Discovery of A Strong Discontinuity P M V Subbarao Associate Professor Mechanical Engineering Department I I T Delhi A Break Through Finding To Operate Supersonic Systems...

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

P throat = p * P exit = p b,critical P exit = p b,design

This back pressure generates choked condition at the throat. This is the back pressure which produces maximum flow rate through the nozzle

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 back pressure. Further lower pressure at throat!?!?!?!? More Mass Flow Rate!?!?!?!? P throat = p * P exit = p b,critical P exit = p *

Convergent-Divergent Nozzle with High Back Pressure P throat< p * ???? p b< p b,critical < p 0 It is impossible to have a pressure lower than p * at the throat. However at any downstream location the pressure can reach p *. P throat = p *

Find out the downstream location, x where p * can be achieved with lower back pressures. p b< p b,critical < p 0 Feasible solution ? M<1 A=? Infeasible solution

Convergent-Divergent Nozzle Under Off-Design Conditions

M>1 M<1 Normal Shock : A large discontinuity

Moving Shock Towards Exit At any location downstream of throat :

If there exist a normal shock at this location: p b,NS is the back pressure which generates a normal shock at location x.

Normal Shock at the exit of the nozzle

Flow Visualization Studies

Design Back Pressure

Steady Cruising Design Conditions

Back Pressure Lower than the design conditions

Ideal Flow Through CD Diffuser In the ideal case, the diffuser will be designed so that at the design Mach number the ratio of the throat to inlet area is equal to the value of A inlet /A * correspond to design Mach number. M>1 M<1M=1

A inlet /A * decreases as M decreases. For a given inlet area, high throat area is required at lower Mach numbers. During aircraft taking off to cruising conditions (Accelerating to design Mach Number), the diffuser will not be able to swallow all the air flowing towards the intake. Under these conditions a normal shock stands ahead of the diffuser. The velocity of air at the inlet becomes subsonic. The air spill over the intake.

Further acceleration of the aircraft leads movement of normal shock towards inlet lip. As the flight Mach number is increased and the throat area becomes closer to the required for the Mach number. There is still a normal shock ahead of the diffuser and spillage still occurs. A higher Mach number than the design Mach number only can move the shock towards the lip of the inlet. At this conditions the shock is attached to the inlet lip. All the air reaching the diffuser will be ingested. This is a conditions of zero spillage.

The Mach number M lip-shock, at which the shock is attached to the lip is found by noting that this set of circumstances is reached beacause the Mach number behind the shock wave is now sufficiently small for the intake to throat ratio to be equal to the value that corresponds to subsonic flow Mach number. M lip-shock is found by using subsonic relations.

Any further slight increase in the Mach number will cause the shock wave to be swallowed by the diffuser. The shock wave then settles in the divergent portion of the diffuser. Thus in order for the fixed area diffuser to swallow the shock, it is necessary to use over-speeding. Once the shock is swallowed, the flight Mach number can be decreased.

Supersonic Missiles