# Parametric Optimisation of a Direct Liquid Cooling–Based Prototype for Electric Vehicles Focused on Pouch-Type Battery Cells

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions in densely populated areas, in recent years HEV/EV vehicles have been one of the global benchmark topics in the mobility sector [1]. Considering batteries as the energy source, these technologies enable 100% zero-emission operation. Today, due to their characteristic large density, high discharge capacity, and low maintenance, lithium-ion–based batteries are the reference energy storage technology in the electric vehicle sector.

## 2. Numerical Model Description

#### 2.1. Physical Model

#### 2.2. Simulation Model Geometry

#### 2.3. Battery Modelling

_{gen}= Q

_{irr}+ Q

_{rev}. Where Q

_{gen}is the total heat generation, Q

_{irr}is the irreversible heat, and Q

_{rev}is the reversible heat. The irreversible heat generation, also referred as Joule effect, is represented by the equation Q

_{irr}= I

^{2}R

_{int}. Where I is the current (A) and R

_{int}the internal resistance of the cell (Ω), which depends on the temperature (T) and the state of charge (SOC). On the other hand, the reversible heat generation is developed by the insertion and disinsertion of lithium ions into the electrodes (anode and cathode). This generation is based on the electrochemical reactions that take place when discharging and charging the lithium-ion cells, reactions that create a variation in the entropic level of the system. This generation is represented by equation Q

_{rev}= IT dE

_{OCV}/dT. Where I is the current (A), T is the temperature (K), and dE

_{OCV}/dT is the variation of the open circuit voltage with the temperature (V/K).

_{OCV}/dT).

^{2}K was defined on the boundary surfaces of the battery cell [20,21], which was experimentally validated.

#### 2.4. Mesh Independence

^{2}K was set. As Figure 5 presents, both maximum temperature and pressure drop curves are stabilised with a mesh of 4,778,025 elements. The results variation maintains below 1% when the elements where increased to 8743816. Thus, it was concluded that the results are independent for the model of 4,778,025 elements [23,24].

## 3. Flow Pattern Design Selection

^{2}. This was a conditioning parameter to define the same heat absorption capacity with the same fluid volume in all flow pattern designs.

#### 3.1. Boundary Conditions

#### 3.2. Results and Discussion

_{max}), temperature homogeneity (ΔT), and the pumping power consumption related to the auxiliary system (P

_{h}) were defined as the output variables. Figure 7 presents the steady state results of each case at flow rates of 0.1, 0.2, 0.4, 0.8, and 1.6 L/min.

**Figure 7.**Geometry comparison results of (

**a**) battery cell maximum temperature (T

_{max}), (

**b**) temperature homogeneity (ΔT), and (

**c**) the pumping power consumption related to the auxiliary system (P

_{h}) at different flow rate.

## 4. Design Optimisation

#### 4.1. Parametrisation of the Geometry

_{f}), the number of cooling channels (N

_{c}), the number of inlet and outlet distributors (N

_{d}), and the flow rate (Q). Figure 9 presents each parameter definition.

#### 4.2. Output Variables

_{max}), temperature homogeneity (ΔT), system volumetric energy density (VED), and system power consumption (P

_{h}). As it is presented in Figure 11, the first two variables (T

_{max}and ΔT) were related to the cell level design to analyse how the strategy controls the thermal behaviour of the battery system. Then, scaling up to a battery module of 24 battery cells, the impact of each cooling strategy on the system volumetric energy density (VED) and system power consumption (P

_{h}) were analysed.

#### 4.3. Optimisation Process Definition

_{f}, N

_{c}, N

_{d}, and Q were determined. To investigate the importance of the defined variables on the output results of the full factorial design, analysis of variance (ANOVA) was employed. This is, a statical model that evaluates the importance of the defined factors by comparing the response variable means at the defined factor levels. To properly develop the regression equations, all variations up to the second order of interaction between the defined factors were first analysed. Then, the most relevant interactions were selected by defining a significance level of 0.05. Once the most influential factors conditioning the output variable were selected, the factorial design was analysed again, and the ANOVA results were extracted. With this information, the regression coefficients were calculated, and regression equations were developed for each output variable. To analyse the reliability of these regression model, values of R

^{2}(Adequate), R

^{2}(Predicted), and R

^{2}(Adjusted) were examined, and the residual normal plots were presented. After the validation, the optimum case was selected considering the composite desirability function, where the optimum case selection process guideline was defined assigning specific weight and importance values for each of the proposed output variables.

#### 4.4. Results and Analysis

_{max}and ΔT, and module level VED and Ph output variable results can be observed for all the possible variations between H

_{f}, N

_{c}, N

_{d}, and Q.

_{max}), cell surface temperature homogeneity (ΔT), system volumetric energy density (VED), and system power consumption (P

_{h}):

_{max}= 27.6 + 0.28 H

_{f}− 0.38 Q

_{f}− 0.014 N

_{c}+ 0.022 N

_{d}− 0.146 Q + 0.008 H

_{f}N

_{d}+ 0.01 H

_{f}Q

_{f}

_{h}= 0.364 − 0.316 H

_{f}+ 0.039 N

_{d}+ 0.302 Q − 0.031 H

_{f}N

_{d}− 0.261H

_{f}Q + 0.035 N

_{d}Q

^{2}(Adequate), R

^{2}(Predicted), and R

^{2}(Adjusted) were analysed. These are significance indexes that present the adequate quality, the quality of the predicted regression models, and the quality of the models after adjustment, respectively. Considering results from Table 3, index values agree for T

_{max}, ΔT, VED, and P

_{h}. Index values for VED were 100% in all R

^{2}cases. This result means that there is not variability on results, as the volumetric energy density VED is the only one proportional to a single parameter (H

_{f}). Therefore, the quality and the correlation of these values demonstrates the reliability of the regression models.

^{2}index values, it is important to make sure that the results of the residuals for each response are consistent. Figure 12 presents the normal residual plots for each output variable. As it is shown the residuals are normally distributed, which means that there is a good agreement between the predicted and actual values. Figure 12c corroborates the interpretation made with R

^{2}index values for the volumetric energy density VED. Therefore, it was confirmed that VED was uniquely and exclusively proportional to H

_{f}. These results demonstrated that the proposed regression models could predict adequately the variability of the output parameters. The reliability of the regression models is therefore justified.

_{f}) and the inlet flow rate definitions (Q) were the main parameters that influences the maximum temperature of the cell body. This means that the influence of the number of channels (N

_{c}) and distributors (N

_{d}) for T

_{max}is negligible. However, the impact of those input parameters is appreciated on the variability of the temperature homogeneity of the battery cell surface (Equation (2)). With a higher N

_{c}number, the temperature difference of the cell surface increases. In contrast, the effect of N

_{d}is the opposite. Therefore, the results recommended to decrease the number of distributors and increase the number of channels to improve the temperature homogeneity of the battery cell surface.

_{f}. Therefore, analysing the results, the objective of developing systems with high volumetric energy density will be achieved by reducing this parameter H

_{f}as much as possible. In this case, the minimum value of 1 mm for H

_{f}is the one that gives the best results of volumetric energy density.

_{h}, it is observed that H

_{f}, Q, and the interaction between them (H

_{f}Q) have more impact than the N

_{d}and related interactions. The power consumption of the system is based on the pressure drop defined by the fluid; therefore, H

_{f}and Q influence is coherent. The pressure drop is related in a quadratic way by the velocity of the fluid [25]. Thus, to decrease the power consumption of the system lower fluid velocity profiles were recommended. Studying the influence of the parameters N

_{c}and N

_{d}it can be observed that the rise in the number of channels and distributors increases the power consumption of the system. Therefore, it is concluded that the quantity of these components should be minimised for achieving the desired fluid distribution to maintain the lowest impact on the power consumption of the system.

_{max}, ΔT, VED, and P

_{h}was implemented. This function calculates, according to the desirability values defined for each output variable, the optimal case within the range of the proposed two-level full factorial model results.

_{max}and ΔT. In this case, the optimum values to ensure the best thermal performance were H

_{f}= 1 mm, N

_{c}= 9, N

_{d}= 10, and Q = 0.4 L/min. This configuration maintains the highest volumetric energy density at the expense of a considerable increase in the P

_{h}output parameter. Therefore, VED and P

_{h}were implemented with a lower weight impact and the same importance on the composite desirability function to develop a multi-objective optimisation that minimises the power consumption of the strategy and maximises the volumetric energy density of the system. For this case, the corresponding values of the design variables were H

_{f}= 1 mm, N

_{c}= 9, N

_{d}= 10, and Q = 0.13 L/min. Maintaining the maximum volumetric energy density of 279.7 Wh/L, this configuration implies an increase in the maximum temperature from 27.02 °C to 27.72 °C, and the temperature difference was increased by 0.3 °C. However, the power consumption of the system was decreased by 90% from 1.16 W to 0.11 W.

## 5. Conclusions

- At flow rates below 0.4 L/min, the flow distribution channels defined on the U-shape design improve the fluid dynamical aspect of the cooling strategy, maintaining the highest thermal performance of the battery cell without increasing the power consumption. It was therefore selected to develop the parametric optimisation process.
- Developed surrogate models presented that the most critical parameters that influence the output variable results were the height of the fluid channel (H
_{f}) and the flowrate definition (Q), which are directly related to the fluid local velocity. - The number of channels (N
_{c}) increases the power consumption of the system (P_{h}) while decreasing the thermal heterogeneity of the battery cell (ΔT). Therefore, it is recommended to decrease the number of channels remaining the thermal distribution of the cell within the optimal range. - The number of distributors (N
_{d}) increases the power consumption of the system (P_{h}) and the thermal heterogeneity of the battery cell (ΔT). However, a minimum number of components to adequately distribute the inflow and outflow are necessary, thus avoiding hot spots in the system. - The proposed parametric optimisation defined the optimum design of the DLC strategy that ensures the optimal relationship among T
_{max}, ΔT, VED, and P_{h}. The corresponding values of the design parameters were H_{f}= 1 mm, N_{c}= 9, N_{d}= 10, and Q = 0.13 L/min. This design case maintains T_{max}at 27.72 and ΔT at 0.65 with the maximum VED value and reducing P_{h}by 90%.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ANOVA | analysis of variance |

CFD | computational fluid dynamics |

DLC | direct liquid cooling |

DoE | design of experiments |

ECM | equivalent circuit model |

EV | electric vehicle |

HEV | hybrid electric vehicle |

HP | heat pipes |

HPPC | hybrid pulse power characterization |

ILC | indirect liquid cooling |

LC | liquid cooling |

NMC | nickel manganese cobalt |

OCV | open circuit voltage |

PCM | phase change material |

SOC | state of charge |

TEC | thermoelectric material |

UDF | user-defined functions |

VED | volumetric energy density |

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**Figure 3.**Battery cell model validation with experimental (

**a**) voltage and (

**b**) surface temperature distribution in a range of 100–20% SOC of a 1C discharge test.

**Figure 4.**Battery cell model heat generation validation with experimental heat generation information (80–20% SOC range).

**Figure 5.**Mesh independence analysis with the maximum temperature of the battery cell (°C) and pressure drop (kPa).

**Figure 8.**Battery cell surface temperature distribution at 0.4 L/min of flow rate for (

**a**) U-shape, (

**b**) convex, (

**c**) honeycomb, and (

**d**) airfoil designs.

**Figure 10.**Battery cell surface temperature distribution for (

**a**) a cooling design without channels and (

**b**) a cooling design without distributors.

**Figure 12.**Residual normal plots for the output variables of (

**a**) T

_{max}, (

**b**) ΔT, (

**c**) VED, and (

**d**) P

_{h}.

Property | Battery Cell | Clamps | Dielectric Fluid |
---|---|---|---|

Material | Battery cell | Aluminium | Mineral oil |

Kinematic Viscosity (mm^{2}/s) | - | - | 4.3 |

Heat Capacity (J/kgK) | 1306 | 871 | 2130 |

Thermal conductivity (W/mK) | x,y: 17.9/z: 0.65 | 202.4 | 0.135 |

Density (kg/m^{3}) | 2183 | 2719 | 774 |

Resistivity (MΩm) | - | - | >5 × 10^{6} |

**Table 2.**The corresponding simulation cases of the two-level full factorial design and the output variable results of each case.

N° Simulations | H_{f} (mm) | N_{c} | N_{d} | Q (L/min) | Cell Level | Module Level | ||
---|---|---|---|---|---|---|---|---|

T_{max} (°C) | ΔT (°C) | VED (Wh/L) | P_{h} (W) | |||||

1 | 3 | 9 | 30 | 0.40 | 27.52 | 0.51 | 248.70 | 0.109 |

2 | 1 | 9 | 30 | 0.40 | 27.00 | 0.37 | 279.78 | 1.455 |

3 | 3 | 3 | 30 | 0.40 | 27.51 | 0.56 | 248.70 | 0.095 |

4 | 1 | 3 | 30 | 0.40 | 26.98 | 0.38 | 279.78 | 1.301 |

5 | 3 | 9 | 10 | 0.40 | 27.56 | 0.47 | 248.70 | 0.076 |

6 | 1 | 9 | 10 | 0.40 | 27.02 | 0.35 | 279.78 | 1.162 |

7 | 3 | 3 | 10 | 0.40 | 27.51 | 0.49 | 248.70 | 0.069 |

8 | 1 | 3 | 10 | 0.40 | 26.98 | 0.36 | 279.78 | 1.060 |

9 | 3 | 9 | 30 | 0.13 | 28.36 | 0.78 | 248.70 | 0.009 |

10 | 1 | 9 | 30 | 0.13 | 27.73 | 0.68 | 279.78 | 0.131 |

11 | 3 | 3 | 30 | 0.13 | 28.31 | 0.84 | 248.70 | 0.007 |

12 | 1 | 3 | 30 | 0.13 | 27.7 | 0.71 | 279.78 | 0.118 |

13 | 3 | 9 | 10 | 0.13 | 28.37 | 0.73 | 248.70 | 0.006 |

14 | 1 | 9 | 10 | 0.13 | 27.72 | 0.65 | 279.78 | 0.115 |

15 | 3 | 3 | 10 | 0.13 | 28.27 | 0.76 | 248.70 | 0.005 |

16 | 1 | 3 | 10 | 0.13 | 27.69 | 0.67 | 279.78 | 0.103 |

**Table 3.**Values of R

^{2}(Adequate), R

^{2}(Predicted), and R

^{2}(Adjusted) for the output variables T

_{max}, ΔT, VED, and P

_{h}.

R^{2} (Adequate) | R^{2} (Predicted) | R^{2} (Adjusted) | |
---|---|---|---|

T_{max} | 90.32% | 85.34% | 88.84% |

ΔT | 99.68% | 99.00% | 99.47% |

VED | 100% | 100% | 100% |

P_{h} | 99.59% | 98.37% | 99.23% |

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**MDPI and ACS Style**

Larrañaga-Ezeiza, M.; Vertiz Navarro, G.; Galarza Garmendia, I.; Fernandez Arroiabe, P.; Martinez-Aguirre, M.; Berasategi Arostegui, J.
Parametric Optimisation of a Direct Liquid Cooling–Based Prototype for Electric Vehicles Focused on Pouch-Type Battery Cells. *World Electr. Veh. J.* **2022**, *13*, 149.
https://doi.org/10.3390/wevj13080149

**AMA Style**

Larrañaga-Ezeiza M, Vertiz Navarro G, Galarza Garmendia I, Fernandez Arroiabe P, Martinez-Aguirre M, Berasategi Arostegui J.
Parametric Optimisation of a Direct Liquid Cooling–Based Prototype for Electric Vehicles Focused on Pouch-Type Battery Cells. *World Electric Vehicle Journal*. 2022; 13(8):149.
https://doi.org/10.3390/wevj13080149

**Chicago/Turabian Style**

Larrañaga-Ezeiza, Manex, Gorka Vertiz Navarro, Igor Galarza Garmendia, Peru Fernandez Arroiabe, Manex Martinez-Aguirre, and Joanes Berasategi Arostegui.
2022. "Parametric Optimisation of a Direct Liquid Cooling–Based Prototype for Electric Vehicles Focused on Pouch-Type Battery Cells" *World Electric Vehicle Journal* 13, no. 8: 149.
https://doi.org/10.3390/wevj13080149