An axial flow compressor stage with 50 reaction has the fol

An axial flow compressor stage with 50 % reaction has the following data: Air inlet stagnation temperature= 290 K, relative flow angle at rotor outlet measured from the axial direction = 32o, flow coefficient = 0.55, relative inlet Mach number onto the rotor = 0, 75. If stage is normal, what is the stagnation temperature rise in the first stage of the compressor?

Solution

GIVEN:- (Inlet Temperature) Tin = 290K, (Work done factor) = 1, cp = 1005 J/kgK, R = 287 J/kg, = 1.4, ( Inlet Pressure) Pin = 101.3 kPa, (Flow coefficient) = Ca/U = 0.55, (Reaction) Rx = 0.50, (Relative flow angle) 2 = 32°, (Mach Number) Rm = 0.75, Assume Ca = 151m/s

TO FIND:- (Stagnation temperature rise) T = ?

SOLUTION:- = 0.55 and tan(2) = 0.625

For Rx = 0.5, tan(1) + tan(2) = U/Ca = 1.82, So tan(1) = 1.82 - 0.625 = 1.195

Also U = 1.82 x Ca = 1.82 x 151 = 274.82 m/s

By formula T = /Cp x U x Ca x [tan(1) - tan(2)] = 1/1005 x 274.82 x 151 x [1.195 - 0.625]

i.e. (Stagnation temperature rise) T = 23.53 K (ANSWER)