(a) Explanation Show the T-s diagram as in Figure (1). Express Prandtl number at state 8. P r 8 = P 8 P 7 P r 7 (I) Here, pressure at state 8 is P 8 , pressure at state 7 is P 7 and Prandtl number at state 7 is P r 7 . Express Prandtl number at state 10. P r 10 = P 10 P 9 P r 9 (II) Here, pressure at state 10 is P 10 , pressure at state 9 is P 9 and Prandtl number at state 9 is P r 9 . Express enthalpy at state 1. h 1 = h f @10 kPa (III) Here, enthalpy of saturation liquid at pressure of 10 kPa is h f @10 kPa . Express specific volume at state 1. v 1 = v f @10 kPa (IV) Here, specific volume of saturation liquid at pressure of 10 kPa is v f @10 kPa . Express initial work input. w pI,in = v 1 ( P 2 − P 1 ) (V) Here, pressure at state 2 and 1 is P 2 and P 1 respectively. Express enthalpy at state 2. h 2 = h 1 + w pI,in (VI) Express quality at state 6. x 6 = s 6 − s f @10 kPa s f g @10 kPa (VII) Here, entropy at state 6 is s 6 , entropy at saturation liquid and evaporation at pressure of 10 kPa is s f @10 kPa and s f g @10 kPa respectively. Express enthalpy at state 6. h 6 = h f @10 kPa + x 6 h f g @10 kPa (VIII) Here, enthalpy at saturation liquid and evaporation at pressure of 10 kPa is h f @10 kPa and h f g @10 kPa respectively. Express the mass flow rate of air in the gas-turbine cycle from energy balance equation. m ˙ air = h 3 − h 2 h 10 − h 11 m ˙ s (IX) Here, enthalpy at state 10 is h 10 , enthalpy at state 11 is h 11 , enthalpy at state 3 and 2 is h 3 and h 2 respectively, and mass flow rate of steam is m ˙ s . Conclusion: Refer Table A-17, “ideal gas properties of air”, and write the enthalpy at state 7 and Prandtl number at state 7 corresponding to temperature at state 7 of 310 K . h 7 = 310.24 kJ / kg P r 7 = 1.5546 Substitute 12 for P 8 P 7 and 1.5546 for P r 7 in Equation (I). P r 8 = 12 ( 1.5546 ) = 18.66 Refer Table A-17, “ideal gas properties of air”, and write the enthalpy at state 8 corresponding to Prandtl number at state 8 of 18.66 using an 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 (X) Here, the variables denote by x and y is Prandtl number at state8 and enthalpy at state 8 respectively. Show the enthalpy at state 8 corresponding to Prandtl number as in Table (1). Prandtl number at state 8 P r 8 Enthalpy at state 8 h 8 ( kJ / kg ) 18.36 ( x 1 ) 628.07 ( y 1 ) 18.66 ( x 2 ) ( y 2 = ? ) 19.84 ( x 3 ) 638.63 ( y 3 ) Substitute 18 .36, 18 .66 and 19 .84 for x 1 , x 2 and x 3 respectively, 628 .07 kJ / kg for y 1 and 638 .63 kJ / kg for y 3 in Equation (X). y 2 = ( 18 .66 − 18 .36 ) ( 638 .63 kJ / kg − 628 .07 kJ / kg ) ( 19 .84 − 18 .36 ) + 628 .07 kJ / kg = 630 .18 kJ / kg = h 8 Thus, enthalpy at state corresponding to Prandtl number at state 8 of 18.66 is, h 8 = 630 .18 kJ / kg Refer Table A-17, “ideal gas properties of air”, and write the enthalpy at state 9 and Prandtl number at state 9 corresponding to temperature at state 9 of 1400 K . h 9 = 1515.42 kJ / kg P r 9 = 450.5 Here, enthalpy at state 9 is h 9 and Prandtl number at state 9 is P r 9 . Substitute 1 12 for P 10 P 9 and 450.5 for P r 9 in Equation (II). P r 10 = 1 12 ( 450.5 ) = 37.54 Refer Table A-17, “ideal gas properties of air”, and write the enthalpy at state 10 s corresponding to Prandtl number at state 10 of 37.54 using an interpolation method. Show the enthalpy at state 10 corresponding to Prandtl number as in Table (2). Prandtl number at state 10 P r 10 Enthalpy at state 10 h 10 ( kJ / kg ) 37.35 ( x 1 ) 767.29 ( y 1 ) 37.54 ( x 2 ) ( y 2 = ? ) 39.27 ( x 3 ) 778.18 ( y 3 ) Use excels and substitutes the values from Table (II) in Equation (X) to get, h 10 = 768.38 kJ / kg Here, enthalpy at state 10 is h 10 . Refer Table A-5, “saturated water-pressure table”, and write the properties at pressure of 10 kPa . h f @10 kPa = 191.81 kJ / kg v f @10 kPa = 0 (b) To determine The rate of total heat input. (c) To determine The thermal efficiency of the combined cycle.

9th Edition

ISBN: 9781259822674

Author: Yunus A. Cengel Dr., Michael A. Boles

Publisher: McGraw-Hill Education

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Chapter 10.9, Problem 108RP

(a)

To determine

The mass flow rate of air in the gas-turbine cycle.

(b)

To determine

The rate of total heat input.

(c)

To determine

The thermal efficiency of the combined cycle.

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Chapter 10.9, Problem 107RP

Chapter 10.9, Problem 109RP

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A new power plant in Malaysia is going to use combined gas-steam power cycle. The gas turbine portion has a pressure ratio of 10. Air enters the compressor at 400 K at a rate of 16 kg/s and is heated to 1700 K in the combustion chamber. The combustion gases leaving the gas turbine are used to heat the steam to 500°C at 12.5 MPa in a heat exchanger. The combustion gases leave the heat exchanger at 380 K. The steam leaving the turbine is condensed at 20 kPa. Assuming all the compression and expansion processes to be isentropic and constant specific heats at room temperature for air. (a) determine the net power output,

QII/ The gas-turbine portion of a combined gas—steam power plant has a pressure ratio of 16. Air enters the compressor at 300 K at a rate of 14 kg/s and is heated to 1500 K in the combustion chamber. The combustion gases leaving the gas turbine are used to heat the steam to 400 0 C at 10 MPa in a heat exchanger. The combustion gases leave the heat exchanger at 420 K. The steam leaving the turbine is condensed at 15 kPa. Assuming all the compression and expansion processes to be isentropic, determine (a) the mass flow rate of the steam, (b) the net power output, and (c) the thermal efficiency of the combined cycle. For air, assume constant specific heats at room temperature. Answers:(a) 1.275 kg/s, (b) 7819 kW, (c) 66.4 percent.

NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. The gas-turbine cycle of a combined gas–steam power plant has a pressure ratio of 8. Air enters the compressor at 290 K and the turbine at 1400 K. The combustion gases leaving the gas turbine are used to heat the steam at 15 MPa to 450°C in a heat exchanger. The combustion gases leave the heat exchanger at 247°C. Steam expands in a high-pressure turbine to a pressure of 3 MPa and is reheated in the combustion chamber to 500°C before it expands in a low-pressure turbine to 10 kPa. The mass flow rate of steam is 12 kg/s. Assume isentropic efficiencies of 100 percent for the pump, 85 percent for the compressor, and 90 percent for the gas and steam turbines. A.) Determine the mass flow rate of air in the gas-turbine cycle. Use steam tables and the table containing the ideal-gas properties of air. The mass flow rate of air in the gas-turbine cycle is ___?___kg/s…

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The mass flow rate of air in the gas-turbine cycle.

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The mass flow rate of air in the gas-turbine cycle.

The rate of total heat input.

The thermal efficiency of the combined cycle.

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