Handbook of Compressible Aerodynamics

Chapter 10

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.

Figure 10.1. Layout of a supersonic nozzle

The nozzle is fed under the initial (stagnation) conditions:

– pressure: P_stj,

– temperature: T_stj.

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 A_E:

– pressure: p_E,

– density : ρ_E,

– temperature: T_E,

– gas velocities: V_E,

– Mach number: M_E.

The area of the throat is denoted by: A_C.

Two quantities are of particular importance for the nozzles:

– the mass flow: q_m,

– 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 ...