Some questions about sutherland laws


I run the case at high Mach and Reynolds number, such as 3 mach and Reynolds 1e4. When I don’t use the viscosity law, it will immediately break with Nanh. But when I use the sutherland’s law, it will run for a while and then crash. I guess if I used the sutherland’s law incorrectly. In dimensional condition, the sutherland law used the unit k. But in dimensionless condition, can I use Twall as the characteristic temperature to nondimensionalize the variable in Sutherland law?

I few things might help here:

1.) As per the User Guide you need to provide the products cpTref and cpTs, where cp is the specific heat capacity at constant pressure. So not just Tref and Ts.

2.) The values/units used for these products should be consistent with those used for the rest of your simulation. So if your whole simulation is setup in SI units then the products should be set to appropriate values in SI units. Similarly if your simulation is non-dimensionalised then the products should be set to appropriate values that are consistent with the non-dimensionalisation.

3.) I realise this is a little fiddly to get right. The reason the products cpTref and cpTs are required as inputs is because we can readily obtain cpT in the code as per PyFR/flux.mako at 843aa641cf3efafc974e651a6145242564ff7f95 · PyFR/PyFR · GitHub (all the cp then all cancel off when the quotients are formed).

4.) You mentioned Twall (which is required if you use an isothermal wall BC). Note that as per the User Guide you need to set cpTw.

Let me know how you get on.


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Thanks for your reply.
Followed your advice. I run the case of Mach 2.15 and Reynolds 1e5, with the Sutherland law. In order to get the appropriate viscosity from the Sutherland law, I set the Tempreture of the free stream 145K, so Reylolds number is 1e5. The the Tempreture of the free stream is used to nondimensionalize the Tref and Ts, which becomes 273.15/145, 110.4/145, then multiply Cp=2.5. When compute at t=6, NaNs appears in the simulation. Did I do the right thing? Is there anything else that needs attention? Of course, and I use the entropy filter.

Not sure I follow. If you are setting up the simulation in SI units then Tref and Ts need to be in SI units too (as does cp). Also, I would suggest trying to get the simulation to run without Sutherlands law first, to confirm that the grid resolution and time step size etc are appropriate. Running ILES/DNS at Re 1e5 is non-trivial and will require a fine (large) mesh. How many mesh elements do you currently have?

First, I use the nondimentional variable.

Second, I run the simulation without Sutherland law, it borken up immediately. And the mesh is 7255 triangular elements with P2. It is Shock Wave/Boundary laminar Layer Interaction.

This, on its own, is a terrible reason for enabling Sutherland’s law. What temperature range do you expect for the flow? If this is large then Sutherland’s law may be important to get the physics correct. However, if you are not expecting a large temperature range then the correction provided by Sutherland’s law is not necessary.

Regards, Freddie.

I’m not sure exactly what the temperature range is. But in the corresponding paper, the Sutherland’s law is required.