Learning Forum

[zhenming.peng]

Dear Ansys Community,

I found in the User Guide that, for improved stability, it is possible to specify a larger solid time step than the fluid time step when performing conjugate heat transfer.

I have a question about this.

Fluent solves the energy equations in the fluid and solid, by default, in a fully coupled manner, meaning that the entire domain, including both fluid and solid zones, is solved together and the energy field in the solids and fluids is updated at every fluid time step.

Therefore, I assume there is a single energy system for both the solid and the fluid in a fully coupled CHT simulation.

If we specify a different solid time step, how is the one energy equation formulated and advanced in time? Why does this not affect the accuracy of the solid and fluid solution?

[SamW]

Hello, while the fluid and solid regions in a CHT simulation are solved in a fully coupled manner, different energy equations are solved for each region. You can see for example the energy equation for solid regions here in the theory guide. Temperature and energy flux continuity is enforced at the solid-fluid interface, but different time steps can be used between zones. 

Also, if you want to get technical, it is also possible to use different time steps for cells within the same zone when you use something like a pseudo-time method.

[SamW]

However, to your final question, the time step specification definitely can affect the accuracy of the solution, especially in transient problems. See the note in the user's guide, section 17.2.2.6: "For general CHT applications, the correct temporal evolution of temperature in the solid can only be obtained when the same time step size / number of iterations is used in fluid and solid zone."

The different time step specifications for solid zones in CHT, or even a pseudo-time method, are usually techniques to artificially advance the solution a further distance in "real" time, usually towards a steady state.

[zhenming.peng]

Thanks a lot for your reply!!

I have a follow up question. Suppose I run a transient simulation where the fluid time step is 0.01 s and the solid time step is 0.1 s.

If the results in both the fluid and the solid are updated at every fluid time step, what solid solution am I looking at when I examine the coupled CHT results at, for example, t = 0.05 s? Is there any temporal interpolation for the solid results? Otherwise, at t = 0.05 s fluid time, the solid corresponds to the state at t = 0.5 s.

[SamW]

Well, the coupling at the interface will typically be enforced each time step in-between your initial and final state in your example. I am not sure I would call it interpolation, but for example the fluid domain will feel the effects of the longer time step in the solid domain along the way as the condition at the interface changes. 

Remember that this is a numerical technique to jump ahead in time towards a steady or quasi-steady state, rather than strictly representative of something you might measure in an experiment, so you can in theory see thermodynamic states that you would not see in a physical laboratory, hence the note about "correct temporal evolution" above.

You can read more about this coupling in the user's guide, in particular 17.2.2.6.1 through 17.2.2.6.3. There are options for looser coupling or time-averaged explicit coupling for transient simulations, which can make it so that the coupling is not enforced every time step. In general I would not worry about these unless you need to accelerate your calculations even further.