Gas Dynamics of Variable Area Ducts P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Development of Efficient and Compact Passive Devices….

System of Equaions

Combine conservation, state equations– can algebraically show So we have three ways to change Mach number of a flow – area change (dA): – friction: f > 0, same effect as –dA – heat transfer: heating, q ’’’ > 0, like –dA cooling, q ’’’ < 0, like +dA

Effect of Shape of duct on Flow Pure shape effects :

Pure Shape Effects …..

Subsonic Nozzle Subsonic Diffuser dA < 0 & M <1 So, du > 0 & dp <0 dA > 0 & M <1 So, du 0

Supersonic Diffuser Supersonic Nozzle dA 1 So, du 0 dA > 0 & M >1 So, du >0 & dp<0

Generation of High Pressure from Supersonic velocity

Generation of Supersonic Velocity from Rest Rocket Nozzle

X – 15 : Hypersonic Research at the Edge of Space The X-15 was air launched from a B-52 aircraft at about 45,000 ft and speeds upward of 500 mph. The airplane first set speed records in the Mach 4-6 range with Mach 4.43 on March 7, 1961; Mach 5.27 on June 23, 1961; Mach 6.04 on November 9, 1961; and Mach 6.7 on October 3, It also set an altitude record of 354,200 feet (67 miles) on August 22, 1963, and provided an enormous wealth of data on hypersonic air flow. Aerodynamic heating, control and stability at hypersonic speeds, reaction controls for flight above the atmosphere, piloting techniques for reentry, human factors, and flight instrumentation.

Intake at Design Altitude p1p1 p2p2 p throat p p2p2 p*p* p1p1

At M=1 Minimum Area = A * : Also called throat

Frictional Adiabatic Flow in A Variable Area Duct 0 Constant Mach number frictional flow