Question 12.CSGP.114: The power plant shown in Fig. 12.21 combines a gas-turbine c......
The power plant shown in Fig. 12.21 combines a gas-turbine cycle and a steam- turbine cycle. The following data are known for the gas-turbine cycle. Air enters the compressor at 100 kPa, 25°C, the compressor pressure ratio is 14, the heater input rate is 60 MW; the turbine inlet temperature is 1250°C, the exhaust pressure is 100 kPa; the cycle exhaust temperature from the heat exchanger is 200°C. The following data are known for the steam-turbine cycle. The pump inlet state is saturated liquid at 10 kPa, the pump exit pressure is 12.5 MPa; turbine inlet temperature is 500°C. Determine
a. The mass flow rate of air in the gas-turbine cycle.
b. The mass flow rate of water in the steam cycle.
c. The overall thermal efficiency of the combined cycle.
a) From Air Tables, A.7: P _{ r 1}=1.0913, \quad h _1=298.66, \quad h _5=475.84 \,kJ / kg
At T _3=1523.2 \,K : P _{ r 3}=515.493, h _3=1663.91 \,kJ / kg
\dot{ m }_{ AIR }=\dot{ Q }_{ H } /\left( h _3- h _2\right)=\frac{60000}{1663.91-634.48}= 5 8 . 2 8 \,k g / s
b)
Steam cycle: – w _{ P } \approx 0.00101(12500-10)=12.615 \,kJ / kg
h _6= h _9- w _{ P }=191.83+12.615=204.45 \,kJ / kg
At 12.5 MPa, 500 °C: h _7=3341.1 \,kJ / kg , \quad s _7=6.4704 \,kJ / kg K
\dot{ m }_{ H _2 O }=\dot{ m }_{ AIR } \frac{ h _4- h _5}{ h _7- h _6}=58.28 \frac{812.68-475.84}{3341.1-204.45}= 6 . 2 5 9 \,kg / s
c)