Question

7. A gas turbine operates on a pressure ratio of 6. The inlet air temperature to the compressor is 300 K and the temperature of air entering to the turbine is 580°C. If the volume rate of air entering the compressor is 250 m3/s. Calculate the net power output of the cycle. Also, calculate the efficiency.​

Answer 1

Answer:

Thermal efficiency = 58.33%, work ratio = 0.583, shaft work = 270.88 kJ/kg

Answer 2

The net power output of the cycle is -212.28615 and the efficiency is 38.2%.

Given,

$P_{1} : P_{2} = 6$

$T_{C} = 300K\\ \\T_{T} = 580^{0} C = 273 + 580 = 863K$

Volume rate = $250m^{3}/s.$

To find,

net power output = $W_{net}$

efficiency = η.

Formula used,

The net power output $W_{net}$ of a gas turbine is equal to the difference of turbine section work and the power needed for the compressor section.

Steady flow energy equations

$-W_{C} = C_{P}dT. --- Compressor.$

$\ W_{T} = C_{P}dT --- Turbine$.

Taking a note of turbines,

$\frac{T}{T_{T} } = [\frac{P_{2} }{P_{1} }] ^{\frac{K-1}{K} }$

$T = 863[\frac{1}{6}] ^{\frac{0.4}{1.4}} \\ \\T = 511.23K$

Therefore,

$W_{C}$ = -1.005 (853 - 300) = -555.765 kJ/kg

$W_{P}$ = 1.005(853-511.23) = 343.47885 kJ/kg

$W_{net} =W_{C} + W_{P}\\ \\ W_{net} = -555.765 + 343.47885 = -212.28615$

Efficiency(η),

Efficiency of turbine is the ratio of the actual work output to the net input supply of energy if fuel form of the turbine.

η =  $\frac{212.28615}{555.765} = 0.382 = %$ 38.2%.

Therefore, the net power output of the cycle is -212.28615 and the efficiency is 38.2%.