# CONVERGENT DIVERGENT VARIABLE NOZZLES

## CONVERGENT NOZZLES

Ideally, the exhaust gases accelerating through a convergent nozzle should reach Mach 1 at the lip of the nozzle and the exit pressure should be reduced to ambient.

This condition gives the maximum obtainable momentum thrust. And zero pressure thrust and occurs when the jet pipe gas pressure is 1.85 times ambient pressure.

If the pressure is lower than this, then the gas will not be able to create the expansion required to give the full momentum thrust. This would occur if the nozzle area were too large.

If the jet pipe pressure were too high then the nozzle would increase the jet stream velocity. And engine thrust until the nozzle choked.

Gas pressure would remain in the exiting jet stream. The expansion would then occur behind the nozzle.

This would produce some pressure thrust and some wasted energy.

If this condition occurs because the nozzle area was too small. The back-pressure felt in the jet-pipe as a result of this will as already stated reduce the turbine pressure ratio. And push the compressor towards the stall.

One question often asked is how can an aircraft fly faster than Mach 1 if the jet-stream velocity cannot exceed Mach 1? The answer is simple!  The speed of sound in air is temperature-dependent. The temperature of the gas at exit is higher than ambient so the speed of sound in air is higher than ambient at the lip of the nozzle.

The jet-stream velocity is actually higher than the ambient value for the speed of sound in the air that the aircraft is flying in. If the exhaust gas velocity were to reach Mach 1 inside the convergent propelling nozzle a choked nozzle condition would occur. Mach 1 gas flow expands faster radially than it does axially.

#### This causes the nozzle to choke.

Once choke occurs the downstream gas velocity cannot increase any further from the value at which the choke occurred regardless of the upstream conditions.

This means that the nozzle will under-expand the gas leaving residual gas pressure in the exit stream. As the gas pressure at exit is now higher than ambient pressure the difference between the exit pressure and ambient pressure will act on the propelling nozzle area to create a forward thrust called pressure thrust.

The nozzle will choke when the gas flow becomes transonic. This is a condition where you would have both sonic and subsonic flow in the exhaust system – Mach one at the propelling nozzle with a sub-sonic upstream flow.

Once a nozzle is choked it can only be un-choked if either the exit velocity is reduced or the gas temperature is increased.

As the speed of sound in is temperature-dependent an increase in jet-pipe gas temperature will raise the sonic speed value. Re-heat systems will do this and permit the jet-stream velocity to rise to a higher Mach 1 value.

### CONVERGENT- DIVERGENT NOZZLES

We know that the jet-stream velocity behind a choked nozzle cannot increase. And that there is an expansion taking place behind the nozzle.

Concorde flies at Mach 2 and no amount of pressure thrust will achieve that. So something else is needed.

You have read that a Mach 1 gas flow expands faster radially than it does axially. Think of a greased metal funnel.

If you were to push a flexible rubber ball down into the apex of the funnel and release it what would happen?

The ball should eject itself from the throat of the funnel. The sideways or radial expansion of the ball would push on the inclined surface of the funnel and produce a reaction force, which ejects the ball.

If a divergent section duct were to be positioned aft of the lip of the convergent propelling nozzle we can create the same effect.

The expanding exit gases would push against the wall of the divergent duct and the resultant reaction force would cause the gases to accelerate rearwards.

There would also be a component of forwarding reaction thrust created on the sloping walls of the divergent nozzle.

The Con-di nozzle is used to produce a jet-stream velocity increase behind a Choked nozzle making maximum use of existing pressure

#### VARIABLE AREA NOZZLES

The only case where you will encounter these nozzles is on Concorde so we will first deal with that type.

The Concorde exhaust system fulfils five major functions:

1. It maintains the correct engine backpressure condition during subsonic and super-sonic airspeeds using a variable area primary propelling nozzle.

2. It maintains the best propulsive efficiency at subsonic and supersonic airspeeds using a variable area secondary nozzle.

3. It maintains the correct engine backpressure during reheat operation.

4. It provides thrust reversal for braking on landing.

5. It provides for noise reduction.

We are only concerned here with the first three requirements.

At subsonic airspeed, the jet stream velocity will be at or below Mach 1.

This means that a normal convergent propelling nozzle will provide the correct exhaust gas expansion to achieve the required jet-stream velocity.

As the aircraft passes through the transonic airspeed range reheat will be used to raise the thrust value to overcome the increasing airframe drag.

When reheat is initiated the jet pipe pressure would rise beyond limits and cause an engine surge if the propelling nozzle area remained unaltered.

There is a need to increase the exhaust nozzle area to control the gas pressure.

The propelling nozzle has a series of 36 moveable flaps connected by links, which are actuated by pneumatic rams.

As the re-heat fuel flow increases the rams progressively open the flaps to control the jet-pipe pressure to compressor delivery pressure ratio within safe limits.

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