Repeat Prob. 9–125, assuming an efficiency of 86 percent for each compressor stage and an efficiency of 90 percent for each turbine stage.
a)
The back work ratio and thermal efficiency of the gas-turbine without regenerator.
Answer to Problem 126P
The back work ratio for the ideal gas-turbine cycle without regenerator is
The thermal efficiency of the gas-turbine without regenerator is
Explanation of Solution
Draw the
Write the pressure ratio relation for the process 1-2.
Here, relative pressure at state 1 is
Write the pressure ratio relation for the process 5-6.
Here, pressure at state 6 is
Write the expression to calculate the work input per kg to the compressors
Here, enthalpy at state 2 is
Write the expression to calculate the work done per kg by the turbines
Here, enthalpy at state 5 is
Write the expression to calculate the back work ratio
Write the expression to calculate the heat input for ideal gas-turbine cycle
Here, enthalpy at state 4 is
Write the expression to calculate the net work output per kg by the gas-turbine cycle
Write the expression to calculate the thermal efficiency of the gas-turbine cycle
Write the expression for the efficiency of the compressor
Here, the specific heat at constant pressure is
Write the expression for the efficiency of the turbine
Conclusion:
From Table A-17, “Ideal-gas properties of air”, obtain the following properties at the temperature of
Substitute 3 for
From the Table A-17, “Ideal-gas properties of air”.
Obtain the value of enthalpy on isentropic state
Write the formula of interpolation method of two variables.
Here, the variables denoted by x and y are relative pressure and enthalpy on isentropic state.
Show relative pressure and enthalpy on isentropic state values from the Table A-17.
Relative pressure | Enthalpy |
4.153 | 411.12 |
4.158 | ? |
4.522 | 421.26 |
Substitute
The enthalpy on isentropic state
Substitute
From Table A-17, “Ideal-gas properties of air”, obtain the following properties at the temperature of
Substitute
From the Table A-17, “Ideal-gas properties of air” obtain the values of enthalpy on isentropic states
Substitute
Substitute
Substitute
Substitute
Thus, the back work ratio for the ideal gas-turbine cycle without regenerator is
Substitute
Substitute
Substitute
Thus, the thermal efficiency of the gas-turbine without regenerator is
b)
The thermal efficiency of the gas turbine with regenerator.
Answer to Problem 126P
The thermal efficiency of the gas turbine with regenerator is
Explanation of Solution
Write the expression to calculate the heat used for the regeneration process
Here, the effectiveness of the regenerator is
Write the expression to calculate the new heat input to the gas-turbine cycle
Write the expression to calculate the thermal efficiency of the gas-turbine with regenerator
Conclusion:
Substitute 0.75 for
Substitute
Substitute
Thus, the thermal efficiency of the gas turbine with regenerator is
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Chapter 9 Solutions
Thermodynamics: An Engineering Approach
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