# What am I missing about rocket nozzle isentropic flow?

Playing a bit with Cpropep-Web, something looked wrong to me about how it models isentropic flow through a CD nozzle.

I'm taking the RS-25 characteristics as an example. I ask for a frozen equilibrium flow computation (to avoid molecular recombination and insure isentropy) and get this result : First, we can see that entropy $$S$$ is conserved from CHAMBER to EXIT, so the whole process is by definition isentropic. (It is not a the throat though, which is weird...)

However, if I try to use isentropic flow relations on this output, things start to get weird.

If my understanding is correct, within an isentropic flow, total temperature $$T_{tot}$$ and pressure $$p_{tot}$$ should be conserved (and should be equal to chamber temperature and chamber pressure, as flow is assumed to be at velocity zero in the chamber).

Then,

at CHAMBER : $$p_{tot_c}=p_c=203.73atm ; T_{tot_c} = T_c = 3609.678K$$

At EXIT, $$M=\frac{I_{sp}}{V_{son}}=5.1245 ; \gamma = 1.28861 ; p_e = 0.153 atm ; T_e = 949.973K$$

Isentropic flow relations give $$\frac{T_e}{T_{tot_e}} = (1 + \frac{\gamma - 1}{2} M^2)^{-1}$$ and $$\frac{p_e}{p_{tot_e}} = \frac{T_e}{T_{tot_e}}^{\frac{\gamma}{\gamma - 1}}$$

Substituting all the values we get at EXIT : $$T_{tot_e} = 4550K ; p_{tot_e} = 166.77 atm$$ which means those quantities were not conserved. Some total pressure was lost and a lot of total temperature was gained.

Is Cpropep-Web wrong or am I missing something here ?

The isentropic relations you quote are derived for constant values of $$\gamma$$ (Gamma in the listing) and in real life $$\gamma$$ varies with temperature. I did a calculation with just the pressures and temperatures in your listing and found that the $$\gamma$$ that fits is 1.1855 which is between the chamber and exit Gamma in the listing. That is to be expected.