CHOKED NOZZLE THRUST
As the exhaust gas passes through the convergent propelling nozzle it accelerates and the pressure and temperature of the gas fall. You should see that if the pressure of the gas falls, the gas will expand as its density decreases. At subsonic velocities this is not significant but, as the gas speed reaches the local speed of sound in air, it becomes significant. At Mach one, the density reduction is enough to cause the gas to significantly expand and attempt a further increase in velocity. As the expansion is in all directions, the propelling nozzle exit orifice becomes choked and no further increase in gas exit velocity is possible. When this occurs, all the pressure in the exhaust gas cannot fully convert to velocity so the gas retains a residual pressure after exit.
This means that when the nozzle chokes there will be a gas pressure in excess of ambient pressure just rear of the engine propelling nozzle orifice.
You should understand that this pressure over ambient did not exist prior to the nozzle choking.
As the engine is surrounded by ambient pressure, the presence of pressure in excess of ambient at the rear of the nozzle will exert a force on the cross-sectional area of the exit orifice.
This is a forward acting force, which is called pressure thrust or choked nozzle thrust.
Pressure thrust=(Exit Gas Pressure – Ambient Pressure) x Nozzle Exit Area
Pressure thrust=(Pj-Pamb) x Area of Nozzle
We now need to revise our ideas about net thrust as follows:
Net Thrust = Gross Thrust + Pressure Thrust – Momentum Drag
The turbo-jet flying at 200m/ s with an air mass flow of 100 kg/s and a jet- stream velocity of 330m/s now has a choked nozzle.
The residual gas pressure in the jet stream is 45KPa gauge and the ambient pressure at the aircraft altitude is 0 KPa gauge. The nozzle area is 0.2 m2
The net thrust is:
Gross Thrust is MVj = 33kN
Momentum drag is MV = 20kN
Pressure thrust= (Pj – Pamb) x A= (45 KPa- 0 KPa) x 0.2m2 = 9kN
Therefore Net thrust= 33kN + 9kN- 20kN = 22kN
So, as you can see, pressure thrust resulting from a choked nozzle is a useful supplement to forward thrust.
Many gas turbine engines running at cruise and above will have a choked nozzle condition.
However, once the nozzle is choked, no increase in jet-stream velocity is possible.
The jet efflux is hot, so, the local speed of sound in air at the propelling nozzle is higher than the ambient figure.
If you further increase the temperature of the gases, for example, push the throttle open or, in some cases, use reheat, the gas temperature rises, the nozzle un-chokes and then re-chokes at a higher gas velocity.