Determine the mass flow rate, the power output of the steam turbine, the net power output of the gas turbine, and the thermal efficiency of the combined cycle.

Transcript: shows a schematic of a combined cycle power plant in which a simple closed loop cycle using helium is added to a vapour power cycle using water. The energy source for heating the helium is a nuclear reactor. The two cycles are connected via an insulated heat exchanger. The steady-state operating conditions are shown in the figure. The water leaves the heat exchanger as saturated vapour at 10 MPa]. The water is passed through a superheater so that it is at 550 [°C] and 10 MPa before entering the steam turbine. The turbine exhaust has a quality of 90% at 10 kPa). Saturated liquid leaves the insulated condenser and enters the pump, where it exits at 47.5 °C and 10 MPa). In the condenser, the energy from the water in the power loop is transferred to cooling water drawn from a lake. The temperature of the cooling water rises from 15 °C] to 35 °C) as it passes through the condenser and its mass flow rate is 1750 kg/s] The helium exits the heat exchanger at 1.38 MPa) and 80 [°C] After passing through the compressor, the helium is at 5.50 (MPaand 407 °C). The helium passes through the reactor and is heated to 760 [°C] with negligible pressure change. After expanding through the gas turbine, the helium is at 1.38 (MPa) and 395 [°C]. The gas turbine shaft work output is used to drive the compressor and to produce a net power output. The compressor, turbines, and pump are also insulated i.e., adiabatic). Neglect changes in potential and kinetic energies. (a) Determine the mass flow rate in the steam power cycle, m'w.in/kg/s). (b) Determine the power output of the steam turbine, Wri, in kW). (c) Determine the net power output of the gas turbine, Wr2t, in [kW]. (d) Determine the thermal efficiency of the combined cycle. (e) On two separate T-u (temperature-specific volume) diagrams, draw process representa- tions for the steam cycle and the helium cycle. On the diagrams, clearly indicate the labelled state points, the process paths (use a dashed line if the path is unknown), and the constant pressure lines that pass through the state points. Indicate state temperature values and saturation temperature values for reference as appropriate. Do any additional work necessary to label the diagram. Labelling v values is optional Po = 5.50 MPa] Tii = 760 [°C] reactor 2 Tio = 407 °C N o | (heater) P1 = PO helium 7 cycle compressor gas WT2,043 Cheat exchanger T = 395 °C turbine heat exchanger P = P Tg = 80°C 8+ P = P. superheater Fun steam 6 saturated og 707T= 550 [°C] W cycle Pape 10 (MPa) steam turbine P = 1.38 (MPa) 5 + P = P. T5 = 47.5°C) Ts = 47.5 [°C] pump saturated liquid P = P3 Ti = 15 [°C] Pi = 100 [kPa] mcw = 1750 [kg/s) condenser Tilaw 3 P = 10 [kPa] 13 = 0.90 T, = 35 [°C P = P lake water