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# 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: 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 ...

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