A gas turbine operates with a regenerator and two stages of reheating and intercooling. Air enters this engine at 14 psia and 60°F, the pressure ratio for each stage of compression is 3, the air temperature when entering a turbine is 940°F, the engine produces 1000 hp, and the regenerator operates perfectly. The isentropic efficiency of each compressor is 88 percent and that of each turbine is 93 percent. Which process of the cycle loses the greatest amount of work potential? The temperature of the heat source is the same as the maximum cycle temperature, and the temperature of the heat sink is the same as the minimum cycle temperature. Use constant specific heats at room temperature.
Which process of the cycle loses the greatest amount of work potential.
Answer to Problem 151P
The exergy destruction associated with process 1-2 and 3-4 is
The exergy destruction associated with process 5-6 and 7-8 is
The exergy destruction associated with process 6-7 and 8-9 is
The exergy destruction associated with process 10-1 and 2-3 is
The exergy destruction associated at regenerator is
During the heat rejection process the highest energy destruction occurs.
Explanation of Solution
Draw the
Write the expression for the temperature and pressure relation for the isentropic process 1-2s.
Here, the pressure ratio is
Write the expression for the efficiency of the compressor
Here, the specific heat at constant pressure is
Write the expression for the temperature and pressure relation ratio for the expansion process 6-7s.
Here, temperature at state 7s for isentropic process is
Write the expression for the efficiency of the turbine
Here, temperature at state 7 is
Write the expression to calculate the heat input for the two-stage gas turbine
Here, the specific heat of air at constant pressure is
Write the expression to calculate the heat output for the two-stage gas turbine
Write the expression for the exergy destruction during the process of as steam from an inlet to exit state.
Here, entropy generation is
Write the expression of exergy destruction for process 1-2
Here, pressure at state 2 is
Write the expression of exergy destruction for process 5-6
Here, pressure at state 5 is
Write the expression of exergy destruction for process 6-7
Here, pressure at state 7 is
Write the expression of exergy destruction for process 10-1
Here, pressure at state 10 is
Write the expression of exergy destruction for regenerator
Conclusion:
Substitute
Substitute
Substitute
Substitute
The regenerator is ideal, the effectiveness is 100% and therefore,
Substitute
Substitute
Substitute
Thus, the exergy destruction associated with process 1-2 and 3-4 is
Substitute
Thus, the exergy destruction associated with process 5-6 and 7-8 is
Substitute
Thus, the exergy destruction associated with process 6-7 and 8-9 is
Substitute
Thus, the exergy destruction associated with process 10-1 and 2-3 is
Substitute
Thus, the exergy destruction associated at regenerator is
During the heat rejection process the highest energy destruction occurs.
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Chapter 9 Solutions
Thermodynamics: An Engineering Approach
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