Question

Assume that air is drawn steadily through a frictionless, adiabatic converging‐diverging nozzle into a frictionless, constant‐area duct with heat addition. The air enters the constant area pipe section at a static pressure of 200 kPa, static temperature of 500K, and velocity of 400 m/s. (a) If 500 kJ/kg is removed from the flow, determine the static pressure, static temperature and velocity of the flow leaving the duct. (b) What is the maximum amount of heat addition for these inflow conditions? (c) Will further addition of heat result in the formation of a normal shock wave within the duct? If it will, explain your answer. If it will not, explain the response of the flow to further heat addition.

Answer 1

a) The sonic velocity at inlet is

Hence

Heat transferred is

Hence

Hence

Using Gas dynamics software in Excel for ME and by trial and error

Hence

Sonic velocity at 2 is

Hence

b) For subsonic flow maximum enthalpy occurs at M=0.845

Since M₁= 0.8924, no heat addition is possible under the given inlet conditions.

c) There will be no normal shock

If heat is added under the given conditions(subsonic), the Rayleigh line must move to a different i.e lower mass flux conditions.