A steam power plant operates on an ideal regenerative Rankine cycle with two open feedwater heaters. Steam enters the turbine at 8 MPa and 550°C and exhausts to the condenser at 15 kPa. Steam is extracted from the turbine at 0.6 and 0.2 MPa. Water leaves both feedwater heaters as a saturated liquid. The mass flow rate of steam through the boiler is 24 kg/s. Show the cycle on a T-s diagram, and determine (a) the net power output of the power plant and (b) the thermal efficiency of the cycle.
(a)
The power output of plant.
Answer to Problem 52P
The power output of the plant is
Explanation of Solution
Draw the schematic diagram of the given ideal regenerative Rankine cycle as shown in
Figure 1.
Draw the
Figure 2.
Here, water (steam) is the working fluid of the regenerative Rankine cycle. The cycle involves three 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
Write the formula for work done by the pump during process 5-6.
Here, the specific volume is
Write the formula for enthalpy
At state 9:
The steam expanded to the pressure of
The quality of water at the exit of the turbine (state 9) is expressed as follows.
The enthalpy at state 9 is expressed as follows.
Here, the enthalpy is
At state 10:
The steam enters the condenser at the pressure of
The quality of water at state 10 is expressed as follows.
The enthalpy at state 10 is expressed as follows.
Here, the subscript 10 indicates the process state 10.
Refer Figure 1 and 2.
Write the formula for heat in
Here, the mass fraction steam extracted from the turbine to the feed water entering the boiler via feed water heater-I
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-II.
Rewrite the Equation (XIV) in terms of mass fraction
Refer Equation (XIII).
Write the energy balance equation for open feed water heater-I.
Rewrite the Equation (XVI) in terms of mass fraction
Write the formula for net power output of the cycle per unit mass.
Write the formula for net power output of the cycle.
Here, the mass flow rate 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-I as a saturated liquid at the pressure of
Refer Table A-5, “Saturated water-Pressure table”.
The enthalpy
At state 5: (Pump III inlet)
The water exits the open feed water heater-II as a saturated liquid at the pressure of
Refer Table A-5, “Saturated water-Pressure table”.
The enthalpy
At state 7:
The steam enters the turbine as superheated vapor.
Refer Table A-6, “Superheated water”.
The enthalpy
From Figure 2.
At state 8:
The steam expanded to the pressure of
Refer Table A-6, “Superheated water”.
The enthalpy
At state 9:
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 10:
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
Equation (III).
Substitute
Substitute
Equation (V).
Substitute
From Figure 1.
Substitute
Substitute
Equation (VIII).
Substitute
Substitute
Equation (X).
Consider the open feed water heater-II alone.
Substitute
Consider the open feed water heater-I alone.
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the power output of the plant is
(b)
The thermal efficiency of the cycle.
Answer to Problem 52P
The thermal efficiency of the cycle is
Explanation of Solution
Write the formula for thermal efficiency of the cycle
Conclusion:
Substitute
Thus, the thermal efficiency of the cycle is
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