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July 31, 2009, 14:58 
Heat flux

#1 
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Luca Cavagna
Join Date: Mar 2009
Location: Stockholm, Sweden
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Hello,
firstly I apologize if my question may sound too trivial. I m a structural engineer dealing with aerothermoelastic analysis. I have an in house code which I ve beed enhancing to allow such kind of analysis. I noticed something which is not so good to me. I calculate the heat flux directly from the gradient of the prescribed wall temperature and the first layer of cell: Q = K * (T_in  T_wall) / Dn where K is the conductivity and Dn is the normal distance between the 2 points. Question: as soon as I change the value of T_wall (coming from the heat transfer module I ve been coupling), T_in changes of very few kelvin. THe problem is that dividing by Dn which is VERY VERY small, Q dramatically change value and then it takes many iterations before to settle. The CFD code uses explicit timestepping RK to converge to steady state. Anybody jas experience with the slow convergence of this kind of problems? Maybe I should also consider some limitation in the timestep considering also the thermal diffusivity (not considered at the moment in the code). Any suggestion is appreciated. Regards Luca 

July 31, 2009, 17:02 

#2 
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I think you've diagnosed your problem accurately.
You should find criteria for the time step limit using explicit timestepping in most texts (sr. level or 1styear graduate). You'll have a choice then: 1. Change the distance between the wall and the nearest node or by cutting the time step to satisfy the criteria. Either of these will also impact the 'accuracy' of your answer  that is, how well does your difference equation approximate the solution to the underlying heat conduction equation. 2. Of course, by cutting the time step, you spend a lot of extra time computing  as you've learned. 3. Switch to an implicit timemarching scheme. Lots of work required and the implicit schemes have their own problems. But, to repeat, I think your diagnosis is correct. Good luck! 

July 31, 2009, 17:11 

#3 
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Luca Cavagna
Join Date: Mar 2009
Location: Stockholm, Sweden
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Hello !
thank you for answering.  I 've been looking into the code and trying to check/modify the calculation of the timestep chosen for each cell. The thermal diffusivity may be involved in the criteria of the time step.  Switching to an implicit method is too much work for me. A massive restyle of the code is involved. The code works very well for flow and I guess I m the first one dealing with such applications. I will also loon into the literature to see if other codes manifest the same slow convergence. A paper I have here with me confirms my fears...  I will examine the problem deeply tomorrow and let you know. Thank you again, Luca 

August 1, 2009, 10:49 

#4 
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[QUOTE=lucav79;224909]Hello !
The thermal diffusivity may be involved in the criteria of the time step. Yes, the thermal diffusivity, the mesh spacing, and the time step are all involved. Again, you can verify that by checking current numerical heat transfer and or CFD books. I didn't mention the diffusivity as something you could change because it would seem to be a part of your structure design. Aren't you stuck with what the mechnical design folks selected? Any, you're clearly on the right track to a solution. It may cost you some computing time! 

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gradient, heat transfer 
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