On LMN calculation under supercritical conditions

[fanxiaojie69-dotcom]

Hello, Xcompact3D author.
I am currently working on a computational case of channel flow under low Mach number, compressible, supercritical conditions. I have modified the equation of state to use a property table under supercritical conditions of 8 MPa and 307.8 K. By fixing the density values on the upper and lower walls of the channel as well as in the entire flow domain, I controlled the temperature, thereby simulating the flow of carbon dioxide within a channel with a hot upper wall and a cold lower wall. The modification to the equation of state is as follows:

By modifying the parameters in the momentum and energy equations, they were adjusted to match the physical properties corresponding to different density values.

Momentum equation

Energy equation:

And also modified the formula for calculating the velocity divergence through the new energy equation

The time advancement part has been changed from advancing temperature to advancing enthalpy.

Currently, the modifications include the energy equation, momentum equation, time advancement part, and the physical properties part of the equation of state. However, the calculated density and temperature seem to develop in a relatively correct trend.

However, the speed is slower on the side with a higher wall temperature and faster on the side with a lower temperature, which is opposite to the actual results.

Also, during the computation iterations, when the iterations reach over seventy thousand steps, the speed diverges and the following situation occurs.



So, I’m not sure where the problem occurred or where the modification hasn’t been successful yet.
Could you give me some suggestions? For example, perhaps the existing variable-coefficient Poisson equation is not suitable for conditions with drastic changes in supercritical properties or other situations.
Thank you, best regards.

[slaizet]

I believe that, with the LMN framework, you are not able to deal with drastic changes in supercritical properties. It is designed for moderate changes.
Best,
Sylvain

[fanxiaojie69-dotcom]

Thank you for your reply. I have now adjusted the time advancement and the ideal gas state for the calculation speed divergence constraint to be suitable for the supercritical variable physical properties. However, I'm not sure if the variable coefficient Poisson equation is applicable to strong variable physical properties. Do I still need to modify the variable coefficient Poisson equation part?

[slaizet]

The variable coefficient Poisson equation is not applicable to strong variable physical properties. Probably best to use a compressible solver.
Sylvain

[fanxiaojie69-dotcom]

Thank you for your reply, I will go search and give it a try.