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.
| Method | Choice order (by performance) | Result | Notes |
|---|---|---|---|
| Liquid Cooling | 1 or 2 | Would be great | Too complicated, too much risk, would take too much time. If done properly, it could work very well. |
| Phase Change Interstitial Material | 1 or 2 | Would work amazing | Unable to acquire / make, would also absorb thermal runaway heat and prevent propagation. Would also mean that we have a fixed amount of thermal mass to heat up, as the pack airflow would be terrible. We can seal the pack completrly with this option though. |
| Forced air cooling | 3 | Works well, must have approriately specced fan | If we get enough air through the modules, it can cool it properly. The fans will require some power when cooling, probably around 20-30W or a little more. We tested the prototype module with a standard 120mm case fan and a Noctua IPPC 3000 fan. |
| Conductive cooling to catamaran | 4 | Ineffective | The catamaran of the car is carbon fiber, and graphite has amazing planar thermal conductivity, but when you will it with epoxy it is terrible. From our testing, it is more conductive through the Z-axis then across the plane |
We selected Forced Air Cooling for our pack.
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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):
| Google drive sheets | ||
|---|---|---|
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We measured the airflow of our Noctua IPPC fan when pulling air through 1 or our prototype modules (see this page), and have an airflow of 15.52m3/h (or 26.3cfm). Looking at the fan curve for the Noctua NF-F12 IPPC 3000 fans mentioned above from Cooling Technique, we see a pressure of about 5.4mmH2O. We will be contacting Noctua to obtain a more accurate P-Q curve for their fan.
| Condition | Airflow (m3/h) | Airflow (CFM) | Static Pressure (from Cooling Technique Testing) | Static Pressure (from Noctua P-Q Curve) |
|---|---|---|---|---|
| Just fan duct | 26.97 | 15.87 | 5.55 | |
| 1 Module and fan duct | 15.52 | 9.13 | 5.6 |
Converted to CFM using this online conversion tool: https://www.convertunits.com/from/cubic+m/hr/to/cfm
So this is the static pressure with 1 module. How does adding more modules (5 modules stacked per fan in our application, with 1 fan pulling air through 5 modules), affect the static pressure? 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
| Variable | Description | Value (Units) |
|---|---|---|
| H | Least amount of heat removed | (W) |
| Cp | Specific heat capacity of the air | 1005 (J/Kg℃) |
| M | Mass of the air | (Kg) |
| ∆T | Temperature difference | Tc - Tamb (℃) |
M = Q x ρ
| Variable | Description | Value |
|---|---|---|
| M | Mass of the air | |
| Q | Flow rate of the air | |
| ρ | Density of the air | ρ = 1.18 Kg/m3 |
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
Discharge Current | Condition | Rate of Temperature Rise (degC / s) | Expected module heat production | Heat Production based on Rate of T Rise |
|---|---|---|---|---|
| 100A | No Fan | 0.015011184 | 570W / 18 = 31.67W | 532W / 18 = 26.56W |
| 100A | Noctua Fan | 0.00384364035 | 570W / 18 = 31.67W | 136W / 18 = 7.56W |
| 0A | No Fan (Cooldown) | -0.0047593750 | 0W | -168W / 18 = -9.373W |
| 0A | Noctua Fan (Cooldown) | -0.0159833 | 0W | -566.6W / 18 = -31.48W |
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:
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