Explanation Draw the T − s diagram for regenerative gas turbine cycle as shown in Figure (1). Write the temperature and pressure relation for the isentropic process 1-2s. T 2 s = T 4 s = T 1 r p ( k − 1 ) / k (I) Here, the pressure ratio is r p , the specific heat ratio is k , temperature at state 1 is T 1 , temperature at state 2 s for isentropic process is T 2 s and temperature at state 4 s for isentropic process is T 4 s . Write the expression for the efficiency of the compressor ( η C ) . η C = c p ( T 2 s − T 1 ) c p ( T 2 − T 1 ) T 2 = T 1 + T 2 s − T 1 η C (II) Here, the specific heat at constant pressure is c p . Write the temperature and pressure relation ratio for the expansion process 6-7 s . T 7 s = T 6 ( 1 r p ) ( k − 1 ) / k (III) Here, temperature at state 7 s for isentropic process is T 7 s and temperature at state 6 for is T 6 . Write the expression for the efficiency of the turbine ( η T ) . η T = c p ( T 6 − T 7 ) c p ( T 6 − T 7 s ) T = T 6 + η T ( T 6 − T 7 s ) (IV) Here, temperature at state 7 is T 7 , Write the expression for the work input per unit mass flow rate to the compressor ( w C,in ) . w C,in = 2 c p ( T 2 − T 1 ) (V) Write the expression for the work done per unit mass flow rate by the turbine ( w T,out ) . w T,out = 2 c p ( T 6 − T 7 ) (VI) Write the expression for to calculate the net work output per unit mass flow rate by the regenerative gas-turbine cycle ( w net ) . w net = w T,out − w C,in (VII) Write the expression to calculate the mass flow rate ( m ˙ ) . m ˙ = W ˙ net w net (VIII) Here, the power produced by the engine is W ˙ net . Write the expression to calculate the rate of heat addition to the cycle ( Q ˙ i n ) . Q ˙ i n = m ˙ c p ( T 6 − T 5 ) + m ˙ c p ( T 8 − T 7 ) = m ˙ c p [ ( T 6 − T 5 ) + ( T 8 − T 7 ) ] (IX) Here, the specific heat at constant pressure is c p , temperature at state 8 for is T 8 . Conclusion. From Table A-2Ea, “Ideal-gas specific heats of various common gases”, obtain the following values for air at room temperature. k = 1.4 c p = 0.24 Btu / lbm ⋅ R Substitute 60 ° F for T 1 , 3 for r p , and 1.4 for k in Equation (I). T 2 s = 60 ° F ( 3 ) 1.4 − 1 / 1.4 = ( 60 + 460 ) R ( 3 ) 0.4 / 1.4 = 711.7 R Substitute 60 ° F for T 1 , 711.7 R for T 2 s , and 88 % for η C in Equation (II). T 2 = 60 ° F + 711.7 R − 60 ° F 88 % = ( 60 + 460 ) R + 711.7 R − ( 60 + 460 ) R 88 ( 1 / 100 ) = 737.8 R Substitute 940 ° F for T 6 , 3 for r p and 1.4 for k in Equation (III). T 7 s = 940 ° F ( 1 3 ) 1.4 − 1 / 1.4 = ( 940 + 460 ) R ( 1 3 ) 0

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ISBN: 9781307573022

Author: CENGEL

Publisher: MCG/CREATE

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Chapter 9.12, Problem 128P

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The change in the rate of heat addition to the cycle.

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Chapter 9.12, Problem 127P

Chapter 9.12, Problem 129P

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The 7FA gas turbine manufactured by General Electric is reported to have an efficiency of 35.9 percent in the simple cycle mode and to produce 159 MW of net power. The pressure ratio is 14.7 and the turbine inlet temperature is 1288°C. The mass flow rate through the turbine is 1,536,000 kg/h. Taking the ambient conditions to be 30°C and 100 kPa, determine the isentropic efficiencies of the turbine and the compressor. Also, determine the thermal efficiency of this gas turbine if a regenerator with an effectiveness of 66 percent is added. Use variable specific heats for air. The isentropic efficiency of the turbine is The isentropic efficiency of the compressor is %. The thermal efficiency of the gas turbine with the regenerator is [ %. %.

The 7FA gas turbine manufactured by General Electric is reported to have an efficiency of 35.9 percent in the simple-cycle mode and to produce 159 MW of net power. The pressure ratio is 14.7 and the turbine inlet temperature is 1288°C. The mass flow rate through the turbine is 1,536,000 kg/h. Taking the ambient conditions to be 20°C and 100 kPa, determine: (a) the isentropic efficiency of the turbine and the compressor, (b) the thermal efficiency of this gas turbine if a regenerator with an effectiveness of 80 percent is added. Answers: (a) 0.849, 0.924 (b) 0.496

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THERMODYNAMICS-SI ED. EBOOK >I<

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The change in the rate of heat addition to the cycle.

Solution Summary: The author explains the change in the rate of heat addition to the cycle. The temperature and pressure relation for the isentropic process is shown in Figure (1).

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