Hi All,

I am thinking about doing Direct Numerical Simulation of a turbulent channel flow. In literature it is common to use periodic boundary conditions for this type of flow in streamwise direction. Now the pressure distribution has a linear decrease in streamwise direction for a channel flow, so a periodic boundary condition cannot be implied directly if one solves for the pressure explicitely (Using a Poisson solver one probably does not have this problem). Does anyone know if there is a way to get around this without having to drop the pressure bc in streamwise direction and still do simulations that have physical relevance?

Guus

Impose periodic + specified pressure drop as your pressure boundary condition.

If you remove the streamwise pressure gradient there is nothing to balance the wall shear stress and your flow will slow to a halt. (Assuming that is what you meant by not dropping the pressure bc).

I meant dropping the periodic bc. It is a typo. I was thinking about specyfing the pressure drop, but will the pressure fluctuations carry over directly from outlet to inlet? I would think the pressure fluctuations are a percentage of the mean values, so just specifying a pressure drop would not be physically relevant as the fluctuations need a scaling factor too?

Guus

I do not understand what you mean by scaling. The pressure b.c. is periodic but with the extra twist of adding a constant difference between inlet and outlet. Hence the pressure fluctuations are identical. So long as the inlet and outlet are far enough apart for the fluctuations to be uncorrelated (if a periodic b.c. was not imposed) the mean statistics will not be affected.

So the mean pressure field and the fluctuating pressure field are not coupled? Is this true for both incompressible and compressible flow.

How about if one were to use a Fourrier spectral method in streamwise direction? The Fourrier disretization asks for a periodic function in streamwise direction; with a linear pressure decrease the function will not be periodic. Will the use of a periodic bc with the pressure drop as you mentioned solve this?

Guus

Hi!

To do a channel flow you can also add the constant dpdx term as a source term to the x-momentum equation. This way the flow is purely periodic in all the variables, the only hitch is that this term has to be taken into account when you compute the temperature in a compressible code. I have done some compressible channel flow calculations and this works out just fine. But then again, I had only incompressible channel flow simulations to compare against!!

Srinivasan.

Aha! Do you know if this method is archived somewhere for compressible flow? And what did you do with the density?

Guus

In terms of it being archived, the original kim's channel paper talsk about it too. If I am not mistaken they too did it with the source terms.

Once all the Q {rho,rho*u,rho*v,rho*w,rho*Et} are available, to compute all the quantities I do this u = Q2/Q1;v=Q3/Q1; etc.

note that nothing needs tobe done for the density - it is solved for. Only for the temperature, you have to be careful now

you get internal energy as

ei = Q5/Q1 - KE

then pressure is computed as

p = (gama-1)*rho*ei - dpdx*(x - x0)

note: you have to do this if dpdx is a source term!!!

then temp. is t = p/(rho*R)

good luck Srinivasan