C & CD Nozzles for Jet Propulsion P M V Subbarao Professor Mechanical Engineering Department Design Vs Off-Design Characteristics…..

Operational Characteristics of Isentropic C Nozzles A converging passage designed to accelerate the a gas flow is considered for study. The concern here is with the effect of changes in the upstream and downstream pressures on the nature of the flow and on the mass flow rate through a nozzle. Four different cases considered for analysis are: Converging nozzle with constant upstream conditions. Converging-diverging nozzle with constant upstream conditions. Converging nozzle with constant downstream conditions. Converging-diverging nozzle with constant downstream conditions.

Pressure Distribution in Under Expanded Nozzle pb=p0 p0 pb,critical<pb3<p0 pb,critical<pb2<p0 pb,critical<pb1<p0 Pb,critical At all the above conditions, the pressure at the exit plane of nozzle, pexit = pb.

Variation of Mass Flow Rate in Exit Pressure 1 1

Variation of in Exit Pressure 1 1

Variation of in Mass Flow Rate 1

Low Back Pressure Operation

Frictional Adiabatic Flow in A Variable Area Duct Sonic Point : M=1

Throat Conditions The capacity of Frictional throat is always lower than ideal throat!!!

The Real Nozzle for Sonic Flow It is impossible to get a sonic flow with real converging nozzle. The flow is always subsonic (transonic) at the throat. A compact real converging nozzle can produce transonic jet. A real nozzle for sonic exit is a CD Nozzle.

Ideal Convergent-Divergent Nozzle Under Design Conditions

Convergent-Divergent Nozzle with High Back Pressure pb1< p0 but > p* Pthroat > p*

Convergent-Divergent Nozzle with High Back Pressure When pb is very nearly the same as p0 the flow remains subsonic throughout. The flow in the nozzle is then similar to that in a venturi. The local pressure drops from p0 to a minimum value at the throat, pthroat , which is greater than p*. The local pressure increases from throat to exit plane of the nozzle. The pressure at the exit plate of the nozzle is equal to the back pressure. This trend will continue for a particular value of back pressure.

Convergent-Divergent Nozzle with High Back Pressure At all these back pressures the exit plane pressure is equal to the back pressure. pthroat> p*

Mass Flow Rate at Higher Back Pressures

Mass flow rate at high back pressure pb At throat with high back pressure pb

For a given value of high back pressure corresponding throat pressure can be calculated. As exit area is higher than throat area throat pressure is always less than exit plane pressure. A decreasing exit pressure produces lowering throat pressure

Variation of Mass Flow Rate in Exit Pressure 1 1

Variation of in Mass Flow Rate 1

Further Decrease the Back Pressure till the throat is just choked…. Define this back pressure as critical back pressure, pb.critical.

This generates choked condition at the throat. This is the back pressure which produces maximum flow rate Through the nozzle. Is this back pressure same as design back pressure? If not??????

Pexit = pb,critical Pthroat = p*

Variation of in Exit Pressure 1 1

Variation of in Throat Pressure 1 1

Variation of in Mass Flow Rate 1

What Next? What happens if back pressure is further reduced? Still the pressure at the exit plane is equal to the throat pressure? Further lower pressure at throat !?!?!

Convergent-Divergent Nozzle with High Back Pressure It is impossible to have a pressure lower than p* at the throat. However at any downstream location the pressure can reach p*. Pthroat = p* pb< pb,critical <p0 Pthroat< p*????

Find out the downstream location, x where p Find out the downstream location, x where p* can be achieved with lower back pressures. A=? pb < pb,critical <p0 Feasible solution Infeasible solution ? M<1 M<1

Convergent-Divergent Nozzle Under Off-Design Conditions

Normal Shock : A large discontinuity

Moving Shock Towards Exit

Flow Visualization Studies

Design Back Pressure

Steady Cruising Design Conditions

Back Pressure Lower than the design conditions

Back Pressure Lower than the design conditions

Back Pressure Lower than the design conditions