A simple Rankine cycle uses water as the working
fluid. The boiler operates at 6000 kPa and the condenser
at 50 kPa. At the entrance to the turbine, the temperature is
450C. The isentropic efficiency of the turbine is 94 percent,
pressure and pump losses are negligible, and the water leaving
the condenser is subcooled by 6.3C. The boiler is sized for a
mass flow rate of 20 kg/s. Determine the rate at which heat is
added in the boiler, the power required to operate the pumps,
the net power produced by the cycle, and the thermal efficiency.
Given data
Operating pressure of boiler P_{H} = 60bar
Operating pressure of condenser low pressure P_{L} = 0.5 bar
Temperature at the entrance of the turbine T_{3 }= 450^{0}C
water is subcooled by 6.30C
Mass flow rate of steam ma = 20kg/sec
Isentropic efficiency of the turbine 94%
To determine
Heat tansfer rater to the boiler.
Power required to operate pump.
Net power produced by the cycle.
Thermal efficiency of the cycle.
As per the given conditions T-S diagram is shown below
1^{1}-1 is subcooling of water
2-3 Heat addition in boiler
4-1 Condensation of steam
1-2 Pump work
Point 1 is the inlet of pump
Point 2 inlet of turbine
Point 3 inlet of turbine
Point 4 inlet of condenser
Point 1^{1} = Saturation point of water at 0.5 bar
Properties of water and steam are taken from the tables
Properties at point 1
boiling point of the water at 0.5 bar is 81.30C. As the water is subcooled by 6.3^{0}C at 0.5 bar properties of water at point 1 are taken at 75^{0}C
To get enthalpy at point 2 we have to calculate pump work
Enthalpy at point 2 is
Enthalpy at point 3 and 4^{1 }is the isentropic efficiency is 100%
From the given isentropic efficiency we get enthalpy at exit of turbine (i.e., point 4)
Heat transfer rate in the boiler is
Pump work is
Turbine work
Net work in the cycle is
Thermal efficiency of the cycle is
Conclusions