Other Gas Power System Applications Helium is used in a

Chapter 9, Problem 93P

(choose chapter or problem)

Helium is used in a combined cycle power plant as the working fluid in a simple closed gas turbine serving as the topping cycle for a vapor power cycle. A nuclear reactor is the source of energy input to the helium. Figure P9.93 provides steady-state operating data. Helium enters the compressor of the gas turbine at \(200 \mathrm{\ lbf} / \mathrm{in} .^{2}, \ 180^{\circ} \mathrm{F}\) with a mass flow rate of \(8 \times 10^{5} \mathrm{\ lb} / \mathrm{h}\) and is compressed to \(800 \mathrm{\ lbf} / \mathrm{in} .^{2}\) The isentropic efficiency of the compressor is 80%. The helium then passes through the reactor with a negligible decrease in pressure, exiting at \(1400^{\circ} \mathrm{F}\). Next, the helium expands through the turbine, which has an isentropic efficiency of 80%, to a pressure of \(200 \mathrm{\ lbf} / \mathrm{in} .^{2}\) The helium then passes through the interconnecting heat exchanger. A separate stream of liquid water enters the heat exchanger and exits as saturated vapor at \(1200 \mathrm{\ lbf} / \mathrm{in}^{2}\) The vapor is superheated before entering the turbine at \(800^{\circ} \mathrm{F}, \ 1200 \mathrm{\ lbf} / \mathrm{in}^{2}\) The steam expands through the turbine to \(1 \mathrm{\ lbf} / \mathrm{in} .^{2}\) and a quality of 0.9. Saturated liquid exits the condenser at \(1 \mathrm{\ lbf} / \mathrm{in} .^{2}\) Cooling water passing through the condenser experiences a temperature rise from 60 to \(90^{\circ} \mathrm{F}\). The isentropic pump efficiency is 100%. Stray heat transfer and kinetic and potential energy effects can be ignored. Determine

(a) the mass flow rates of the steam and the cooling water, each in lb/h.

(b) the net power developed by the gas turbine and vapor cycles, each in Btu/h.

(c) the thermal efficiency of the combined cycle.