Application of the One-Dimensional Theoryto the Calculation of Supersonic Nozzles
10.1. General definition of a supersonic nozzle
A supersonic propulsion nozzle with a convergent–divergent shape ensures the expansion of propellants from a subsonic state, in the combustion chamber, turbine outlet, or even after the postcombustion chamber, to a supersonic state in the exit plane (E). In most cases, the nozzles are axisymmetric. Such a supersonic nozzle is shown in Figure 10.1. It must include a throat (C) where the Mach number is equal to 1. The nozzles of this type also equip supersonic wind tunnels.
The nozzle is fed under the initial (stagnation) conditions:
– pressure: Pstj,
– temperature: Tstj.
In these notations, we have introduced the index j to denote a propulsion jet. We denote with the index E the conditions in the exit plane whose section has an area AE:
– pressure: pE,
– density : ρE,
– temperature: TE,
– gas velocities: VE,
– Mach number: ME.
The area of the throat is denoted by: AC.
Two quantities are of particular importance for the nozzles:
– the mass flow: qm,
– the thrust: F.
These quantities can be calculated using the theory of one-dimensional flows. The results thus obtained are approximate, the flow in a real nozzle being not strictly one-dimensional. A precise calculation of the performance of a nozzle must ...