Performance Evaluation and Optimization of Series Flow Channel Water-Cooled Plate for IGBT Modules

Abstract

The stability in the operation of insulated gate bipolar transistor (IGBT) modules plays a crucial role in wind power generation. It is essential to improve the thermal performance of the heat sink of IGBT modules in wind power converters and reduce the power consumption of liquid cooling systems, in order to optimize the heat dissipation of IGBT modules in wind power converters. In this paper, a simulation model of the liquid-cooled heat sink of the IGBT module is established and the performance of three different series flow channel structures is compared by computational fluid dynamics (CFD). Moreover, based on the orthogonal test design, the three factors (channel width, channel height, and cold plate wall thickness) affecting the performance of the water-cooled plate were ranked and optimized. The results show that the water-cooled plate with double-helical-type flow channel structure has the best comprehensive performance. In addition, for the double-helical-type structure, the optimal combination of channel structure parameters about channel width, channel height, and cold plate wall thickness is obtained. After optimization, the maximum IGBT temperature, thermal resistance, and pressure drop of the cold plate are reduced by 3.13%, 5.78%, and 18.87%, respectively, compared with the double-S structure in parameter case one. The proposed methods and results are expected to provide theoretical guidance for the thermal management of IGBT modules in wind power converters.

1. Introduction

With the increasing environmental, climate, and energy problems, countries around the world are investing more and more in new energy industries and environmental protection. Wind power generation is getting more and more attention as a clean and renewable energy source [1,2]. As the core device of wind turbine variable voltage grid-connected systems [3], the performance and reliability of the insulated gate bipolar transistor (IGBT) modules of the wind power converter are important factors affecting the power generation quality of wind power systems [4,5,6]. In recent years, with the increasing power generation of wind turbines, the switching frequency of IGBT modules has increased significantly, and their power loss and heat flow density levels have increased significantly [7]. If the heat generated by the IGBT module cannot be eliminated in time, the chip junction temperature exceeds the threshold value and overheating damage will occur [8,9], which will directly threaten the stability of wind power converter operation. Therefore, the heat dissipation problem of IGBT modules has become a key issue that needs to be urgently solved in the development of wind power converters.

Various methods have been proposed for thermal management of IGBTs, which can be broadly divided into two categories: those aimed at controlling the power loss of IGBT modules and those aimed at optimizing the cooling system of IGBT modules. The former is mainly used to regulate the switching frequency by hysteresis control to minimize the power loss and junction temperature swing of the IGBT module under various operating conditions [10,11,12]. The junction temperature of the IGBT module is also affected by external cooling conditions, and proper thermal design is necessary to maintain the performance and reliability of the IGBT over its lifetime. So far, many methods have been investigated for cooling IGBT modules, including air cooling, direct liquid cooling, indirect liquid cooling, jet impingement cooling, thermoelectric cooling, and heat pipe cooling [13,14,15,16]. Air cooling is the most reliable, simple, and cost-effective method. However, as a high heat flow density electronic device, the conventional air natural convection and forced convection can no longer meet the requirements of its thermal design [17,18], especially when the power consumption exceeds 1500 W [19]. Among these technologies, indirect liquid cooling has been considered as an effective method to deal with heat dissipation in high-power electronics [20]. It has the advantages of high heat exchange efficiency and compact structure [21]. Therefore, it is well suited for the thermal design of IGBT modules in wind power converters.

For indirect cooling, the coolant usually flows in the channels of the water-cooled plate and does not come into contact with the cooling object. The cold plate can be classified into two main types according to the flow channel form: the parallel-type flow channel and the series-type flow channel. Some studies have been conducted to explore the performance of these two types of cold plates. Chen et al. [22] designed a water-cooled plate with parallel U-type flow channels and investigated the effect of flow rate scheduling of the parallel channels on the performance of the cold plate. The experimental results showed that the thermal objectives could be achieved and energy consumption reduced by scheduling the coolant flow rate during the cooling process. Lu and Wang [23,24] investigated the effect of five inlet and outlet arrangements on the performance of parallel flow channel pattern cold plates, including Z-type, L-type, I-type, ]-type, and Γ-type arrangements. For the same inlet velocity, the inlet and outlet arrangements of I-type and Γ-type provide the best heat transfer performance. This study confirms the uneven fluid velocity distribution and inhomogeneity of the temperature field in parallel-type flow channels. To improve the heat transfer performance and uneven flow distribution of parallel-type flow channel cold plates, Liu and Yu [25] numerically analyzed the heat transfer and flow performance of four parallel channel cold plates using baffles. The simulation results show that the uneven flow distribution of the heat sink can be improved by uneven baffles, thus improving the uniformity of the cold plate temperature distribution.

The series flow channel can destroy the fully developed boundary layer through the corners of the flow channels and the secondary flow structure (Dean vortex), thus improving fluid mixing and heat transfer [26]. Therefore, a lot of research has been conducted on the series flow channel cold plates to improve the comprehensive performance of the series flow channel cold plates. For example, Jarrett and Kim [27] used a sequential quadratic programming (SQP) algorithm to design the width and position of the series channel in the cold plate. The optimization achieved an average temperature reduction of 14% and a pressure drop and temperature difference reduction of more than 50%. Chen et al. [28] proposed a multi-objective optimization method for the series flow channel heat sink to reduce the thermal resistance and pressure drop of the heat sink by optimizing four design variables: the number of channels, channel width, channel height, and inlet velocity. Zheng et al. [29,30,31] enhanced the turbulence intensity of the fluid and thus the heat transfer performance of the heat sink by designing a spoiler column structure in each of the series channels of the water-cooled plate. Some researchers used energy and exergy analysis methods to explore the performance of parallel and series flow channel pattern cold plates [32,33,34]. It was found that the series flow channel cold plate has better heat transfer performance and temperature uniformity, and the parallel flow channel cold plate has better flow properties.

According to the above research results, the series flow channel cold plates have the advantages of good heat dissipation, uniform flow distribution, and water savings. However, there is a large pressure loss since there is only one water path in the series flow channel, which leads to a significant increase in pumping power. The existing studies mainly focus on the optimization of the conventional S-type flow channel structure. There are fewer studies related to the performance comparison of different series channel structures and the influence of multiple interaction parameters on the performance of cold plates. Therefore, in this study, the IGBT modules were cooled by the series-type channel cold plate. Numerical methods are used to investigate the performance of cold plates with S-type, double-helical-type, and double-S-type flow channel structures. The maximum static temperature of the IGBT, and the inlet and outlet pressure drop of the cold plate are used as indexes to study the channel structure that takes into account the heat dissipation performance and pressure drop. In addition, the interaction among the channel width, channel height, and wall thickness of the cold plate, and their effects on the performance of the cold plate are analyzed. The results of this study will provide key insights into water-cooled plates applied to the thermal management of wind power converter IGBT modules.

2. Methodology

2.1. Physical Model

In this study, three IGBT modules are arranged on the water-cooled plate, as shown in Figure 1e. Among them, the power loss of each IGBT module is 1451 W. Figure 1a,b, and c show the schematic diagrams of the conventional S-type flow channel, the double-helical-type flow channel, and the double-S-type flow channel, respectively. The cross-sectional dimensions of the channels are shown in Figure 1d. The same dimensional parameters in the three models are shown in

Table 1. Model parameters.

Parameters	L	L1	W	W1	W2	d
Dimension (mm)	335	295	330	30	10	10

.

2.2. Mathematical Model

2.2.1. Model Assumptions

To analyze the heat transfer and flow characteristics of the water-cooled model, the following assumptions were made:

• The fluid in the cold plate is a Newtonian fluid with no internal heat source and is incompressible;
• The effects of volume forces and thermal radiation are neglected;
• The various physical parameters of the cold plate material and fluid are invariant with the temperature change.

2.2.2. Equations

The governing equations based on the above assumptions are as follows.

Mass conservation equation:

$$\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z}=0$$

(1)

where u, v, and w are the velocity components of the fluid velocity in the x, y, and z directions.

Momentum conservation equation:

$$\left\{\begin{array}{c}{\rho }_f\left(\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}+w\frac{\partial u}{\partial z}\right)=-\frac{\partial P}{\partial x}+\mu \left(\frac{{\partial }^{2}u}{\partial x^2}+\frac{{\partial }^{2}u}{\partial y^2}+\frac{{\partial }^{2}u}{\partial z^2}\right)\\ {\rho }_f\left(\frac{\partial v}{\partial t}+u\frac{\partial v}{\partial x}+v\frac{\partial v}{\partial y}+w\frac{\partial v}{\partial z}\right)=-\frac{\partial P}{\partial y}+\mu \left(\frac{{\partial }^{2}v}{\partial x^2}+\frac{{\partial }^{2}v}{\partial y^2}+\frac{{\partial }^{2}v}{\partial z^2}\right)\\ {\rho }_f\left(\frac{\partial w}{\partial t}+u\frac{\partial w}{\partial x}+v\frac{\partial w}{\partial y}+w\frac{\partial w}{\partial z}\right)=-\frac{\partial P}{\partial z}+\mu \left(\frac{{\partial }^{2}w}{\partial x^2}+\frac{{\partial }^{2}w}{\partial y^2}+\frac{{\partial }^{2}w}{\partial z^2}\right)\end{array}\right.$$

(2)

where ${\rho }_f$ is the fluid density, P is the pressure, and $\mu$ is the dynamic viscosity of the fluid.

Energy conservation equation:

$${\rho }_f{C}_p\left(\frac{\partial T}{\partial t}+u\frac{\partial T}{\partial x}+v\frac{\partial T}{\partial y}+w\frac{\partial T}{\partial z}\right)=\lambda \left(\frac{{\partial }^{2}T}{\partial x^2}+\frac{{\partial }^{2}T}{\partial y^2}+\frac{{\partial }^{2}T}{\partial z^2}\right)$$

(3)

where $C_p$ is the specific heat capacity, T is the temperature, and $\lambda$ is the thermal conductivity of the fluid.

2.2.3. Cold Plate Heat Transfer Model

The heat transfer between IGBT modules and the cold plate belongs to heat conduction, so it can be simplified as a heat conduction model and its heat flow equation is as follows:

$${\varnothing }_1=\lambda A_1\frac{t_{w1}-t_{w2}}{\delta }$$

(4)

where ${\varnothing }_1$ is transferred heat in the heat conduction process, $t_{w1}$ is the temperature of the IGBT module surface, $t_{w2}$ is the temperature of the cold plate surface, $\delta$ is the thermal conductivity thickness, $\lambda$ is thermal conductivity coefficient, and A₁ is the thermal conductivity area.

The heat transfer between the cold plate and the coolant belongs to convective heat transfer, so it can be simplified as a thermal convection model and its heat flow equation is as follows:

$${\varnothing }_2=h{A}_2\left(t_{w2}-t_f\right)$$

(5)

where ${\varnothing }_2$ is transferred heat in the convective heat transfer process, $t_f$ is the coolant temperature, h is the convective heat transfer coefficient, and A₂ is the heat transfer area.

2.3. Numerical Simulation

2.3.1. Boundary Condition Setting

The material of the cold plate is 6063 aluminum alloy and the cooling medium is water. The physical parameters of the material in this numerical simulation are shown in

Table 2. The physical parameters of the material.

Material	Density (kg/m3)	Specific Heat (J/(kg.k))	Thermal Conductivity (w/m.k)	Dynamic Viscosity (Ps.s)
6063 Al	2710	902	218	-
Coolant	997.0	4200	0.609	9.028 × 10−4

. The boundary conditions of inlet and outlet are set as velocity inlet and pressure outlet respectively. Inlet flow velocity is set to 2 m/s, while inlet water temperature is set to 25 °C at all time. The upper surface of the cold plate is in contact with the IGBT simulated heat source, and the three IGBT simulated heat sources are set to heat the surface with constant heat flow, all with 1451 W power.

ANSYS-Icepak (version 16.0) software is utilized to obtain the iterative solution for the algebraic equations. A zero-equation turbulence model is constructed to calculate the flow domain. The SIMPLE algorithm is used in coupling velocity and pressure. The residual criterion for the flow is set to 10⁻³ and that for the energy is set to 10⁻⁷.

2.3.2. Grid Independence Test

In order to balance the simulation accuracy and computational efficiency, an S-type flow channel with structural parameters Hc = 12, Wc = 30, Hb = 4 is used as an example to check the mesh independence. As shown in

Table 3. Grid independence validation.

Mesh	Elements (Million)	T (°C)	Difference (%)	ΔP (Pa)	Difference (%)
Mesh1	0.60	54.41	−2.5581	4876	4.5903
Mesh2	1.28	55.84	0.5868	4662	1.4360
Mesh3	1.67	55.52	0.1879	4596	0.1962
Mesh4	2.08	55.41	-	4587	-

, the maximum temperature is 55.52 °C and the pressure difference is 4596 Pa for a grid number of 1.67 million. When the grid is refined to 2.08 million, the rates of change of temperature and pressure are 0.1879% and 0.1962%, respectively. Therefore, the recommended grid scheme is Mesh 3. Moreover, this grid parameter setting is also applicable to other models.

2.3.3. Model Validation

Taking the S-type flow channel with structural parameters Hc = 12, Wc = 30, Hb = 4 as an example, the accuracy of the simulation is verified by comparing the numerical simulation and experimental test results of the model. As shown in Figure 2, the overall trend of the simulated data and the experimental data are consistent. Moreover, from the data of the maximum temperature of IGBT and pressure drop, the relative errors of simulation and experiment are both controlled at about 10%, which is within the error tolerance. This confirms the reliability of the computational model and meets the computational requirements for engineering applications.

3. Results and Discussion

3.1. Simulation Analysis

The channel width Wc, channel height Hc, and cold plate wall thickness Hb are important structural parameters in the design of water-cooled plate channels. In order to compare the heat transfer and flow properties of the three flow channel structures and to ensure the reliability of the results, three different sets of structural parameters were designed in this section, as shown in

Table 4. Geometrical parameters of Case1–3.

	Case 1	Case 2	Case 3
Wc (mm)	24	30	21
Hc (mm)	12	12	16
Hb (mm)	3	4	2

.

3.1.1. Analysis of Channel Performance under Different Parameter Combinations

Figure 3 shows the performance of heat transfer and flow under the three sets of structural parameters for the different flow channel designs.

As shown in Figure 3, the maximum IGBT temperatures obtained for the double-helical structure are all lower than that of the S-type structure for different combinations of parameters. However, there is a large fluctuation in the maximum IGBT temperature obtained with different combinations of channel parameters for the double-S structure. In the first group of parameters, the double-S-type flow channel has the worst heat transfer performance; in the second group of parameters, the double-S-type flow channel shows the best heat transfer performance; in the third group of parameters, the heat transfer performance of the double-S-type structure is between the double-helical structure and the S structure.

The pressure drops for different structures are shown in Figure 3. Under different combinations of parameters, the double-helical-type structure has the smallest flow resistance, followed by the S-type structure, and the double-S-type structure has the largest inlet and outlet pressure drop. Moreover, at the three sets of parameters, the pressure drop obtained for the double-S structure increased by an average of 731 Pa compared to the double-helical structure and by an average of 631 Pa compared to the S structure.

3.1.2. Analysis of Channel Performance at the Same Flow Velocities

Figure 4 presents the distribution cloud plot of surface temperature of the cold plate with different flow channel designs at an inlet flow velocity of 2 m/s for the first set of parameter combinations. For all the channel structures, the highest temperatures of the water-cooled plates are distributed downstream of the coolant flow direction. This is mainly because, along the direction of coolant flow, the temperature of the liquid is getting higher and the temperature difference between the liquid and the channel wall is getting smaller. Therefore, the heat carried by the coolant gradually decreases and the temperature of the cold plate rises. As shown in Figure 4, the double-helical-type structure has a lower maximum temperature on the surface of the cold plate compared to the other two structures. Therefore, its heat transfer performance is better.

Figure 5 presents the pressure drop distributions for different flow channel designs at an inlet flow velocity of 2 m/s for the first set of parameter combinations. For all the channel structures, the pressure drop is greatest near the inlet of the coolant, while a minimum pressure drop exists near the outlet of the coolant. At the same time, the pressure drop in the flow channel is stepped, and the pressure drop is more uniform in the straight part of the flow channel and increases significantly at the corners. This is because of the local pressure loss at the corners. At the same flow rate, the channel design effectively affects the pressure drop of the cold plate. As shown in Figure 5, the double-helical-type structure has a lower pressure drop. Among them, the pressure drop is reduced by 200.58 Pa compared to the conventional S-type structure and by 1278.54 Pa compared to the double-S-type structure. Therefore, it has better flow properties.

Table 5. The combined average length of the horizontal and vertical flow channels.

Models	S-Type	D-H-Type	D-S-Type
Channel length (mm)	1900	1980	1980
Horizontal length (mm)	240	640	640
Horizontal average length (mm)	48	128	106.67
Vertical length (mm)	1660	1340	1340
Vertical average length (mm)	276.67	223.33	191.43
Combined average length (mm)	162.34	175.67	149.05

shows the total length of the channels and the combined average length of the horizontal and vertical flow channels. As shown in Figure 5, the number of corners is 10 for both the double-helical and S-type structures. However, the double-helical structure achieves better flow properties when the total length of the flow channel is larger than that of the S-type structure. By analyzing the data in Table 5, it is clear that this is because the combined average length of the horizontal and vertical flow channels of the double-helical structure is greater than that of the S-type structure, i.e., the average spacing between the corners of the double-helical structure is larger. Therefore, the double-helical structure can still obtain better flow properties even if the total length of the flow channel is larger than that of the S-type structure. The double-S-type flow channel has the worst flow properties due to the long flow channels, many corners and the shortest combined average length of the horizontal and vertical flow channels.

The combined average length of the horizontal and vertical flow channels is positively correlated with the corner spacing of the channels. Based on the above analysis, the corner spacing of the channels is also an important factor affecting the flow properties of the cold plate. Under the same conditions, the larger the average corner spacing, the better the flow properties of the cold plate.

3.1.3. Analysis of Channel Performance at Different Flow Velocities

Figure 6 illustrates the distribution of the maximum temperature of the IGBT module caused by the variation of the flow velocity for different structural designs under the first set of parameter combinations.

For the range of flow velocity under study, the maximum IGBT temperature decreases as the flow velocity increase for all channel structures. This trend is evident at low flow velocity and slows down as the flow velocity increases. This is because the effect of increasing coolant flow velocity on the heat transfer coefficient gradually decreases, so the heat dissipation increment of the IGBT module also gradually decreases. As shown in Figure 6, the basic ordering of the maximum IGBT temperature at different inlet flow velocities is: double-helical-type < S-type < double-S-type. Among them, the maximum IGBT temperature of S-type structure is the lowest when the inlet flow velocity is 3 and 4 m/s. However, the difference in temperature between the double-helical-type structure and it is very small, only 0.04 °C and 0.11 °C, respectively.

Figure 7 illustrates the distribution of the pressure drop caused by the variation in the flow velocity for different structural designs under the first set of parameter combinations.

For the range of flow velocity under study, the pressure drop increases as the flow velocity increases for all channel structures. At low flow velocities, the difference in pressure drop between the different flow channel structures is small. As the flow velocity increases, the pressure drop difference between different structures increases sharply. This is because the head loss along the coolant is proportional to the quadratic of the flow velocity, so the pressure drop of the liquid cooling plate increases faster. As shown in Figure 7, the basic ordering of the pressure drop at different inlet flow velocities is: double-helical-type < S-type < double-S-type. Among them, the pressure drop of the double-S structure tends to increase a bit faster, which makes the pressure drop difference between it and the other two structures increasing.

The analysis of the numerical simulation results shows that the double-helical-type structure has the best comprehensive performance among the three flow channel structures. Therefore, this flow channel structure will be used as a model for the subsequent search for the optimal configuration of the flow channel structure parameters.

3.2. Multivariate Analysis

3.2.1. Orthogonal Experimental Design

The above analysis shows that the double-helical-type channel has relatively better comprehensive performance. In order to obtain better heat transfer performance and flow properties, the water-cooled plate must be optimized by adjusting its channel structural parameters to control its maximum temperature and pressure drop in an optimal range.

To ensure that the results have a certain degree of accuracy and control the number of experiments, an orthogonal test table with three factors and four levers (L16(4⁵)) is used to study the effect of multiple factors on the comprehensive performance of the water-cooled plate in

Table 6. Factors and levels of flow channel structure parameter.

Levers	Factors
	A (mm)	B (mm)	C (mm)
1	10	21	2
2	12	24	3
3	16	27	4
4	20	30	5

, in which A, B, and C are the three factors (A is the channel height, B is the channel width, and C is the wall thickness of the cold plate). The evaluation indexes are maximum temperature, and inlet and outlet pressure drop, and the results are shown in

Table 7. L₁₆(4⁵) orthogonal array and results.

Test Number	Test Factors			Test Results
	A (mm)	B (mm)	C (mm)	Tmax (°C)	△P (Pa)
1	10	21	2	51.7422	6175
2	10	24	3	51.8447	5543
3	10	27	4	52.2739	5326
4	10	30	5	52.6885	5042
5	12	21	3	52.5431	5384
6	12	24	2	55.6067	4913
7	12	27	5	53.9930	4742
8	12	30	4	55.4061	4601
9	16	21	4	55.5149	4949
10	16	24	5	57.1487	4735
11	16	27	2	61.6008	4595
12	16	30	3	61.1789	4584
13	20	21	5	58.7400	4513
14	20	24	4	61.4269	4645
15	20	27	3	64.1011	4659
16	20	30	2	67.8940	4645

.

In order to investigate the effect of factors and levels on the results and the importance of each factor, the results of the experiment are analyzed by range analysis (RA) and analysis of variance (ANOVA).

3.2.2. Analysis Results of Maximum Temperature and Pressure Drop

The maximum temperature and pressure drop are the most important evaluation parameters for the water-cooled plate performance.

Table 8. Range analysis results of the maximum static temperature.

Levers	Factors
	A (mm)	B (mm)	C (mm)
$\overline{K_{j1}}$	52.1373	54.6351	59.2109
$\overline{K_{j2}}$	54.3872	56.5068	57.4170
$\overline{K_{j3}}$	58.8608	57.9922	56.1555
$\overline{K_{j4}}$	63.0405	59.2919	55.6426
$R_J$	10.9032	4.6568	3.5684
Importance of factors	1	2	3
Best solution	A1 B1 C4

and

Table 9. Range analysis results of the pressure drop.

Levers	Factors
	A (mm)	B (mm)	C (mm)
$\overline{K_{j1}}$	5522	5255	5082
$\overline{K_{j2}}$	4910	4959	5043
$\overline{K_{j3}}$	4716	4831	4880
$\overline{K_{j4}}$	4616	4718	4758
$R_J$	906	537	324
Importance of factors	1	2	3
Best solution	A4 B4 C4

show results of the range based on the following expressions.

$$R_J=\max \left(\overline{K_{j1}},\overline{K_{j2}},\dots ,\overline{K_{jm}}\right)-\min (\overline{K_{j1}},\overline{K_{j2}},\dots ,\overline{K_{jm}})$$

(6)

where $K_{jm}$ is the sum of the test indexes corresponding to the jth factor m level and $\overline{K_{jm}}$ is the average value of $K_{jm}$. The magnitude of $\overline{K_{jm}}$ can determine the optimal level of j factors and the combination of levels of each factor, i.e., the optimal combination.

$R_J$ is the range of the jth factor, which reflects the magnitude of the change in the test index when the level of the jth factor changes. The larger the $R_J$, the greater the influence of the factor on the test index, and therefore the more important. Thus, based on the magnitude of $R_J$, the priority of the factor can be judged.

As shown in Table 8 and Table 9, the factors affecting the highest static temperature of IGBT and pressure drop have the same order of importance, which is A > B > C. The scheme of the best heat transfer performance of the cold plate is A1B1C4. The scheme of the best flow performance of the cold plate is A4B4C4. Because heat transfer characteristics are the main indicator of cold plate performance and factor A has the greatest effect on the maximum static temperature of the IGBT, for both indicators, the channel height is best at the A1. At the same time, in order to make the cold plate obtain better heat transfer characteristics and take into account its flow performance, for the two indicators, the flow channel width is the best to take the B4. Because the best solution of cold plate wall thickness for both indicators is C4, for the two indicators, the cold plate wall thickness is the best to take the C4. Therefore, in order to obtain a better comprehensive performance of the water-cooled plate, the optimized design of the channel structure is channel height A = 10 mm, channel width B = 30 mm, and cold plate wall thickness C = 5 mm.

The range analysis only reflects the importance of the factors and does not provide an accurate quantitative estimate of the importance of the factors. To compensate for the lack of range analysis, analysis of variance is used and the results of variance analysis are shown in

Table 10. Variance analysis results of the maximum static temperature.

Factors	f	SS	MS	F
A	3	281.509	93.8362	546.83
B	3	48.112	16.0375	93.46
C	3	30.291	10.0968	58.84
E	6	1.030	0.1716
T	15	360.941
Fα	F0.05(3,6) = 4.757		F0.01(3,6) = 9.780

and

Table 11. Variance analysis results of the pressure drop.

Factors	f	SS	MS	F
A	3	1,978,515	659,505	17.10
B	3	644,064	214,688	5.57
C	3	269,450	89,817	2.33
E	6	231,395	38,566
T	15	3,123,423
Fα	F0.05(3,6) = 4.757		F0.01(3,6) = 9.780

.

$$\overline{x}=\frac{1}{n}\sum _{i=1}^m\sum _{j=1}^r{x}_{ij}$$

(7)

$$S{S}_T=\sum _{i=1}^m\sum _{j=1}^r{(x_{ij}-\overline{x})}^2$$

(8)

$$S{S}_A=\sum _{i=1}^m\sum _{j=1}^r{({\overline{x}}_i-\overline{x})}^2=r\sum _{i=1}^m{({\overline{x}}_i-\overline{x})}^2$$

(9)

$$S{S}_E=S{S}_T-\left(S{S}_A+S{S}_B+S{S}_C\right)$$

(10)

$$F_A=\frac{S{S}_A/f_A}{S{S}_E/f_E}$$

(11)

where, $\overline{x}$ indicates the total mean of the sample data, n is the number of orthogonal trials (n = 16), m indicates the number of levels of the factor (m = 4), and r indicates the number of independent trials conducted at each level (r = 4). SS_T denotes the sum of squared total deviations; SS_A denotes the sum of squared deviations of factor A (the expressions for factors B and C are the same); SS_E denotes the sum of squared error deviations; f_A is the degrees of freedom of SS_A; f_E is the degrees of freedom of SS_E; and F_A is the variance ratio of factor A, which is used to assess whether the effect of the examined factors on the index is significant.

Table 10 shows the ANOVAs for the maximum IGBT temperatures, where F_A, F_B, and F_C are greater than F_0.01(3,6). It can be seen that the level of variation of the three factors has a significant effect on the maximum IGBT temperature at a significance level of 0.01. According to the F value, the degree of influence of three factors on the maximum temperature of IGBT can be ranked from largest to smallest: channel height > channel width > cold plate wall thickness.

Table 11 shows the ANOVAs for pressure drop, where F_A and F_B are greater than F_0.05(3,6) and F_C is less than F_0.05(3,6). It can be seen that the level changes of factor A and factor B have a significant effect on the inlet and outlet pressure drop at the significance level of 0.05; the significance of factor C is negligible, which is obvious because the thickness of the cold plate does not affect the flow state of the coolant. According to the F value, the three factors can be arranged in descending order of influence on the pressure drop: channel height > channel width > cold plate wall thickness.

In summary, the ANOVA results of the two evaluation indicators were consistent with the RA results, i.e., the primary and secondary order of the factors was the order of significance. The optimal structural parameter combination scheme is A1B4C4.

3.2.3. Optimization Effect Analysis

At an inlet flow velocity of 2 m/s, the results of the comprehensive performance comparison between the optimized cold plate and the three flow channel structures under the first set of structural parameters are shown in

Table 12. Optimization effect analysis.

Models	S-Type	D-H-Type	D-S-Type	Optimal
Tmax (°C)	54.32	53.94	54.38	52.68
θ (°C/KW)	6.74	6.65	6.75	6.36
ΔP (Pa)	5511	5313	6216	5043

. As can be seen from Table 12, the comprehensive performance of the optimized cold plate is significantly improved. Among them, the maximum temperature, overall thermal resistance, and pressure drop of the optimized cold plate decreased by 3.13%, 5.78%, and 18.87%, respectively, compared with the double-S-type structure, which is under the first set of structural parameters.

4. Conclusions

In this study, the effects of three different series-type flow channel structures on the performance of water-cooled plate were studied. Furthermore, the structural parameters of channels were optimized by an orthogonal test with two test indexes. The main conclusions are as follows:

(1)

The analysis of the numerical simulation results shows that the double-helical-type channel has the best comprehensive performance among the three series-type flow channel structures.

(2)

The corner spacing of the flow channel is also an important factor affecting the flow characteristics of the cold plate. Under the same conditions, the larger the corner spacing, the better the flow characteristics of the cold plate.

(3)

The importance of the influencing factors (channel width, channel height, and cold plate wall thickness) on the maximum IGBT temperature is ranked as follows: channel height > channel width > cold plate wall thickness. Among them, the level variation of the three factors has a significant effect on the maximum IGBT temperature.

(4)

The importance of the influencing factors (channel width, channel height, and cold plate wall thickness) on the pressure drop is ranked as follows: channel height > channel width > cold plate wall thickness. Among them, the level variation of channel height and channel width has a significant effect on the pressure drop at the inlet and outlet, and the effect of the wall thickness of the cold plate is negligible.

(5)

Through orthogonal test analysis, the comprehensive performance of the double-helical-type cold plate is the best when the channel width is 30 mm, the channel height is 10 mm, and the wall thickness of the cold plate is 5 mm. The maximum IGBT temperature, overall thermal resistance, and pressure drop of this cold plate decreased by 3.13%, 5.78%, and 18.87%, respectively, compared with the double-S-type structure in parameter case one. This combination was verified to be the optimal channel structure parameter configuration in the parameter study range. This paper has certain guiding significance for the cold plate design of series flow channel structures.