Battery Pack Cooling

Due to the internal resistance of battery cells, they produce heat when a current is applied to them. We must dissipate this heat somewhere to stop the cells from heating up.

Several methods for cooling the pack have been discussed and some were tested.

We selected Forced Air Cooling for our pack.

With this selection, the next challenge is to figure out how much air we need to move through the pack, and how we will move that air through.

We will not be doing simulation of any of our battery pack cooling due to lack of experience and lack of time, but will be doing hand calcs and basic Python modelling.

How to Move Air

The obvious answer here is to use a fan, but which fan to use and understanding the specifications is a whole other beast.

Let's start with the manufacturer specs.

A fan manufacturer (at least in the PC case fan world) will generally give 2 specifications for their fans:

1. (Maximum) Static Pressure (usually in mmH2O)
   1. When amount of pressure generated when there is no airflow
   2. Ex - fan sitting horizontally on a table with the air being pushed in to the table
2. (Maximum) Airflow (usually in CFM - cubic feet per minute, or in m3/h - meters cubed per hour)
   1. When there is no restriction to the airflow, this is the amount of air that the fan will move
   2. Ex - fan sitting on a table with nothing in front and nothing behind

Neither of these specifications are useful on their own to tell us how much air we will be moving through the pack, as we will have both airflow and pressure. So, we will be somewhere in the middle of the Static Pressure - Airlfow (P-Q) curve of the fan. This curve is different for every fan, and changes based on blade design, frame design, and many other factors. Reputable fan manufacturers will either publish their P-Q curves or will be able to provide one upon request. If a manufacturer cannot supply a P-Q curve, I would not buy from them as it may be a sign that they do not completely understand their fans (apparently some PC case fan manufacturers are in this boat). For more info on the P-Q curves, see the following links:

Resources - P-Q Curves of Fans

P-Q Curves explanation and measurement principles: http://www.arx-group.com/pq.html

P-Q Curves of some Noctua fans: https://noctua.at/en/nf-a12x25-performance-comparison-to-nf-f12-and-nf-s12a

Google spreadsheet comparing P-Q curves of various computer fans (made by the guy in the following youtube video): 

YouTube Video explaining some of the P-Q curves of fans, and manufacturers: 

3rd party testing of some P-Q curves of many fans - NF-F12 iPPC 3000: http://www.coolingtechnique.com/recensioni/air-cooling/ventole/1532-noctua-ippc-nf-f12-e-nf-a14-3000rpm-pwm-tabelle-prestazionali-analisi-spettrometrica-e-video-in-hd.html?start=1

Fans in Series and Parallel

Fans in parallel (side by side) will double the airflow at a given pressure.

Fans in series (stacked) will double the pressure at a given airflow.

https://www.sodeca.com/Content/img/en/InformacioTecnica_01_EN.pdf

We will have multiple fans in parallel to cover to whole width of the battery box, but might have more if required.

Pressure in our application

We are interested in finding the amount of pressure that pulling air through our battery modules adds to the system. Once this is figured out, then we can figure out the airflow required with some heat calculations, and then move on to choosing a proper fan for the battery box.

We measured the airflow of our Noctua IPPC fan when pulling air through 1 or our prototype modules (see this page). We will be contacting Noctua to obtain a more accurate P-Q curve for their fan.

Converted to CFM using this online conversion tool: https://www.convertunits.com/from/cubic+m/hr/to/cfm

So it seems as if there is not much added static pressure by introducing a module into the airflow path. There was more room for the air to move over the top of the modules than there will be in the final pack, but this gives us a good baseline. We should test again, but forcing the air through the cells with extra airflow guides.

I presume that by forcing the air through more modules, the static pressure that must be overcome will be added. The easiest way to figure this out would be to test it with some more modules in series, but some calculations may also be possible.

Anything in the airflow path is essentially an impedance to said airflow, and can be thought of as a resistor in an electrical circuit, with the current being the airflow.

Have a look at the airflow page: http://www.arx-group.com/airflow1.html for an explanation on system impedance, which is sort of what I was trying to calculate here.

Required Airflow

Now we need to figure out how much air we need to move through the battery box. We will be using this page as a reference for these calculations: http://www.arx-group.com/airflow.html

The first step is to figure out how much heat is produced in the battery system. See this page for the estimations of the amount of heat produced. Our total pack resistance is around 57mOhms.

Temperature Limit of our system - air output temp: 45 degrees Celsius (Tc)

Surrounding Air Temperature - air input temp (summer, middle of US): 35 degrees Celsius (Tamb)

This page goes through the rest of the calculations required for the flow rate required. The equations below are copied from the page: http://www.arx-group.com/airflow1.html

Essentially, if we have a given amount (mass) of air moving through the module, and we heat it up by X degreeds Celsius, then with the specific heat capacity of air, we can determine how much energy was transferred to the air (and thus removed from the system).

H = Cp × M × ∆T

M = Q x ρ

Rearranging the equations above, we get the following:

Q = H / (Cp × ρ × ∆T)

Q = H / (1005 J/Kg℃ x 1.18 Kg/m3 x 10℃)      Units: m³/s

With 15.52 m³/h of airflow (tested value with 1 fan, 1 module), we should be able to remove 50W of heat.

With 4 fans (planned number in the battery pack) generating 60 m³/h of airflow, we should be able to remove around 190W of heat.

This amount of heat removal will allow around 50A of continuous to be drawn from the pack, and keep the temperature rise to under 10 degrees celcius.

Since our motors have a max continuous rating of 4kW, which equates to 30A at nominal pack voltage, we will be able to operate at maximum steady state condition without any issues.

Next, we will look at the conditions when climbing hills at higher current draws, and determine the maximum length of a hill that we can climb while staying under the 10 degree rise. For this however, we cannot necessarily assume that the pack will be at ambient before the start of the hill.

Now we need to ensure that the fans we spec will be able to produce the required amount of airflow with the amount of static pressure they must overcome.

Graph of airflow and heat removal (theoretical, 

Comparing against measured results

With the fan, we were able to remove 26.56 - 7.56 = 19W of heat with a Noctua iPPC 3000 fan. The 50W of heat removal that was previously calculated is assuming that the system has reached a steady state and that the difference in temperature from the input to the output is in fact 10 degrees C. With the 5 modules in a row (giving the air a longer time to heat up) and more heat to dissipate in the first place, I believe that the calculation of 50W is accurate to within 20% - we should be able to remove 40W of heat.

The other way that I would still like to compare is looking at the cool down rate of temperature decrease with and without the fan. This should give us a similar value. As can be seen on the cooldown slope of the noctua fan graph above, the rate of cooldown decreases as the temperature difference decreases. For the rate of decrease with the fan, I tried to capture the steepest part of the slope at the beginning of the cooling phase. With the addition of the fan on the cooldown portion, we were able to remove 31.48 - 9.373 = 22.1W of heat with the Noctua fan.

Please note, that these values for the rate of temperature rise were calculated using the average of the rate of temperature rise of the individual cells. Because there is such a large temperature variation between the cells (which affects the amount of cooling potential due to the delta between the cell temp and the air temp), these values are not to be taken as 100% true - they are experimental and could be improved with better airflow paths, better measuring equipment, etc.

As a conclusion to this testing data, I will restate what I mentioned earlier - that I believe we will be able to remove more heat once we stack all 5 modules. However, I will add that due to the uncertainty in the measurements, temperature distributions, and difficulty in simulating everything, I strongly advise to allow a safety factor of 2 when specifying the fan airflow requirements.

Might be useful, sometime and thought I would throw a link here - an interesting way to measure airflow in a closed pipe or duct:

Thermal Flow Measuring Principle: http://www.coolingtechnique.com/70-guide/metodologie-di-test/399-galleria-del-vento.html?start=1