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#1 |
New Member
Delhi
Join Date: Jul 2017
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Hello everyone!
I am slightly confused about the validity of the law of temperature. I tried to go over literature and I couldn't find a concrete answer. I was wondering if the law of wall for temperature shifts when we can change the wall temperature. I ran RANS simulations in an in-house code for a flat plate case with different wall temperature (isothermal boundary condition). I selected Twall/Tfreestream as 1.03, 1.04, 1.05, 1.1. I observed that T+ vs y+ was varying for both SA and k-w SST turbulence models. I wondering if anyone ran a similar simulation in any other code. I want to check if this behavior is expected or not. It would be great to have the opinion of the CFD community about it. Thank you very much |
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#2 |
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Delhi
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It would be great if someone could give me their opinion regarding it from their experience or relevant literature.
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#3 |
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Lane Carasik
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#4 |
Senior Member
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Also, show us what you mean by varying (some plots would be useful), how did you define your T+ and y+, your grid parameters, what other bc you used for your case, the properties you used (are you sure the Pr number is the same?).
As it is not expected in general, the first thing I can think of is that your grid is in a gray area, and as you changed the temperature difference, the y+ range chenaged as well. You should be aware that these WF are not perfect, they typically have some variability if you change your y+. |
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#5 | |
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Delhi
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Quote:
Keeping this un-necessary discussion aside. Can you please give any technical advice to my question? Thank you! ![]() |
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#6 | |
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Delhi
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Quote:
I defined my variables as: ![]() where, I take ![]() ![]() where ![]() and ![]() ![]() ![]() ![]() I should mention that this dependence on wall temperature is not due to the absolute value of Twall but the difference with the freestream temperature ( ![]() The results are shown as follows and can be found here: https://drive.google.com/file/d/1wma...ew?usp=sharing Note that here Twall = 1.03 in the legend is basically Twall = 1.03*T_freestream. Where T_freestream is 300 K for all the simulations. The prandtl number (=0.71) and c_p are constant with temperature. These are not wall function simulations, they are low-Reynolds number turbulence model simulations with y+ < 0.1. I did mesh convergence study and the result is not varying. It is important to tell here that the U+ vs y+ profile is almost identical to the analytic one for all wall temperatures. I understand your point about grid variability, however I am not running wall functions. It's the turbulence model solved to the wall with y+ < 0.1. The BC I used for the wall is isothermal wall. The case is exactly the 2-D flat plate case in NASA turbulence modeling resource. Unfortunately, they don't provide heat transfer data for validation. The velocity profile shows good agreement with CFL3D data. |
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#7 |
Senior Member
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Let us assume that you are computing a constant density flow, otherwise things get much more involved (or, in any case, let us assume that density variations are negligible).
Let us also assume that the viscosity variation with temperature is negligible, as this is the case under which classical law of the walls actually hold. In this scenario, your definition of ![]() ![]() Second, how do you compute ![]() In any case, my experience is with the channel flow where, using a temperature bc instead of a fixed flux one, I also experienced non collapsing profiles, but that was for different Re numbers, which might be a different scenario. |
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#8 |
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Delhi
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Quote:
![]() ![]() I computed ![]() ![]() ![]() ![]() ![]() ![]() ![]() Last edited by aviral2000; March 29, 2019 at 11:39. |
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#9 |
Senior Member
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Everything seems legit to me. As I said, I found a similar behavior when changing the Re number, for fixed wall temperature, in a periodic channel flow. Maybe the two things are related.
Yet, the fact that it gets worst with decreasing temperature difference, which is at your T+ numerator, is suspicious... maybe there is a utau dependence from the temperature difference? |
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#10 | |
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Hmm, I don't think that there is ![]() ![]() ![]() Thanks for suggestions. ![]() |
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#11 | |
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![]() ![]() ![]() At lower mach number (M = 0.1), the T+ vs y+ curve for different wall temperature were matching perfectly. I also tried removing the viscous dissipation term from the RANS solver and observed that even though my St number result is different now (expected behaviour), the temperature profile for different mach numbers are matching nicely. Most of the T+ vs y+ curves and studies are for incompressible solver which does not model viscous dissipation term. Also, for higher compressible flows, Van-Driest or other similar transformations are used to convert to velocity and temperature profile to analytic ones. The case I was doing was in sort of a gray area as I was using a compressible solver for a low-speed flow without using these transformations for the velocity profile. That's my opinion regarding the issue. It will be great to have an opinion from you and other members of CFD community regarding it. Feel free to point out any mistakes in my reasoning or suggestions for additional verification tests. Thank you! ![]() |
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#12 | |
Senior Member
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Quote:
In more general terms, I would conclude that the main mistake was in applying an incompressible law to a compressible case. Thus, besides the viscous dissipation term, a varying density and, in case, viscosity, might invalidate it as well. |
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Tags |
heat transfer, law of wall, temperature, turbulence modeling |
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