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Validation Case: Battery Pack Cooling

This validation case belongs to conjugate heat transfer, with the case of a battery pack cooling test. The aim of this project is to demonstrate the validity of SimScale’s CHTv2 solver by performing a conjugate heat transfer analysis of an air-cooled battery pack by comparing the following parameters:

  • Temperature of solid bodies
  • Temperature of fluid
  • Flow velocity profiles

The simulation results from SimScale were compared to the results presented in the reference paper [JILTE]\(^1\).

Geometry

The battery pack consists of a 3×3 cell configuration, as illustrated in Figure 1:

battery cell pack model simscale
Figure 1: Geometry model for the battery pack

The cell geometry dimensions are taken from the parameters given in the reference paper\(^1\), except for the cell’s top tab, whose proportions are approximated from the pictures. The value for the number of cells \((N)\) is 9. The dimension values are given in Table 1:

ParameterVariableValue \([mm]\)
Cell diameter\(D\)42.4
Cell height\(H\)97.7
Tab diameter\(d\)15
Tab height\(h\)3.7
Cell spacing\(S_L\)63.6
Enclosure width\(W_E\)212
Enclosure height\(H_E\)140.1
Table 1: Geometry parameters

Analysis Type and Mesh

Tool Type: OpenFOAM®

Analysis Type: Conjugate Heat Transfer v2

Mesh and Element Types:

The meshes were computed using the SimScale’s Standard meshing algorithm:

Mesh
#
Mesh TypeNumber of
Cells
Setup
1Standard2829369Fineness 7
2Standard2853925Fineness 5, manual refinement 0.002 \(m\) and boundary layers
3Standard13970254Fineness 5, manual refinement 0.001 \(m\) and boundary layers
4Standard4176543Fineness 5, manual refinement 0.0015 \(m\) and boundary layers
Table 2: Mesh refinement per case
battery pack cooling mesh simscale
Figure 2: Standard mesh 1, clipped for showing the hexahedral core and tetrahedral surface. Such visualization can be created with the ‘Mesh quality‘ tool.

Simulation Setup

Model:

  • Flow compressibility: Incompressible/Compressible
  • Time dependency: Steady state
  • Turbulence model: Laminar
  • Incompressible Working Fluid (Air):
    • (\(\nu\)) Kinematic viscosity: 1.529e-5 \(m^2/s\)
    • (\(\rho\)) Density: 1.196 \(kg/m^3\)
    • Thermal expansion coefficient: 3.43e-3 \(1/K\)
    • (\(T_0\)) Reference temperature: 273.1 \(K\)
    • (\(Pr_{lam}\)) Laminar Prandtl number: 0.713
    • (\(Pr_{t}\)) Turbulent Prandtl number: 0.85
    • Specific heat: 1004 \(J/(kg.K)\)
  • Compressible Working Fluid (Air):
    • (\(M_m\)) Molar mass: 28.97 \(kg/kml\)
    • Transport: Const
    • (\(\mu\)) Dynamic viscosity: 1.83e-5 \(kg/s.m\)
    • (\(Pr\)) Prandtl number: 0.713
    • (\(Pr_{t}\)) Turbulent Prandtl number: 0.85
    • Thermal model: hConst (Constant entalphy)
    • Specific heat: 1004 \(J/(kg.K)\)
    • Equation of state: Perfect gas
  • Solid Material (Cells):
    • Conductivity type: Isotropic
    • (\(\kappa\)) Thermal conductivity: 1 \(W/(m.K)\)
    • Specific heat: 837.4 \(J/(kg.K)\)
    • Equation of state: Constant density
    • (\(\rho\)) Density: 2008 \(kg/m^2\)

Two simulations were run using the compressible fluid model, in order to test the accuracy of the Boussinesq approximation in the incompressible solver.

Boundary Conditions:

  • Velocity Inlet: 0.1 \(m/s\)
  • Pressure Outlet: 101 325 \(Pa\) – Fixed value
  • Absolute power source on cells: 0.35 \(W\)
  • External walls: No slip flow, adiabatic.
battery cell pack boundary conditions simscale
Figure 3: Illustration of the boundary conditions and cell numbering

Reference Solution

The reference solution for the battery pack cooling is of the numerical type, as developed in [JILTE]\(^1\). It was computed using the Ansys FLUENT 6.3 CFD package. The reference simulation is transient, thus approximations were required to compare the results to SimScale’s steady-state CHT v2 solver.

The reference solutions are the temperature and velocity fields, measured at different locations:

  • Area average temperatures at cells 4, 5 and 6 (refer to Figure 3).
  • Converged temperature profile in two planes perpendicular to the flow direction, between rows 1 and 2 (Plane 1) and between rows 2 and 3 (Plane 2) of the cells. The profile is reported along lines at two different heights in the planes, 25 and 50 \(mm\).
  • Flow velocity magnitude profile for Plane 1 at heights as described above.
locations where results for lpu battery pack cooling are analyzed
Figure 4: Illustration of planes and heights at which the data will be analyzed

Results Comparison

For the average temperature across cells, the comparison of the different meshes shows the convergence behavior:

Temperature LocationMesh 1 \([°C]\)Mesh 2 \([°C]\)Mesh 3 \([°C]\)Mesh 4 \([°C]\)Final Deviation
Cell 4 Average25.2025.2026.6026.301.14 %
Cell 5 Average27.5026.7028.6028.600.00 %
Cell 6 Average27.4027.1028.9028.900.00 %
Table 3: Temperature results \((°C)\) for the mesh convergence study. Final deviation is between Mesh 3 and Mesh 4.

It was found that Mesh 4 is optimal because it captures the converged results while using a smaller cell count than mesh 3.

Comparison of the computed values in SimScale with Mesh 3 (finest) and the reference solution is shown below:

Temperature LocationSimScale Result
(Mesh 3)
Reference ResultDeviation
Cell 4 Average26.6027.17-2.10 %
Cell 5 Average28.6027.324.69 %
Cell 6 Average28.9027.186.33 %
Table 4: Comparison of temperature results \((°C)\) against the reference values\(^1\)

A maximum temperature deviation of 1.7 \(°C\) is observed at Cell 6, between SimScale and the reference results. This corresponds to an error of 6.33% in the battery pack cooling strategy.

The temperature profiles comparison in Plane 1 is presented at two heights, 25 and 50 \(mm\). ‘Reference’ curves correspond to the paper results, and ‘SimScale’ curves correspond to the Mesh 3 results.

battery pack cooling temperature results simscale
Figure 5: Comparison of temperature profiles at Plane 1

The same comparison is performed for Plane 2:

battery pack cooling temperature results simscale
Figure 6: Comparison of temperature profiles at Plane 2

The deviation of air temperature with respect to reference values is within 2 \(°C\). Similar to cell temperatures, air temperature values are mostly over predicted.

The comparison of flow velocity magnitude profiles for Plane 1 is presented below:

battery pack cooling velocity results simscale
Figure 7: Comparison of flow velocity magnitude profiles at Plane 1

The maximum velocity values are over-predicted by SimScale by a maximum of around 0.06 \(m/s\). This error can be attributed to the comparison of steady-state to transient results.

Finally, for the verification of the Boussinesq approximation, the temperature and velocity profiles are compared for results of runs using compressible and incompressible flow models. The velocity magnitude and temperature profiles are presented for Plane 1:

boussinesq temperature results simscale
Figure 8: Temperature profiles for the incompressible model using Boussinesq approximation and compressible flow model
boussinesq velocity results simscale
Figure 9: Velocity magnitude profiles for incompressible model using Boussinesq approximation and compressible flow model

Good correlation is achieved between profiles using Boussinesq approximation and compressible flow, thus it is determined that the air velocity profile is independent of the approximation.

temperature and velocity results simscale
Figure 10: Temperature of the cells and flow velocity at 50 \(mm\) height

References

  • R.D. Jilte, Raviden Kumar – Numerical investigation on cooling performance of Li-ion battery thermal management system at high galvanostatic discharge – Engineering Science and Technology, an International Journal – Elsevier – Octuber 2018

Note

If you still encounter problems validating you simulation, then please post the issue on our forum or contact us.

Last updated: June 7th, 2021

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