Question 12.CSGP.125: Consider a gas turbine cycle with two stages of compression ......
Consider a gas turbine cycle with two stages of compression and two stages of expansion. The pressure ratio across each compressor stage and each turbine stage is 8 to 1. The pressure at the entrance of the first compressor is 100 kPa, the temperature entering each compressor is 20°C, and the temperature entering each turbine is 1100°C. 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.
\begin{aligned}& P _2 / P _1= P _4 / P _3= P _6 / P _7= P _8 / P _9=8.0 \\& P _1=100 \,kPa \\& T _1= T _3=20{ }^{\circ} C , \quad T _6= T _8=1100{ }^{\circ} C\end{aligned}
Cold air and s _2= s _1 \text { and } s _4= s _3
T _4= T _2= T _1\left\lgroup\frac{ P _2}{ P _1} \right\rgroup^{\frac{ k -1}{ k }}=293.15(8)^{0.286}=531 \,K
Total – w _{ C }=2 \times\left(- w _{12}\right)=2 C _{ P 0}\left( T _2- T _1\right)=2 \times 1.004(531-293.15)= 4 7 7 . 6 ~ k J / k g
Also s _6= s _7 \text { and } s _8= s _9: \Rightarrow T _7= T _9= T _6\left\lgroup \frac{ P _7}{ P _6} \right\rgroup^{\frac{ k -1}{ k }}=1373.15\left\lgroup \frac{1}{8} \right\rgroup^{0.286}=758 \,K
Total w _{ T }=2 \times w _{67}=2 C _{ P 0}\left( T _6- T _7\right)=2 \times 1.004(1373.15-758)=1235.2\, kJ / kg
w _{ NET }=1235.2-477.6=757.6 \,kJ / kg
Ideal regenerator: T _5= T _9, T _{10}= T _4 so the actual one has
