Finite Difference Numerical Methods in EES

[tenghensen]

Hey there,

So I'm solving for a hypothetical situation of thermal runaway in Li-ion batteries. The goal is to find the ideal insulating material to ensure that the functional battery does not get above 100 C. Assume that the failing battery is separated from a non-failing battery by a 2 mm thick insulation, and that the battery is 10 mm thick and 200 mm tall. Due to the construction of the battery, the thermal conductivity is anisotropic: 1 W m-1 K-1 and 26 W m-1 K-1 in the x and y directions, respectively. The volumetric heat capacity of the battery is 2.2 kJ L-1 k-1. The failing cell is represented by imposing a 500°C constant surface temperature on the left side of the insulation, and the battery is attached on the top and bottom to cold plates for cooling. The cold plate is represented by a constant surface temperature of 25°C on the top and bottom surfaces of the battery. You are also to assume that the right side of the battery is thermally insulated, and that there is no thermal contact resistance between the insulation and the battery.

Here's the idealized picture.

https://fbcdn-sphotos-c-a.akamaihd....0_10153197526196064_5579259681756965913_o.jpg

I know that this can be approximated with Ansys and a few other softwares, but I need to solve this using numerical methods.

So far, I have begun doing a nodal analysis to solve it as a 2D finite difference problem. I've found a few basic code formats for this in EES, and would like to be able to build off of them. They're attached to this post. I am thinking that it may be wise to run a separate simulation for the insulation and the battery, so that I can plug in conductivity values for the insulation without having to run the entire system.

If you've seen anything like this before and have some input, it would be great. I'll post updates as I move along in the solution.

Cheers

 

[prex]

What's EES?
A 2D problem like this one can be simply solved in Excel. Even a 3D version can be set up, if a quite coarse mesh is acceptable.

prex
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[IRstuff]

The wording you used suggests a homework problem, but your other postings do not.

There's unlikely a closed form solution, but there are numerical approximations that could be taken, like:

http://www.electronicsprotectionmagazine.com/images/ATS-2.pdf

http://www.electronics-cooling.com/...-for-estimating-thermal-spreading-resistance/

http://www.electronics-cooling.com/1998/01/calculating-spreading-resistance-in-heat-sinks/

The articles aren't 100% applicable, so you should do a search on something like "heat spreading

The anisotropy makes it interesting. Possibly, you could scale the horizontal dimension of the battery by 20x, but keep the net heat capacity the same?

TTFN
faq731-376

Need help writing a question or understanding a reply? forum1529


Of course I can. I can do anything. I can do absolutely anything. I'm an expert!
There is a homework forum hosted by engineering.com:

http://www.engineering.com/AskForum/aff/32.aspx

 

[tenghensen]

@prex EES is Engineering Equation Solver. It's a program used frequently for thermodynamic and fluids calculations. The coarsest mesh possible is 2mm because it is necessary to have a nod on the outside of the insulation and one on the contact surface with the battery. If you have done anything similar to this in Excel, could I see an example? I'm much more comfortable with excel myself.

 

[IRstuff]

Upon rereading your OP and this last reply, I'm a bit confused. You seem to proposing to reinvent the wheel, as it were, since you're talking about doing a finite-element solution, which is exactly what ANSYS is.

So, is this homework?

TTFN
faq731-376

Need help writing a question or understanding a reply? forum1529


Of course I can. I can do anything. I can do absolutely anything. I'm an expert!
There is a homework forum hosted by engineering.com:

http://www.engineering.com/AskForum/aff/32.aspx

 

[tenghensen]

@IRstuff I realized after your first comment that this should definitely be in the homework forum, so I went ahead and threw it in there as well. Thanks for the heads up on that. I just kept it in here as well because of prez's reply for convenience. Do I need to take it down from this forum?

 

[IRstuff]

No, that's fine. Engineering.com's homework forum is still sparsely populated, and there may be some utility to having this thread staying here.

TTFN
faq731-376

Need help writing a question or understanding a reply? forum1529


Of course I can. I can do anything. I can do absolutely anything. I'm an expert!
There is a homework forum hosted by engineering.com:

http://www.engineering.com/AskForum/aff/32.aspx

 

[prex]

You have it. It's a relatively rough setup (in 2D), that can easily be made better (e.g. dx different from dy, use of symmetry,...). It also possibly contains errors.
To use it: set [tt]start=1[/tt] to start the calculation. If dt is too large, you go into troubles, then use [tt]start=0[/tt] to come back to initial conditions.
Then instruct Excel to use iterations, to use manual recalc, and a fair number of iterations (1000?).
Each time you hit the recalc button, when recalculation ends, you see the temperatures at [tt]time=t[/tt]

prex
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