Estimating Thermal Time Constant for Cooling Battery Pack

I have made a first attempt at estimating the thermal time constant for the Leaf battery pack. The thermal time constant is the time it takes for the temperature differential to decrease by 63.2%. I drove my Leaf home after being parked in the shade at work and parked in my underground parking garage where there is no solar loading and ambient temperature is fairly constant (changes slowly, negligible over 2 hours). Maximum battery pack temperature decreased 2 degrees F. over 2 hours using the Leaf Battery App.

Assuming that the battery pack obeys Newtons law of cooling we get:

Delta T(at time t) = Delta T(orginal) * e^(-t/Time Constant)

My data:

10 degree F. original temperature differential = 5.55 degrees C.
8 degree F. temperature differential at 2 hours = 4.44 degrees C.

So per equation shown in attachment below:

4.44 = 5.55 * e^(-2/Time Constant)

Conclusion: Time Constant is about 9 hours.

The next big question is
Will the measured Temp match the estimated Temp in 9 hours.

KJD said:

The next big question is
Will the measured Temp match the estimated Temp in 9 hours.

Click to expand...

Actually, it's a bit more complicated than that for a variety of reasons:

1) I used maximum battery pack temperature sensor, perhaps average would be better
2) While the temp differential was pretty close to 2 degrees, I didn't record it to 0.1 degree increment
3) Shorter time periods are more reliable, because there is less likely to be drift in ambient temperature (parking garage isn't that stable in temperature)
4) Larger temperature differentials are probably more reliable, because small errors/drift in temperature measurements will have less effect on the calculation
5) If the Time Constant doesn't follow the predicted curve at all temperature differentials, it will still be useful since the main thing one wants to know is how quickly temps cool down when there is a significant difference between ambient temp and battery pack temp. Once you get to 3-4 degrees F. from ambient it doesn't matter much as a practical matter if the rate changes.
6) The measured change was a couple of days ago, so I can't wait another 9 hours to see what happens
7) You can't charge your Leaf or move it out of the parking garage during the testing period, since driving will heat the battery pack (or cool it if the ambient temp is much lower than battery pack temp) and solar loading will affect the result. I did drive my Leaf for a bit today.

Next test will probably involve two changes to see if the Time Constant calculation gives roughly the same result.

1) Testing a larger temperature differential
2) Testing for a longer period of time (e.g., 4-6 hours)

Thanks for the information. Looking forward to reading about the next test results.

OK, I went back and found data from my log from last night and this morning to do more precise calculations. The main problem is that I am not sure what the exact ambient temperature was when I got home. Therefore, I did the analysis with 2 slightly different temperatures, 68 degrees and 69.5 degrees F. The time between readings in the log was much longer--16.55 hours. Unfortunately, I also did 40 minutes of charging after about 12 hours, which probably raised the ending battery temperature about 1.2 degrees based on my previous estimate. Thus the calculated values are actually an upper bound for the time constant. I calculated the time constant for each temperature sensor and also took an average. I then recalculated subtracting 1.2 degrees F. from the final temperature, which probably gives a more accurate estimate of the time constant.

Conclusions:

1) Time constant varies for each temperature sensor - probably around 9-14 hours (first column in first attachment)
2) Constant is probably around 11 hours average, but could be as low as 8 hours average (second column in first attachment)
3) In order to get a more accurate calculation, I need a more accurate digital thermometer to take ambient temp readings over several hours, and I need to make sure I don't charge in the morning before taking the battery pack temperature readings. Still the values are fairly similar to my rough off the cuff estimate using a much shorter time and much less temperature change. That is reassuring.

Thanks for investigating this issue; this aspect of managing battery temps is one of the most interesting with use of the new battery app. Your rule of thumb figures for battery heating/cooling are a great help in understandng thermal behavior. I've noted my cap has decreased quickly over the last month and I'll be Interested to know if the capacity bars are directly tied to the cap parameter. I should know soon since I'm at 86%.

Thanks, Stoaty! Nice work!

So it appears the thermal time constant when sitting is on the order of 10 hours, which seems like a reasonable result to me. Unfortunately, such a long time constant means that when you park the LEAF it takes a LONG time to cool. Also note that the temperatures within the cells are almost certainly higher than those seen at the sensors since the heat is not dissipated at the sensors.

The thermal time constant when driving is likely much lower since the moving air greatly reduces the thermal resistance from the batteries to ambient. My guess is that it is around two hours when driving. That is a good thing when the ambient temperature is lower than the internal battery temperature. But it is a very bad thing when the ambient temperature is above the internal battery temperature since it hastens the heating of the battery. It is for this reason that I hesitate to take the LEAF out of the garage on days when it is 80F in the garage but 100F outside.

RegGuheert said:

So it appears the thermal time constant when sitting is on the order of 10 hours, which seems like a reasonable result to me. Unfortunately, such a long time constant means that when you park the LEAF it takes a LONG time to cool. Also note that the temperatures within the cells are almost certainly higher than those seen at the sensors since the heat is not dissipated at the sensors.

Click to expand...

Yes, 10 hours is a good estimate. T1 is an outlier at 14 hours, but part of the explanation may be the 40 minutes of charging, which in my experience increases the T1 sensor temperature significantly more than the other temperature sensors. I expect that when charging is eliminated from the test the T1 sensor will be closer to the other sensors, although it may be that the physical arrangement of the pack causes it to equilibrate more slowly. I would be interested to see the location of the sensors on a 3D cutout of the pack.

The thermal time constant when driving is likely much lower since the moving air greatly reduces the thermal resistance from the batteries to ambient. My guess is that it is around two hours when driving.

Click to expand...

What makes you think it is so low? I don't see any change in battery pack temperature during a 35-40 minute drive when ambient is 10 degrees cooler than pack temperature. Of course there are two competing forces there: the heating of the pack from driving (includes a significant elevation gain for me with constant 20 kw output for about 10 minutes) and the increased cooling from driving. I don't know a good way to estimate the time constant while driving at significant speeds. Once I get better data on the time constant, my next experiment will be to put a fan under my Leaf over night to see how much that speeds up the cooling (if any).

Stoaty said:

What makes you think it is so low?

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As I said, it is only a guess.

FWIW, here is my thinking:
- The thermal capacitance is roughly the same in both the stationary and moving cases.
- In the stationary case, there are two big changes to thermal resistance: 1) Airflow horizontally across the bottom of the steel battery case is stopped, and 2) the air which is trapped between the plastic cover and the battery becomes an additional thermal resistance between the battery and ambient. Because the air in that space is located horizontally under the battery, there is very little convection flow generated by "chimney effect", so the air is quite static. Dead air is known the be a very good thermal insulator and it is the main insulator used in homes around the world. This addition of nearly-dead air thermal resistance plus an increase in the resistance between the metal baseplate and the air will result in several times more thermal resistance when the car is not moving, hence my estimate of a several times reduced time constant due to motion.

Stoaty said:

Once I get better data on the time constant, my next experiment will be to put a fan under my Leaf over night to see how much that speeds up the cooling (if any).

Click to expand...

That should be an interesting test! I'll look forward to seeing further results. Thanks again for all the testing!

Very interesting topic, now knowing that we need to keep the battery temp below 86*f. Any further updates on the testing?

This morning I was reading through old threads and saw a post from "abasile" (I think it was him) talking about driving through a stream which rapidly cooled the battery by one bar, then tried to spray water under the car to see if that would also work to cool the battery.

If this was the case, couldn't we hook up some type of water misting system at the cooling air intake to use while driving in those +100*f days? Has anything like this been tried or tested?

Graffi said:

This morning I was reading through old threads and saw a post from "abasile" (I think it was him) talking about driving through a stream which rapidly cooled the battery by one bar, then tried to spray water under the car to see if that would also work to cool the battery.

Click to expand...

:lol: Yes, that was me. Looking back on that experience, here are my thoughts:
- The instantaneous drop of one temp bar almost certainly arose from rapidly cooling one or more of the temperature sensors, not the pack itself. It would take more than a 15 second dunk to really cool the pack.
- The ensuing evaporative cooling associated with having a very wet car bottom likely did measurably cool the pack.

A simple aid in hot, dry climates might be a very basic misting system set up at home underneath the car.

The real solution, of course, will be a better battery system. I am hopeful that the announced 2014 chemistry changes will adequately address the problem of hyper heat sensitivity.

I know this thread is old, but it is a good topic and it is relatively timeless.

I have a 2013 SL. It has only 3 sensors. I think T3 was removed in 2013. The three sensor defiantly have different time constants. T1 is the slowest and T2 is only a little faster. T4 has the fastest time constant.

I calculated the fastest time constant today. That is T4. My T4 sensor has a time constant of about 4 hours.

We need to have these measurements made several times by independent, technically savvy owners. If we did, I think we would find that we get distinctly different reading for the 3 or 4 sensors. I believe the OP calculations for T1 and T2.

Any fans would effect T4 the first,

How this would apply to battery longevity requires a lot more information than we have. I am sure that Nissan does have that data. I expect that Nissan chose T1 to be close to the highest temperature point in the pack If internal heating is the driving factor, and T4 to be the highest temperature point if the external heating is the driving factor, with T2 in between and becoming the highest temperature point when you have both internal and external heating.

Thanks,
Dan