Here we illustrate how we designed and tested our fireproof casing.

There are two physical phenomenon at play:

- lithium ion cell providing energy to the casing

- the casing which radiates energy as it becomes hotter

# Theoretical considerations

## Energy released by a cell

A significant portion of the total energy released during thermal runaway is carried away by the vented gases and ejected particles/ejecta. Simulations showed that for an 18650 LG cell, 78.3% of the total energy (74.9 kJ) was released through the ejecta and vented gases during thermal runaway.

References:

Intersting conversion:

75kJ = 20Wh

## Casing thermal absorption

We make the following hypothesis:

- all the energy released by a cell gas is transmitted to the casing (which is not true if we vent the fumes outside the casing)

- this energy transfert is instantaneaous

To compute the temperature elevation (ΔT) of a volume of aluminum when given a certain amount of energy (E), we can use the following formula:

Where:

ΔT is the change in temperature (in °C or K)

E is the amount of energy supplied (in Joules, J)

m is the mass of the aluminum (in kg)

c is the specific heat capacity of aluminum (897 J/kg°C)

## Casing radiation

To calculate the energy radiated by aluminum surface at a specific temperature, we can use the Stefan-Boltzmann law.

The rate of energy radiated (E) by a black body is given by:

Where:

ε is the emissivity of the surface (dimensionless)

σ is the Stefan-Boltzmann constant (5.67 x 10^-8 W/m^2K^4)

A is the surface area (m^2)

T is the absolute temperature (K)

For a perfect black body, the emissivity ε = 1. However, for real surfaces like aluminum, the emissivity is less than 1.From the search results:

- For unoxidized aluminum at 25°C (298K), the emissivity ε = 0.02

- For oxidized aluminum at 199°C (472K), the emissivity ε = 0.11

# Interval of propagation

From our observations, it takes a certain amount of time between each TR of cells. This is understandable also when we think that only 25% of the cell energy is transfered to the honeycomb (the rest being ejected as gas).

Heat is then transfered through the plastic by heat diffusion and through the tabs. Both are heat conduction so we can use Fourier’s law, the heat transfert in (W) is:

where k is the thermal conductivity and A is the cross section, (w) is the distance between cells centers.

For the diffusion through plastic:

where L is the length of the cell and D its diameter

From this reference we know that the TR has high probability of starting if

m is the mass of a cell (in kg).

c is the specific heat capacity of a NMC cell (1040 J/kg°C) from here

References:

# Experimental testing

We first step was to validate the thermal propagation between the cells through the spacer.

The we measured the heat transfert through the contacts

This gave us the right parameters to determine a time between cell firing. Then we moved on with real test on a aluminum casing using various number of cells (from 4 to 90).

The temperatures measured on the casing where matching the model giving us the proper way to design the casing that can withstand a complete thermal runaway of the pack.