Consider a steam power plant that operates on a regenerative Rankine cycle and has a net power output of 150 MW. Steam enters the turbine at 10 MPa and 500°C and the condenser at 10 kPa. The isentropic efficiency of the turbine is 80 percent, and that of the pumps is 95 percent. Steam is extracted from the turbine at 0.5 MPa to heat the feedwater in an open feedwater heater. Water leaves the feedwater heater as a saturated liquid. Show the cycle on a T-s diagram, and determine (a) the mass flow rate of steam through the boiler and (b) the thermal efficiency of the cycle. Also, determine the exergy destruction associated with the regeneration process. Assume a source temperature of 1300 K and a sink temperature of 303 K.
(a)
The mass flow rate of steam through the boiler.
Answer to Problem 98RP
The mass flow rate of steam through the boiler is
Explanation of Solution
Draw the
Here, water (steam) is the working fluid of the regenerative Rankine cycle. The cycle involves two pumps.
Write the formula for work done by the pump during process 1-2.
Here, the specific volume is
Write the formula for enthalpy
Write the formula for work done by the pump during process 3-4.
Here, the specific volume is
Write the formula for enthalpy
At state
The steam expanded to the pressure of
The quality of water at state
The enthalpy at state
Here, the enthalpy is
The isentropic efficiency for the process 5-6 is expressed as follows.
At state
The steam enters the condenser at the pressure of
The quality of water at state
The enthalpy at state
Here, the subscript
The isentropic efficiency for the process 5-7 is expressed as follows.
Here, the subscript
Write the formula for heat in
Here, the mass fraction steam extracted from the turbine to the inlet mass of the boiler
Write the general equation of energy balance equation.
Here, the rate of net energy inlet is
At steady state the rate of change of net energy of the system
Refer Equation (XIII).
Write the energy balance equation for open feed water heater.
Rewrite the Equation (XIV) in terms of mass fraction
Write the formula for net work output of the cycle.
Write the formula for mass flow rate of steam.
Here, the net power output of the cycle is
At state 1: (Pump I inlet)
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: (Pump II inlet)
The water exits the open feed water heater as a saturated liquid at the pressure of
Refer Table A-5, “Saturated water-Pressure table”.
The enthalpy
At state 5:
The steam enters the turbine as superheated vapor.
Refer Table A-6, “Superheated water”.
The enthalpy
Refer Figure 1.
At state
The steam expanded to the pressure of
Refer Table A-5, “Saturated water-Pressure table”.
Obtain the following properties corresponding to the pressure of
At state
The steam enters the condenser at the pressure of
Refer Table A-5, “Saturated water-Pressure table”.
Obtain the following properties corresponding to the pressure of
Conclusion:
Substitute
Substitute
Substitute
Substitute
From Figure 1.
Substitute
Substitute
Equation (VI).
Substitute
Substitute
Substitute
Equation (IX).
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the mass flow rate of steam through the boiler is
(b)
The thermal efficiency of the cycle and the exergy destruction associated with the regeneration process.
Answer to Problem 98RP
The thermal efficiency of the cycle is
Explanation of Solution
Write the formula for thermal efficiency of the cycle
Write the formula for exergy destruction associated with the regeneration cycle.
Here, the entropy generation is
Conclusion:
Substitute
Thus, the thermal efficiency of the cycle is
Consider the regeneration process- open feed water heater, process states 6,2,3.
Here,
Substitute
Thus, the exergy destruction associated with the regeneration process is
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