Rocket Nozzles

Converging Diverging Nozzle

This is also referred to as the Laval nozzle. For generating supersonic flows in jet engines, rocket propulsion, supersonic wind tunnels, etc. the nozzle has a converging - diverging shape. Without such a shape, supersonic flow cannot be produced at the outlet.

We start with the description of one-dimensional compressible flow in a duct (same analysis as before)

Continuity

Momentum

For M <1

For M > 1

dV = 0, no change in speed

converging

dV > 0, good as speed is increased

dV < 0, once M = 1 is reached, the diverging design will reduce the speed. Not good as we need to increase M

diverging

dV < 0, speed decreases - this is called a diffuser

dV > 0, once M = 1 is reached, a diverging design is needed to increase the Mach number further

Therefore, for a fluid starting from rest, to have an exit Mach number greater than one - a converging -diverging design is essential.

M = 1 must be at the throat (the junction between the converging and diverging sections)

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