Consider a combined gas–steam power plant that has a net power output of 280 MW. The pressure ratio of the gas-turbine cycle is 11. Air enters the compressor at 300 K and the turbine at 1100 K. The combustion gases leaving the gas turbine are used to heat the steam at 5 MPa to 350°C in a heat exchanger. The combustion gases leave the heat exchanger at 420 K. An open feedwater heater incorporated with the steam cycle operates at a pressure of 0.8 MPa. The condenser pressure is 10 kPa. Assuming isentropic efficiencies of 100 percent for the pump, 82 percent for the compressor, and 86 percent for the gas and steam turbines, determine (a) the mass flow rate ratio of air to steam, (b) the required rate of heat input in the combustion chamber, and (c) the thermal efficiency of the combined cycle.
(a)
The mass flow rate ratio of the air to the steam.
Answer to Problem 86P
The mass flow rate ratio of the air to the steam is
Explanation of Solution
Show the
Refer Figure 1.
Consider the gas cycle (topping cycle) and their respective process states such as 8, 9,
At state 8:
The air enters the compressor at the temperature of
Refer Table A-17, “Ideal-gas properties of air”.
The enthalpy
Write the relative pressure and absolute pressure relation for the process 8-9-
Here, the relative pressure is
Write the formula for isentropic efficiency of compressor for the process 8-9-
Here, the enthalpy is
At state 10:
The air enters the turbine at the temperature of
Refer Table A-17, “Ideal-gas properties of air”.
The enthalpy
Write the relative pressure and absolute pressure relation for the process 10-11-
Write the formula for isentropic efficiency of gas turbine
At state 12: (heat exchanger)
The enthalpy
Refer Figure 1.
Consider the steam cycle (bottoming cycle) and their respective process states such as 1, 2, 3, 4, 5, 6,
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 2:
Write the formula for work done by the pump during process 1-2.
Here, the specific volume is
Write the formula for 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 4:
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 5:
The steam enters the turbine as superheated vapour.
Refer Table A-6, “Superheated water”.
The enthalpy
At state
The steam expanded to the pressure of
The quality of water at state
The enthalpy at state
Here, the enthalpy is
Refer Table A-5, “Saturated water-Pressure table”.
Obtain the following properties corresponding to the pressure of
The isentropic efficiency of the steam turbine for the process 5-6-
At state
The steam enters the condenser at the pressure of
The quality of water at state
The enthalpy at state
Here, the subscript
Refer Table A-5, “Saturated water-Pressure table”.
Obtain the following properties corresponding to the pressure of
The isentropic efficiency of the steam turbine for the process 5-7-
Here, the subscript
Write the general energy rate balance equation.
Here, the rate of energy in is
Consider the heat exchanger operates on steady state. Hence, the rate of change in net energy of the system is zero.
The Equation (XVI) is reduced as follows for the heat exchanger.
Here, the mass flow rate of air is
Conclusion:
Substitute
Refer Table A-17, “Ideal-gas properties of air”.
The enthalpy
Substitute
Substitute
Refer Table A-17, “Ideal-gas properties of air”.
The enthalpy
Substitute
Substitute
Substitute
Substitute
Equation (VII).
Substitute
From Figure 1.
Substitute
Substitute
Equation (X).
Substitute
Substitute
Substitute
Equation (XIII).
Substitute
Substitute
Thus, the mass flow rate ratio of the air to the steam is
(b)
The required rate of heat input in the combustion chamber.
Answer to Problem 86P
The required rate of heat input in the combustion chamber is
Explanation of Solution
Refer Equation (XV).
Consider the open feed water heater operates on steady state. Hence, the rate of change in net energy of the system is zero.
Write the energy rate balance equation for open feed water heater.
Rewrite the Equation (XVII) in terms of mass fraction
Here, the mass fraction steam extracted from the turbine to the inlet mass of the boiler
Write the formula for work output of the steam turbine.
Write the formula for net work output of the steam cycle.
Write the formula for net work output of the gas cycle.
Write the formula for the net work output of the gas-steam cycle per unit mass of gas.
Write the formula for mass flow rate of air through the compressor.
Write the formula for rate of heat input to the combustion chamber.
Conclusion:
Substitute
Equation (XVIII).
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Equation (XXIV).
Thus, the required rate of heat input in the combustion chamber is
(c)
The thermal efficiency of the combined cycle.
Answer to Problem 86P
The thermal efficiency of the combined cycle is
Explanation of Solution
Write the formula for thermal efficiency.
Conclusion:
Substitute
Thus, the thermal efficiency of the combined cycle is
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