Flow Loss Analysis and Structural Optimization of Multiway Valves for Integrated Thermal Management Systems in Electric Vehicles

: The multiway valve is the core component of the integrated thermal management system in an electric vehicle, and its heat transfer loss and pressure loss signiﬁcantly impact the performance of the whole thermal management system. In this paper, heat transfer loss and pressure loss in multiway valves are investigated using three-dimensional unsteady numerical simulations. Heat transfer loss and pressure loss under different operating modes are revealed, and relationships between pressure loss and mass ﬂow rate, inlet temperature, and valve materials are studied. The results show that the signiﬁcant temperature gradient around the control shaft results in heat transfer loss and pressure loss mainly occurs around the junction of the control shaft and the shell, where the ﬂow direction changes sharply. The pressure loss is nonlinearly and positively correlated with the mass ﬂow rate. Furthermore, the main geometric parameters of the pipeline and the control shaft are optimized. The pressure loss ﬁrstly increases and then decreases, with the increasing curvature of the inner walls of the pipe corners in four ﬂow channels. Compared with the structural optimization at the pipe corners, increasing the curvature of the inner wall of the control shaft and the shell corners reduces pressure loss continuously. Moreover, this study obtains an optimal structure with minimum pressure loss using coupled structure optimization at the control shaft and shell corners.


Introduction
With the continuous advancement of electric vehicle (EV) technology, thermal management systems have been a crucial part of electric vehicles and are evolving toward high integration [1,2]. The performance of an integrated thermal management system (ITMS), which consists of an air conditioning (AC) system, battery thermal management system (BTMS), and drive motor thermal management system [3][4][5], significantly impacts the mileage, performance, and lifespan of EVs [6,7].
The multiway valve is a key innovation and an indispensable component in the present ITMS. Unlike traditional valves, multiway valves generally contain multiple flow paths. By switching among these paths, it is possible to highly integrate the various coolant loops and accurately control the flow in each loop, thereby achieving temperature control of each subsystem in the ITMS. The application of the multiway valve directly decreases the number and length of pipes, which greatly upgrades the efficiency of the whole system. However, since the temperature of the coolant in different loops of the multiway valve is not consistent during operation, the temperature difference inevitably induces heat conduction from high-temperature coolant to low-temperature coolant through the valve body [8], resulting in heat transfer loss in the valve. On the other hand, multiway valves generally possess more intricate flow channel configurations than traditional valves. As the coolant flows through a multiway valve, the fluid frequently undergoes multiple changes in flow direction, which unavoidably leads to high local pressure loss [9]. Numerous studies have already demonstrated the significant impact of pressure drop and heat transfer loss caused by valves or pipelines on the performance of ITMSs for EVs [10,11]. Therefore, it is of great importance to investigate both the heat transfer loss and flow loss of multiway valves in order to enhance the overall performance of IMTSs.
Since a multiway valve is a novel directional valve that has emerged in recent years with the development of ITMSs, studies on its internal heat transfer and flow characteristics are rarely reported. However, researchers have conducted extensive studies on heat transfer loss in traditional valves using experimental investigation and numerical simulation over the past few decades, and have also proposed diverse structural optimization methods. For instance, research on heat characteristics in reversing and check valves was carried out by Li et al. [4], and the results showed that a flow channel with high pressure had greater heat loss than a flow channel with low pressure. Oshman et al. [12] found that heat transfer occurred across the thermal valve due to significant temperature differences inside the valve, as well as between the valve and environment. The heat transfer has caused the difference temperature between the inlet and outlet, and the uneven temperature distribution resulted in thermal stress, reducing structural reliability [13]. Bao et al. [14] studied the flow characteristics of a Tesla valve and put forward that heat transfer loss can be reduced by decreasing disturbance in the tubes. Similarly, Monika et al. [15] and Lu et al. [16] investigated the effect of structural parameters in Tesla valves, such as the number of channels, the angles, and the distance between adjacent flow channels, on thermal performance. The authors indicated that heat transfer loss could be reduced by decreasing the channel number and increasing the distance between channels.
In addition to heat transfer loss, the pressure loss in traditional valves is also pronounced. Several studies have proven that valves with high pressure loss can increase energy consumption and reduce thermal performance in thermal management systems [17,18]. Specifically, pressure loss consists of friction pressure loss and local pressure loss. Friction pressure loss refers to pressure loss that occurs when fluid flows through the multiway valve, overcoming the viscosity of the fluid and the friction of the wall. When the flow's cross-sectional area and direction change, a vortex is generated, and local pressure loss occurs. Hemamalini et al. [19] showed that the pressure drop in the control valve was 68 times larger than that in pipes. Edvardsen et al. [20] measured the pressure drop in the shut-in valve at 55 kPa. The pressure losses in rotary tubular spool valves [9], reversing valves [21], and Tesla valves [14] are proportional to the flow rate and viscosity of the fluid, and inversely proportional to the change in flow area [22]. Moreover, Liu et al. [23] demonstrated that triangular rib tubes have lower pressure loss than square pipes. Ye et al. [24] found that there was a sudden change in pressure around the valve spool in the needle valve due to the flow direction changing suddenly. In summary, pressure drops are related to the velocity and temperature of the fluid and the structure of the flow channel, influencing the performance of the whole system.
For pressure loss within the diverse types of valves mentioned above, researchers have made great efforts to optimize valve structure [25], and structural optimization can be adopted to reduce pressure loss [26]. Zong et al. [27] studied the effect of the length and inner diameter of pipes and inlet mass flow rate in safety valves on pressure drop, and an optimal structure with lower pressure loss was obtained. Zhang et al. [28] changed the spacing, slot width, and depth of each trench to decrease flow resistance in a bionic valve. To reduce the pressure loss in spool valves and needle valves, Okhotnikov et al. [9] and Ye et al. [24] reduced the areas of pipe corners and sections where cross-sectional flow areas changed suddenly by changing their shapes to circular arcs. However, the abovementioned studies related to heat transfer loss and pressure loss mainly focused on traditional valves, and knowledge on the basic flow characteristics of multiway valves is still insufficient. The analysis of heat transfer loss and pressure loss in multiway valves is essential to facilitating the targeted optimization of their design. Additionally, although existing methods are only designed for traditional valves, they provide guidance for the structural optimization of multiway valves.
Energies 2023, 16, 5040 3 of 22 In this paper, the characteristics of heat transfer loss and pressure loss in a multiway valve are numerically investigated. Effects of main parameters, including mass flow rate, inlet temperature, and valve materials, on the flow characteristics of a multiway valve are studied. Furthermore, structural optimization at different sections, such as pipe corners, the control shaft, and shell corners, is conducted to obtain minimum flow resistance.

Physical Model and Mesh Generation
The structure of the multiway valve in this study is shown in Figure 1a, and it is composed of a shell, a sealing gasket, and a control shaft. A simplified geometric model is shown in Figure 1b. There are four flow channels in the multiway valve, and the inlet and outlet of flow channels 1, 3, and 4 are squares with an area of 441 mm 2 , and the pipe shape of flow channel 2 is a rectangle with an area of 714 mm 2 . According to the working principle of the valve, the flow direction of each flow channel is marked. There are six fluid regions, and two of the fluid domains are nonflowing, as shown in Figure 1c. Except the two nonflowing domains, coolant flows through the pipe in the shell, and when the coolant flows to the control shaft, the flow direction changes by 90 • in each fluid channel. Similarly, the change in flow direction occurs when the coolant flows from the control shaft to the pipe in the shell. essential to facilitating the targeted optimization of their design. Additionally, although existing methods are only designed for traditional valves, they provide guidance for the structural optimization of multiway valves. In this paper, the characteristics of heat transfer loss and pressure loss in a multiway valve are numerically investigated. Effects of main parameters, including mass flow rate, inlet temperature, and valve materials, on the flow characteristics of a multiway valve are studied. Furthermore, structural optimization at different sections, such as pipe corners, the control shaft, and shell corners, is conducted to obtain minimum flow resistance.

Physical Model and Mesh Generation
The structure of the multiway valve in this study is shown in Figure 1a, and it is composed of a shell, a sealing gasket, and a control shaft. A simplified geometric model is shown in Figure 1b. There are four flow channels in the multiway valve, and the inlet and outlet of flow channels 1, 3, and 4 are squares with an area of 441 mm 2 , and the pipe shape of flow channel 2 is a rectangle with an area of 714 mm 2 . According to the working principle of the valve, the flow direction of each flow channel is marked. There are six fluid regions, and two of the fluid domains are nonflowing, as shown in Figure 1c. Except the two nonflowing domains, coolant flows through the pipe in the shell, and when the coolant flows to the control shaft, the flow direction changes by 90° in each fluid channel. Similarly, the change in flow direction occurs when the coolant flows from the control shaft to the pipe in the shell. The meshes of both solid and fluid computational domains of the valve were generated as unstructured polyhedral meshes using ANSYS Fluent Meshing, as shown in Figure 2. Moreover, the inlet and outlet of the computational domain were extended 60 mm in order to avoid backflow and maintain inlet velocity stability. Shared topology was applied between the solid and fluid computational domains. Since the control shaft is cylindrical and the bulkhead is relatively thin, local sizing with a curvature normal angle of 10° The meshes of both solid and fluid computational domains of the valve were generated as unstructured polyhedral meshes using ANSYS Fluent Meshing, as shown in Figure 2. Moreover, the inlet and outlet of the computational domain were extended 60 mm in order to avoid backflow and maintain inlet velocity stability. Shared topology was applied between the solid and fluid computational domains. Since the control shaft is cylindrical and the bulkhead is relatively thin, local sizing with a curvature normal angle of 10 • at the control shaft was adopted. The curvature normal angle of the surface mesh for other regions was 12 • . The offset method type of boundary layers was uniform, and the at the control shaft was adopted. The curvature normal angle of the surface mesh for other regions was 12°. The offset method type of boundary layers was uniform, and the growth rate was set as 1.1. The maximum and minimum cell lengths were 0.85 mm and 0.1 mm, respectively.

Numerical Simulation and Boundary Conditions
Various turbulence models are available, accounting for different studies, and the appropriate turbulence model for each study should be verified [29]. At present, the k-ε model is used to assess the turbulence flow field in valves. The RNG k-ε model is an improvement on the standard k-ε model [30]. The RNG k-ε model performs well in simulating the turbulence flow field with a low Reynolds number [31]. Zhu et al. [31] utilized the RNG k-ε model to investigate the complicated flow field of a volute-type discharge passage, and the results showed evidence of flow separation and a vortex and that the velocity distribution was uneven. Therefore, the flow fields with flow separation and vortexes can be simulated using the RNG k-ε model.
Since the wall condition has a significant impact on flow characteristics near the wall, the wall function approach can be promoted to resolve all the flow scales at the walls [30]. Therefore, the RNG k-ε model together with standard wall functions was adopted for multiway valve simulation. The RNG k-ε model is defined by Equations (1) and (2) [32]: where k is the turbulence energy; αk and αε are generations of kinetic energy due to the mean velocity gradients and the buoyancy; µeff is the turbulence viscosity; Gk and Gb are the generation of turbulence kinetic energy due to the mean velocity gradients and the buoyancy; ε is the turbulence dissipation rate; YM is the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate; C1ε and C2ε are constants, and their values are 1.42 and 1.68, respectively. This turbulence model was used to calculate the pressure drop in turbulence flow through a pipe in a fluent validation case [33], and the error between the result of 21,429 Pa and the true value of 21,744 Pa was only 1.44%. A pressure correction based an iterative SIMPLE algorithm was utilized for discretizing the convective transport terms. The convergence accuracy of the energy equation, the turbulence kinetic energy, and the turbulence dissipation rate was 1 × 10 −6 . The gradient of the spatial discretization was set as least

Numerical Simulation and Boundary Conditions
Various turbulence models are available, accounting for different studies, and the appropriate turbulence model for each study should be verified [29]. At present, the k-ε model is used to assess the turbulence flow field in valves. The RNG k-ε model is an improvement on the standard k-ε model [30]. The RNG k-ε model performs well in simulating the turbulence flow field with a low Reynolds number [31]. Zhu et al. [31] utilized the RNG k-ε model to investigate the complicated flow field of a volute-type discharge passage, and the results showed evidence of flow separation and a vortex and that the velocity distribution was uneven. Therefore, the flow fields with flow separation and vortexes can be simulated using the RNG k-ε model.
Since the wall condition has a significant impact on flow characteristics near the wall, the wall function approach can be promoted to resolve all the flow scales at the walls [30]. Therefore, the RNG k-ε model together with standard wall functions was adopted for multiway valve simulation. The RNG k-ε model is defined by Equations (1) and (2) [32]: where k is the turbulence energy; α k and α ε are generations of kinetic energy due to the mean velocity gradients and the buoyancy; µ eff is the turbulence viscosity; G k and G b are the generation of turbulence kinetic energy due to the mean velocity gradients and the buoyancy; ε is the turbulence dissipation rate; Y M is the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate; C 1ε and C 2ε are constants, and their values are 1.42 and 1.68, respectively. This turbulence model was used to calculate the pressure drop in turbulence flow through a pipe in a fluent validation case [33], and the error between the result of 21,429 Pa and the true value of 21,744 Pa was only 1.44%. A pressure correction based an iterative SIMPLE algorithm was utilized for discretizing the convective transport terms. The convergence accuracy of the energy equation, the turbulence kinetic energy, and the turbulence dissipation rate was 1 × 10 −6 . The gradient of the spatial discretization was set as least squares cell-based. The second-order format for pressure and the second-order upwind format for momentum, turbulent kinetic energy, turbulent dissipation rate, and energy equations were used.
The valve is composed of acrylonitrile butadiene styrene plastic (ABS), and its physical properties are listed in Table 1. The outside wall of the valve was set as adiabatic, and the inside wall was regarded as smooth and no-slip. BASF G40 was adopted as the coolant. Since the physical properties of the coolant vary with temperature, a piecewise linear function was implemented in numerical simulations to accurately capture the fluid's behavior. As for the boundary conditions, the parameters of each boundary condition in the present study refer to the actual operation data provided by China Automotive Research Corporation. The inlet boundary was set as a mass flow inlet of 0.6 kg/s, and the outlet was a pressure outlet with standard atmospheric pressure. Moreover, the inlet temperatures of flow channels 1 to 4 were set at 318 K, 313 K, 323 K, and 310 K, individually.

Grid Independence Verification
Three computational models, for which the cell numbers were 7.88 billion, 3.50 billion, and 159 billion, were adopted in grid independence verification to ensure accuracy and computational efficiency. The inlet mass flow rate was 0.6 kg/s, and the inlet temperature was 318 K. The approximate relative error e 21 a , the extrapolated relatively error e 21 ext , and the fine-grid convergence index GCI 21 f ine can be expressed as Equations (3)-(12) [34]: where z is a representative cell; N is the total number of cells; ∆V i is the volume of the ith cell; φ is the pressure drop in the flow channel; p is the apparent order. The discretization errors are listed in Table 2. The numerical uncertainty in the fine-grid solution for the pressure drop was 0.026%.

Heat Transfer Loss
As shown in Figure 3, two sections are arranged at the center of the two rows of flow channels, and the temperature field distribution on the sections is observed. Since the temperature of the coolant in different flow channels is different and the bulkheads of the control shaft are thin, the temperature gradient is significant around the control shaft, indicating that the heat transfer mainly occurs across the control shaft. Moreover, the heat transfer between flow channels 2, 3, and 4 is distinct, while that in flow channel 1 is inconspicuous. The temperature gradient of the fluid regions that are nonflowing is great. However, the heat transfer is little, and the outlet temperatures change slightly. Thus, the heat transfer loss is inconspicuous.

Heat Transfer Loss
As shown in Figure 3, two sections are arranged at the center of the two rows of flow channels, and the temperature field distribution on the sections is observed. Since the temperature of the coolant in different flow channels is different and the bulkheads of the control shaft are thin, the temperature gradient is significant around the control shaft, indicating that the heat transfer mainly occurs across the control shaft. Moreover, the heat transfer between flow channels 2, 3, and 4 is distinct, while that in flow channel 1 is inconspicuous. The temperature gradient of the fluid regions that are nonflowing is great. However, the heat transfer is little, and the outlet temperatures change slightly. Thus, the heat transfer loss is inconspicuous. The temperature difference ∆tf inevitably leads to heat transfer loss, and the heat exchange power Q can be obtained by Equation (13).
where h is the convective heat transfer coefficient; A is the cross-sectional area of the flow channel; Δ is the logarithmic mean temperature difference; is the mass flow rate of the coolant; c is the specific heat capacity. Figure 4 shows the temperature difference and the heat exchange power of each channel. It can be seen that the temperature difference in each flow channel is −0.006 K, 0.016 The temperature difference ∆t f inevitably leads to heat transfer loss, and the heat exchange power Q can be obtained by Equation (13). where h is the convective heat transfer coefficient; A is the cross-sectional area of the flow channel; ∆t is the logarithmic mean temperature difference; . m is the mass flow rate of the coolant; c is the specific heat capacity. Figure 4 shows the temperature difference and the heat exchange power of each channel. It can be seen that the temperature difference in each flow channel is −0.006 K, 0.016 K, −0.020 K, and 0.016 K, and the heat exchange power is −2.98 W, 7.31 W, 9.59 W, and 7.12 W, respectively. When the temperature difference and the heat exchange power are positive, the coolant flowing through the flow channel absorbs heat, while heat is released when the temperature difference and heat exchange power are negative numbers. The temperature differences in flow channels 2, 3, and 4 are larger than that in channel 1. The coolant has a high specific heat capacity of about 2500 J/(kg·K) and a low thermal conductivity of about 0.28 W/(m·K). This shows that the temperature of the coolant changes slightly in the valve. K, −0.020 K, and 0.016 K, and the heat exchange power is −2.98 W, 7.31 W, 9.59 W, and 7.12 W, respectively. When the temperature difference and the heat exchange power are positive, the coolant flowing through the flow channel absorbs heat, while heat is released when the temperature difference and heat exchange power are negative numbers. The temperature differences in flow channels 2, 3, and 4 are larger than that in channel 1. The coolant has a high specific heat capacity of about 2500 J/(kg·K) and a low thermal conductivity of about 0.28 W/(m·K). This shows that the temperature of the coolant changes slightly in the valve.

Pressure Loss
The pressure distribution of each channel is shown in Figure 5a. The pressure decreases constantly from inlet to outlet in four flow channels, and the pressure distribution is not steady around the control shaft, since the flow direction changes suddenly. A large pressure gradient can be observed at the control shaft. By distinguishing the colors of the pressure contours, the pressure drop between the inlet and outlet of each channel is different, with channels 1 and 4 exhibiting higher inlet pressure compared to channels 2 and 3. In order to define the regions where pressure loss mainly occurs, quantitative analysis was adopted. Taking flow channel 1 as an example, the pressure at each section is listed in Figure 5b. Section analyses were carried out before and after changes in the flow direction or cross-sectional area of the channels. The pressure drops between surfaces 4 and 5, as well as between surfaces 6 and 7 are large. The pressure drops in the two regions are 1411 Pa and 1883 Pa, and 25.8% and 34.47% of the total pressure drop, respectively. This indicates that the flow direction varies suddenly, resulting in an inhomogeneous pressure field. Moreover, a large loss of pressure occurs in the regions after the changes in flow direction.

Pressure Loss
The pressure distribution of each channel is shown in Figure 5a. The pressure decreases constantly from inlet to outlet in four flow channels, and the pressure distribution is not steady around the control shaft, since the flow direction changes suddenly. A large pressure gradient can be observed at the control shaft. By distinguishing the colors of the pressure contours, the pressure drop between the inlet and outlet of each channel is different, with channels 1 and 4 exhibiting higher inlet pressure compared to channels 2 and 3. In order to define the regions where pressure loss mainly occurs, quantitative analysis was adopted. Taking flow channel 1 as an example, the pressure at each section is listed in Figure 5b. Section analyses were carried out before and after changes in the flow direction or crosssectional area of the channels. The pressure drops between surfaces 4 and 5, as well as between surfaces 6 and 7 are large. The pressure drops in the two regions are 1411 Pa and 1883 Pa, and 25.8% and 34.47% of the total pressure drop, respectively. This indicates that the flow direction varies suddenly, resulting in an inhomogeneous pressure field. Moreover, a large loss of pressure occurs in the regions after the changes in flow direction. The pressure drop of the coolant in the four flow channels is depicted in Figure 6 With a mass flow rate of 0.6 kg/s, the pressure drops in the four flow channels are 5467.2 Pa, 2650.81 Pa, 3235.55 Pa, and 6265.60 Pa, respectively. The coolant in flow channel 4 ex periences the most significant pressure drop, followed by that in channels 1 and 3, and th smallest pressure drop of the coolant occurs in channel 2. The length of flow channels and 4 is larger, and the flow field is more complex than that of flow channels 2 and 3. I addition, the diameter of flow channel 2 is larger than that of the other three flow channel and the velocity of flow channel 2 is lower than that of other flow channels at the sam mass flow rate. The friction pressure loss and local pressure loss are both small at low velocity. However, adopting the pressure drop between the inlet and the outlet is insuffi cient to evaluate the pressure loss in different structures, and thus the flow resistance co efficient is adopted in this section to reveal the detailed flow loss in the flow channels. Th expression of the flow resistance coefficient ξ is as follows: where Δ is the pressure drop between the inlet and the outlet of each flow channel. The pressure drop of the coolant in the four flow channels is depicted in Figure 6. With a mass flow rate of 0.6 kg/s, the pressure drops in the four flow channels are 5467.22 Pa, 2650.81 Pa, 3235.55 Pa, and 6265.60 Pa, respectively. The coolant in flow channel 4 experiences the most significant pressure drop, followed by that in channels 1 and 3, and the smallest pressure drop of the coolant occurs in channel 2. The length of flow channels 1 and 4 is larger, and the flow field is more complex than that of flow channels 2 and 3. In addition, the diameter of flow channel 2 is larger than that of the other three flow channels, and the velocity of flow channel 2 is lower than that of other flow channels at the same mass flow rate. The friction pressure loss and local pressure loss are both small at low velocity. However, adopting the pressure drop between the inlet and the outlet is insufficient to evaluate the pressure loss in different structures, and thus the flow resistance coefficient is adopted in this section to reveal the detailed flow loss in the flow channels. The expression of the flow resistance coefficient ξ is as follows: where ∆p v is the pressure drop between the inlet and the outlet of each flow channel.  As shown in Figure 6, the flow resistance coefficient of flow channel 2 is the largest, followed by that of flow channels 4 and 1, and the smallest is that of flow channel 3. The higher the flow resistance, the larger the pressure loss. Based on this, the pressure loss from large to small is flow channels 2, 4, 1, and 3. This phenomenon is different from that obtained by analyzing the pressure drop. Compared with the pressure drop, the flow resistance, as the evaluation index for pressure loss, is only related to the structure, eliminating the influence of flow velocity on pressure loss.

Mass Flow Rate
The effect of different mass flow rates on the temperature difference of the coolant in each channel is shown in Figure 7a. The temperature difference between the inlet and outlet decreases with an increase in the mass flow rate, and the rate of decrease in temperature difference slows down. Thus, a higher mass flow rate leads to a smaller temperature difference between the inlet and outlet and lower heat transfer loss. With a mass flow rate of 0.1 kg/s, the maximum temperature difference and heat transfer power are 0.02 K and 9.59 W, respectively. Equation (1) reveals that the temperature difference between the inlet and outlet is a function of the mass flow rate and the logarithmic mean temperature difference, with the same geometric structure and material of the valve. Since the change in logarithmic mean temperature difference is only 0.0002 K under different working conditions, the temperature difference between the inlet and outlet is only positively correlated with . . As shown in Figure 6, the flow resistance coefficient of flow channel 2 is the largest, followed by that of flow channels 4 and 1, and the smallest is that of flow channel 3. The higher the flow resistance, the larger the pressure loss. Based on this, the pressure loss from large to small is flow channels 2, 4, 1, and 3. This phenomenon is different from that obtained by analyzing the pressure drop. Compared with the pressure drop, the flow resistance, as the evaluation index for pressure loss, is only related to the structure, eliminating the influence of flow velocity on pressure loss.

Mass Flow Rate
The effect of different mass flow rates on the temperature difference of the coolant in each channel is shown in Figure 7a. The temperature difference between the inlet and outlet decreases with an increase in the mass flow rate, and the rate of decrease in temperature difference slows down. Thus, a higher mass flow rate leads to a smaller temperature difference between the inlet and outlet and lower heat transfer loss. With a mass flow rate of 0.1 kg/s, the maximum temperature difference and heat transfer power are 0.02 K and 9.59 W, respectively. Equation (1) reveals that the temperature difference between the inlet and outlet is a function of the mass flow rate and the logarithmic mean temperature difference, with the same geometric structure and material of the valve. Since the change in logarithmic mean temperature difference is only 0.0002 K under different working conditions, the temperature difference between the inlet and outlet is only positively correlated with Energies 2023, 16, x FOR PEER REVIEW 9 of 22 As shown in Figure 6, the flow resistance coefficient of flow channel 2 is the largest, followed by that of flow channels 4 and 1, and the smallest is that of flow channel 3. The higher the flow resistance, the larger the pressure loss. Based on this, the pressure loss from large to small is flow channels 2, 4, 1, and 3. This phenomenon is different from that obtained by analyzing the pressure drop. Compared with the pressure drop, the flow resistance, as the evaluation index for pressure loss, is only related to the structure, eliminating the influence of flow velocity on pressure loss.

Mass Flow Rate
The effect of different mass flow rates on the temperature difference of the coolant in each channel is shown in Figure 7a. The temperature difference between the inlet and outlet decreases with an increase in the mass flow rate, and the rate of decrease in temperature difference slows down. Thus, a higher mass flow rate leads to a smaller temperature difference between the inlet and outlet and lower heat transfer loss. With a mass flow rate of 0.1 kg/s, the maximum temperature difference and heat transfer power are 0.02 K and 9.59 W, respectively. Equation (1) reveals that the temperature difference between the inlet and outlet is a function of the mass flow rate and the logarithmic mean temperature difference, with the same geometric structure and material of the valve. Since the change in logarithmic mean temperature difference is only 0.0002 K under different working conditions, the temperature difference between the inlet and outlet is only positively correlated with . . The variation in pressure drops with mass flow rates is demonstrated in Figure 7b. The larger the mass flow rate is, the higher the pressure drop is, and the faster the pressure drop increases. With a mass flow rate of 0.8 kg/s, the pressure drops in each flow channel reach their maximum values of 9313.16 Pa, 4599.46 Pa, 5468.78 Pa, and 10,882.36 Pa, respectively. It is evident from the Darcy-Weisbach Formula [35] and the equation for calculating local loss [36] that the pressure drop is proportional to the square of the velocity, signifying that mass flow rate has a significant impact on pressure loss. In addition, the flow channel with a pronounced pressure drop has high sensitivity to changes in mass flow rate.

Inlet Temperature
The temperature differences with the increase in the inlet temperature are shown in Figure 8a. As the inlet temperature rises, the temperature difference among different channels is insignificant, resulting in a slight change in heat transfer power. This implies that the inlet temperature has a negligible impact on heat transfer loss. Conversely, Figure 8b demonstrates the pressure drop in each flow channel with the increase in the inlet temperature. As the inlet temperature increases, the pressure drop declines continuously. The maximum pressure drops during the inlet temperature changing from 34 • C to 46 • C are 292.08 Pa, 88.14 Pa, 198.25 Pa, and 188.48 Pa, respectively, with pressure drops within this temperature range being 5.4%, 3.4%, 6.3%, and 3.0%. Specifically, the viscosity of the coolant decreases with the increase in coolant temperature. Consequently, an increase in inlet temperature leads to a decrease in pressure loss. However, the influence of inlet temperature on pressure loss is less significant compared to that of mass flow rate. The variation in pressure drops with mass flow rates is demonstrated in Figure 7b. The larger the mass flow rate is, the higher the pressure drop is, and the faster the pressure drop increases. With a mass flow rate of 0.8 kg/s, the pressure drops in each flow channel reach their maximum values of 9313.16 Pa, 4599.46 Pa, 5468.78 Pa, and 10,882.36 Pa, respectively. It is evident from the Darcy-Weisbach Formula [35] and the equation for calculating local loss [36] that the pressure drop is proportional to the square of the velocity, signifying that mass flow rate has a significant impact on pressure loss. In addition, the flow channel with a pronounced pressure drop has high sensitivity to changes in mass flow rate.

Inlet Temperature
The temperature differences with the increase in the inlet temperature are shown in Figure 8a. As the inlet temperature rises, the temperature difference among different channels is insignificant, resulting in a slight change in heat transfer power. This implies that the inlet temperature has a negligible impact on heat transfer loss. Conversely, Figure 8b demonstrates the pressure drop in each flow channel with the increase in the inlet temperature. As the inlet temperature increases, the pressure drop declines continuously. The maximum pressure drops during the inlet temperature changing from 34 °C to 46 °C are 292.08 Pa, 88.14 Pa, 198.25 Pa, and 188.48 Pa, respectively, with pressure drops within this temperature range being 5.4%, 3.4%, 6.3%, and 3.0%. Specifically, the viscosity of the coolant decreases with the increase in coolant temperature. Consequently, an increase in inlet temperature leads to a decrease in pressure loss. However, the influence of inlet temperature on pressure loss is less significant compared to that of mass flow rate.

Valve Materials
Diverse new materials, such as TC4 (a titanium alloy) and carbon fiber-reinforced polymer (CFRP), and gray cast iron, which is commonly used in valves, were utilized to explore the influence of the valve materials on valve performance. The sidewall remained smooth, and the influence of the wall's roughness on flow characteristics were ignored. The physical properties of these materials are listed in Table 3.

Valve Materials
Diverse new materials, such as TC4 (a titanium alloy) and carbon fiber-reinforced polymer (CFRP), and gray cast iron, which is commonly used in valves, were utilized to explore the influence of the valve materials on valve performance. The sidewall remained smooth, and the influence of the wall's roughness on flow characteristics were ignored. The physical properties of these materials are listed in Table 3. The temperature difference between the inlet and outlet using different valve materials is shown in Figure 9. The temperature differences are −0.005 K, −0.060 K, −0.070 K, and −0.119 K for ABS, TC4, CFRP, and gray cast iron at a mass flow rate of 0.6 kg/s, taking flow channel 3 as an example. The temperature difference increases accordingly, and this trend is also observed in other flow channels, resulting in an increase in heat transfer loss. Notably, gray cast iron has higher thermal conductivity than the other materials, leading to increased heat transfer through the valve. However, the temperature difference is not significantly different between the model with CFRP and TC4, due to the lower specific heat capacity of CFRP, despite the thermal conductivity of CFRP being 30% higher than that of TC4. Hence, materials with low thermal conductivity and high specific heat capacity should be used to minimize heat transfer loss. Furthermore, the pressure drops remain relatively constant despite changes in valve material. Valve materials have a negligible impact on pressure drop. Although the valve's material can affect heat transfer in each channel, the temperature difference and change in viscosity can be neglected. Moreover, since the roughness of the sidewall is neglected in the numerical simulation, the valve materials cannot impact the friction pressure loss of the multiway valve.
Energies 2023, 16, x FOR PEER REVIEW 11 of 22 The temperature difference between the inlet and outlet using different valve materials is shown in Figure 9. The temperature differences are −0.005 K, −0.060 K, −0.070 K, and −0.119 K for ABS, TC4, CFRP, and gray cast iron at a mass flow rate of 0.6 kg/s, taking flow channel 3 as an example. The temperature difference increases accordingly, and this trend is also observed in other flow channels, resulting in an increase in heat transfer loss. Notably, gray cast iron has higher thermal conductivity than the other materials, leading to increased heat transfer through the valve. However, the temperature difference is not significantly different between the model with CFRP and TC4, due to the lower specific heat capacity of CFRP, despite the thermal conductivity of CFRP being 30% higher than that of TC4. Hence, materials with low thermal conductivity and high specific heat capacity should be used to minimize heat transfer loss. Furthermore, the pressure drops remain relatively constant despite changes in valve material. Valve materials have a negligible impact on pressure drop. Although the valve's material can affect heat transfer in each channel, the temperature difference and change in viscosity can be neglected. Moreover, since the roughness of the sidewall is neglected in the numerical simulation, the valve materials cannot impact the friction pressure loss of the multiway valve.

Structure Optimization
Given the negligible heat transfer loss in the multiway valve, the structural optimization focuses on minimizing pressure loss. The velocity vector distribution of the coolant inside the valve is shown in Figure 10. The vortexes in specific regions, including the pipe corners, control shaft, and shell corners, are revealed. Owing to the significant change in flow direction and flow cross-sectional area in these regions, there is a large pressure.

Structure Optimization
Given the negligible heat transfer loss in the multiway valve, the structural optimization focuses on minimizing pressure loss. The velocity vector distribution of the coolant inside the valve is shown in Figure 10. The vortexes in specific regions, including the pipe corners, control shaft, and shell corners, are revealed. Owing to the significant change in flow direction and flow cross-sectional area in these regions, there is a large pressure. The temperature difference between the inlet and outlet using different valve materials is shown in Figure 9. The temperature differences are −0.005 K, −0.060 K, −0.070 K, and −0.119 K for ABS, TC4, CFRP, and gray cast iron at a mass flow rate of 0.6 kg/s, taking flow channel 3 as an example. The temperature difference increases accordingly, and this trend is also observed in other flow channels, resulting in an increase in heat transfer loss. Notably, gray cast iron has higher thermal conductivity than the other materials, leading to increased heat transfer through the valve. However, the temperature difference is not significantly different between the model with CFRP and TC4, due to the lower specific heat capacity of CFRP, despite the thermal conductivity of CFRP being 30% higher than that of TC4. Hence, materials with low thermal conductivity and high specific heat capacity should be used to minimize heat transfer loss. Furthermore, the pressure drops remain relatively constant despite changes in valve material. Valve materials have a negligible impact on pressure drop. Although the valve's material can affect heat transfer in each channel, the temperature difference and change in viscosity can be neglected. Moreover, since the roughness of the sidewall is neglected in the numerical simulation, the valve materials cannot impact the friction pressure loss of the multiway valve.

Structure Optimization
Given the negligible heat transfer loss in the multiway valve, the structural optimization focuses on minimizing pressure loss. The velocity vector distribution of the coolant inside the valve is shown in Figure 10. The vortexes in specific regions, including the pipe corners, control shaft, and shell corners, are revealed. Owing to the significant change in flow direction and flow cross-sectional area in these regions, there is a large pressure.  Since analysis on the regions generating pressure loss via the velocity field is insufficient, the entropy production analysis method was adopted in the present study to determine the specific regions of the energy loss. Entropy production is generated by irreversible processes and represents the irreversibility of the system and the resulting energy loss [37]. Moreover, it can be mathematically expressed as: The entropy production rate of the section planes is shown in Figure 11. It is evident that the entropy production rate is high at the connection between the pipe of the shell and the control shaft. Furthermore, a comparison with Figure 10 reveals that the location where the velocity vector exists is characterized by a high level of entropy production. Therefore, the following structural optimizations mainly focus on the geometric optimization of the pipe corner, control shaft, and shell corner. Shape optimization was put forward to change the inner wall curves, where the flow direction and the flow cross-sectional area change, to make the fluid field steady without changing the appearance of the multiway valve. As the radius of inner wall curve increases, changes in flow direction and flow cross-sectional area slow down, and the flow characteristics are improved. However, the valve consists of three parts, which requires limiting the potential increase in inner wall curves to ensure that the curves do not exceed the junction of different parts. Since analysis on the regions generating pressure loss via the velocity field is insufficient, the entropy production analysis method was adopted in the present study to determine the specific regions of the energy loss. Entropy production is generated by irreversible processes and represents the irreversibility of the system and the resulting energy loss [37]. Moreover, it can be mathematically expressed as: The entropy production rate of the section planes is shown in Figure 11. It is evident that the entropy production rate is high at the connection between the pipe of the shell and the control shaft. Furthermore, a comparison with Figure 10 reveals that the location where the velocity vector exists is characterized by a high level of entropy production. Therefore, the following structural optimizations mainly focus on the geometric optimization of the pipe corner, control shaft, and shell corner. Shape optimization was put forward to change the inner wall curves, where the flow direction and the flow cross-sectional area change, to make the fluid field steady without changing the appearance of the multiway valve. As the radius of inner wall curve increases, changes in flow direction and flow cross-sectional area slow down, and the flow characteristics are improved. However, the valve consists of three parts, which requires limiting the potential increase in inner wall curves to ensure that the curves do not exceed the junction of different parts.

Pipe Corners
Flow channels 1, 2, and 4 contain pipe corners within their respective shells, leading to sudden changes in flow direction and cross-sectional area. Therefore, taking the adjacent walls as tangents and specifying the radius, the inner wall curves of flow channels 1, 2, and 4 are drawn and determined. The schematic diagram is shown in Figure 12, and the specific schemes are listed in Table 4.

Pipe Corners
Flow channels 1, 2, and 4 contain pipe corners within their respective shells, leading to sudden changes in flow direction and cross-sectional area. Therefore, taking the adjacent walls as tangents and specifying the radius, the inner wall curves of flow channels 1, 2, and 4 are drawn and determined. The schematic diagram is shown in Figure 12, and the specific schemes are listed in Table 4.   Figure 13 illustrates the changes in flow cross-sectional area and pressure drop for varying curve radii. As the radii of the wall curves increase, the pressure drop initially decreases to a minimum, and then increases, while the flow cross-sectional area continues to decline. The optimal curve radii for flow channels 1, 2, and 4 are 12 mm, 60 mm, and 10 mm, respectively. The corresponding maximum pressure drop reductions achieved are 36.68 Pa, 44.83 Pa, and 5.78 Pa. This demonstrates that a large surface radius leads to a slow change in flow direction and a decrease in pressure loss. However, the continuous reduction in flow cross-sectional area with increasing surface curvature results in an increase in local pressure loss.   Figure 13 illustrates the changes in flow cross-sectional area and pressure drop for varying curve radii. As the radii of the wall curves increase, the pressure drop initially decreases to a minimum, and then increases, while the flow cross-sectional area continues to decline. The optimal curve radii for flow channels 1, 2, and 4 are 12 mm, 60 mm, and 10 mm, respectively. The corresponding maximum pressure drop reductions achieved are 36.68 Pa, 44.83 Pa, and 5.78 Pa. This demonstrates that a large surface radius leads to a slow change in flow direction and a decrease in pressure loss. However, the continuous reduction in flow cross-sectional area with increasing surface curvature results in an increase in local pressure loss. Figure 14 depicts the flow fields of both the original and optimized multiway valve models. The synergy between the wall shape and flow field resulting from structural optimization induces distinct weakened flow separation in the optimized model. Furthermore, the change in wall shape effectively stabilizes the flow field, which in turn reduces pressure loss. However, despite the improvements achieved using structural optimization, the pressure drop reduction remains relatively small. Further analysis of the velocity vector and entropy production rate distributions, as shown in Figure 11, reveals that the entropy production rate in the pipe corners is low, despite the presence of flow separation, compared with that of the regions at the control shaft. Consequently, the impact of structural optimization in these areas on overall valve performance is less significant.
decreases to a minimum, and then increases, while the flow cross-sectional area continues to decline. The optimal curve radii for flow channels 1, 2, and 4 are 12 mm, 60 mm, and 10 mm, respectively. The corresponding maximum pressure drop reductions achieved are 36.68 Pa, 44.83 Pa, and 5.78 Pa. This demonstrates that a large surface radius leads to a slow change in flow direction and a decrease in pressure loss. However, the continuous reduction in flow cross-sectional area with increasing surface curvature results in an increase in local pressure loss.  Figure 14 depicts the flow fields of both the original and optimized multiway valve models. The synergy between the wall shape and flow field resulting from structural optimization induces distinct weakened flow separation in the optimized model. Furthermore, the change in wall shape effectively stabilizes the flow field, which in turn reduces pressure loss. However, despite the improvements achieved using structural optimization, the pressure drop reduction remains relatively small. Further analysis of the velocity vector and entropy production rate distributions, as shown in Figure 11, reveals that the entropy production rate in the pipe corners is low, despite the presence of flow separation, compared with that of the regions at the control shaft. Consequently, the impact of structural optimization in these areas on overall valve performance is less significant.   Figure 14 depicts the flow fields of both the original and optimized multiway valve models. The synergy between the wall shape and flow field resulting from structural optimization induces distinct weakened flow separation in the optimized model. Furthermore, the change in wall shape effectively stabilizes the flow field, which in turn reduces pressure loss. However, despite the improvements achieved using structural optimization, the pressure drop reduction remains relatively small. Further analysis of the velocity vector and entropy production rate distributions, as shown in Figure 11, reveals that the entropy production rate in the pipe corners is low, despite the presence of flow separation, compared with that of the regions at the control shaft. Consequently, the impact of structural optimization in these areas on overall valve performance is less significant.

Control Shaft
As the coolant flows from the inlet pipe to the control shaft, it undergoes a 90-degree rotation and experiences a sudden increase in flow cross-sectional area. This abrupt change in geometry creates vortices and contributes to the high entropy production rates observed in Figures 10 and 11. Thus, structural optimization along radial and axial directions was proposed for the control shaft, as shown in Figure 15. The influence of the radius of the curve along the radial direction on pressure drop is demonstrated in Figure 16. The

Control Shaft
As the coolant flows from the inlet pipe to the control shaft, it undergoes a 90-degree rotation and experiences a sudden increase in flow cross-sectional area. This abrupt change in geometry creates vortices and contributes to the high entropy production rates observed  Figures 10 and 11. Thus, structural optimization along radial and axial directions was proposed for the control shaft, as shown in Figure 15. The influence of the radius of the curve along the radial direction on pressure drop is demonstrated in Figure 16. The pressure drops in four flow channels increase as the radius increases. The maximum pressure drops increase by 57.36 Pa, 56.88 Pa, 96.52 Pa, and 115.29 Pa, respectively. Therefore, increasing the radius of mode 1 cannot reduce pressure loss, as it leads to a smaller flow cross-sectional area and a larger pressure drop compared with the original model.  The impact of the radius of the curve along the axial direction on the pressure drop is shown in Figure 17. When the radii of curves are 19.5 mm, the pressure losses of each flow channel are minimized, with reductions in pressure drop of 496.55 Pa, 112.21 Pa, 181.40 Pa, and 946.39 Pa, resulting in an improvement in flowability of 9.13%, 4.31%, 5.59%, and 14.89%, respectively. Moreover, as the radius increases, the pressure drops of flow channels 1, 2, and 4 continue to fall, and the trends of the decreasing pressure drop slow down. However, the trend in flow channel 3 is different in that the pressure drop first declines, then rises as the radius rises from 6 mm to 8 mm, and finally declines again. Figure 17 shows the flow field of channel 3 with a radius of 0 mm, 6.0 mm, 8.0 mm, and 19.5 mm. The vortex in location 1 continues to decline as the radius decreases. Additionally, an area with low speed increases in location 2, when the radius changes from 0 mm to 8 mm. This phenomenon of flow separation intensifies when the radius changes between 6 mm and 8 mm. Although the vortexes in location 1 decrease, the pressure loss increases due to the intensified flow separation at location 2. However, if the radius continues to increase from 8.0 mm to 19.5 mm, the vortexes at location 1 and location 2 decrease, with the velocity gradient decreasing, and the flow field uniformity increases.  The impact of the radius of the curve along the axial direction on the pressure drop is shown in Figure 17. When the radii of curves are 19.5 mm, the pressure losses of each flow channel are minimized, with reductions in pressure drop of 496.55 Pa, 112.21 Pa, 181.40 Pa, and 946.39 Pa, resulting in an improvement in flowability of 9.13%, 4.31%, 5.59%, and 14.89%, respectively. Moreover, as the radius increases, the pressure drops of flow channels 1, 2, and 4 continue to fall, and the trends of the decreasing pressure drop slow down. However, the trend in flow channel 3 is different in that the pressure drop first declines, then rises as the radius rises from 6 mm to 8 mm, and finally declines again. Figure 17 shows the flow field of channel 3 with a radius of 0 mm, 6.0 mm, 8.0 mm, and 19.5 mm. The vortex in location 1 continues to decline as the radius decreases. Additionally, an area with low speed increases in location 2, when the radius changes from 0 mm to 8 mm. This phenomenon of flow separation intensifies when the radius changes between 6 mm and 8 mm. Although the vortexes in location 1 decrease, the pressure loss increases due to the intensified flow separation at location 2. However, if the radius continues to increase from 8.0 mm to 19.5 mm, the vortexes at location 1 and location 2 decrease, with the velocity gradient decreasing, and the flow field uniformity increases. The impact of the radius of the curve along the axial direction on the pressure drop is shown in Figure 17. When the radii of curves are 19.5 mm, the pressure losses of each flow channel are minimized, with reductions in pressure drop of 496.55 Pa, 112.21 Pa, 181.40 Pa, and 946.39 Pa, resulting in an improvement in flowability of 9.13%, 4.31%, 5.59%, and 14.89%, respectively. Moreover, as the radius increases, the pressure drops of flow channels 1, 2, and 4 continue to fall, and the trends of the decreasing pressure drop slow down. However, the trend in flow channel 3 is different in that the pressure drop first declines, then rises as the radius rises from 6 mm to 8 mm, and finally declines again. Figure 17 shows the flow field of channel 3 with a radius of 0 mm, 6.0 mm, 8.0 mm, and 19.5 mm. The vortex in location 1 continues to decline as the radius decreases. Additionally, an area with low speed increases in location 2, when the radius changes from 0 mm to 8 mm. This phenomenon of flow separation intensifies when the radius changes between 6 mm and 8 mm. Although the vortexes in location 1 decrease, the pressure loss increases due to the intensified flow separation at location 2. However, if the radius continues to increase from 8.0 mm to 19.5 mm, the vortexes at location 1 and location 2 decrease, with the velocity gradient decreasing, and the flow field uniformity increases.  Figure 18 shows the flow field of the original model and optimized model, taking flow channel 1 as an example. It can be observed that the flow field of the optimized model is more stable than that of the original model. The synergy between the shape of the control shaft and the flow field is improved. This approach of optimizing the control shaft's structure using mode 2 leads to a slower change in flow direction and a reduction in vortex formation, ultimately decreasing pressure loss and improving the valve's performance.

Shell Corners
These regions, known as shell corners and highlighted in Figure 19, involve a 90° change in flow direction. As the coolant flows through the shell corners, the pressures of the flow channels drop significantly. The influence of wall shape on pressure drop is shown in Figure 20. The pressure drops in the four flow channels continue to decrease as the radius of the shell corner increases, and the trend of the descent rate drops. With a  Figure 18 shows the flow field of the original model and optimized model, taking flow channel 1 as an example. It can be observed that the flow field of the optimized model is more stable than that of the original model. The synergy between the shape of the control shaft and the flow field is improved. This approach of optimizing the control shaft's structure using mode 2 leads to a slower change in flow direction and a reduction in vortex formation, ultimately decreasing pressure loss and improving the valve's performance.  Figure 18 shows the flow field of the original model and optimized model, taking flow channel 1 as an example. It can be observed that the flow field of the optimized model is more stable than that of the original model. The synergy between the shape of the control shaft and the flow field is improved. This approach of optimizing the control shaft's structure using mode 2 leads to a slower change in flow direction and a reduction in vortex formation, ultimately decreasing pressure loss and improving the valve's performance.

Shell Corners
These regions, known as shell corners and highlighted in Figure 19, involve a 90° change in flow direction. As the coolant flows through the shell corners, the pressures of the flow channels drop significantly. The influence of wall shape on pressure drop is shown in Figure 20. The pressure drops in the four flow channels continue to decrease as the radius of the shell corner increases, and the trend of the descent rate drops. With a

Shell Corners
These regions, known as shell corners and highlighted in Figure 19, involve a 90 • change in flow direction. As the coolant flows through the shell corners, the pressures of  Figure 20. The pressure drops in the four flow channels continue to decrease as the radius of the shell corner increases, and the trend of the descent rate drops. With a radius of 7.0 mm, the pressure drop differences are 987.48 Pa, 809.40 Pa, 851.38 Pa, and 997.10 Pa of four flow channels, and the flow characteristics improve by 18.16%, 31.06%, 26.23%, and 15.68%, respectively. This improvement indicates that optimizing the shell corner can effectively reduce pressure loss. The velocity fields of the original and optimized models are compared in Figure 21, taking flow channel 3 as an example. The velocity contour shows that the velocity gradient of the optimized model is smaller, resulting in a more uniform flow field with reduced high-speed zones and decreased vortex.  Figure 21, taking flow channel 3 as an example. The velocity contour shows that the velocity gradient of the optimized model is smaller, resulting in a more uniform flow field with reduced high-speed zones and decreased vortex.      Figure 21, taking flow channel 3 as an example. The velocity contour shows that the velocity gradient of the optimized model is smaller, resulting in a more uniform flow field with reduced high-speed zones and decreased vortex.      Figure 21, taking flow channel 3 as an example. The velocity contour shows that the velocity gradient of the optimized model is smaller, resulting in a more uniform flow field with reduced high-speed zones and decreased vortex.      a clear reduction. The shell corner has the most significant impact on the structural optimization's effect, followed by the control shaft and pipe corner. Moreover, the sensitivity of pressure loss reduction decreases. The improved flow channel at shell corners causes maximum percentage reduction in flow resistance coefficients of 18  As the wall shapes at the control shaft along the axial direction and shell corner have a considerable impact on pressure loss, structural optimizations at different regions were coupled to obtain the optimal valve construction. The percentage reduction in the flow resistance coefficient of the optimized models is listed in Figure 23. The maximum pressure drops of the four flow channels are 3960.31 Pa, 1748.20 Pa, 2332.78 Pa, and 4601.99 Pa, and the minimum reductions in flow resistance coefficient are 27.56%, 34.05%, 27.90%, and 26.79%, respectively, by coupling the optimization of control shaft and shell corners. Therefore, the multiway valve has lower pressure loss using coupled optimization. Figure  24 depicts the entropy production rate of the original and optimized models. The area of regions with a high entropy production rate in the optimized model declines distinctly, indicating that the coupled structural optimization works to reduce pressure loss. Consequently, the optimal model with the lowest pressure loss and the best flowability is achieved using structural optimization.  As the wall shapes at the control shaft along the axial direction and shell corner have a considerable impact on pressure loss, structural optimizations at different regions were coupled to obtain the optimal valve construction. The percentage reduction in the flow resistance coefficient of the optimized models is listed in Figure 23. The maximum pressure drops of the four flow channels are 3960.31 Pa, 1748.20 Pa, 2332.78 Pa, and 4601.99 Pa, and the minimum reductions in flow resistance coefficient are 27.56%, 34.05%, 27.90%, and 26.79%, respectively, by coupling the optimization of control shaft and shell corners. Therefore, the multiway valve has lower pressure loss using coupled optimization. Figure 24 depicts the entropy production rate of the original and optimized models. The area of regions with a high entropy production rate in the optimized model declines distinctly, indicating that the coupled structural optimization works to reduce pressure loss. Consequently, the optimal model with the lowest pressure loss and the best flowability is achieved using structural optimization.  As the wall shapes at the control shaft along the axial direction and shell corner have a considerable impact on pressure loss, structural optimizations at different regions were coupled to obtain the optimal valve construction. The percentage reduction in the flow resistance coefficient of the optimized models is listed in Figure 23. The maximum pressure drops of the four flow channels are 3960.31 Pa, 1748.20 Pa, 2332.78 Pa, and 4601.99 Pa, and the minimum reductions in flow resistance coefficient are 27.56%, 34.05%, 27.90%, and 26.79%, respectively, by coupling the optimization of control shaft and shell corners. Therefore, the multiway valve has lower pressure loss using coupled optimization. Figure  24 depicts the entropy production rate of the original and optimized models. The area of regions with a high entropy production rate in the optimized model declines distinctly, indicating that the coupled structural optimization works to reduce pressure loss. Consequently, the optimal model with the lowest pressure loss and the best flowability is achieved using structural optimization.

Conclusions
In this study, heat transfer loss and pressure loss in a multiway valve were investigated using numerical simulations. Effects of various impact factors, such as the mass flow rate of the coolant, inlet temperature, and valve materials, on the flow characteristics of the valve were revealed. Furthermore, structural optimization of the pipe corners, control shaft, and shell corners was conducted to decrease pressure loss, and the sensitivity of pressure loss to diverse structural optimization was thoroughly analyzed. The main conclusions are drawn below: 1. The heat transfer loss in the multiway valve of the integrated thermal management system in an electric vehicle is deemed negligible, with the primary cause of flow loss within the valve being attributed to pressure loss. Additionally, the pressure loss demonstrates a positive correlation with the mass flow rate of the coolant while exhibiting a negative correlation with the inlet temperature. 2. Structural optimization along the direction of change in flow direction at the pipe corners, control shaft, and shell corners can be adopted to effectively improve the multiway valve performance. However, structural optimization along the other directions at the control shaft does not reduce pressure loss. Structural optimization at shell corners causes maximum percentage reductions in flow resistance coefficient of 18.16%, 31.06%, 26.23%, and 15.68% in the four flow channels.

Conclusions
In this study, heat transfer loss and pressure loss in a multiway valve were investigated using numerical simulations. Effects of various impact factors, such as the mass flow rate of the coolant, inlet temperature, and valve materials, on the flow characteristics of the valve were revealed. Furthermore, structural optimization of the pipe corners, control shaft, and shell corners was conducted to decrease pressure loss, and the sensitivity of pressure loss to diverse structural optimization was thoroughly analyzed. The main conclusions are drawn below: 1.
The heat transfer loss in the multiway valve of the integrated thermal management system in an electric vehicle is deemed negligible, with the primary cause of flow loss within the valve being attributed to pressure loss. Additionally, the pressure loss demonstrates a positive correlation with the mass flow rate of the coolant while exhibiting a negative correlation with the inlet temperature.

2.
Structural optimization along the direction of change in flow direction at the pipe corners, control shaft, and shell corners can be adopted to effectively improve the multiway valve performance. However, structural optimization along the other directions at the control shaft does not reduce pressure loss. Structural optimization at shell corners causes maximum percentage reductions in flow resistance coefficient of 18.16%, 31.06%, 26.23%, and 15.68% in the four flow channels.

3.
Simultaneous optimization of the curvatures of the inner walls of the shell corners and control shaft yields the minimum flow resistance coefficient for multiway valves. The optimal model exhibits percentage reductions of 27.56%, 34.05%, 27.90%, and 26.79% in flow resistance coefficient for the different flow channels. Data Availability Statement: Not applicable.

Conflicts of Interest:
The authors declare no conflict of interest. The component of velocity in the y-direction, m/s. w The component of velocity in the z-direction, m/s. ∆t The logarithmic mean temperature difference, K. ∆t f Temperature difference between inlet and outlet, K. ∆p v Pressure drop between inlet and outlet, Pa. S PRO,D Entropy production rate by distinct dissipation, W/(m 3 ·K). S PRO,D Entropy production rate by turbulent dissipation, W/(m 3 ·K). S PRO Entropy production rate, W/(m 3 ·K). Greek symbols α k Generation of kinetic energy due to mean velocity gradients, kg/(m·s 2 ). α ε Generation of kinetic energy due to buoyancy, kg/(m·s 2 ).