Superheated steam at 84 bars and 485 degree C exits the boiler of a vapor power

Question

Superheated steam at 84 bars and 485 degree C exits the boiler of a vapor power plant. Heat transfer and frictional effects in the line connecting the boiler and the turbine reduce the pressure and temperature at the turbine inlet to 79 bars and 445 degree C, respectively. The pressure at the exit of the turbine is 0.15 bars, and the turbine operates adiabatically. Liquid leaves the condenser at 9 kPa, 36 degree C. The pressure is increased to 9.2 MPa across the pump. The turbine and pump isentropic efficiencies are 88%. The mass flow rate of steam is 79.53 kg/s. Determine The net power output, in kW The thermal efficiency. The rate of heat transfer from the line connecting the steam generator and the turbine, in kW. The mass flow rate of condenser cooling water, in kg/s, if the cooling water enters at 15 degree C and exits at 35 degree C with negligible pressure change.

Explanation / Answer

a)At turbine inlet, specific enthalpy = 3261.84 kJ/kg (from steam table).

Had the process been isentropic, dryness fraction of water = .799 (by equating specific entropy). At this point, specific enthalpy would have been 2120.69 kJ/kg.

Using 88% isentropic efficiency of turbine, actual specific enthalpy = 2257.63 kJ/kg.

Hence, turbine output = (difference in specific enthalpy) x mass flow rate = (3261.84 - 2257.63) x 79.53 = 79864.82 kW.

But, net power output will be obtained after subtracting power input to pump, which is given by the product of specific volume at inlet of pump, pressure difference across pump, and the mass flow rate. This equals 0.001 x (9.2 - .009) x 10^6 x 79.53 W = 730.96 kW.

Hence, net power output = 79864.82 - 730.96 = 79133.85 kW.

b) Thermal efficiency is equal to net power output/power supplied in boiler.

Power supplied = (3356.92 - 1372.66)*79.53 kW = 157,808.198 kW

Hence, thermal efficiency = 79133.85/157,808.198 = 0.5 (or 50%)

c) Loss in enthalpy across the line connecting the steam generator and turbine = (3356.92 - 3261.84) kJ/kg = 95.08 kJ/kg (from steam tables).

Now, rate of heat transfer is simply the product of the difference in specific enthalpies and the mass flow rate, hence it equals 95.08 x 79.53 kW = 7561.71 kW.

d)Heat exchanged in condenser = (difference in specific enthalpies across the condenser) x (mass flow rate of water) = (2257.63 - 150.83) x 79.53 = 167,553.80 kW. This is equal to the product of mass flow rate of the cooling water, the temperature difference (20 degrees celcius), and specific heat capacity of water (4.2 kJ/kg/K). Hence, mass flow rate is 1994.68 kg/s, or approximately 2 tonnes/s.

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