Reconsider Prob. 10–83. Determine which components of the combined cycle are the most wasteful of work potential.
10–83 A combined gas–steam power cycle uses a simple gas turbine for the topping cycle and simple Rankine cycle for the bottoming cycle. Atmospheric air enters the gas turbine at 101 kPa and 20°C, and the maximum gas cycle temperature is 1100°C. The compressor pressure ratio is 8; the compressor isentropic efficiency is 85 percent; and the gas turbine isentropic efficiency is 90 percent. The gas stream leaves the heat exchanger at the saturation temperature of the steam flowing through the heat exchanger. Steam flows through the heat exchanger with a pressure of 6000 kPa and leaves at 320°C. The steam-cycle condenser operates at 20 kPa, and the isentropic efficiency of the steam turbine is 90 percent. Determine the mass flow rate of air through the air compressor required for this system to produce 100 MW of power. Use constant specific heats for air at room temperature.
Which component of the combined cycle is the most wasteful of work potential.
Answer to Problem 85P
The combustor of the gas-steam cycle has largest exergy destruction
Explanation of Solution
Show the
Refer Figure 1.
Consider the gas cycle (topping cycle) and their respective process states such as 5, 6,
Write the temperature and pressure relation at isentropic state and for the process 5-6-
Here, the temperature is
Write the formula for isentropic efficiency of compressor for the process 5-6-
Here, the enthalpy is
Rearrange and rewrite the equation (II) to obtain
Write the temperature and pressure relation at isentropic state and for the process 7-8-
Write the formula for isentropic efficiency of gas turbine
Rearrange and rewrite the equation (V) to obtain
At state 9: (heat exchanger)
The temperature
Refer Table A-5, “Saturated water-Pressure table”.
The saturation temperature corresponding to the pressure of
Refer Figure 1.
Consider the steam cycle (bottoming cycle) and their respective process states such as 1, 2, 3, 4,
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 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: (Turbine inlet)
The steam enters the turbine as superheated vapour.
Refer Table A-6, “Superheated water”.
The enthalpy
From Figure 1,
At state 4: (Turbine exit or condenser inlet)
The steam exits the condenser as a saturated liquid at the pressure of
The quality of water at the exit of the turbine is expressed as follows.
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
Write the formula for isentropic efficiency of the steam turbine
Rearrange the Equation (XI) to obtain the enthalpy
Write the formula for net work output of the gas cycle.
Here, the specific heat of air at constant pressure is
Write the formula for net work output of the steam cycle.
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 (XV) is reduced as follows for the heat exchanger.
Here, the mass flow rate of air is
Write the formula for mass flow rate of air through the compressor.
Write the formula for the exergy destruction for the process 3-4 (turbine).
Write the formula for the exergy destruction for the process 4-1 (condenser).
Write the formula for the exergy destruction for heat exchanger.
Write the formula for the exergy destruction for the process 5-6 (compressor).
Write the formula for the exergy destruction for the process 6-7 (combustion chamber).
Write the formula for the exergy destruction for the process 7-8 (gas turbine).
Here, the specific heat at constant pressure of air is
Refer Table A-2, “Ideal-gas specific heats of various common gases”.
The specific heat at constant pressure
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Here,
Substitute
Substitute
Equation (X).
Substitute
Substitute
Substitute
Equation (XIV).
Substitute
When, the mass flow rate of air is
Substitute
Thus, the Equation (XXIV) describes that
Substitute
Thus, the mass flow rate of the air through the air compressor required for this system to produce
Substitute
Consider the process 1 to 2 (Pump).
Here, the pump is isentropic. Hence the exergy destruction during the process 1-2 is zero.
Consider the process 3 to 4 (steam turbine).
Here,
Substitute
Thus, the exergy destruction during process 3-4 is
Substitute
Substitute
Substitute
Substitute
Substitute
The calculated exergy destruction value is greater for component combustor that is
Hence, the combustor of the gas-steam cycle has largest exergy destruction of all other components and that is the most wasteful of work potential.
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