrialization. However, the key to resolving the problem lies in the power cycle. The supercritical carbon dioxide (SCO₂) Brayton cycle represents a developing power cycle system that boasts a number of key advantages, including simple cycle layout, high cycle efficiency at moderate turbine inlet temperature, and low efficiency loss using dry cooling. These features underpin its extensive utilization across pivotal energy domains, such as nuclear, solar, and coal-fired power generation, underscoring its relevance and versatility in diverse energy landscapes [1,2,3,4,5,6]. The heat exchange devices, including the precooler, recuperators, and heater, are the main parts of the SCO₂ Brayton cycle. The printed circuit heat exchanger (PCHE) is a compact plate heat exchanger that exhibits excellent heat transfer performance, high temperature and pressure resistance, and other advantageous characteristics and demonstrates notable adaptability and stability under extreme operating conditions [7]. Compared to a traditional shell-and-tube heat exchanger, PCHE can deliver the same heat transfer effect with a reduction in volume [8]. Hence, it is employed in a variety of power cycle systems.

Extensive research has been conducted on the flow and heat transfer characteristics of supercritical carbon dioxide (SCO₂) in traditional identical-size unit channel configurations of PCHE. Concurrent studies have explored the thermal–hydraulic performance of identical-size unit channel configurations with diverse channel structures, collectively providing a critical foundational reference for the present work. The channel structures of PCHE can be categorized into continuous and discontinuous types. Primary continuous configurations include straight channel [9], zigzag channel [10,11], and sinusoidal channel [12], etc. For the discontinuous types, there are S-shaped fin channels [13,14], airfoil fin channels [15], etc. Hasan et al. [16] analyzed the performance impact of four different cross-sectional shapes (square, circular, triangular, and trapezoidal) on a straight channel PCHE, revealing superior overall performance in the square channel. Shi et al. [17] found that using the airfoil channel inside the recuperator led to better overall performance compared to straight and zigzag channels. Cheng et al. [18] conducted experimental research into the thermo-hydraulic characteristics of SCO₂-water in a 100 kW class PCHE. The findings reveal that the inlet Reynolds number and temperature of SCO₂ and water are the primary factors influencing the heat transfer. Hu et al. [19] numerically analyzed the condensation flow and heat transfer characteristics of condensate in a semicircular PCHE channel. The occurrence of different flow patterns in the channel was observed, and the pressure drop and heat transfer correlations were established, with good predictive results. Wen et al. [20] investigated the local heat transfer and flow characteristics of SCO₂ in a sinusoidal-channel PCHE numerically. It was found that the complex interactions between varying thermophysical properties, buoyancy force, and periodically varying centrifugal force were pivotal to the shaping of the flow field. The results of Wang et al. [21] showed that the overall performance of a rectangular channel on the hot side of the PCHE was improved compared to a semicircular channel, but the opposite was observed on the cold side. Xu et al. [22] inserted several hemispherical dimples to periodically destroy the flow boundary, which improved thermal performance with increased pressure loss. In summary, the comprehensive performance of PCHE varies significantly across different channel configurations, making the optimization of channel geometry a critical pathway to enhance the thermal efficiency of power cycles. Existing studies have extensively investigated the thermal–hydraulic performance of identical-size unit channel configuration (traditional one-to-one channel configuration) under conditions with comparable thermal resistance between hot and cold fluids. However, these efforts predominantly focus on optimizing channel geometry types and cross-sectional parameters while neglecting the influence of channel configuration strategies—particularly the unexplored potential of hybrid-size unit channel configuration (asymmetric one-to-two channel configuration). Therefore, systematic investigation into the effects of channel configuration under smaller thermal resistance ratios is imperative to unlock advanced PCHE design.

In recent years, a proportion of the research on PCHE has also been related to the nuclear energy field. Utilizing the conventional channel configuration (identical-size unit channel configuration), the conjugate heat transfer characteristics and heat exchanger performance of lead–bismuth eutectic (LBE) and SCO₂ in PCHE have been examined, thus providing a foundation for the optimization of PCHE [23,24]. Moreover, the research revealed that LBE has the potential to corrode solid domains in the flow heat transfer process, thereby generating debris and leading to scaling. In turn, this results in the obstruction of the channel, thereby compromising the safe operation of the equipment. It is therefore recommended that the LBE side should be used with a large equivalent-diameter channel to prevent clogging [25]. Based on the aforementioned considerations, a hybrid-size channel configuration is typically adopted in research, featuring a single hot-side channel with a larger hydraulic diameter coupled with multiple cold-side channels of smaller hydraulic diameters. This configuration demonstrates superiority over traditional symmetric configurations in operational performance. Liu et al. [26] have proposed a new configuration of PCHE, the conclusion of which states that superior heat transfer performance is provided when the optimal channel diameter ratio is determined to be 2.5. In their research, Qiao et al. [27] employed the NSGA-II multi-objective method to enhance the geometrical configuration of the channels of a semicircular PCHE. The outcomes demonstrate that the optimal performance and economic advantages were achieved when the channel diameter ratio was set at 4.1. This configuration was identified as a key factor in the optimization of the PCHE design. Liu et al. [28] compared the overall performance of a hybrid-size channel configuration of a straight-channel PCHE with a traditional channel configuration. The findings revealed that the hybrid-size channel configuration can achieve superior heat transfer efficiency when the fixed plate thickness and the channel diameter ratio are set to 2.25. It was further demonstrated that the hybrid-size channel configuration is capable of achieving optimal results. Current research on hybrid-size unit channel configuration remains limited, predominantly confined to applications in nuclear reactor primary heat exchangers under lower thermal resistance ratios. The adaptability of these configurations to other thermal resistance regimes has yet to be systematically explored, representing a critical frontier for advancing a heat exchanger design. Furthermore, while prior studies have generated valuable insights, they universally neglect the impact of channel configurations on unit channel volume, a key parameter governing system compactness and manufacturing costs. Consequently, future investigations must rigorously integrate volumetric constraints into channel configuration optimization.

The aforementioned research findings reveal that due to the inherently compact nature of supercritical Brayton cycles, the spatial footprint of all components must be rigorously optimized during system design, including critical elements like heat exchangers. This constraint necessitates strict limitations on the overall volume of heat exchangers integrated into such cycles, as their physical dimensions directly impact the feasibility of achieving high power density in advanced energy systems. The above studies were conducted to compare and analyze the performance of PCHE in different channel configurations while keeping the mass flow rate at the inlet of the unit channel constant on both the cold and hot sides. It was demonstrated that the hybrid-size channel configurations have superior heat transfer and flow performance in comparison to the conventional channel configurations, disregarding the alteration in the volume of the heat exchanger consequent to the modification in channel configuration. However, when the number of channels on both sides changes from 1:1 to 1:2 and above, the ratio of mass flow rates at the inlets of the unit channels on both the hot and cold sides is bound to change. The inlet conditions in extant studies are not well defined, which has a detrimental effect on the accuracy of the performance evaluation of different channel configurations. Furthermore, existing studies on novel configurations are predominantly confined to nuclear energy applications, leaving their applicability under other thermal resistance ratios (r = R_h/R_c) uncertain, given that the thermal resistance ratio is also a critical factor influencing overall heat transfer performance. Therefore, comparative analyses under varying thermal resistance ratios are essential to gain deeper insights into the suitability of different channel configurations.

Therefore, under the constraints of fixed heat exchanger volume and constant total mass flow rate, this study conducted a performance comparison between conventional standard-size channel configurations and novel hybrid-size channel configurations in a straight-channel PCHE. The investigation focuses on evaluating the overall performance of both configurations under varying thermal resistance ratios, verifying the applicability of the novel configuration, and providing design optimization references for PCHE.

2. Model and Methodology

2.1. Working Fluid

To investigate the applicability of both configurations under different fluid thermal resistance ratios (r = R_h/R_c), two pairs of working fluids were selected:

(1)

Pair 1 (small thermal resistance r): Hot-side fluid is LBE, and cold-side fluid is SCO₂.

(2)

Pair 2 (large thermal resistance r): Hot-side fluid is SCO₂, and cold-side fluid is water.

Technical specifications of the working fluids employed in this study require explicit elaboration: First, supercritical carbon dioxide (SCO₂) exhibits hybrid gas–liquid properties: its density surpasses typical gases, while its viscosity remains gas-like, significantly lower than conventional liquids. The thermal expansion coefficient is moderately higher than common gases and 10–100 times greater than most liquids, resulting in enhanced transport properties and superior heat transfer efficiency. The physical property data for SCO₂ were obtained from the National Institute of Standards and Technology (NIST) Reference Fluid Thermodynamics and Transport Properties (REFPROP) database [29]. Secondly, lead–bismuth eutectic (LBE) demonstrates significantly higher density and viscosity compared to conventional fluids, yet exhibits superior thermal conductivity, which qualifies it as an optimal primary coolant for Generation IV nuclear reactor systems, particularly lead-cooled fast reactors (LFRs). The physical property data of LBE were obtained from the physical property equations obtained by fitting the experimental data of LBE using the least-squares method in the work of Liu et al. [28] The physical property formula for LBE is shown below:

$${\rho }_{LBE}=11113.6+1.34T$$

(1)

$$c_{p,LBE}=246.8T^{-0.08}$$

(2)

$${\lambda }_{LBE}=4.51+1.2\times {10}^{-2}T$$

(3)

$${\mu }_{LBE}=4.94\times {10}^{-4}exp\left({\displaystyle \frac{757.1}{T}}\right)$$

(4)

2.2. Conservation Equations

The following continuity, momentum, and energy equations are used in the heat transfer solution process.

The continuity equation:

$${\displaystyle \frac{\mathit{\partial }\rho }{\mathit{\partial }t}}+{\displaystyle \frac{\mathit{\partial }{\rho u}_j}{\mathit{\partial }{x}_j}}=0$$

(5)

The momentum equation:

$${\displaystyle \frac{\mathit{\partial }{\rho u}_i}{\mathit{\partial }t}}+{\displaystyle \frac{\mathit{\partial }{\rho u}_i{u}_j}{\mathit{\partial }{x}_j}}=-{\displaystyle \frac{\mathit{\partial }P}{\mathit{\partial }{x}_i}}+{\displaystyle \frac{\mathit{\partial }}{\mathit{\partial }{x}_j}}\left[\rho \left(\upsilon +{\upsilon }_t\right){\displaystyle \frac{\mathit{\partial }{u}_i}{\mathit{\partial }{u}_j}}\right]+\rho g_i$$

(6)

The energy equation:

$${\displaystyle \frac{\mathit{\partial }\rho h}{\mathit{\partial }t}}+{\displaystyle \frac{\mathit{\partial }\rho h{u}_j}{\mathit{\partial }{x}_j}}+{\displaystyle \frac{\mathit{\partial }\rho K{u}_j}{\mathit{\partial }{x}_j}}+{\displaystyle \frac{\mathit{\partial }\rho K}{\mathit{\partial }t}}={\displaystyle \frac{\mathit{\partial }P}{\mathit{\partial }t}}+\rho u_i·g_i+{\displaystyle \frac{\mathit{\partial }}{\mathit{\partial }x}}\left[\rho \left(\alpha +{\alpha }_t\right){\displaystyle \frac{\mathit{\partial }h}{\mathit{\partial }{x}_j}}\right]$$

(7)

where, u_i, P, h, and K are used to represent velocity, pressure, specific heat capacity, and specific kinetic energy, respectively; g_i is employed to denote the gravity source term; ρ, denotes density; and υ and α are the molecular kinematic viscosity and molecular heat diffusion coefficient of the fluid.

2.3. Numerical Model

2.3.1. Physical Model Selection and Calculation Conditions

Given the spatial constraints imposed by supercritical Brayton cycles on the heat exchanger footprint, this study focuses on evaluating the impact of configuration modifications on thermal–hydraulic performance under a fixed total heat exchanger volume. The investigation is conducted with a standardized overall dimension of 200 × 12 × 15 mm, within which two distinct straight-channel configurations are implemented. Both configurations maintain a minimum inter-channel spacing of 0.5 mm between hot and cold channels. Detailed geometric parameters of the unit channels for each configuration are illustrated in Figure 1.

Under the fixed total dimensions, the identical-size unit channel configuration contains 24 hot-side channels and 24 cold-side channels, whereas the hybrid-size channel configuration reduces the channel counts to 18 (hot) and 9 (cold). Consequently, if the total inlet mass flow rate remains constant, the inlet mass flow rate of the single channel on both the hot and cold sides in the hybrid-size unit channel configuration will be increasing. If an identical inlet mass flow rate of the single channel on the same side under different configurations is maintained, the total mass flow rate entering the heat exchanger would inherently differ between configurations. Therefore, the total heat entering the heat exchanger would also be different, thus affecting the reasonableness of the results of the comparison of heat exchanger performances. Additionally, this would also ignore the effect of the channel configurations on the volume of the unit channel. Therefore, this study asserts that maintaining identical total mass flow rates across all channel configurations is a prerequisite for scientifically defensible comparisons of heat exchanger performance.

The total mass flow rate of the heat exchanger was employed in the study to maintain a consistent level, and the individual channel mass flow rates were calculated separately by the number of channels on each side as the inlet conditions for the unit channels. The counter-flow configuration is used. The operating conditions are shown in

Table 1. Calculation conditions.

		Hot Side				Cold Side
	Case	Th,in (K)	Mh,in (kg/s)	mh,in (kg/s) (1-1)	mh,in (kg/s) (1-2)	Tc,in (K)	Mc,in (kg/s)	mc,in (kg/s) (1-1)	mc,in (kg/s) (1-2)
Pair 1	1	700	1.44	0.060	0.160	420	0.0336	0.0014	0.00186
	2	700	1.68	0.070	0.186	420	0.0336	0.0014	0.00186
	3	700	1.92	0.080	0.213	420	0.0336	0.0014	0.00186
	4	700	2.16	0.090	0.240	420	0.0336	0.0014	0.00186
	5	600	1.68	0.070	0.186	420	0.0336	0.0014	0.00186
	6	800	1.68	0.070	0.186	420	0.0336	0.0014	0.00186
	7	1000	1.68	0.070	0.186	420	0.0336	0.0014	0.00186
	8	700	1.68	0.070	0.186	420	0.0216	0.0009	0.00120
	9	700	1.68	0.070	0.186	420	0.0264	0.0011	0.00146
	10	700	1.68	0.070	0.186	420	0.0384	0.0016	0.00213
Pair 2	11	363.15	0.01130	0.000471	0.001256	293.15	0.03015	0.001256	0.001675
	12	363.15	0.01507	0.000628	0.001675	293.15	0.03015	0.001256	0.001675
	13	363.15	0.01884	0.000785	0.002094	293.15	0.03015	0.001256	0.001675
	14	363.15	0.02261	0.000942	0.002512	293.15	0.03015	0.001256	0.001675
	15	358.15	0.01507	0.000628	0.001675	293.15	0.03015	0.001256	0.001675
	16	368.15	0.01507	0.000628	0.001675	293.15	0.03015	0.001256	0.001675
	17	378.15	0.01507	0.000628	0.001675	293.15	0.03015	0.001256	0.001675
	18	363.15	0.01507	0.000628	0.001675	293.15	0.02261	0.000942	0.001256
	19	363.15	0.01507	0.000628	0.001675	293.15	0.02639	0.001099	0.001466
	20	363.15	0.01507	0.000628	0.001675	293.15	0.03392	0.001413	0.001884

. The solid material is stainless steel 304 (SUS304). The mass flow rate inlet has been selected for the inlet conditions on both the hot and cold sides. The pressure outlet has been chosen for the outlet conditions. Periodic boundary conditions have been set on the outer wall of the model. The fluid–solid coupling interface has been set as the coupling boundary, and the front and rear solid walls have been set as the adiabatic boundary.

2.3.2. Flow and Heat Transfer Numerical Model

Numerical simulations were conducted utilizing the Fluent software, employing the SIMPLEC algorithm to manage the coupling of pressure and velocity. All equations were formulated in second-order windward format. In prior studies, the SST k-ω turbulence model has demonstrated superior accuracy in predicting heat transfer performance for fluids with variable thermophysical properties. Extensively validated by numerous scholars, this model exhibits minimal deviations from experimental data and is particularly effective for simulating the flow and heat transfer processes of SCO₂ in PCHE [30,31,32]. Regarding turbulence modeling for LBE, several scholars have compared the standard k-ε model, the realizable k-ε model, and the SST k-ω model. The findings of these studies have indicated that the SST k-ω model achieves higher predictive precision for near-wall flow and heat transfer characteristics, exhibiting minimal deviation from experimental data. These findings confirm its applicability for simulating LBE thermal–hydraulic behavior. Given these advantages, the SST k-ω model is selected to simulate the flow and heat transfer processes in PCHE for this study [33,34,35]. Moreover, the Prandtl number of LBE is lower than that of conventional fluids. In addition, molecular heat conduction dominates in the heat transfer process. It is therefore necessary to use an effective Prandtl number model combined with the SST k-ω model to simulate the flow heat transfer in LBE. A review of relevant literature reveals that some scholars have compared various turbulent Prandtl number (${Pr}_t$) models, and the Cheng-Tak [36] turbulent Prandtl number (${Pr}_t$) model, when combined with the SST k-ω model, has demonstrated promising results [37]. To this end, Cheng-Tak’s model was used to calculate the turbulent Prandtl number, as follows:

$${Pr}_t=\left\{\begin{array}{c}4.12, Pe \le 2000\\ {\displaystyle \frac{0.01Pe}{{\left[0.018{Pe}^{0.8}-\left(7.0-A\right)\right]}^{1.25}}}, 1000<Pe \le 6000\end{array}\right.$$

(8)

$$A=\left\{\begin{array}{c}4.5, Pe \le 1000\\ 5.4-9\times {10}^{-4}Pe, 1000<Pe \le 2000\\ 3.6, Pe>2000\end{array}\right.$$

(9)

2.3.3. Model Verification

The computational domain of the unit channel is meshed using ICEM software, and in order to meet the requirements of the SST k-ω model, the boundary layer is encrypted to ensure that y + <1, and the grids of two models are shown in Figure 2. In the context of the investigation, grid independence verification was conducted separately for both channel configurations. Convergence of the calculations can be determined by monitoring the outlet temperatures on both the hot and cold sides and determining that they remain constant and that the residual difference is less than 10⁻¹⁰. The outcomes of the grid independence are presented in Figure 3 and Figure 4. It is evident from these figures that when the number of grids exceeds 1,420,954 and 3,090,727, respectively, the variation in the outlet temperatures of the hot and cold sides under the two channel configurations is less than 1%. In order to ensure the accuracy of the results and save computation time, the grids with the numbers 1,420,954 and 3,090,727 are selected for the two channel configurations for the subsequent calculations, respectively.

In view of the lack of experimental studies about hybrid-size channel configuration, the experimental data from Park et al. [38] of identical-size unit channel configuration was used for comparison. For experimental boundary conditions, the hot-side fluid is SCO₂ at a pressure of 7.5 MPa, with an inlet Reynolds number Re of 14,400 and an inlet temperature of 346.15 K. The cold-side fluid is water. The inlet temperature of water is 309.8 K. As demonstrated in Figure 4, the simulated and experimental values demonstrate a strong correlation, accurately reflecting the overall trend, with a maximum discrepancy of 1.01% on the hot side and 0.98% on the cold side. This variation falls within the acceptable range, substantiating the reliability of the numerical simulation method.

2.4. Data Reduction

The channel hydraulic diameters of the various models have been calculated from the dimensional parameters of these models. The hydraulic diameter D_h is defined as follows:

$$D_h={\displaystyle \frac{4V}{A_c}}$$

(10)

where V is used to denote the volume of the fluid domain within the channel and A_c is used to denote the cross-sectional area of the channel.

The evaluation of the heat transfer performance of the heat exchanger is conducted through the assessment of two key metrics: the overall heat transfer rate Q of the PCHE unit and the heat transfer rate per unit volume Q/V. The overall heat transfer rate, Q, is defined by the following equation:

$$Q=m·(h_{in}-h_{out})$$

(11)

Here, the average mass flow rate of a single channel on the hot side is denoted by m_in. The enthalpy of the inlet and outlet on the hot side is denoted by h_in and h_out, respectively. Finally, the volume of the PCHE unit is denoted by V.

In order to visually compare the overall thermal–hydraulic performance of all channel configurations of the PCHE, the ratio of the average heat transfer rate to the pumping power η is used to evaluate the overall performance, where η is defined by the following equation:

$$\eta ={\displaystyle \frac{Q_{ave}}{{PP}_{{CO}_2}+{PP}_{LBE}}}={\displaystyle \frac{(Q_{{CO}_2}+Q_{LBE})/2}{{\left(\frac{m}{\rho }\Delta P\right)}_{{CO}_2}+{\left(\frac{m}{\rho }\Delta P\right)}_{LBE}}}$$

(12)

In the above equation, Q_ave is the average heat transfer rate of the PCHE unit, and PP_CO2 and PP_LBE are the pumping power of the hot and cold sides, respectively.

3. Results and Discussion

3.1. Axial Profiles of Bulk Temperature and Velocity

This section commences with an exploration of the effects of the two channel configurations. Under the constraint of an identical total heat exchanger footprint, the transition from identical-size unit channel configuration to hybrid-size channel configuration results in a reduction in the number of channels for both hot and cold sides while maintaining constant total mass flow rates. The variation in flow velocity within the channel is the primary factor contributing to the substantial discrepancy in pressure drop observed between the two channel configurations. However, under different thermal resistance ratios, there is a significant difference in the effect of the channel configuration on the heat transfer performance.

Utilizing Case 2 as a demonstrative example, the subsequent Figure 5 and Figure 6 illustrate the bulk temperature of the fluid and the velocity within the channels on both the hot and cold sides for both channel configurations. For Pair 1 (LBE and SCO₂), there is no significant difference in fluid temperature between the hot and cold sides under the different configurations; the velocity in the channels is significantly different, with the velocity in the channel on the hot side of the identical-size unit channel configuration almost 1.5 times that on the hot side of the hybrid-size channel configuration. Although the hybrid-size unit channel configuration increases the hot-side heat transfer area to enhance thermal exchange, it concurrently reduces the hot-side flow velocity. This velocity reduction diminishes flow-induced turbulence within channels and fails to thin the thermal boundary layer, thereby weakening convective heat transfer intensity. Due to the inherently thick thermal boundary layer in LBE, where molecular conduction dominates, the hot-side heat transfer efficiency experiences only a marginal decline. Consequently, the hot-side fluid temperature remains nearly constant as the suppressed convective effects are counterbalanced by sustained conductive heat transfer through the boundary layer. Additionally, the increased flow velocity of SCO₂ enhances fluid mixing through intensified turbulence within the channel while simultaneously disrupting the thermal boundary layer to elevate convective heat transfer intensity. Under the hybrid-size unit channel configuration, despite comparable inlet and outlet temperatures between configurations, the higher cold-side flow velocity accelerates heat removal rates. This phenomenon results in minimal difference in cold-side bulk temperature between both configurations, as the augmented cold-side convective capacity compensates for the thermal load transferred from the hot side.

For Pair 2 (SCO₂-Water), taking Case 12 as an example, the hybrid-size unit channel configuration (one-to-two arrangement) increases the hot-side mass flow rate but significantly reduces the flow velocity within hot channels. This velocity reduction suppresses turbulence generation, thereby weakening thermal boundary layer disruption and fluid mixing, ultimately diminishing convective heat transfer intensity. As SCO₂ relies predominantly on convective heat transfer, the elevated thermal resistance on the hot side leads to a notable decline in overall heat transfer efficiency. Conversely, the cold-side mass flow rate of the single channel increases, driving a substantial rise in flow velocity that enhances cold-side convective heat transfer. These observations unequivocally demonstrate that channel configurations modulate heat exchange performance primarily through velocity-dependent alterations.

3.2. Effect of Hot-Side Mass Flow Rate

The present section is concerned with an investigation of the effect of hot-side mass flow rate on the flow and heat transfer performance for two thermal resistance ratio conditions, corresponding to cases 1–4 and cases 11–14, respectively. The temperature difference between the inlet and outlet of the hot and cold sides (ΔT_hot and ΔT_cold), as well as the pressure drop per unit length (ΔP_hot/L and ΔP_cold/L) in the channel, were analyzed directly for two thermal resistance ratios. As depicted in Figure 7, the increasing total mass flow rate at the hot-side inlet shortens the thermal exposure time of the hot-side fluid. However, this simultaneously amplifies turbulence intensity within the hot-side channels, enhancing heat transfer efficiency through intensified thermal boundary layer disruption. Consequently, the ΔT of the hot and cold streams exhibit opposing trends. In this scenario, the ΔT_hot and ΔT_cold are reduced. In the identical-size unit channel configuration, a greater ΔT_hot and ΔT_cold are observed; however, this difference between the hybrid-size and identical-size unit channel configurations is less pronounced.

For both thermal resistance ratios, the ΔT_hot and ΔT_cold with higher thermal resistance are more significantly affected by the channel configuration. For Pair 1, the hybrid-size unit channel configuration increases the hot-side heat transfer area to enhance thermal exchange but simultaneously reduces the hot-side flow velocity of the channel. This velocity reduction suppresses turbulence generation and fails to thin the thermal boundary layer, thereby diminishing convective heat transfer intensity. Due to the thicker thermal boundary layer of LBE, which is dominated by molecular thermal conductivity, there is a slight increase in the heat transfer intensity on the hot side, and the ΔT_hot is minimal. Concurrently, the elevated cold-side flow velocity intensifies turbulence, effectively disrupting the cold-side thermal boundary layer and amplifying convective heat transfer. The accelerated cold-side flow also rapidly evacuates absorbed heat, mitigating the impact of the slightly reduced heat transfer intensity on the cold side. Consequently, the ΔT_cold across both configurations remains comparable. The hybrid-size channel configuration exhibits a maximum reduction in ΔT_hot of 2.0% and a 3.4% decrease in ΔT_cold, indicating minor disparities in heat transfer performance between the two configurations. For Pair 2, the hybrid-size unit channel configuration increases the mass flow rate of the hot-side channel but significantly reduces the flow velocity within the channel. This velocity reduction suppresses turbulence generation and weakens thermal boundary layer disruption, thereby diminishing convective heat transfer intensity. Since SCO₂ primarily relies on convective heat transfer, the overall hot-side thermal performance degrades, leading to a reduction in the ΔT_hot. On the cold side, the elevated mass flow rate substantially increases the flow velocity of the channel, enhancing cold-side convective heat transfer. However, the reduced thermal exposure time causes a decrease in the ΔT_cold. The hybrid-size channel configuration demonstrates a maximum reduction of 20.9% in ΔT_hot and 30.0% in ΔT_cold, signifying a significant deterioration in heat transfer performance compared to the baseline identical-size unit channel configuration.

By conducting a thorough analysis of the pressure drop per unit length of both hot and cold sides (ΔP_hot/L and ΔP_cold/L), taking into account the variations in thermal resistance ratios for the two channel configurations illustrated in Figure 8. It was observed that as the hot-side total mass flow rate increased, a corresponding gradual rise in ΔP_hot/L was recorded for both channel configurations. Conversely, a relatively stable ΔP_cold/L was recorded on the cold side of both channel configurations. The ΔP_hot/L in the identical-size unit channel configuration is significantly higher than that of the hybrid-size channel configuration, with the disparity progressively amplifying as the hot-side total mass flow rate increases. This phenomenon arises from the configuration-induced disparity in the number of channels. This results in diminished velocity on the hot side and augmented velocity on the cold side of the hybrid-size channel configuration. Consequently, there is a reduction in pressure drop on the hot side and an augmentation in pressure drop on the cold side. For Pair 1, the hybrid-size channel configuration achieves a maximum reduction of 80.0% in ΔP_hot/L and a 68.7% increase in ΔP_cold/L. For Pair 2, the hybrid-size channel configuration yields a 79.7% reduction in ΔP_hot/L but incurs a 57.6% rise in ΔP_cold/L, reflecting configuration-dependent hydraulic trade-offs under distinct thermal resistance regimes. The hybrid-size channel configuration produces a similar effect on the hydraulic performance of the hot and cold sides for both thermal resistance ratio conditions. That is to say, it substantially improves the pressure drop on the hot side, but also increases the pressure drop on the cold side.

It is noteworthy that under both thermal resistance ratio conditions, the two channel configurations exhibit divergent outcomes in terms of heat transfer rate per volume (Q/V) and ratio of average heat transfer rate to pumping power (η). As illustrated in Figure 9, under the Pair 1 conditions, cold-side heat transfer exerts a dominant influence on overall thermal performance. The enhanced convective intensity on the cold side offsets localized hot-side performance degradation, resulting in minimal variation in global heat transfer intensity. Consequently, the total heat transfer capacity increases proportionally with unit channel volume expansion, causing the hybrid-size unit channel configuration (one-to-two arrangement) to exert minimal impact on the volumetric heat transfer rate of the heat exchanger. The hybrid-size channel configuration minimally impacts the Q/V, peaking at a mere 2.0% reduction, while significantly elevating the η, achieving a staggering 349.5% enhancement by the reduction in the pressure drop in the channel. Moreover, under the Pair 2 conditions, the overall heat transfer performance is predominantly governed by the convective heat transfer intensity of the hot-side SCO₂. The hybrid-size unit channel configuration significantly reduces this intensity due to suppressed turbulence and thickened thermal boundary layers, leading to a marked decline in global heat transfer efficiency. Although the elevated hot-side mass flow rate delivers additional thermal energy, the resultant increase in total heat transfer capacity is substantially outweighed by the expanded unit channel volume, ultimately causing a 28.9% reduction in Q/V and a declining trend in the η. However, when the hot-side mass flow rate is increased to 0.01884 kg/s, the hybrid-size channel configuration demonstrates a transient superiority with η, peaking at 44.0% higher than the baseline identical-size unit channel configuration. But this performance enhancement is confined to specific operational cases.

3.3. Effect of Hot-Side Inlet Temperature

The hot-side inlet temperature constitutes a critical factor influencing heat exchanger performance. This section systematically examines the thermal–hydraulic impacts induced by hot-side inlet temperature. As shown in Figure 10, increasing the hot-side inlet temperature amplifies the thermal driving force between the hot and cold sides, leading to a concurrent rise in ΔT_hot and ΔT_cold. Notably, ΔT_hot exhibits more pronounced sensitivity to inlet temperature variations under both thermal resistance ratios. It is noteworthy that ΔT_hot is more susceptible to the influence of the hot-side inlet temperature, given the presence of two distinct thermal resistance ratios.

Under the Pair 2 conditions, the hybrid-size unit channel configuration increases the mass flow rate of the hot-side single channel but significantly reduces the flow velocity within hot channels. This velocity reduction suppresses turbulence generation and impedes thermal boundary layer disruption and fluid mixing enhancement, thereby diminishing convective heat transfer intensity. Since SCO₂ heat transfer primarily relies on convective mechanisms, the weakened hot-side heat transfer efficiency directly reduces the ΔT_hot. Consequently, compounded by the weakened hot-side heat transfer, the ΔT_cold also decreases. For Pair 1, the hybrid-size channel configuration exhibits maximum reductions of 3.1% in ΔT_hot and 3.7% in ΔT_cold, indicating negligible thermal performance disparities between configurations. In stark contrast, Pair 2 demonstrates substantial reductions of 18.7% in ΔT_hot and 30.0% in ΔT_cold under the hybrid-size channel configuration, highlighting its enhanced efficacy in high thermal resistance ratio regimes.

The trend of ΔP_hot/L and ΔP_cold/L for different inlet temperatures on the hot side is indicative of the prevailing conditions, as demonstrated in Figure 11. Under the Pair 1 conditions, as the hot-side inlet temperature increases, the ΔP_hot/L in both configurations demonstrates a gradual decrease, while the ΔP_cold/L exhibits a progressive increase, governed by divergent thermophysical responses of the working fluids. Under the Pair 2 conditions, both channel configurations exhibit relatively flat pressure drop trends on the hot and cold sides, likely attributable to the thermophysical properties of the working fluids within the studied temperature range. This indicates that under high thermal resistance ratio conditions, variations in hot-side inlet temperature exert minimal influence on the pressure drop of both configurations. For Pair 1, the hybrid-size channel configuration achieves a maximum reduction of 80.0% in ΔP_hot/L while incurring a 68.3% increase in ΔP_cold/L. For Pair 2, the hybrid-size channel configuration demonstrates analogous effects, with a 78.9% ΔP_hot/L reduction and a 57.6% ΔP_cold/L increase. It is evident that both thermal resistance ratio conditions yield analogous effects.

As illustrated in Figure 12, the evolution trends of both the Q/V and the η for the two channel configurations are delineated under varying hot-side inlet temperatures. The influence of elevated hot-side inlet temperature on the Q/V diverges markedly between the two thermal resistance ratios. Under Pair 2 conditions, the overall heat transfer performance is predominantly governed by the convective heat transfer intensity of the SCO₂. The hybrid-size unit channel configuration significantly reduces this intensity due to suppressed turbulence and thickened thermal boundary layers, leading to a marked decline in global heat transfer efficiency. Although the elevated mass flow rate of the hot-side single channel delivers additional thermal energy, the resultant increase in total heat transfer capacity is substantially outweighed by the expanded unit channel volume, ultimately causing a 28.7% reduction in Q/V. Concurrently, the increased pressure drop across unit channels reduces the η, with a maximum observed decline of 15.4%. However, under Pair 1, the enhanced convective heat transfer intensity on the cold side compensates for localized thermal performance variations, resulting in minimal changes to the global heat transfer intensity. Consequently, the total heat transfer capacity increases proportionally with the expanded unit channel volume, leading to a negligible impact on the Q/V. For Pair 1, the hybrid-size channel configuration incurs a maximum reduction of 3.1% in Q/V while achieving a remarkable 298.5% enhancement in the η.

3.4. Effect of Cold-Side Mass Flow Rate

To investigate the impact of cold-side mass flow rate, analyses were conducted across varying cold-side inlet flow conditions under two thermal resistance ratios. As illustrated in Figure 13, increasing the total cold-side mass flow rate amplifies turbulent disturbances and enhances the fluid-mixing effects within the cold-side channels, thereby accelerating heat extraction from the hot side. Concurrently, the ΔT_hot exhibits a gradual rise under both thermal resistance ratios, while the ΔT_cold follows an opposing trend.

Under the Pair 2 conditions, the hybrid-size unit channel configuration increases the mass flow rate of the hot-side single channel but significantly reduces the flow velocity within hot channels. This velocity reduction suppresses turbulence generation and weakens fluid mixing effects, thereby diminishing convective heat transfer intensity. Since SCO₂ heat transfer primarily relies on convective mechanisms, the weakened hot-side heat transfer efficiency directly reduces the hot-side thermal performance. Consequently, compounded by the diminished heat transfer intensity on the hot side, the ΔT_cold and ΔT_hot decrease. The disparity predominantly manifests between the two thermal resistance ratio regimes, with significantly amplified differences between that observed in Pair 2 compared to Pair 1. This observation further substantiates that variations in the thermal resistance ratio amplify the disparities in heat transfer performance between different channel configurations, particularly accentuating the divergence between identical-size and hybrid-size unit channel configurations. For pair 1, although the hot-side heat transfer intensity decreases, the enhanced cold-side convective heat transfer intensity compensates for this reduction, resulting in minimal variation in global thermal performance. Specifically, the hybrid-size channel configuration achieves maximum reductions of 5.4% in ΔT_hot and 5.6% in ΔT_cold. Additionally, under the Pair 2 conditions, the hybrid-size channel configuration exhibits significantly larger reductions of 18.5% for ΔT_hot and 29.6% for ΔT_cold. This marked contrast between thermal resistance ratio regimes underscores the imperative of incorporating the thermal resistance ratio into configuration selection protocols for PCHE.

Thorough analysis of the variation trends in ΔP_hot/L and ΔP_cold/L with respect to cold-side total mass flow rate, as illustrated in Figure 14. Under both thermal resistance ratio conditions, the ΔP_hot/L remains essentially invariant with changes in cold-side total mass flow rate, while the ΔP_cold/L exhibits a monotonic increase in proportional cold-side total mass flow rate. This phenomenon arises because the cold-side mass flow rate dominantly governs the ΔP_cold/L, with minimal coupling to the hot-side hydraulic behavior. For Pair 1, the hybrid-size channel configuration achieves a maximum reduction of 80.3% in ΔP_hot/L while incurring a 68.6% increase in ΔP_cold/L. Under Pair 2, the hybrid-size channel configuration demonstrates analogous trends but with amplified penalties of a 79.1% reduction in ΔP_hot/L coupled with a 58.6% surge in ΔP_cold/L. The effect of channel configuration on the hydraulic performance of the hot and cold sides is found to be essentially similar for different thermal resistance ratios.

As illustrated in Figure 15, within the investigated operational range, the Q/V for both channel configurations increase with cold-side total mass flow rate across all thermal resistance ratios. However, the η exhibits diametrically opposed trends. For Pair 2, under identical total cold-side mass flow rates, the overall heat transfer performance is predominantly governed by the convective heat transfer intensity of the SCO₂. The hybrid-size unit channel configuration significantly reduces this intensity due to suppressed turbulence and thickened thermal boundary layers, leading to a marked decline in global thermal efficiency. Although the elevated hot-side mass flow rate of the single channel delivers additional thermal energy, the resultant increase in total heat transfer capacity is substantially outweighed by the expanded unit channel volume, ultimately causing a 28.4% reduction in Q/V. Additionally, the increase in total cold-side mass flow rate leads to a slower rise in heat transfer capacity compared to the amplified cold-side pressure drop. This disparity accelerates the decline of the η in the hybrid-size unit channel configuration, accompanied by a 23.6% deterioration in η. When the cold-side total mass flow rate exceeds 0.03015 kg/s, the η value of the hybrid-size channel configuration falls below that of the identical-size unit channel configuration. This finding further demonstrates that the thermal resistance ratio critically governs the integrated performance of heat exchangers. For Pair 1, the hybrid-size channel configuration exhibited a maximum 5.2% reduction in Q/V while achieving a 352.6% enhancement in η.

3.5. Discussion on Different Thermal Resistance Ratios

The two fluid pairs (Pair 1: LBE-SCO₂ and Pair 2: SCO₂-water) exhibit significant differences in thermal resistance ratios, which critically influence the heat exchanger’s thermal–hydraulic performance. Under the operational conditions in this study, the two pairs of fluids exhibit distinct thermal resistance ratio (r = R_h/R_c) ranges, with the thermal resistance ratios further modulated by channel configuration layouts, as illustrated in Figure 16. For Pair 1, its thermal resistance ratio deviates more significantly from unity compared to Pair 2, indicating a more pronounced thermal resistance disparity between the hot and cold fluids under the Pair 1 conditions, which constitutes a critical consideration. As indicated in Figure 17, under the Pair 1 conditions, the hybrid-size channel configuration exhibited negligible variation in Q/V within the investigated parameter range, yet its η surpassed that of the identical-size unit channel configuration. However, for Pair 2, both the Q/V and the η under the identical-size unit channel configuration demonstrated consistently higher values compared to the hybrid-size channel configuration. Hence, the hybrid-size and identical-size unit channel configurations exhibit distinct applicability under varying operational conditions. Configuration selection must be tailored to the thermophysical properties of the pair of fluids to achieve optimal performance, requiring comprehensive consideration of thermal resistance disparities and pressure-drop distributions between hot and cold fluids. Under the Pair 1 conditions, where the pressure drop across unit channels is predominantly dominated by the hot side, the hybrid-size unit channel configuration significantly reduces the hot-side pressure drop, thereby lowering the overall channel pressure drop and improving hydraulic performance. In contrast, under the Pair 2 conditions, where the pressure drop distribution shifts toward the cold side, the hybrid-size configuration increases the cold-side pressure drop, leading to a rise in total channel pressure drop and consequently degrading the comprehensive performance metrics. Therefore, in scenarios with a substantial thermal resistance disparity between hot and cold fluids, where pressure drop is predominantly dominated by the hot side, the hybrid-size unit channel configuration enhances comprehensive performance metrics by trading a marginal reduction in heat transfer efficiency for a significant pressure drop reduction. Conversely, under balanced thermal resistance ratios, the identical-size unit channel configuration preserves heat transfer efficiency while maintaining superior overall performance, particularly in systems requiring thermal equilibrium under extreme thermal gradients.

4. Conclusions

This study investigated the effects of flow channel configurations on the thermal–hydraulic performance of heat exchangers through numerical simulations, prioritizing compact design constraints. A comparative analysis of two channel configurations was conducted under varying thermal resistance ratios, with fixed volumetric dimensions and invariant total mass flow rate. Key findings are summarized as follows:

(1)

The two configurations exhibited configuration-dependent thermal performance under varying thermal resistance ratios. For LBE-SCO₂ with a low thermal resistance ratio, the hybrid-size channel configuration achieved an 80.3% maximum reduction in hot-side pressure drop per unit length while maintaining a comparable heat transfer rate per unit volume (≤5.2% variation), thereby substantially enhancing hot-side hydraulic performance.

(2)

For SCO₂-water with a high thermal resistance ratio, the hybrid-size channel configuration induced a pronounced 28.9% maximum degradation in heat transfer rate per unit volume. However, this hybrid-size channel configuration simultaneously achieved a substantial 79.7% decrease in hot-side pressure drop per unit length, which counterbalanced the elevated cold-side hydraulic resistance.

(3)

When evaluating the ratio of the average heat transfer rate to the pumping power η, the hybrid-size channel configuration demonstrated superior efficacy under low thermal resistance ratios. The significantly reduced hot-side pressure drop in this configuration led to a 352.6% maximum enhancement in η compared to the identical-size unit channel configuration as the minimized cumulative pump power consumption. However, under elevated high thermal resistance ratios, the hybrid-size channel configuration compromised the η, with a peak reduction of 23.6%.

(4)

Based on the comprehensive performance comparison between the two configurations under varying thermal resistance ratios, under scenarios with substantial thermal resistance disparity between hot and cold fluids, the identical-size unit channel configuration preserved thermal performance with minimal hydraulic penalties, thereby avoiding the risks of comprehensive performance degradation associated with the adoption of hybrid-size unit channel configuration. When pressure drop was predominantly dominated by the hot-side fluid, the hybrid-size unit channel configuration demonstrated superior viability in balanced thermal resistance ratios by a substantial pressure drop reduction. This configuration significantly enhanced comprehensive performance, offering a strategic pathway to optimize PCHE through improved channel configuration.