Isentropic Relations for Real Gas in Converging-Diverging nozzle

Jonny6001

Hello,

I am looking at a problem concerning flow through a converging-diverging nozzle. The governing equations are relatively straight-forward for gasses that closely follow the ideal gas law. However I am looking at an unusual gas which is certainly not represented by the ideal gas assumption.

I am curious how you would go about calculating the maximum flow rate through the nozzle when the flow is choked at the throat, I do not want to use CFD initially.
My first thoughts would be to use the isentropic assumption that the stagnation enthalpy is constant throughout the nozzle. From having access to thermodynamic properties of the gas via 'refprop' it should be possible to iterate the temperature in the nozzle to achieve the same stagnation enthalpy as the inlet conditions. But the enthalpy is also dependent on the pressure so I thought I could use the isentropic pressure-temperature relation to couple the pressure to the temperature so that everything at the throat would be defined from knowing the temperature. But it using the isentropic law P0/P1=(T0/T1)^(gamma-1/gamma) assuming that the gas behaves according to the ideal gas law?

Thank you

boneh3ad

Yes, the typical isentropic relations - [itex]p/p_0 = (\rho_\rho_0)^{\gamma} = (T/T_0)^{\gamma/(\gamma-1)}[/itex] - directly follow from the equation of state for an ideal gas. If you had an equation of state for your real gas you could likely come up with an equivalent set of isentropic relations for your real gas. Otherwise, you may be able to approximate it with a polynomial. The only other option beyond that would be to do it computationally.