A stationary gas turbine engine is used for generating electricity during times of peak demand. Dry air at Tamb= 20oC and Patm = 1 atm enters the compressor. The pressure of the air is increased to Pc,out = 6 atm in the compressor. The isentropic efficiency of the compressor is ηc=0.76. The air leaving the compressor is mixed with methane that enters at T fuel= Pc,out and then mixture is combusted. The methane flow rate is adjusted so that the combustion reaction uses 300% excess air. The combustion products are expanded in a turbine with an isentropic efficiency of ηt=0.83. A generator mounted on the same shaft as the turbine and compressor produces Wgen=500kW of electrical power with a generator efficiency of ηgen =0.92. Pressure in the piping can be neglected in this analysis. However, there are thermal losses from the combustor where you can simulate it as six horizontal cylinder of 10cm diameter and 20cm length with a surface temperature of 700 oC in ambient condition.
a) Determine the temperature of the air entering the combustor (at the exit of the compressor).
b) Determine the temperature of the combustion products leaving the combustor and entering the turbine.
c) Determine the volumetric flow rate of the air entering the compressor.
d) What is the second law efficiency of the system? Discuss this number.
e) Determine the efficiency of the gas turbine engine relative to the lower heating value of the methane. (LHVmethane = 50,032 kJ/kg).
f) What happens to the above calculated parameters if the reduce the excess to 150%? Does this make sence?