# The Design and Investigation of a Cooling System for a High Power Ni-MH Battery Pack in Hybrid Electric Vehicles

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## Abstract

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## Abstract

## 1. Introduction

#### 1.1. Literature Review

#### 1.2. Contributions and Organization

## 2. Preliminary Design

#### 2.1. Parameters of the Battery Pack

#### 2.2. Structure of the Cooling Plate

## 3. Theoretical Analysis

_{a}and S

_{b}are the cross-sectional area of the main pipe and serpentine pipe, respectively.

#### 3.1. Heat Generation Process

_{r}), polarization heat (Φ

_{p}), side reaction heat (Φ

_{s}), and Joule heat (Φ

_{j}) [38]. The operation process is divided into two phases: the normal charge–discharge phase and the overcharge phase. The calorific value is related to the magnitude and direction of the current (I). Because the SOC working range is controlled within 30%~70% to avoid overcharging in HEVs, the sub reaction heat is approximately zero. According to the exothermic charge and endothermic discharge, the total reaction heat can be ignored by using alternating current.

_{p}) and electronic resistance (R

_{e}) cannot be calculated directly, the total internal DC resistance (R

_{t}) is used for the equivalent calculation, which is the sum of the polarization resistance and electronic resistance. The internal resistance of the cells is treated as a constant, which means that it does not vary with changes in the state of charge (SOC), temperature, or other parameters.

#### 3.2. Heat Transfer Process

_{1}, R

_{2}, and R

_{3}, we find:

_{4}, is:

_{H}, and the heat conductivity of fluid k

_{f}, using Equation (8):

_{b}is the length of the branch pipe, and μ is the dynamic viscosity (subscript f and w represent the fluid temperature and wall temperature, respectively). The Reynolds number Re and Prandtl number (for the temperature of the fluid) Pr

_{f}are:

_{4}can also be calculated from Equations (7)–(10).

_{c}is the equivalent heat resistance within the battery cell and is determined by the cell’s materials, components, and dimensions. T

_{c}is the maximum temperature in the cell, T

_{s}is the temperature of the battery’s steel shell, and Φ is the heat flow at the contact surface.

_{c}

_{,i,j}, can be obtained by the following equation:

#### 3.3. Thermal–Hydraulic Performance

_{a}

_{–b}is calculated from the experimental equations in [42,43]:

_{bend}is calculated from the experimental equations in [42,43]. L/2 is the bending radius (half of the cell’s center distance L in Figure 3c).

_{fri,i}comprises the loss along each segment in the main pipe and branch pipe for the cooling plate in Group Set A:

_{C}, so:

_{i}and Q

_{1}~Q

_{n}has been established, and the flow of different channels (the bias flow rate β) can be obtained by iterative calculations according to Equation (17). According to the heat transfer formula introduced in Section 3.2, the maximum temperature and temperature difference corresponding to different flows can also be calculated.

- Five diameters of the main pipe were used: D = 12 mm (δ = 0.484), D = 14.5 mm (δ = 0.707), D = 17 mm (δ = 0.973), D = 19.5 mm (δ = 1.278), and D = 22 mm (δ = 0.1627).
- The boundary conditions for the simulation were as follows: The maximum current must not exceed 35 A, the maximum inlet temperature of the coolant must not exceed 30 °C, and the coolant flow must be greater than 5 L/min.

## 4. Numerical Simulation

#### 4.1. Geometry Model and Parameter Settings

- A steady flow with a certain temperature at the inlet;
- Free flow at the outlet with zero pressure;
- A conjugated boundary at the solid–fluid interface;
- Uniform heat generation in the cells;
- Adiabatic at all other outer surfaces of the cells and pipes.

#### 4.2. Grid Independence

_{total}= 5 L/min, I = 25 A, N = 0. The seven different levels of grid systems, with grid numbers ranging from 3000 to 260,000, are presented in Table 4. Figure 8 shows a grid sectional view at the mid-symmetry plane of grid level 1, 4, and 7. The Nusselt number Nu, pressure loss Δp, and maximum temperature T

_{max}on the battery surface were selected to be the parameters of validation. The results obtained by these systems are shown in Figure 9a. It can be seen that when the grid number exceeds 50,000 (i.e., when the grid number increases significantly), all three parameters change slightly. Thus, to balance the accuracy and computational cost, a level 4 grid system was selected for the numerical models.

_{0}, Δp

_{0}, and the numerical results are represented as Nu, Δp. The results show good agreement, and the relative errors are within 10%. Further, the Nusselt number results for the numerical simulation are larger than those for the theoretical simulation based on Sieder–Tate correlation. The main reason that the pipe appears to be a straight pipe in Equation (10) but has a serpentine-like shape in practice is to enhance the heat exchange. The heat transfer coefficient or Nusselt number of a curved pipe’s surface is larger than that of a straight pipe under the same inlet conditions. Thus, the results are reasonable.

#### 4.3. Study of Internal Parameters

_{max}and T

_{diff}at a flow rate of Q = 5 L/min when N = 0. When the cross-sectional area ratio δ increase, the bias rate β, the pressure loss Δp, the maximum temperature T

_{max}, and the temperature difference T

_{diff}all decrease. The bias rate β and pressure loss Δp tend to become smaller as δ increases, and when δ is large enough, the trend gradually becomes slower. Similarly, the maximum temperature T

_{max}and the temperature difference T

_{diff}also become smaller as δ increases; when δ = 0.484, Tmax exceeds 40 °C, and Tdiff exceeds 5 °C. Considering the influence of δ on the cooling performance and actual size of the main cooling pipe, the final selection of δ is 0.973.

_{max}, and T

_{diff}are smaller than ratio δ. When the wall number N increase, the bias rate β, the maximum temperature T

_{max}, and the temperature difference T

_{diff}all decrease, but the pressure loss Δp increases dramatically. When N = 9, the maximum pressure loss reaches 3.75 kPa, thereby exceeding the maximum acceptable pressure loss limit. Thus, we fixed N at medium number 6 to balance the maximum heat transfer and pressure loss.

#### 4.4. Study of Boundary Conditions

_{diff}on the same monitoring surface between the battery cells is below 3 °C, and the maximum temperature T

_{max}of the battery is 36.86 °C. The maximum and minimum cell temperatures (at the surface opposite the cooling area) exist at the two corners of the pack. Because the flow consistency in each branching serpentine pipe was optimized in the previous section, the temperature difference T

_{i}between cells corresponding to the different branching serpentine pipes is well controlled. The temperature difference T

_{j}between the cells increases as the temperature of the coolant in the cooling channel gradually increases, but the total temperature difference T

_{diff}correctly meets the design expectations.

## 5. Experiment

#### 5.1. Test Sample and Experiment Preparation

#### 5.2. Experiment Environment Setup

#### 5.3. Bench Test Results

#### 5.4. Experiment on a Vehicle

## 6. Conclusions

- A simplified one-dimensional heat transfer model from the battery interface to the coolant was established; the mathematical relationship between head loss H
_{i}and coolant flow Q_{1}~Q_{n}was also established, and the flow Q_{i}in each serpentine pipe was calculated iteratively. The design parameters of the cooling plate and reasonable ranges of boundary conditions were obtained through these two models, which provided theoretical guidance for the simulation and reduced the number of combinations required for the simulation. - The cross-section ratio affects the flow rate deviation β and results in temperature differences. As the cross-section ratio δ increases from 0.484 to 1.627 at Q
_{total}= 5 L/min, the flow rate deviation β decreases by about 40%, and the temperature difference decreases by about 2.5 °C. The inner support wall N can enhance heat transfer to reduce the maximum temperature but will cause a definite increase of the pressure drop in the pipeline. The pressure drop in the pipe when N = 9 (Q_{total}= 5 L/min) increases by 2.5 kPa compared to that when N = 0, while the maximum temperature decreases by 3 °C. - The optimized cross-section ratio is δ = 0.973 (D = 17 mm), and the number of supporting walls is N = 6. The maximum RMS current allowed by the cooling plate does not exceed 30 A, the maximum inlet temperature of the coolant does not exceed 30 °C, and the coolant flow is greater than 5 L/min at least. The ranges of the solution at various input conditions provide the basic data for BMS dynamic control.

## 7. Patents

- Patent: A kind of Power Battery Module;
- Applicant: Corun CHS Technology Co., Ltd. (2880 Wanfeng Road, Fengjing town, Jinshan District, Shanghai, China);
- Inventor: Minghuan Zhang, Faping Zhong, Aihua Chu, Chunhua Wu, Wei Tan, Chenquan Zhou, Yunpeng Zong;
- Application No.: 201720406483.4;
- Application Date: 2017-04-18

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

A | area of the contact region between the battery and serpentine pipe (m^{2}) |

A_{f} | area of the pipe—fluid interface (m^{2}) |

C_{p} | heat capacity (J (kg K)^{−1}) |

d | diameter of the main pipe (m) |

d_{H} | hydraulic diameter of the serpentine pipe (m) |

g | gravity acceleration (m s^{−2}) |

h | heat transfer coefficient of convection (W (m^{−2}·K^{−1})) |

H | head loss (m) |

k | coefficient of heat conductivity (W (m^{−1}·K^{−1})) |

L | length (m) |

$\dot{m}$ | mass flow rate (kg s^{−1}) |

N | the number of internal walls within one serpentine pipe |

Nu | Nusselt number |

Δp | pressure loss (Pa) |

Pr | Prandtl number |

q | heat generation in the battery cell (W) |

Q_{total} | total volume flow rate in one water bag (m^{3}·s^{−1}) |

Q_{i} | volume flow rate in serpentine pipe i (m^{3}·s^{−1}) |

Re | Reynolds number |

S_{a} | Section area of the main pipe (m^{2}) |

S_{b} | Section area of the serpentine pipe (m^{2}) |

t | thickness of the serpentine pipe wall (m) |

T_{i,j} | average temperature on cell j, serpentine i (K) |

T_{f,i,j} | average fluid temperature corresponding to cell j, serpentine i (K) |

T_{in,i,j} | average inlet temperature corresponding to cell j, serpentine i (K) |

T_{out,i,j} | average outlet temperature corresponding to cell j, serpentine i (K) |

V | velocity of fluid in the system (m·s^{−1}) |

DC-IR | DC internal resistance (Ω) |

Greek letters | |

β | bias rate of the flow in serpentine pipes |

δ | ratio of the section area of the main pipe to the total section area of serpentine pipes |

λ | frictional loss coefficient of pipes |

μ | dynamic viscosity (Pa·s) |

ν | kinematic viscosity (m^{2}·s^{−1}) |

ξ | local loss coefficient of pipes |

ρ | density (kg·m^{−3}) |

Subscripts | |

a | main pipe |

b | serpentine pipe |

diff | difference |

s | steel shell of battery |

f | fluid |

i | index of the serpentine pipe in one module |

j | index of the cell along one serpentine line |

max | maximum |

pvc | Polyvinyl chloride layer of the battery |

pad | thermal pad of Silicon layer |

total | total |

turn | turning of pipes |

wall | wall of pipes |

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**Figure 3.**Liquid-cooling system. (

**a**) A 3D view of the two cooling modules, including the in/out rubber pipes connected in parallel; (

**b**) schematic of the cooling module; (

**c**) schematic side view of the cooling module and the battery cell; (

**d**) cross-sectional view of the serpentine pipe (with internal walls).

**Figure 4.**A single cell heat transfer model. (

**a**) Schematic of the heat transfer pass of a single cell (

**b**) presented as heat resistance.

**Figure 7.**Geometry models: (

**a**) battery cells with a cooling plate; (

**b**) single-battery heat transfer model (grid level 1).

**Figure 8.**Sectional view of the grids at the mid-symmetry plane: (

**a**) grid level 1; (

**b**) grid level 4; (

**c**) grid level 7.

**Figure 9.**Grid independence. (

**a**) Nusselt number, pressure loss, and maximum temperature calculated by different grid systems; (

**b**) comparison of the Nusselt number and pressure loss of the theoretical and numerical results.

**Figure 10.**The effect of δ on several parameters, at Q = 5 L/min, N = 0: (

**a**) β and Δp; (

**b**) T

_{max}and T

_{diff}.

**Figure 11.**The effect of N on several parameters at Q = 5 L/min, δ = 0.973: (

**a**) β and Δp; (

**b**) T

_{max}and T

_{diff}.

**Figure 12.**The temperature field at the worst working condition with an effective current at 25 A and δ = 0.973, Q = 5 L/min, and N = 6: (

**a**) batteries; (

**b**) coolant.

**Figure 13.**Battery pack with a cooling plate under a test: (

**a**) the battery pack’s internal structure and the cooling plate in details; (

**b**) the thermocouple placement and fixing method.

**Figure 15.**Temperature test result on a vehicle: (

**a**) temperature curve during the complete test process; (

**b**) temperature histogram of 20 thermocouples after temperature equilibration.

**Figure 16.**Test conditions and test results of the temperature on vehicles: (

**a**) road spectrum, transient current spectrum, and RMS current over ten minutes; (

**b**) ambient temperature inside the battery pack temperature trends from six sensors, and temperature difference curves.

Technology Readiness Level | Air | Liquid | PCM | HP | Emerging |
---|---|---|---|---|---|

TRL 9—Complete industrialization | Ο | Ο | |||

TRL 8—Optimization | Ο | Ο | |||

TRL 7—Entry into production | Ο | Ο | |||

TRL 6—Application development in product | Ο | Ο | Ο | Ο | |

TRL 5—Verification in production equipment | Ο | Ο | Ο | Ο | |

TRL 4—Verification in representative prototype | Ο | Ο | Ο | Ο | |

TRL 3—Verification in the laboratory | Ο | Ο | Ο | Ο | Ο |

TRL 2—Feasibility and profitability analysis | Ο | Ο | Ο | Ο | Ο |

TRL 1—Investigation of the fundamentals of technology | Ο | Ο | Ο | Ο | Ο |

Items | Cell | L5 Module | Pack |
---|---|---|---|

Number of cells | 1 | 5 | 240 |

Normal Voltage (V) | 1.2 | 6 | 288 |

Capacity (Ah) | 6 | 6 | 6 |

Energy (Wh) | 7.2 | 36 | 1728 |

DC-IR (mΩ) | 2.5 | 12.5 | 600 |

Discharge power ^{1} (W) | 185 | 925 | 40,000 ^{2} |

^{1}25 °C, 50% SOC, 10 s.

^{2}The total power of the battery pack is smaller than the theoretical value because of the consistency of the battery cells.

Material | Density kg/m^{3} | Specific Heat Capacity J/(kg·K) | Thermal Conductivity W/(m·K) |
---|---|---|---|

50% ethylene glycol | 1082 | 3300 | 0.4 |

Cell material | 3270 | 1537 | 15.1(Axial)/1(Radial) |

Surface steel | 7870 | 448 | 80 |

Polyvinyl chloride film | 1140 | 1670 | 0.2 |

Thermal silica gel pad | 2600 | 2190 | 1.5 |

Aluminum alloy cooling plate | 2700 | 903 | 237 |

Grid level No. | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|

Number of grids | 3698 | 9850 | 29,978 | 47,426 | 79,335 | 159,777 | 258,299 |

Number of prism layers | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

Group | 1 ^{1} | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
---|---|---|---|---|---|---|---|---|---|---|---|

Heat | I_{rms} (A) | 25 | 25 | 25 | 25 | 30 | 30 | 30 | 30 | 35 | 35 |

Power (W) | 375 | 375 | 375 | 375 | 540 | 540 | 540 | 540 | 735 | 735 | |

Rate (W/m^{3}) | 30,791 | 30,791 | 307,91 | 30,791 | 44,339 | 44,339 | 44,339 | 44,339 | 60,350 | 60,350 | |

Coolant | T_{inlet} (°C) | 25 | 25 | 30 | 30 | 25 | 25 | 30 | 30 | 25 | 30 |

Q (L/min) | 5 | 10 | 5 | 10 | 5 | 10 | 5 | 10 | 10 | 10 |

^{1}Group NO.1 was described in detail as an example.

Test Order | Boundary Conditions | Simulation | Experiment | Judgment | ||||
---|---|---|---|---|---|---|---|---|

I_{rms} (A) | T_{inlet} (°C) | Q (L/min) | T_{max} (°C) | T_{diff} (°C) | T_{max} (°C) | T_{diff} (°C) | ||

1 ^{1} | 25 | 25 | 5 | 37.6 | 3.0 | 38.7 | 3.0 | Pass |

2 | 25 | 10 | 36.8 | 2.8 | 38.3 | 2.9 | Pass | |

3 | 30 | 5 | 41.1 | 2.7 | 42.3 | 2.6 | Pass | |

4 | 30 | 10 | 40.2 | 2.1 | 41.3 | 2.4 | Pass | |

5 | 30 | 25 | 5 | 40.4 | 3.5 | 41.3 | 3.2 | Pass |

6 | 25 | 10 | 40.2 | 2.9 | 41.1 | 2.8 | Pass | |

7 | 30 | 5 | 43.9 | 3.1 | 45.1 | 2.9 | Pass | |

8 | 30 | 10 | 43.2 | 2.5 | 44.8 | 2.7 | Pass | |

9 | 35 | 25 | 10 | 45.3 | 3.9 | 46.3 | 4.1 | Fail |

10 | 30 | 10 | 48.6 | 4.0 | 49.7 | 3.8 | Fail |

^{1}The process and results of the NO.1 experiments are described in detail as examples.

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## Share and Cite

**MDPI and ACS Style**

Chu, A.; Yuan, Y.; Zhu, J.; Lu, X.; Zhou, C. The Design and Investigation of a Cooling System for a High Power Ni-MH Battery Pack in Hybrid Electric Vehicles. *Appl. Sci.* **2020**, *10*, 1660.
https://doi.org/10.3390/app10051660

**AMA Style**

Chu A, Yuan Y, Zhu J, Lu X, Zhou C. The Design and Investigation of a Cooling System for a High Power Ni-MH Battery Pack in Hybrid Electric Vehicles. *Applied Sciences*. 2020; 10(5):1660.
https://doi.org/10.3390/app10051660

**Chicago/Turabian Style**

Chu, Aihua, Yinnan Yuan, Jianxin Zhu, Xiao Lu, and Chenquan Zhou. 2020. "The Design and Investigation of a Cooling System for a High Power Ni-MH Battery Pack in Hybrid Electric Vehicles" *Applied Sciences* 10, no. 5: 1660.
https://doi.org/10.3390/app10051660