A gas turbine has two stages of compression, with an intercooler between the sta

Question

A gas turbine has two stages of compression, with an intercooler between the stages and two stages of expansion. Air enters the first stage of compression at 100kPa and 300K. The pressure ratio across each compressor stage is 5:1, and each stage has an isentropic efficiency of 82%. Air exits the intercooler at 330K. The temperature entering each turbine is 1373K. A regenerator is also incorporated into the cycle, and it has an efficiency of 70%. Determine the compressor work, the turbine work and the thermal efficiency of the cycle.

Explanation / Answer

P1 = 100 kPa, T1 = 300 K State 7: P7 = Po = 100

kPa

State 3: T3 = 330 K; State 6: T6 = 1373 K, P6 = P4

P2 = 5 P1 = 500 kPa; P4 = 5 P3 = 2500 kPa

Ideal compression T2s = T1 (P2/P1)

(k-1)/k = 475.4 K

1st Law: q + hi = he + w; q = 0 => wc1 = h1 - h2 = CP(T1 - T2)

wc1 s = CP(T1 - T2s) = -176.0 kJ/kg, wc1 = wc1 s/ ? = -214.6

T2 = T1 - wc1/CP = 513.9 K

T4s = T3 (P4/P3)

(k-1)/k = 475.4 K

wc2 s = CP(T3 - T4s) = -193.6 kJ/kg; wc2 = -236.1 kJ/kg

T4 = T3 - wc2 / CP = 565.2 K

Ideal Turbine (reversible and adiabatic)

T7s = T6(P7/P6)

(k-1)/k = 597.4 K => wTs = CP(T6 - T7s) = 905.8 kJ/kg

1st Law Turbine: q + h6 = h7 + w; q = 0

wT = h6 - h7 = CP(T6 - T7) = ?Ts wTs = 0.86

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