Question

How do the momentum and pressure terms in the thrust equation vary between an over- expanded, optimally expanded, and under-expanded nozzle? Why are the characteristic velocity (c*) and thrust coefficient (C used to compare rocket performance? What factors affect these two parameters? Why a bell-shaped nozzle performs better than a conical nozzle rocket. Give several reasons?

Answer 1

1) where the external pressure is higher than the exit pressure, is referred to as over expanded. When an over expanded flow passes through a nozzle, the higher atmospheric pressure causes it to squeeze back inward and separate from the walls of the nozzle. This "pinching" of the flow reduces efficiency because that extra nozzle wall is wasted and does nothing to generate any additional thrust. Ideally, the nozzle should have been shorter to eliminate this unnecessary wall.

            The opposite situation, in which the atmospheric pressure is lower than the exit pressure, is called under expanded. In this case, the flow continues to expand outward after it has exited the nozzle. This behavior also reduces efficiency because that external expansion does not exert any force on the nozzle wall. This energy can therefore not be converted into thrust and is lost. Ideally, the nozzle should have been longer to capture this expansion and convert it into thrust.

Thrust equation is same for all but only the pressure is difference in two cases.In the optimal expanded nozzle the exit pressure equals to ambient pressure.

2)The "Characteristic Velocity" c* depends mainly on propellant properties. The Thrust Coefficient cF depends on propellant properties throughγ (or equivalent), but mainly on the pressure ratio and nozzle geometry. So by the definitions of cF and c* we have managed to separate the effects of propellant properties and the effects of nozzle geometry into the two factors of c. This separation, though demonstrated only for ideal gases, holds also for the more general situation of complex chemically reacting propellants.

The pressure ratio and nozzle geometry may effecting.

3) Conical nozzle have small angle.A small angle produces greater thrust ,because it maximizes the axial component of exit velocity and produces a high specific impulse.In case of bell-shaped nozzle the divergent angle is very small compared conical nozzle.The angle is 2-8 degrees. Because of this angle difference its minimize the weight and maximize the performance 10-25% than conic.