Question 1.7: Consider an axial flow gas turbine in which air enters at th......
Consider an axial flow gas turbine in which air enters at the stagnation temperature of 1050 K. The turbine operates with a total pressure ratio of 4:1. The rotor turns at 15500 rpm and the overall diameter of the rotor is 30 cm. If the total-to-total efficiency is 0.85, find the power output per kg per second of airflow if the rotor diameter is reduced to 20 cm and the rotational speed is 12,500 rpm. Take γ = 1.4.
Using the isentropic P – T relation:
T^′_{02} = T_{01} \left(\frac{P_{02}} {P_{01}}\right)^\frac{(γ-1)}{2} = (1050)\left(\frac{1}{4}\right)^{0.286} = 706.35 K
Using total-to-total efficiency,
T_{01} -T_{02} = (T_{01} -T_{02})η_{tt}= (343.68)(0.85) = 292.13 K
and
W_1 = c_pΔT_0 = (1.005)(292.13) = 293.59 kJ/kg
W_2 = \frac{W_1N_2^2D_{2}^2} {N^2_1 D^2_1} =\frac{(293.59 \times 10^3)(12,500)^2(0.20)^2}{(15,500)^2(0.30)^2}
= 84, 862 J/kg
∴ Power output = 84.86 kJ/kg