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Question

The following data relate to a high pressure ratio single shaft gas turbine cycle with reheat. Total ambient condition = 1.01 bar, 288 K, total compressor pressure ratio = 32, polytropic efficiency = 0.9 for compressor and turbine both, turbine both, turbine inlet temperature = 1600 K pressure loss in first combustor = 2% of compressor delivery pressure loss in second combustor = 4% of HP turbine, exhaust pressure, total turbine exhaust pressure = 1.05 bar, mechanical efficiency for assembly = 0.97, combustion efficiency of both combustor = 0.96, alternator efficiency = 0.97, alternator power output = 240 MW, lower calorific value of fuel = 42000 kJ/kg, CPa=1.005kJ/kgk,Cpg=1.15kJ/kgK. For optimum power output, the reheating pressure under. ideal condition should be

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Solution

The correct option is **C** 5.492

For polytropic compression and expansion, the value of (n−1)/n has to be evaluated and polytropic efficiency will help in evaluating their values,

for compression process, n−1n=γ−1γηpc

=0.41.4×0.9=0.3174

for expansion process, n−1n=(γ−1)ηptγ=0.4×0.91.4=0.2571

for actual compression process

1−2′:T′02=T01(P02P01)n−1n=288(32)0.3174=865.22K

P03=0.98×32×1.01=31.673bar

and P06=1.05bar

For optimum power output, the reheating pressure under ideal condition should be

p4=px=√pt=√P03P06=√31.6731.05

= 5.492

For polytropic compression and expansion, the value of (n−1)/n has to be evaluated and polytropic efficiency will help in evaluating their values,

for compression process, n−1n=γ−1γηpc

=0.41.4×0.9=0.3174

for expansion process, n−1n=(γ−1)ηptγ=0.4×0.91.4=0.2571

for actual compression process

1−2′:T′02=T01(P02P01)n−1n=288(32)0.3174=865.22K

P03=0.98×32×1.01=31.673bar

and P06=1.05bar

For optimum power output, the reheating pressure under ideal condition should be

p4=px=√pt=√P03P06=√31.6731.05

= 5.492

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