a) Explanation Draw the T − s diagram regenerative gas turbine as shown in Figure (1). Write the expression to calculate the pressure ratio for the regenerative gas turbine ( r p ) . r p = P 2 / P 1 . (I) Here, pressure at state 1 is P 1 and pressure at state 2 is P 2 . Write the pressure ratio relation for the process 3-4. P r 4 = P 4 P 3 P r 3 . (II) Here, pressure at state 4 is P 4 and pressure at state 3 is P 3 . Write the efficiency of the turbine ( η T ) . η T = h 3 − h 4 h 3 − h 4 s . (III) Here, enthalpy at state 3 is h 3 , enthalpy at state 4 is h 4 and isentropic enthalpy at state 4 s is h 4 s . Write the expression to calculate the heat added due to regeneration ( q regen ) . q regen = ε ( h 4 − h 2 ) . (IV) Here, the effectiveness of the regenerator is ε . Conclusion: From Table A-17, “Ideal-gas properties of air”, obtain the properties of air at 295 K ( T 1 ) , 650K ( T 2 ) and 1400 K ( T 3 ) ,as 310.24 kJ / kg for h 1 , 659.84 kJ / kg for h 2 , 1 , 515.42 kJ / kg for h 3 and 450.5 for P r 3 respectively. Substitute 900 kPa for P 2 , and 100 kPa for P 1 in Equation (I). r p = 900 kPa / 100 kPa = 9 Substitute 1 9 for P 4 P 3 , and 450.5 for P r 3 in Equation (II). P r 4 = ( 1 9 ) ( 450.5 ) = 50.06 From the Table A-17, “Ideal-gas properties of air”. Obtain the value of isentropic enthalpy at state 4 s ( h 4 s ) at the relative pressure ( P r 4 ) of 50.06 by using interpolation method. Write the formula of interpolation method of two variables. y 2 = ( x 2 − x 1 ) ( y 3 − y 1 ) ( x 3 − x 1 ) + y 1 (V) Here, the variables denoted by x and y are relative pressure and enthalpy b) To determine The thermal efficiency of the turbine.

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Author: CENGEL

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Chapter 9.12, Problem 116P

To determine

The amount of heat transfer in the regenerator.

To determine

The thermal efficiency of the turbine.

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Chapter 9.12, Problem 115P

Chapter 9.12, Problem 117P

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Chapter 9 Solutions

EBK THERMODYNAMICS: AN ENGINEERING APPR

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The amount of heat transfer in the regenerator.

Solution Summary: The author explains the amount of heat transfer in the regenerator and the pressure ratio relation for the process 3-4.

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The amount of heat transfer in the regenerator.

The thermal efficiency of the turbine.

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