I am confused about the definition of total temperature and total pressure in a turbulent flow with non-negligible kinetic energy of fluctuation k.

I use an isentropic law to define the total pressure :

T0 = T + V**2/(2Cp) + k/2(Cp)

p0 = p*(T0/T)**(g/(g-1))

but this gives me strange evolution of total pressure (increasing total pressure). Can you enlight me on this subject ?

Thanks

Carl

You are most likely looking for the Reynolds averaged total temp and pressure, right? Be careful with your definition of the RA total temperature. If you are solving for compressible flow, one of your governing equations is the energy equation. If that's the case, you should actually have the total energy (which includes k) already available as variable. Simply define the total temperature by use of the total enthalpy which you get from total energy and pressure.

In any event, to validate that your result is consistent, verify that total temperature does not change in time, unless there's work being done. What kind of flow is it?

Thank you for responding

You're right. I'am looking at the RA total temperature and pressure. The flow is a stator of a compressor.

The total temperature is evolving correctly but not the total pressure which diminishes in the region of important value of k and then growes again. Is there a different definition of the total pressure that includes the kinetic energy of the fluctuation ?

There is only one definition of the total pressure.

I can imagine mixing to lead to redistribution of total energy. What you should check is that the average total pressure on the exit plane is lower than the average total pressure at the inlet, while exit and inlet average total temperatures must be the same in case of the stator. If there is anything wrong with the pressure you will see discrepancies in other flow quantities (e.g. total temp) as well. If not, your solution may simply not be converged.

I will check that.

Thank you for your help.