Question 4.7: A centrifugal compressor is running at 10,000 rpm and air en......
A centrifugal compressor is running at 10,000 rpm and air enters in the axial direction. The inlet stagnation temperature of air is 290 K and at the exit from the impeller tip the stagnation temperature is 440 K. The isentropic efficiency of the compressor is 0.85, work input factor ψ = 1.04, and the slip factor σ = 0.88. Calculate the impeller tip diameter, overall pressure ratio, and power required to drive the compressor per unit mass flow rate of air.
Temperature equivalent of work done:
T_{02} – T_{01} = \frac{σψU_2^2}{C_p} \text{or} \frac{(0.88)(1.04)(U_2^2)}{1005}
Therefore, U_2 = 405.85 m/s
and D = \frac{60U_2} {\pi N} = \frac{(60)(405.85)}{(\pi)(10,000)} = 0.775 m
The overall pressure ratio is given by:
\frac{P_{03}} {P_{01}} = \left[1 + \frac{η_cσψU_2^2}{C_pT_{01}}\right]^{γ/(γ – 1)}
= \left[1 + \frac{(0.85)(0.88)(1.04)(405.85^2)}{(1005)(290)}\right]^{3.5} = 3.58
Power required to drive the compressor per unit mass flow:
P = mψσU_2 ^2 = \frac{(1)(0.88)(1.04)(405.85^2)}{1000} = 150.75 kW