The 424 battery cooling model

Amandine Martin

Project 424 100% electric hypercar needs an optimum cooling system to fit with its high-performance lithium-ion batteries.

This study is part of a collaboration between PERRINN and SEGULA Technologies.

In the framework of my mission for the engineering Group SEGULA Technologies, I have taken care of the 424 battery cooling system for 6 months. The aim was to choose the best suited geometry and the most efficient cooling fluid as well as creating a model that will be implemented in the 424 driving simulation to display the battery temperature in live timing. Discover below all the details of the resourceful approach lying behind this extensive study.

The objective is to study the performance of the battery cooling system. The architecture of the system is as follows: the fluid passes through 84 channels, installed along each battery module, 10 in number; each module being composed of 36 cells, of the Lithium Ion type.

Representation of the passage of coolant through a module/cell/perforation

Numerical simulations

For this, we produce numerical models in 2D, 3D and 1D.

Through the models, we test the influence of the configuration of the modules (series or parallel) in addition to studying the thermal behavior of the cells:

2D model

The first 2D model aims to test the fluid, i.e. to study its temperature rise along the circuit in order to size the system. The cells are not studied here.

The 2D modeling looks like this:

The flux imposed on the inner walls is slightly overestimated. It was averaged on the basis of the heat emitted by a module over one lap of the circuit. All other walls are considered adiabatic. At the circuit inlet, the fluid is injected with an inlet temperature set at 15°C and a flow rate of 160 L/min.

2D results

Evolution of the temperature for a series configuration – Water

Water is therefore a better cooling fluid. The temperature difference between the outlet and the inlet is the smallest.

The temperature differences are explained by different thermal properties for the two fluids.

Simplified 3D model

On a two-cell model with two symmetries, we study the temperature reached by the cells as a function of the flow.

Numerical model and imposed conditions: inlet temperature set at 15°C and 708 kW/m3 in volume flow applied to each cell (heat flow from the same data as the 2D model to remain consistent).

Simplified 3D model results

Results in steady state:

Temperature gradient for water and Opticool-H at 160 L/min

A maximum temperature of 70°C for the cells imposes demanding specifications. For the moment, the first results show that it is necessary to improve our system because this temperature is too often approached/exceeded. However, the results are obtained in a steady state.

The 1D model that we will develop later will give us more information because the simulation will be unsteady. We will thus be able to evaluate the temperature of the cells according to the position where 424 is on the circuit.

Detailed 3D model

The last step before approaching the 1D model is to determine the transfer coefficient h, representative of the performance of the cooling system.

This coefficient was difficult to determine due to the lack of formulas and literature. There is no documentation to calculate an equivalent coefficient for several pipes in parallel.

A more detailed 3D model is designed. A double symmetry is no longer valid due to the more complex geometry. Only one is applied.

Limit condition: surface heat flux applied to each part of inter-cell aluminum:

Detailed 3D model results

Temperature of the contact surfaces and the contour of the perforations in steady state

The calculation of this coefficient by the software is very approximate. Based on the reference temperature Tfluid, this makes the coefficient very dependent on this temperature:

By averaging, the global coefficients representing all the perforations are obtained:

The q value of the flux varies for each element of the mesh, which leads to strong variations. It is therefore difficult to determine the most representative coefficient of the cooling performance of the battery cells.

1D model

The last step is to create a 1D model taking into account all the elements of the system in order to be able to follow the temperature of the cells according to the portion of the circuit where 424 is located :

Theoretical 1D model

1D model (serial configuration)

1D model (parallel configuration)

1D model results

Comparison of the two fluids on the two configurations

As expected, water is a better coolant and the parallel configuration seems more optimized.

The cooling system seems to be well dimensioned and meets the maximum temperature criterion which is 70°C maximum.

Reduced model results

As we want to display the temperature of the battery in the 424 Unity driving simulation, we need to create a specific model for this purpose. Indeed, the "Unity" software requires writing code in C# language, it is therefore impossible to simply provide the simulation file.

This is why through the theoretical formulas, a "reduced" model has been set up.

Module 10 Temperature Profile Comparisons for Different Models - Series Configuration

A difference is notable between the curve of the 1D model and the theoretical curve for water. This is in particular due to the simulation software. Indeed, the latter adapts the time step dynamically to prevent the simulation from diverging. Thus, the reduced model having been produced with a fixed time step (0.5s), the differences are therefore created naturally over the course of the simulation.

However, this reduced model curve follows more or less the behaviour of the 1D model curve. This gives an idea of the temperatures obtained.

The work carried out focused on the analysis of the temperature behavior of the battery of the 424 hypercar on the Nürburgring circuit. For this, 2D, 3D and 1D digital models have been set up.

The 2D model made it possible to evaluate the performance of the two fluids envisaged (water and Opticool-H) to circulate around the modules. Then the 3D models made it possible to estimate the exchange coefficient between the fluid and the cells in order to be implemented later in the 1D software. Finally, the 1D model coupled with the data provided by PERRINN made it possible to obtain temperature evolution profiles as a function of time, taking into account the layout of the Nürburgring.

Despite the assumptions of the different models, it was still possible to conclude that the cooling system is well dimensioned. The system would be able to keep a cell temperature below the set 70°C.