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, $C_{P_a}=1.005kJ/kgk,C_{p_g}=1.15kJ/kgK.$ For optimum power output, the reheating pressure under. ideal condition should be

• A. 3.421
• B. 6.425
• C. 5.492
• D. 4.521

Answer 1

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, $\frac{n-1}{n}=\frac{\gamma -1}{\gamma {\eta }_{pc}}$

$=\frac{0.4}{1.4\times 0.9}=0.3174$

for expansion process, $\frac{n-1}{n}=\frac{(\gamma -1){\eta }_{pt}}{\gamma }=\frac{0.4\times 0.9}{1.4}=0.2571$

for actual compression process

$1-2^{\prime }:T_{02}^{\prime }=T_{01}{\left(\frac{P_{02}}{P_{01}}\right)}^{\frac{n-1}{n}}=288(32{)}^{0.3174}=865.22K$

$P_{03}=0.98\times 32\times 1.01=31.673bar$

and $P_{06}=1.05bar$

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

$p_4=p_x=\sqrt{pt}=\sqrt{\frac{P_{03}}{P_{06}}}=\sqrt{\frac{31.673}{1.05}}$

= 5.492