Numerical Simulation and Field Synergy Analysis of IGBT Air-Cooled Heat Exchanger for EMUs

2.1 Physical model

The IGBT air-cooled heat exchanger consists of a baseplate and fins (Figure 1). For the baseplate, several IGBT modules are installed on one side, while fins with a height of 116 mm are on the other side. At present, the flat fin is generally used in the IGBT air-cooled heat exchanger of the EMUs. To realize heat transfer, the IGBT heat source first transfers heat to the baseplate through thermal conduction, and then the fins for secondary heat dissipation are used to transfer heat by convection heat transfer to the cooling air. The flow channel formed between the fins is an important space for heat exchange. Traditionally, a straight fin structure has been designed to reduce air flow resistance. However, as higher requirements have been proposed for heat exchange by the electrical components of the EMU, the ACHE structure should be more compact, and have higher flow resistance. In order to enhance the turbulence and heat transfer performance, the traditional straight fin should be changed to a corrugated structure.

Figure 2 shows a schematic plan of the cooling air flowing in the flow channel of the ACHE with improved fin, in which①-④ indicate the positions of the 4 monitoring points in the flow channel; the air in the flow channel continuously changes the direction of movement, increasing the flow (heat transfer) distance and enhancing the turbulent performance of fluid flow. Figure 3 is a three-dimensional view of the ACHE with the improved aluminum-made fin, the copper-made heat-conducting baseplate, and heat-insulating baffle plate. Using the tools such as stretching and array in Creo, a three-dimensional model was generated, as shown in Figure 3. Then, it’s imported into Gambit software for grid processing, and finally analyzed and calculated in Fluent software.

From Figure 3, the overall structure size of the ACHE fin model: 690mm×400mm×116mm. The geometric parameters of the simplified calculation area of the ACHE are shown in Table 1, where, λ is corrugation Height, β is the corrugation width, θ is the corrugation angle, x is the fin spacing, and L is the fin length. Figure 2 shows the mathematical relationship between λ, β, and θ, namely,

$\tan \frac{\theta }{2}=\frac{\beta }{2\lambda }$      (1)

From Eq. (1), λ, β, and θ are correlated, and the change of the corrugation angle will also lead to changes in corrugation height and width. To explore the influence of corrugated fins on the ACHE, the corrugation height was determined first, and the corresponding corrugation width was calculated at different corrugation angles in the three-dimensional modeling of fins.

According to the overall size of the ACHE and the requirements for heat exchange amount, comprehensive consideration was taken to determine the corrugation height for 14mm, under the condition that the total number of fins is determined.

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Figure 1. Structure diagram of traditional IGBT air-cooled heat exchanger

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Figure 2. Plan view of improved fins

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Figure 3. Three-dimensional view of improved fin

Table 1. Geometric structure parameters of IGBT air-cooled heat exchanger fins

2.2 ACHE calculation equations

The convection heat exchange was conducted between the fluid working medium air and the fins, involving the flow problem. The system satisfied the law of conservation of mass and momentum. There were additional equations for turbulent motion.

The mathematical model was based on the following assumptions:

(1) The Newtonian fluid is used as working medium;

(2) The fluid is in a stable flow state;

(3) The buoyancy caused by the density difference is ignored;

(4) The effect of viscous dissipation is ignored.

For single-phase incompressible fluids, the governing equations in the three-dimensional rectangular coordinate system are as follows:

1. Mass conservation equation:

$\frac{\partial \left( \rho u \right)}{\partial x}+\frac{\partial \left( \rho v \right)}{\partial y}+\frac{\partial \left( \rho w \right)}{\partial z}=0$   (2）

where, ρ is the density; u, v, and w are the components of the velocity vector in the x, y, and z directions, respectively.

2. Momentum conservation equation:

$\frac{\partial uu}{\partial x}+\frac{\partial uv}{\partial y}+\frac{\partial uw}{\partial z}=\nu \left( \frac{{{\partial }^{2}}u}{\partial {{x}^{2}}}+\frac{{{\partial }^{2}}u}{\partial {{y}^{2}}}+\frac{{{\partial }^{2}}u}{\partial {{z}^{2}}} \right)-\frac{\partial p}{\partial x}$     （3）

$\frac{\partial vu}{\partial x}+\frac{\partial vv}{\partial y}+\frac{\partial vw}{\partial z}=\nu \left( \frac{{{\partial }^{2}}v}{\partial {{x}^{2}}}+\frac{{{\partial }^{2}}v}{\partial {{y}^{2}}}+\frac{{{\partial }^{2}}v}{\partial {{z}^{2}}} \right)-\frac{\partial p}{\partial y}$    （4）

$\frac{\partial wu}{\partial x}+\frac{\partial wv}{\partial y}+\frac{\partial ww}{\partial z}=\nu \left( \frac{{{\partial }^{2}}w}{\partial {{x}^{2}}}+\frac{{{\partial }^{2}}w}{\partial {{y}^{2}}}+\frac{{{\partial }^{2}}w}{\partial {{z}^{2}}} \right)-\frac{\partial p}{\partial z}$      （5）

where, ν is the kinematic viscosity; p is the pressure on the fluid element.

3. Energy conservation equation:

$\frac{\partial uT}{\partial x}+\frac{\partial vT}{\partial y}+\frac{\partial wT}{\partial z}=a\left( \frac{{{\partial }^{2}}T}{\partial {{x}^{2}}}+\frac{{{\partial }^{2}}T}{\partial {{y}^{2}}}+\frac{{{\partial }^{2}}T}{\partial {{z}^{2}}} \right)$     （6）

where, T is the temperature; a is the thermal diffusivity of the fluid.

4. Turbulence equation:

When the fluid flows in the flow channel of the new fin structure, the turbulence and turbulence dissipation rate of the fluid increased due to the change of the flow channel structure. The turbulent kinetic energy of fluid [21] is calculated in Eq. (7):

$\begin{align} & \frac{\partial \left( \rho \kappa  \right)}{\partial t}+\frac{\partial \left( \rho {{u}_{j}}\kappa  \right)}{\partial {{x}_{j}}}= \\ & {{C}_{\kappa }}-\rho \varepsilon +{{S}_{\kappa }}+\frac{\partial }{\partial {{x}_{j}}}\left[ {{\alpha }_{\kappa }}\left( \mu +{{\mu }_{t}} \right)\frac{\partial \kappa }{\partial {{x}_{j}}} \right] \\\end{align}$      （7）

where, u_j is the velocity component in the j direction; κ is turbulent kinetic energy; ε is the turbulent dissipation rate; α_κ is fluid Prandtl number corresponding to turbulent kinetic energy; C_κ is turbulent kinetic energy term caused by velocity gradient; S_κ is the turbulent kinetic energy term of the fluid.

The turbulent dissipation rate of the fluid [22] is calculated as:

$\begin{align} & \frac{\partial \left( \rho \varepsilon  \right)}{\partial t}+\frac{\partial \left( \rho {{u}_{j}}\varepsilon  \right)}{\partial {{x}_{j}}}={{C}_{\xi 1}}\frac{\varepsilon }{\kappa }{{C}_{\kappa }}- \\ & {{C}_{\xi 2}}\rho \frac{{{\varepsilon }^{2}}}{\kappa }+{{S}_{\varepsilon }}+\frac{\partial }{\partial {{x}_{j}}}\left[ {{\alpha }_{\varepsilon }}\left( \mu +{{\mu }_{t}} \right)\frac{\partial \varepsilon }{\partial {{x}_{j}}} \right] \\\end{align}$    （8）

where, μ_t is turbulence viscosity, $\mu_{t}=\frac{\rho C \kappa^{2}}{\varepsilon}$ ; μ is fluid viscosity; α_ε is fluid Prandtl number of turbulent dissipation rate; C_ξ1, C_ξ2, C are empirical constants; S_ε is the source term of fluid turbulence dissipation rate.

2.3 Grid independence verification

Grid is a geometric expression form of CFD model and an important carrier for simulation analysis. The quality of the grid affects the calculation accuracy and efficiency of CFD. For the specific issue, the quality of the grid is closely related to its geometric characteristics, flow characteristics and flow field solving algorithms. This model contains many thin fin plates with very small dimensions. The tetrahedral unstructured grids were generated. In order to ensure the accuracy of the numerical simulation calculation results, the independence verification was conducted on the fin model with corrugation angle θ=120° using the three different numbers of grid. Figure 4 shows the changes of the average cross-sectional temperature at each monitoring point under different grid numbers. With the number of grids 1.47×10⁶ and 1.62×10⁶, the average cross-sectional temperature of the ACHE at different monitoring points was different from that with the number of grids 1.58×106 by -2.3×10^-4~26×10^-4 and 2.3×10^-4~11×10^-4, respectively. Considering the calculation accuracy and time, the number of grids was finally determined to be 1.58×10⁶ in the simulation calculation process.

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Figure 4. The average cross-sectional temperature of the ACHE fin at different monitoring points under different grid numbers

2.4 Boundary conditions and algorithms

The inlet boundary condition was set as the velocity inlet at the inlet end of the calculation area, and the value of the inlet velocity was given in the direction perpendicular to the inlet boundary; the cooling air inlet temperature was set to 40℃; the outlet end of the calculation area was set as the pressure outlet; the ambient pressure was standard atmospheric pressure. The solid wall of the ACHE adopted a non-slip boundary. In Fluent calculation, the residual was set to 1×10^-7. The model was solved in a 3D rectangular coordinate system, to calculate the Reynolds number Re in the flow channel for 2.44×10⁴. The RNGκ-ε turbulence model was used; the separation variable implicit method was adopted for iterative solution; the semi-implicit SIMPLE algorithm was taken as the velocity and pressure coupling method; the interpolation method adopted the second-order upwind scheme. The air was regarded as cooling medium, and its physical properties are shown in Table 2. In actual operation, the air is forced to flow by a fan at a low working temperature. The calculation was based on the following assumptions: the physical properties of the air are constants; the air flow is constant; the natural convection is not considered; the viscous dissipation of the fluid is ignored; the flow rate of the inlet fluid is evenly distributed; the flow channel formed by the fins is evenly spaced; the resistance effect of the fin thickness to the fluid flow is ignored.

Table 2. Thermophysical properties of dry air

Through the field synergy analysis for the ACHE fins with different corrugation angles, this paper explores the influence of the gas flow channel structure generated by the corrugation angle on the field synergy.

4.1 Synergy analysis of velocity field and temperature field

According to literature [17], the general relationship between the Nusselt number of turbulent convective heat transfer and the local velocity field and temperature field is given as:

$Nu=RePr\int_{0}^{l}{\left( \overline{U}\cdot \nabla \overline{T} \right)}dY$       (11)

where, Nu，Re，Pr are Nusselt number, Reynolds number and Prandtl number respectively; $\bar{U}$ is the time average velocity; $\nabla \bar{T}$ is the time average temperature gradient.

The integrated factor can be expressed as:

$\overline{U}\cdot \nabla \overline{T}=\left| \overline{U} \right|\cdot \left| \nabla \overline{T} \right|\cos \alpha $        (12)

In Eq. (12) above, α is the angle between the velocity vector and the temperature gradient vector (heat vector). The physical meaning of this dimensionless integral is the sum of the intensity of the dimensionless heat source in the thickness section of the thermal boundary layer at x. Under certain conditions of velocity and temperature gradient, reducing the angle between them can achieve enhanced heat transfer. The synergy angle is expressed as:

$\alpha =\arccos \frac{\overline{U}\cdot \nabla \overline{T}}{\overline{\left| U \right|}\left| \nabla \overline{T} \right|}$      (13)

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Figure 13. Nephograms of the synergy angle between the velocity and the temperature gradient at the monitoring point 3

Due to the limited length of the paper, Figure 13 only shows the nephograms of the synergy angle between the velocity and the temperature gradient at the monitoring point 3 section (away from the inlet and outlet position). It can be seen from the figure that as the fin corrugation angle θ decreased, the synergy angle between the velocity and the temperature gradient changed significantly. When using the straight fin (θ=180°), the distribution of θ at the monitoring point was very uneven, and there was a very obvious change gradient in the flow channel, indicating that the velocity and temperature gradient in the flow field are not stable enough, and the heat transfer effect in the channel is not the best; the comparison shows that when θ is equal to 150° and 120°, the synergy angles are uniformly distributed in the flow channel, and they’re less than 90°, indicating a significant heat transfer effect. Figure 14 shows a broken line graph of the average synergy angle between the velocity and the temperature gradient at different monitoring points in the flow channel with different fin angles θ. From this figure, it can be seen clearly that the average synergy angle of the straight fin was the minimum for 72° only on the cross section of point 1 at the inlet, and the average synergy angle at other flow field positions was not much different from 120°, but it fluctuated more obviously in the entire flow field; the average value α of the whole field was calculated to be 82° when using the straight fin; at θ=120°, the synergy angle in the entire field had the smallest fluctuation, indicating that the heat transfer enhancement effect in the entire flow field is more uniform than other angles, and the average value of the entire flow field α was 83.6°.

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Figure 14. The average synergy angle of velocity and temperature gradient at each monitoring point

4.2 Synergy analysis between velocity and pressure gradient

For the enhanced convective heat transfer of the heat exchanger, it is generally necessary to increase the pump power or fan power. Considering the mutual coordination between the temperature field, pressure field, and velocity field of the heat medium in the heat exchanger, the heat exchange can also be enhanced by improving the synergy of the temperature field of the cold and hot fluid. According to the literature [17], the synergy relationship between velocity and pressure gradient is shown in (14):

$\overline{U}\cdot \left( -\nabla \overline{P} \right)=\left| \overline{U} \right|\left| -\nabla \overline{P} \right|\cos \beta $      (14)

Then, the synergy angle β can be derived as:

$\beta =\arccos \frac{\overline{U}\cdot \left( -\nabla \overline{P} \right)}{\left| \overline{U} \right|\left| -\nabla \overline{P} \right|}$     (15)

Based on the principle of field synergy, when $\bar{U} \cdot(-\nabla \bar{P})$ is constant, the smaller the β angle, the smaller the power consumption of the fluid.

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Figure 15. The average synergy angle of velocity and pressure gradient at each monitoring point

Figure 15 shows that except for the monitoring point 4 (the outlet position), the synergy angles at the other monitoring points were less than 90°; as the corrugation angle decreased, the synergy angle at each cross-section presents a more complicated change, indicating that the change of the corrugated angle has a greater impact on the flow resistance. Based on the average synergy angle β, it can be found that at 120°<θ<180°, the average synergy angle increases with the decrease of θ, indicating that the smaller the corrugation angle, the greater the flow resistance, but when it’s less than 120°, the influence of corrugation angle on the resistance is reduced. This is mainly because the reduction of the corrugation angle will decrease the size of its internal space, so that less fluid enters the angle space during fluid flow, and the resistance is also reduced.

It can be seen from Table 3 that based on the principle of field synergy, the smaller the synergy angle α, the stronger the fluid convection heat transfer; the smaller the synergy angle β, the smaller the fluid flow resistance; as the fin heat transfer coefficient changes with the corrugation angle, 120° is a demarcation point, i.e., at 180°~120°, the smaller the angle, the greater the heat transfer coefficient, while at less than 120°, the heat transfer coefficient decreases instead. When selecting the corrugation angle of 120°, the average β was increased by 29.6% compared with the traditional fin, and the heat transfer coefficient was by about 65%. This angle can not only achieve the purpose of strengthening convection heat transfer of the ACHE, but also avoid the large increase in the flow resistance.

Table 3. The average synergy angle and fin heat transfer coefficient of different corrugation angles