[Andrew2]

Hello,

I'm PhD student trying to modify a code to model the compressible flow in a centrifugal compressor. The code uses a pressure based fractional step method to solve for the compressible Navier-Stokes equations. To relate density to pressure, the code uses the differential form of the equation of state p=p(rho,s).

dp = c^2 * drho + (drho/ds)*ds

where c^2 = dp/drho

This relation is then used to find the time derivative of pressure

dp/dt = c^2 * drho/dt + (drho/ds)*ds/dt

The code in it's current form assumes that ds/dt is zero. My question is whether this a reasonable assumption to make and how much of an impact this assumption will have on turbulence and shock modelling. All of the literature I have been able find assumes that the flow homentropic (ds=0) and disregards entropy, but turbulence and shock generation aren't isentropic processes and I don't think assuming ds=0 is a good assumption. If entropy can't easy be disregard if turbulence and shock modelling are important, does entropy need to be calculated with a separate scalar equation?

Any suggestions for papers or books on this topic would be greatly appreciated.

Thank you,
Andrew

[FMDenaro]

Originally Posted by Andrew2

Hello,

I'm PhD student trying to modify a code to model the compressible flow in a centrifugal compressor. The code uses a pressure based fractional step method to solve for the compressible Navier-Stokes equations. To relate density to pressure, the code uses the differential form of the equation of state p=p(rho,s).

dp = c^2 * drho + (drho/ds)*ds

where c^2 = dp/drho

This relation is then used to find the time derivative of pressure

dp/dt = c^2 * drho/dt + (drho/ds)*ds/dt

The code in it's current form assumes that ds/dt is zero. My question is whether this a reasonable assumption to make and how much of an impact this assumption will have on turbulence and shock modelling. All of the literature I have been able find assumes that the flow homentropic (ds=0) and disregards entropy, but turbulence and shock generation aren't isentropic processes and I don't think assuming ds=0 is a good assumption. If entropy can't easy be disregard if turbulence and shock modelling are important, does entropy need to be calculated with a separate scalar equation?

Any suggestions for papers or books on this topic would be greatly appreciated.

Thank you,
Andrew

If you are solving the 3D compressible form of the NS equations, you can use mass, momentum and total energy (kinetic plus internal) along with the pressure state equation to have all you need for taking into account entropy changes in the flow. You do not need to compute the entropy equation to solve the system.
Turbulence and shock (actually high gradients for viscous flows) induce strong entropy variation so that you can get ds/dt=0 only for steady flows but having gradient of entropy.