Longhorn Racing Cell Spacing Optimization

In thermals, one of the main things we drive on the car is the cell spacing within our battery segments. This has a direct impact on overall battery spaceclaim and packaging in the car. However, more critically, cell spacing has a great impact on our pressure drop and cooling effectiveness, which heavily drives fan selection.

To drive cell spacing, I used the staggered Zukauskas Flow Across a Bank of Tubes correlation as it is representative of how we cool cylindrical cells. With this correlation, given an inlet velocity, transverse spacing, longitudinal spacing, segment s&p count, and ambient conditions, a pressure drop and average convection coefficient for the battery segments can be determined.

Using the equations, tables, and graphs that define the staggered Zukauskas correlation, I was able to create a three layered optimizer to find the optimal cell spacing and inlet velocity to maximize the following value: 

This value represents the overall cooling effectiveness accounting for fan power consumption. Cooling is improved with a higher convection coefficient, but we want to do so at minimal fan power consumption, which is equivalent to the fan’s flow rate times pressure drop, which is proportional to the value in the denominator.

Using the equations, I was able to map out (at a fixed velocity), how the convection coefficient, pressure drop, and optimized value change as cell spacing changes. As can be seen, h increases with a tighter transverse spacing, although this comes at the cost of a higher pressure drop and less air heat capacity (leading to hotter air, which would ineffectively cool cells towards the back of the segment).

This results in our optimized value performing best when the transverse pitch is maximized. Although longitudinal pitch does seem to suffer as it is brought closer, the change in pressure drop as longitudinal pitch changes is small and can instead be driven by battery packaging concerns instead.

When building the optimizer to pick out the best cell spacing and inlet velocity, I not only designed it to maximize the above value, also ensured that the selected configuration adequately removed the heat generated from all cells in the pack. I did this with an iterative approach that determined how the air temperature changed as it moved through the segment and calculated the subsequent heat rejection per cell.

Given our segment configuration of 13s5p, which looked like the below, I had to set up the bounds transverse spacings for optimization. 

Our longitudinal spacing was fixed at 11.8mm due to spaceclaim. Since the smallest fan we could get with this configuration was 92mm, I looked at if the pressure drop was manageable with this width, targeting a value of 500 pa or lower: 

Given this extreme pressure drop, I was not going to pursue a 92mm fan. The next size up was up to a 120mm fan. After talking with battery, body, and dynamics members over impacts of spacing on the rest of the car, such as passing SES rules, center of gravity impacts, and doing a tolerance stackup, I had a new bound for my transverse spacing. These were the much more managable results, alongside the heat dissipated and air temperature per segment row: 

From here, next step is to run fan selection, optimizing for weight and power consumption. Since the total width of the segment in this configuration is 109mm, we can still use a 92mm fan with this setup. Since I already know the optimized inlet velocity (1.7m/s), translating results for a 92mm fan, and the required pressure drop, all I have to do is find a fan that can supply 53.5 CFM at 461 pa by analyzing their fan curves.

Here is the GitHub to my cell spacing optimization programs, called CellStaggeredSpacing.py and CellStaggeredSpacingRunner.py. Reach out to me if you have any questions. 

https://github.com/AadiVasa1/Thermal_Modeling