A steam power plant operates on an ideal reheat–regenerative Rankine cycle with one reheater and two feedwater heaters, one open and one closed. Steam enters the high-pressure turbine at 15 MPa and 600°C and the low-pressure turbine at 1 MPa and 500°C. The condenser pressure is 5 kPa. Steam is extracted from the turbine at 0.6 MPa for the closed feedwater heater and at 0.2 MPa for the open feedwater heater. In the closed feedwater heater, the feedwater is heated to the condensation temperature of the extracted steam. The extracted steam leaves the closed feedwater heater as a saturated liquid, which is subsequently throttled to the open feedwater heater. Show the cycle on a T-s diagram with respect to saturation lines. Determine (a) the fraction of steam extracted from the turbine for the open feedwater heater, (b) the thermal efficiency of the cycle, and (c) the net power output for a mass flow rate of 42 kg/s through the boiler.
(a)
The fraction of steam extracted from the turbine for the open feed water heater.
Answer to Problem 110RP
The fraction of steam extracted from the turbine for the open feed water heater is
Explanation of Solution
Draw the schematic layout of the given power plant that operates on an ideal reheat-regenerative Rankine cycle as shown in Figure 1.
Draw the
Figure 2.
Here, water (steam) is the working fluid of the ideal 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
Write the formula for enthalpy
The quality of water at state 13 is expressed as follows.
The enthalpy at state 13 is expressed as follows.
Here, the enthalpy is
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 (VIII).
Write the energy balance equation for open feed water heater.
Here, the mass fraction steam extracted from the turbine to the inlet mass of the boiler
Rewrite the Equation (IX) in terms of mass fraction
For the open FWH,
Here, the mass fraction steam extracted from the turbine to the inlet mass of the boiler
Solving Equation (XI).
Conclusion:
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
Substitute
Substitute
From the Table A-5, “Saturated water-temperature Table” obtains the value of the enthalpy
Substitute
Substitute
From the Table A-5, “Saturated water-temperature Table” obtains the value of the enthalpy
Here, the temperature at the state 6
Substitute
From the Table A-6, “Superheated water” obtains the value of the enthalpy
From the Table A-6, “Superheated water” obtains the value of the enthalpy
Here, the entropy at the state 9
From the Table A-6, “Superheated water” obtains the value of the enthalpy
Refer Table A-6, “superheated water”, and write the enthalpy at state 11 at pressure of
Here, enthalpy of saturation liquid at pressure of
Write the formula of interpolation method of two variables.
Here, the variables denote by x and y is specific entropy and specific enthalpy at state 11 respectively.
Show the specific enthalpy at state 11 corresponding to temperature as in Table (1).
Specific entropy at state 11 |
Specific enthalpy at state 11 |
7.7097 | 3270.8 |
7.7642 | |
8.0041 | 3483.4 |
Substitute
Substitute
Similarly repeat the Equation (XIV) for specific enthalpy at state 11 corresponding to the pressure of
From the Table A-5, “Saturated water” obtains the value of the specific entropy of saturated liquid
Substitute
Substitute
Substitute
Substitute
Thus, the fraction of steam extracted from the turbine for the open feed water heater is
(b)
The thermal efficiency of the cycle.
Answer to Problem 110RP
The thermal efficiency of the cycle is
Explanation of Solution
Write the formula for heat in
Write the formula for net power output of the cycle per unit mass.
Write the formula for thermal efficiency of the cycle
Conclusion:
Substitute
Substitute 0.06215 for
Substitute
Substitute
Thus, the thermal efficiency of the cycle is
(c)
The net power output for mass flow rate of
Answer to Problem 110RP
The net power output for mass flow rate of
Explanation of Solution
Write the expression for net power output for mass flow rate of
Here, the mass flow rate through the boiler is
Conclusion:
Substitute
Thus, the net power output for mass flow rate of
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