# Design of Parallel Air-Cooled Battery Thermal Management System through Numerical Study

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## Abstract

**:**

## 1. Introduction

## 2. Models

#### 2.1. Illustration of the Parallel Air-Cooled BTMS

#### 2.2. Computational Fluid Dynamics Calculation

## 3. Numerical Procedure

#### 3.1. Parameters of the Numerical Cases

#### 3.2. Grid Dependence Analysis

#### 3.3. Validation of the CFD Method

## 4. Influences of the System Parameters on Performance

#### 4.1. Influence of the Discharge Rate

#### 4.2. Influence of the Inlet Air Temperature

#### 4.3. Influence of the Inlet Airflow Rate

#### 4.4. Influence of Cell Spacing

#### 4.5. Influence of the Angles of the Divergence Plenum and Convergence Plenum

- Situation 1: Let ${w}_{1}=20$ mm, and consider the value of ${w}_{2}$ as 1 mm, 5 mm, 10 mm, 15 mm and 20 mm, respectively.
- Situation 2: Let ${w}_{1}={w}_{2}$, and consider the values as 1 mm, 5 mm, 10 mm, 15 mm and 20 mm, respectively.
- Situation 3: Let ${w}_{2}=20$ mm, and consider the value of ${w}_{1}$ as 1 mm, 5 mm, 10 mm, 15 mm and 20 mm, respectively.

#### 4.6. Optimization of Plenum Widths

- Set ${w}_{2}$ as the fixed value and set the initial range of ${w}_{1}$ as $\left[{w}_{11},{w}_{12}\right]$. Calculate the middle point of the range $\left[{w}_{11},{w}_{12}\right]$ as ${w}_{13}=\left({w}_{11}+{w}_{12}\right)/2$.
- Let ${w}_{1}$ equal ${w}_{11}$, ${w}_{12}$ and ${w}_{13}$, respectively. Evaluate the values of $\Delta {T}_{\mathrm{max}}$ of these three BTMSs using the CFD calculation, respectively, denoting them as $\Delta {T}_{\mathrm{max},1}$, $\Delta {T}_{\mathrm{max},2}$ and $\Delta {T}_{\mathrm{max},3}$.If $\Delta {T}_{\mathrm{max},1}<\Delta {T}_{\mathrm{max},3}$,let ${w}_{11}={w}_{11},{w}_{12}={w}_{13},{w}_{13}=\left({w}_{11}+{w}_{12}\right)/2$, then return to Step 2 and continue the process.else if $\Delta {T}_{\mathrm{max},2}<\Delta {T}_{\mathrm{max},3}$,let ${w}_{11}={w}_{13},{w}_{12}={w}_{12},{w}_{13}=\left({w}_{11}+{w}_{12}\right)/2$, then return to Step 2 and continue the process.elsego to Step 3.
- The range for ${w}_{1}$ is reduced through using the following strategy. Let ${w}_{14}=\left({w}_{11}+{w}_{13}\right)/2$ and ${w}_{15}=\left({w}_{13}+{w}_{12}\right)/2$. Evaluate the values of $\Delta {T}_{\mathrm{max}}$ of the two BTMSs with ${w}_{1}={w}_{14}$ and ${w}_{1}={w}_{15}$ using CFD calculation, respectively, denoting them as $\Delta {T}_{\mathrm{max},4}$ and $\Delta {T}_{\mathrm{max},5}$.If $\Delta {T}_{\mathrm{max},4}<\Delta {T}_{\mathrm{max},3}$,let ${w}_{11}={w}_{11},{w}_{12}={W}_{13},{w}_{13}={w}_{14},\Delta {T}_{\mathrm{max},1}=\Delta {T}_{\mathrm{max},1},\Delta {T}_{\mathrm{max},2}=\Delta {T}_{\mathrm{max},3},\Delta {T}_{\mathrm{max},3}=\Delta {T}_{\mathrm{max},4}$.else if $\Delta {T}_{\mathrm{max},5}<\Delta {T}_{\mathrm{max},3}$,let ${w}_{11}={w}_{13},{w}_{12}={w}_{12},{w}_{13}={w}_{15},\Delta {T}_{\mathrm{max},1}=\Delta {T}_{\mathrm{max},3},\Delta {T}_{\mathrm{max},2}=\Delta {T}_{\mathrm{max},2},\Delta {T}_{\mathrm{max},3}=\Delta {T}_{\mathrm{max},5}$.elselet ${w}_{11}={w}_{14},{w}_{12}={w}_{15},{w}_{13}={w}_{13},\Delta {T}_{\mathrm{max},1}=\Delta {T}_{\mathrm{max},4},\Delta {T}_{\mathrm{max},2}=\Delta {T}_{\mathrm{max},5},\Delta {T}_{\mathrm{max},3}=\Delta {T}_{\mathrm{max},3}$.
- If $\left({w}_{13}-{w}_{11}\right)$ and $\left({w}_{12}-{w}_{13}\right)$ are both smaller than a specified threshold, the optimization process is stopped; otherwise, return to Step 3, and continue the process.

#### 4.7. Performance with Fixed Power Consumption

## 5. Conclusions

- The temperature rise and the temperature difference of the battery pack increase as the discharge rate increases, but the discharge rate cannot be controlled effectively.
- Reducing the inlet air temperature can reduce the absolute temperature of the battery pack, but cannot effectively reduce the temperature rise and the temperature difference of the system.
- As the inlet airflow rate increases, the maximum temperature of the battery pack is reduced, but the temperature difference of the battery pack and the power consumption to maintain the flow rate are both increased.
- As the cell spacings decrease, the temperature and the temperature difference of the battery pack are both reduced effectively. However, the decrease of the cell spacing increases the power consumption of the system significantly.
- The angles of the plenums remarkably influence the performance of the BTMS. The maximum temperature and the maximum temperature difference of the battery pack can be reduced effectively through optimizing the angles of the plenums, without increasing the total volume and the power consumption of the BTMS.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

${C}_{1},{C}_{2}$ | parameters of the $k\sim \epsilon $ turbulence model, 1 |

${C}_{\mu}$ | parameter of the $k\sim \epsilon $ turbulence model, 1 |

${c}_{p,\mathrm{air}}$ | heat capacities of the air, $\mathrm{J}/(\mathrm{kg}\xb7\mathrm{K})$ |

${c}_{p,\mathrm{b}}$ | heat capacities of the battery cell, $\mathrm{J}/(\mathrm{kg}\xb7\mathrm{K})$ |

${d}_{0}$ | cell spacing among the battery cells, m |

${l}_{\mathrm{b}},{w}_{\mathrm{b}},{h}_{\mathrm{b}}$ | length, width and height of the battery cell, m |

I | discharge current of the battery cell, A |

k | turbulent kinetic energy, ${\mathrm{m}}^{2}/{\mathrm{s}}^{2}$ |

M | number of the rows for the battery pack, 1 |

N | number of the columns for the battery pack, 1 |

p | Reynolds-averaged pressure, Pa |

${Q}_{0}$ | inlet airflow rate, ${\mathrm{m}}^{3}/\mathrm{s}$ |

R | the equivalent resistance of the battery cell, $\mathsf{\Omega}$ |

${T}_{0}$ | temperature of the inlet airflow, K |

${T}_{\mathrm{air}}$ | temperature of the air, K |

${T}_{\mathrm{b}}$ | temperature of the battery cell, K |

${T}_{max}$ | maximum temperature of the battery pack, K |

$\Delta {T}_{max}$ | maximum temperature difference of the battery pack, K |

${u}_{i}$, ${u}_{j}$ | the i-th and the j-th Reynolds-averaged velocity components, m/s |

${V}_{\mathrm{cell}}$ | volume of the battery cell, ${\mathrm{m}}^{3}$ |

${w}_{1}$ | width of the divergence plenum, m |

${w}_{2}$ | width of the convergence plenum, m |

${w}_{\mathrm{in}}$ | inlet width, m |

${w}_{\mathrm{out}}$ | outlet width, m |

${W}_{\mathrm{p}}$ | power consumption of the BTMS, W |

$x,y,z$ | coordinates of the domain, m |

## Greek Symbols

${\lambda}_{\mathrm{air}}$ | thermal conductivity of the air, $\mathrm{W}/(\mathrm{m}\xb7\mathrm{K})$ |

${\lambda}_{\mathrm{b}}$ | thermal conductivity of the battery cell, $\mathrm{W}/(\mathrm{m}\xb7\mathrm{K})$ |

$\mu $ | the molecular dynamic viscosity coefficient of the air, $\mathrm{kg}/(\mathrm{m}\xb7\mathrm{s})$ |

${\mu}_{\mathrm{t}}$ | the turbulent dynamic viscosity coefficient, $\mathrm{kg}/(\mathrm{m}\xb7\mathrm{s})$ |

${\varphi}_{\mathrm{b}}$ | heat generation rate of the battery cell, $\mathrm{W}/{\mathrm{m}}^{3}$ |

$\rho $ | density of the air, $\mathrm{kg}/{\mathrm{m}}^{3}$ |

${\rho}_{\mathrm{b}}$ | density of the battery cell, $\mathrm{kg}/{\mathrm{m}}^{3}$ |

${\sigma}_{\epsilon}$ | parameter of the $k\sim \epsilon $ turbulence model in the $\epsilon $ equation, 1 |

${\sigma}_{k}$ | parameter of the $k\sim \epsilon $ turbulence model in the k equation, 1 |

${\sigma}_{T}$ | parameter of the $k\sim \epsilon $ turbulence model in the temperature equation, 1 |

${\theta}_{1}$ | angle of the divergence plenum, degree |

${\theta}_{2}$ | angle of the convergence plenum, degree |

$\epsilon $ | turbulent kinetic energy dissipation, ${\mathrm{m}}^{2}/{\mathrm{s}}^{3}$ |

## Subscripts

$\mathrm{b}$ | battery cell |

$\mathrm{in}$ | inlet cross-section |

max | maximum |

$\mathrm{out}$ | outlet cross-section |

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**Figure 2.**Schematic of the parallel air-cooled battery thermal management system (BTMS). (

**a**) Orthographic view of the BTMS; (

**b**) Side view of the BTMS.

**Figure 5.**Comparison of the numerical results by 2D calculation and 3D calculation. (

**a**) Maximum temperature; (

**b**) maximum temperature difference.

**Figure 6.**Comparison of the numerical results of the present study and the experiment data in the reference.

**Figure 7.**Comparison of numerical results for various inlet air temperatures. (

**a**) Maximum temperature; (

**b**) maximum temperature difference.

**Figure 8.**Comparison of results for various inlet airflow rates. (

**a**) Flow rate in the cooling channel; (

**b**) maximum temperature; (

**c**) maximum temperature difference.

**Figure 9.**Comparison of the results for various cell spacings. (

**a**) Flow rate in the cooling channel; (

**b**) maximum temperature; (

**c**) maximum temperature difference.

**Figure 10.**Comparison of numerical results for various angles of the plenums. (

**a**) Pressure; (

**b**) pressure drop.

**Figure 12.**Comparison of the maximum temperature and the maximum temperature difference of the battery pack with time with fixed power consumption. (

**a**) Maximum temperature; (

**b**) maximum temperature difference.

Property | Air | Battery Cell [22] |
---|---|---|

Density ($\mathrm{kg}/{\mathrm{m}}^{3}$) | 1.165 | 2700 |

Specific heat ($\mathrm{J}/(\mathrm{kg}\xb7\mathrm{K})$) | 1005 | 900 |

Dynamic viscosity ($\mathrm{kg}/(\mathrm{m}\xb7\mathrm{s})$) | $1.86\times {10}^{-5}$ | - |

Thermal conductivity ($\mathrm{W}/(\mathrm{m}\xb7\mathrm{K})$) | 0.0267 | 240 |

Initial temperature (K) | 300 | 300 |

${l}_{\mathrm{b}}$ (mm) | - | 16 |

${h}_{\mathrm{b}}$ (mm) | - | 151 |

${w}_{\mathrm{b}}$ (mm) | - | 65 |

**Table 2.**Comparison of numerical results at the end of the five-current (5C) discharge process by 2D calculation and 3D calculation.

${\mathit{Q}}_{0}$ | 3D Calculation | 2D Calculation | |||
---|---|---|---|---|---|

(${\mathbf{m}}^{3}/\mathbf{s}$) | ${\mathit{T}}_{max}$ (K) | $\Delta {\mathit{T}}_{max}$ (K) | ${\mathit{T}}_{max}$ (K) | $\Delta {\mathit{T}}_{max}$ (K) | |

0.005 | 329.5 | 4.4 | 329.5 | 4.4 | |

0.010 | 327.1 | 6.6 | 327.2 | 6.6 | |

0.012 | 326.4 | 7.2 | 326.5 | 7.3 | |

0.015 | 325.4 | 8.0 | 325.6 | 8.2 |

**Table 3.**Properties of battery cell used for testing the temperature calculation [31].

Property | Value [31] |
---|---|

Size (mm × mm × mm) | 70 × 27 × 90 |

Density ($\mathrm{kg}/{\mathrm{m}}^{3}$) | 2335 |

Specific heat ($\mathrm{J}/(\mathrm{kg}\xb7\mathrm{K})$) | 935 |

Thermal conductivity (${\lambda}_{x},{\lambda}_{y},{\lambda}_{z}$, $\mathrm{W}/(\mathrm{m}\xb7\mathrm{K})$) | 0.26/0.7/0.26 |

Equivalent heat generation rate ($\mathrm{W}/{\mathrm{m}}^{3}$) | $1.27\times {10}^{5}$ |

Discharge Rate | ${\mathit{T}}_{max}$ (K) | ${\mathit{T}}_{min}$ (K) | $\Delta {\mathit{T}}_{max}$ (K) |
---|---|---|---|

3C | 313.5 | 308.5 | 5.0 |

4C | 320.0 | 313.7 | 6.3 |

5C | 326.5 | 319.2 | 7.3 |

6C | 333.5 | 325.1 | 8.4 |

${\mathit{T}}_{0}$ (K) | ${\mathit{T}}_{max}$ (K) | $\left({\mathit{T}}_{max}-{\mathit{T}}_{0}\right)$ (K) | $\Delta {\mathit{T}}_{max}$ (K) |
---|---|---|---|

290 | 316.5 | 26.5 | 7.3 |

295 | 321.5 | 26.5 | 7.3 |

300 | 326.5 | 26.5 | 7.3 |

305 | 331.5 | 26.5 | 7.3 |

310 | 336.5 | 26.5 | 7.3 |

${\mathit{Q}}_{0}$ (${\mathbf{m}}^{3}/\mathbf{s}$) | ${\mathit{T}}_{max}$ (K) | $\Delta {\mathit{T}}_{max}$ (K) | ${\mathit{W}}_{\mathbf{p}}$ (W) |
---|---|---|---|

0.005 | 329.5 | 4.4 | 0.0371 |

0.010 | 327.2 | 6.6 | 0.2295 |

0.012 | 326.5 | 7.3 | 0.3794 |

0.015 | 325.6 | 8.2 | 0.7094 |

0.020 | 324.3 | 9.3 | 1.6132 |

${\mathit{d}}_{0}$ (mm) | ${\mathit{T}}_{max}$ (K) | $\Delta {\mathit{T}}_{max}$ (K) | ${\mathit{W}}_{\mathbf{p}}$ (W) |
---|---|---|---|

1 | 322.7 | 4.5 | 4.0044 |

2 | 324.0 | 4.7 | 0.7023 |

3 | 326.5 | 7.3 | 0.3794 |

4 | 329.5 | 11.0 | 0.3149 |

5 | 330.5 | 12.4 | 0.3056 |

${\mathit{w}}_{1}$ (mm) | ${\mathit{w}}_{2}$ (mm) | ${\mathit{T}}_{max}$ (K) | $\Delta {\mathit{T}}_{max}$ (K) | ${\mathit{W}}_{\mathbf{p}}$ (W) | |
---|---|---|---|---|---|

20 | 1 | 329.1 | 11.0 | 0.4721 | |

20 | 5 | 328.0 | 9.5 | 0.4361 | |

Situation 1 | 20 | 10 | 327.2 | 8.4 | 0.4097 |

20 | 15 | 326.8 | 7.8 | 0.3922 | |

20 | 20 | 326.5 | 7.3 | 0.3794 | |

1 | 1 | 326.3 | 6.7 | 0.6296 | |

5 | 5 | 326.2 | 7.7 | 0.4991 | |

Situation 2 | 10 | 10 | 326.3 | 7.6 | 0.4379 |

15 | 15 | 326.5 | 7.5 | 0.4032 | |

20 | 20 | 326.5 | 7.3 | 0.3794 | |

1 | 20 | 324.0 | 3.1 | 0.4682 | |

5 | 20 | 325.0 | 5.8 | 0.4315 | |

Situation 3 | 10 | 20 | 325.7 | 6.7 | 0.4063 |

15 | 20 | 326.2 | 7.1 | 0.3905 | |

20 | 20 | 326.5 | 7.3 | 0.3794 |

Step | ${\mathit{w}}_{11}$ | ${\mathit{w}}_{14}$ | ${\mathit{w}}_{13}$ | ${\mathit{w}}_{15}$ | ${\mathit{w}}_{12}$ | |||||
---|---|---|---|---|---|---|---|---|---|---|

${\mathit{w}}_{1}$ (mm) | $\Delta {\mathit{T}}_{max}$ (K) | ${\mathit{w}}_{1}$ (mm) | $\Delta {\mathit{T}}_{max}$ (K) | ${\mathit{w}}_{1}$ (mm) | $\Delta {\mathit{T}}_{max}$ (K) | ${\mathit{w}}_{1}$ (mm) | $\Delta {\mathit{T}}_{max}$ (K) | ${\mathit{w}}_{1}$ (mm) | $\Delta {\mathit{T}}_{max}$ (K) | |

1 | 1.00 | 3.08 | - | - | 3.00 | 5.10 | - | - | 5.00 | 5.80 |

2 | 1.00 | 3.08 | - | - | 2.00 | 4.43 | - | - | 3.00 | 5.10 |

3 | 1.00 | 3.08 | - | - | 1.50 | 3.92 | - | - | 2.00 | 4.43 |

4 | 1.00 | 3.08 | - | - | 1.25 | 3.61 | - | - | 1.50 | 3.92 |

5 | 1.00 | 3.08 | - | - | 1.13 | 3.32 | - | - | 1.25 | 3.61 |

6 | 1.00 | 3.08 | - | - | 1.06 | 3.21 | - | - | 1.13 | 3.32 |

Step | ${\mathit{w}}_{11}$ | ${\mathit{w}}_{14}$ | ${\mathit{w}}_{13}$ | ${\mathit{w}}_{15}$ | ${\mathit{w}}_{12}$ | |||||
---|---|---|---|---|---|---|---|---|---|---|

${\mathit{w}}_{1}$ (mm) | $\Delta {\mathit{T}}_{max}$ (K) | ${\mathit{w}}_{1}$ (mm) | $\Delta {\mathit{T}}_{max}$ (K) | ${\mathit{w}}_{1}$ (mm) | $\Delta {\mathit{T}}_{max}$ (K) | ${\mathit{w}}_{1}$ (mm) | $\Delta {\mathit{T}}_{max}$ (K) | ${\mathit{w}}_{1}$ (mm) | $\Delta {\mathit{T}}_{max}$ (K) | |

1 | 15.00 | 3.45 | - | - | 17.50 | 3.25 | - | - | 20.00 | 3.08 |

2 | 17.50 | 3.25 | - | - | 18.75 | 3.16 | - | - | 20.00 | 3.08 |

3 | 18.75 | 3.16 | - | - | 19.38 | 3.12 | - | - | 20.00 | 3.08 |

4 | 19.38 | 3.12 | - | - | 19.69 | 3.10 | - | - | 20.00 | 3.08 |

5 | 19.69 | 3.10 | - | - | 19.84 | 3.09 | - | - | 20.00 | 3.08 |

6 | 19.84 | 3.09 | - | - | 19.92 | 3.09 | - | - | 20.00 | 3.08 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Chen, K.; Li, Z.; Chen, Y.; Long, S.; Hou, J.; Song, M.; Wang, S.
Design of Parallel Air-Cooled Battery Thermal Management System through Numerical Study. *Energies* **2017**, *10*, 1677.
https://doi.org/10.3390/en10101677

**AMA Style**

Chen K, Li Z, Chen Y, Long S, Hou J, Song M, Wang S.
Design of Parallel Air-Cooled Battery Thermal Management System through Numerical Study. *Energies*. 2017; 10(10):1677.
https://doi.org/10.3390/en10101677

**Chicago/Turabian Style**

Chen, Kai, Zeyu Li, Yiming Chen, Shuming Long, Junsheng Hou, Mengxuan Song, and Shuangfeng Wang.
2017. "Design of Parallel Air-Cooled Battery Thermal Management System through Numerical Study" *Energies* 10, no. 10: 1677.
https://doi.org/10.3390/en10101677