Question about heat transfer simulation convergence

Anna Tian · May 8, 2013, 16:04

Hi,

Heat transfer convergence usually takes much more time than the velocity convergence. For fluid dynamics simulation, when the velocity residual and mass flow residual is very small, then we can basically say that the simulation has already converged.

But for heat transfer simulation, this convergence criteria may not work. I'm wondering what could be the convergence criteria for the heat transfer simulation?

rmh26 · May 9, 2013, 11:52

Transient or Steady State? How are the equations being solved? What exactly do you mean by convergence?

Are you using a commercial code or something you wrote youself?

Anna Tian · May 9, 2013, 12:38

Quote:

Originally Posted by rmh26

Transient or Steady State? How are the equations being solved? What exactly do you mean by convergence?

Are you using a commercial code or something you wrote youself?

It's steady state conjugate heat transfer simulation. NS equations and total energy equations are solved by FVM. Convergence means the heat transfer rate doesn't change a lot anymore even thought the residual is still reduced. CFX is used.

rmh26 · May 9, 2013, 15:14

If the physical parameter you are interested in, ( a heat flux), is converged to a level that is good enough for you then stop there. There residual does not directly reflect how far your solution is from the correct solution, it tells you how accurately you are solving the equations. Also because the flow depends only weakly on the temperature it make sense that it will converge quickly, the temperature field depends strongly on the velocity field so that a small update to the velocity field can cause a large change to the convective terms in your heat equation. But I would say that if you flux is not changing by much then your answer is probably good enough and running the simulation for longer will not give you much more accuracy.

ghorrocks · May 9, 2013, 18:11

CHT simulations commonly have this problem where the residuals are well converged but the imbalances are not and converge quite slowly. The problem is caused by the different time scales in the solid and fluid regions - the solid region is much slower than the fluid region, so a sensible time step for the fluid region only advances the solid region very slowly.

The answer is to use a solid time scale factor. This accelerates the time step in the solid region. As the equation solved in the solid region is just the heat equation and it is linear and well-behaved you can accelerate it by a large amount - I typically use factors like 100 or 1000. This usually makes the solid region converge just as fast as the fluid region and speeds up CHT simulations many times.

And this is also why it is vital that CHT simulations have convergence criteria on both residuals and imbalances. If you just use residuals or look at the convergence of parameters of interst you can get answers which are wrong by miles.

Anna Tian · May 10, 2013, 04:14

Quote:

Originally Posted by ghorrocks

CHT simulations commonly have this problem where the residuals are well converged but the imbalances are not and converge quite slowly. The problem is caused by the different time scales in the solid and fluid regions - the solid region is much slower than the fluid region, so a sensible time step for the fluid region only advances the solid region very slowly.

The answer is to use a solid time scale factor. This accelerates the time step in the solid region. As the equation solved in the solid region is just the heat equation and it is linear and well-behaved you can accelerate it by a large amount - I typically use factors like 100 or 1000. This usually makes the solid region converge just as fast as the fluid region and speeds up CHT simulations many times.

And this is also why it is vital that CHT simulations have convergence criteria on both residuals and imbalances. If you just use residuals or look at the convergence of parameters of interst you can get answers which are wrong by miles.

1) What do you mean by 'factors like 100 or 1000'?

2) Is there a way to setup to change the time step during the simulation running automatically? Then I can use large time step firstly then change to small step. I really need a automatic way to do this time step shifting. Because I have more than 300 this kind of simulations to run. I can't change the time step manually every time.

3) Could I setup a simulation stopping criteria like 'the outlet temperature doesn't change a lot anymore' in CFX? So that the simulation can be stopped by this criteria automatically and in this way the next simulation can be started earlier. This can save some computation time.

4) How to decide the length of the time step I need to use at the beginning to solve the solid temperature distribution?

RicochetJ · May 10, 2013, 04:48

Quote:

Originally Posted by ghorrocks

CHT simulations commonly have this problem where the residuals are well converged but the imbalances are not and converge quite slowly. The problem is caused by the different time scales in the solid and fluid regions - the solid region is much slower than the fluid region, so a sensible time step for the fluid region only advances the solid region very slowly.

The answer is to use a solid time scale factor. This accelerates the time step in the solid region. As the equation solved in the solid region is just the heat equation and it is linear and well-behaved you can accelerate it by a large amount - I typically use factors like 100 or 1000. This usually makes the solid region converge just as fast as the fluid region and speeds up CHT simulations many times.

And this is also why it is vital that CHT simulations have convergence criteria on both residuals and imbalances. If you just use residuals or look at the convergence of parameters of interst you can get answers which are wrong by miles.

I agree! Just compare solid time scales to fluid time scales and you quickly appreciate why the imbalances don't reduce as much as you want to! (And it's usually the energy equation - no suprises there!)

However in transient simulations surely you can't set a timescale for the solid region, and a different time scale for the fluid region?

Using your method described above (coincidentally is the same method I use) you're restricted to steady state calculations using "false" physical timesteps.

ghorrocks · May 10, 2013, 23:47

Yes, the solid time scale factor is only applicable to steady state runs. In transient runs you have to model it with the physical time step the same in both regions.

Shoushou:
I mean set a solid time scale factor in the range of 100-1000.

You do not need to change the time step during a run. You can start it with this high factor.

For CHT simulations I recommend using the residuals AND imbalances as convergence tolerances. Do a sensitivity study to check your settings are OK and then use that setting on all your runs.

Setting time step size: Just try it out and see if it works. It is goes slow then make it bigger, If it diverges then make it smaller.

May 8, 2013, 16:04	Question about heat transfer simulation convergence	#1
Anna Tian Senior Member Shoushou Tian Join Date: Jul 2012 Posts: 192 Rep Power: 2	Hi, Heat transfer convergence usually takes much more time than the velocity convergence. For fluid dynamics simulation, when the velocity residual and mass flow residual is very small, then we can basically say that the simulation has already converged. But for heat transfer simulation, this convergence criteria may not work. I'm wondering what could be the convergence criteria for the heat transfer simulation? __________________ Best regards, Shoushou

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May 9, 2013, 11:52		#2
rmh26 Member Join Date: Jul 2011 Posts: 46 Rep Power: 3	Transient or Steady State? How are the equations being solved? What exactly do you mean by convergence? Are you using a commercial code or something you wrote youself?

May 9, 2013, 15:14		#4
rmh26 Member Join Date: Jul 2011 Posts: 46 Rep Power: 3	If the physical parameter you are interested in, ( a heat flux), is converged to a level that is good enough for you then stop there. There residual does not directly reflect how far your solution is from the correct solution, it tells you how accurately you are solving the equations. Also because the flow depends only weakly on the temperature it make sense that it will converge quickly, the temperature field depends strongly on the velocity field so that a small update to the velocity field can cause a large change to the convective terms in your heat equation. But I would say that if you flux is not changing by much then your answer is probably good enough and running the simulation for longer will not give you much more accuracy.

May 9, 2013, 18:11		#5
ghorrocks Super Moderator Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 6,940 Rep Power: 59	CHT simulations commonly have this problem where the residuals are well converged but the imbalances are not and converge quite slowly. The problem is caused by the different time scales in the solid and fluid regions - the solid region is much slower than the fluid region, so a sensible time step for the fluid region only advances the solid region very slowly. The answer is to use a solid time scale factor. This accelerates the time step in the solid region. As the equation solved in the solid region is just the heat equation and it is linear and well-behaved you can accelerate it by a large amount - I typically use factors like 100 or 1000. This usually makes the solid region converge just as fast as the fluid region and speeds up CHT simulations many times. And this is also why it is vital that CHT simulations have convergence criteria on both residuals and imbalances. If you just use residuals or look at the convergence of parameters of interst you can get answers which are wrong by miles.

May 10, 2013, 23:47		#8
ghorrocks Super Moderator Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 6,940 Rep Power: 59	Yes, the solid time scale factor is only applicable to steady state runs. In transient runs you have to model it with the physical time step the same in both regions. Shoushou: I mean set a solid time scale factor in the range of 100-1000. You do not need to change the time step during a run. You can start it with this high factor. For CHT simulations I recommend using the residuals AND imbalances as convergence tolerances. Do a sensitivity study to check your settings are OK and then use that setting on all your runs. Setting time step size: Just try it out and see if it works. It is goes slow then make it bigger, If it diverges then make it smaller.