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Compute  Plenum-face conditions for known thrust and combustion temperature

Assumptions: 1-D, axisymmetric, isentropic, compressible, To=Combustion temperature, perfect gas
Subsonic Plenum, Supersonic Exit
Knowns:
Gamma = , R = m^2/(s^2 K)
If the axisymmetric nozzle Geometry is specified:


















Plenum-face Diameter =  m,    Throat Diameter =  m,   Exit Diameter =  m
We can
Area Ratios: 
                  Ap/A* =  ,                    Ae/A* =
and Mach numbers:
  Mplenum =  ,                                               Mexit =
Thrust is defined as
Thrust=(Pe-Pinf)Ae + rho_e*Ve*VeAe
where the subscript e is for exit plane.
If we use the fact that
rho*V*V=rho*M*M*a*a=Gamma*M*M*P
Then we can get Pe as a function of the thrust, exit area and Pinf.
To compute Pinf, we need the
Reference Conditions:
For Altitude = m, the following are
Ref. Density = Kg/m^3, Ref. Pressure = Pa, Ref. Sound Speed = m/s
For a specified Thrust= N
We can Pe from this value using the Thrust equation (See exit conditions below).
From the static exit pressure, the Stagnation pressure can be

using 1-D compressible flow relations
P0 = Pa
If we also specify
Combustion temperature:= K
The stagnation density can also be

using perfect gas relations.
rho0 = Kg/m^3
Conditions at the plenum and exit faces: Using 1-D Compressible flow relations, and known stagnation values. 

plenum-face conditions            Throat conditions               Exit conditions
   Pp =  Pa             P* =  Pa              Pe =  Pa
rho_p =  Kg/m^3        rho* =  Kg/m^3        rho_e =  Kg/m^3
Non-Dimensionalization for the above conditions is 
        Non-D rho_p = rho_p/rho_inf =                   Non-D rho_e = rho_e/rho_inf =  
Non-D Up = Up/a_inf = Mp*(ap/a_inf) =           Non-D Ue = Ue/a_inf = Me*(ae/a_inf) =  
         Non-D Pp = Pp/(Gamma*Pinf) =                    Non-D Pe = Pe/(Gamma*Pinf) =  
                Non-D rho_* = rho_*/rho_inf =  
                Non-D U* = U*/a_inf = (a*/a_inf) =  
                Non-D P* = P*/(Gamma*Pinf) =