Consider a steam power plant that operates on a reheat Rankine cycle. Steam enters the high-pressure turbine at 10 MPa and 500°C and the low-pressure turbine at 1 MPa and 500°C. Steam leaves the condenser as a saturated liquid at a pressure of 10 kPa. The isentropic efficiency of the turbine is 80 percent, and that of the pump is 95 percent. Determine the exergy destruction associated with the heat addition process and the expansion process. Assume a source temperature of 1600 K and a sink temperature of 285 K. Also, determine the exergy of the steam at the boiler exit. Take P0 = 100 kPa.
The exergy destruction associated with the heat addition, the expansion process, and the exergy of the steam at the boiler exit.
Answer to Problem 62P
The exergy destruction during the heating process is
The exergy destruction during the expansion process is
The exergy of the steam at the boiler exit is
Explanation of Solution
Draw the
Here, water is the working fluid.
Write the formula for work done by the pump during process 1-2 with the consideration of isentropic efficiency
Here, the specific volume is
Write the formula for enthalpy
Before reheating,
At state
The isentropic efficiency is expressed as follows.
After reheating,
At state 5:
The reheating occurs at constant pressure. Hence, the pressure at state 4 and state 5 are equal.
At state
The steam is expanded to the pressure of
The quality of water at the exit of the L.P turbine (state 6) is expressed as follows (actual).
The enthalpy at state 6 is expressed as follows.
Here, the enthalpy is
The isentropic efficiency is expressed as follows.
Here, the subscript
Write the formula for heat input
Write the formula for the exergy destruction for the combined heat addition and pumping process 1-5.
Here, the entropy
Write the formula for the exergy destruction for pumping process 1-2.
Here, the work input of pump at actual process 1-2 is
Write the formula for exergy destruction for heat addition processes 2-3, 4-5.
Write the formula for the exergy destruction for the expansion process 3-4, 5-6.
Write the formula for exergy of the steam at boiler exit
Here, the enthalpy is
Neglect the kinetic energy
At state 1:
The water exits the condenser as a saturated liquid at the pressure of
Refer Table A-5, “Saturated water-Pressure table”.
The enthalpy
At state 3: (H.P. Turbine inlet)
The steam enters the as superheated vapor.
Refer Table A-6, “Superheated water”.
The enthalpy
At state
From Figure 1.
Refer Table A-6, “Superheated water”.
The enthalpy
At state 5: (L.P. Turbine inlet)
The steam is reheated to superheated at the pressure of
Refer Table A-6, “Superheated water”.
The enthalpy
At state
From Figure 1.
Refer Table A-5, “Saturated water-Pressure table”.
Obtain the following properties corresponding to the pressure of
Here, the sink temperature is equal to the surrounding temperature.
The surrounding pressure
Refer Table A-4, “Saturated water-Temperature table”.
The enthalpy
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Equation (V).
Substitute
Refer Table A-5, “Saturated water-Pressure table”.
Obtain the vapor enthalpy
The calculated enthalpy at state 6 is greater than the vapor enthalpy at this state. Hence, the steam is at superheated state.
Substitute
Consider the process 1 to 5 (combined heat addition and boiler).
Here,
Substitute 285 K for
Substitute
Substitute
Thus, the exergy destruction during the heating process is
Consider the process 3-4 and 5-6 (H.P. turbine expansion and L.P. turbine expansion).
Here,
Substitute 285 K for
Thus, the exergy destruction during the expansion process is
Substitute
Thus, the exergy of the steam at the boiler exit is
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Chapter 10 Solutions
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