# Temperature dependent thermal expansion coefficient

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 May 16, 2019, 11:22 Temperature dependent thermal expansion coefficient #1 New Member   Emil Helgren Join Date: Feb 2019 Posts: 7 Rep Power: 7 I am modelling natural convection of water in the temperature range (0 C -> 21 C) using the Boussinesq approximation, and the thermal expansion coefficient of water is changing around 4 degree Celsius, but i'm only able to input a constant value. I tried creating a define property UDF and loaded that, but i was only able to choose the UDF on the other material properties (where piecewise linear and other options are also available). Is there any way i can have a non-constant thermal expansion coefficient when using boussinesq density?

 May 16, 2019, 11:39 #2 Senior Member   Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,677 Rep Power: 66 No. Even if your UDF worked I wouldn't do it because you'll break other things. Just use a different equation of state for density (not Boussinesq).

 May 17, 2019, 03:50 #3 New Member   Emil Helgren Join Date: Feb 2019 Posts: 7 Rep Power: 7 Thanks for the reply! Do you maybe have a specific method you would recommend? I am modelling phase change as well by the way, using the solidification/melting module. I've tried using a piecewise linear density instead of boussinesq in 2D, and the solution didn't converge on any of the timesteps even at 50 iterations pr. step(!) as long as there was still ice present in the simulation. After all the ice was melted, it congerveged after 2-5 iterations each step, so i assume the problem is at least related to the phase change solving. I would really like to get a nice converging solution before taking the time to do a 3D simulation I assume ANSYS just uses fully compressible navier-stokes when the density is defined piecewise linear? (can you confirm this?) Do you think the problem is the enthalpy-porosity method used by the module having a hard time or is it something else? (maybe there is a better way of simulating this phase change?) Any kind of advice is much appreciated! I would love to post the details of my setup if needed

May 17, 2019, 12:31
#4
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Lucky
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Piecewise density should work in place of a temperature dependent boussinesq.

Yes, Fluent always uses a fully compressible navier-stokes even when you use constant density.

Quote:
 Originally Posted by emilhelgren I've tried using a piecewise linear density instead of boussinesq in 2D, and the solution didn't converge on any of the timesteps even at 50 iterations pr. step(!)
it converged with Boussinesq or did you not try it? That would be a hint as to what is stalling convergence.

May 20, 2019, 04:32
#5
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Emil Helgren
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Quote:
 Originally Posted by LuckyTran it converged with Boussinesq or did you not try it? That would be a hint as to what is stalling convergence.
Yes with Boussinesq it converged at about the 10th iteration each step, and when the ice was completely melted it only used 2 iterations.

Interestingly, it looks like the the problem is with continuity (i hope i succeded in attaching an image of my residuals). I would think that a residual of 1 is pretty bad :S.

I read somewhere that if your solution doesn't converge, it doesn't necessarily mean you can't trust your results, but you certainly can't trust the time - as in, the flow development and interaction is right, but how fast things are happening is probably not true, would you agree with that, or is that too general a statement?

I don't really know what to change next, do you have any ideas?
Attached Images
 residuals.PNG (29.3 KB, 38 views)

 May 20, 2019, 09:12 #6 Senior Member   Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,677 Rep Power: 66 A residual of 1 for continuity means the flow solution is not changing. That is, your velocity field is not changing. This can happen when there is no flow. You should see some residual reduction vs iteration within each time-step and it looks like your energy residual is just constant. You've got some wonky setting in your case.

October 8, 2021, 20:38
#7
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Henry
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Quote:
 Originally Posted by LuckyTran No. Even if your UDF worked I wouldn't do it because you'll break other things. Just use a different equation of state for density (not Boussinesq).
I am also facing the same dilemma in simulating natural convection in water (single phase). The thermal expansion coefficient changes by 25% in my temperature range ([293, 305 K]) and should be taken into account.

May I ask why the volumetric expansivity can only be designated as constant in ANSYS Fluent? What's the rationale behind it?

If so, how could we model natural convection in water? Choosing the density as a polynomial fit with temperature?

October 9, 2021, 05:09
#8
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Lucky
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Quote:
 Originally Posted by haiteng I am also facing the same dilemma in simulating natural convection in water (single phase). The thermal expansion coefficient changes by 25% in my temperature range ([293, 305 K]) and should be taken into account. May I ask why the volumetric expansivity can only be designated as constant in ANSYS Fluent? What's the rationale behind it? If so, how could we model natural convection in water? Choosing the density as a polynomial fit with temperature?

Are you using the Boussinesq approach? If so, the limitations should be obvious. If you don't make the assumptions that make a model Boussinesq, well then it's not Boussinesq anymore. The whole point of the Boussinesq approach is to ignore those variations.

If you want to take these things into account, don't do Boussinesq. It's that simple.

October 10, 2021, 00:50
#9
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Henry
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Quote:
 Originally Posted by LuckyTran Are you using the Boussinesq approach? If so, the limitations should be obvious. If you don't make the assumptions that make a model Boussinesq, well then it's not Boussinesq anymore. The whole point of the Boussinesq approach is to ignore those variations. If you want to take these things into account, don't do Boussinesq. It's that simple.
Yes, I chose "Boussinesq" in the density drop-list. As far as I know, Boussinesq approximation ignores variation in density. It is acceptable in my case where the temperature range in water is [293, 305 K] and as a result, the density variation is indeed negligible.

Meanwhile, Boussinesq approximation does NOT require the variation of other physical properties (conductivity, viscosity, thermal expansion coefficient, etc.) to be small. As in my case, thermal expansion coefficient changes in the ranger from 0.00021 to 0.00032 (1/K), while the Boussinesq approximation still holds. Besides, ANSYS Fluent does offer option to include the variation of conductivity, viscosity and specific heat when Boussinesq is activated in the density drop-list. I am amazed why similar options have not been provided for thermal expansion coefficient...

I look forward to hear your comment on this. Cheers!

 October 10, 2021, 04:33 #10 Senior Member   Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,677 Rep Power: 66 The Boussinesq approximation linearizes the buoyancy force about the reference temperature and reference density. By the way, this is why other transport properties are NOT required to be constant (they don't have anything to do with this buoyancy force). If your thermal expansion coefficient changes over this interval, then this force is not linear anymore. Then it's not Boussinesq. Volume expansivity is just the linear term when you write down the total differential for density (i.e. the partial derivative of density with respect to temperature). You can't tell me that density changes are negligible and then tell me that volume expansivity changes are significant. That's a plain self-contradiction. Just use a variable density model... and everything will be theoretically sound... It's not that difficult... Last edited by LuckyTran; October 10, 2021 at 11:29.

 October 10, 2021, 07:11 #11 Senior Member   Lorenzo Galieti Join Date: Mar 2018 Posts: 374 Rep Power: 12 Agree, you can't say density change with temperature is negligible but allow the thermal expansion ( change in volume due to temperature change) coefficient to change with temperature. Last edited by LoGaL; October 10, 2021 at 15:02.

 Tags boussinesq, natural convection

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