Other Gas Power System Applications A simple gas turbine

Chapter 9, Problem 97P

(choose chapter or problem)

A simple gas turbine is the topping cycle for a simple vapor power cycle (Fig. 9.22). Air enters the compressor of the gas turbine at \(60^{\circ} \mathrm{F}, \ 14.7 \mathrm{\ lbf} / \mathrm{in} .^{2}\), with a volumetric flow rate of \(40,000 \mathrm{\ ft}^{3} / \mathrm{min}\). The compressor pressure ratio is 12 and the turbine inlet temperature is \(2600^{\circ} \mathrm{R}\). The compressor and turbine each have isentropic efficiencies of 88%. The air leaves the interconnecting heat exchanger at \(840^{\circ} \mathrm{F}, \ 14.7 \mathrm{\ lbf} / \mathrm{in} .^{2}\) Steam enters the turbine of the vapor cycle at \(1000 \mathrm{lbf} / \mathrm{in} .^{2},\ 900^{\circ} \mathrm{F}\), and expands to the condenser pressure of \(\) Water enters the pump as saturated liquid at \(1 \mathrm{\ lbf} / \mathrm{in} .^{2}\) The turbine and pump efficiencies are 90 and 70%, respectively. Cooling water passing through the condenser experiences a temperature rise from 60 to \(80^{\circ} \mathrm{F}\) with a negligible change in pressure. Determine

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

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

(c) the thermal efficiency of the combined cycle.

(d) a full accounting of the net exergy increase of the air passing through the combustor of the gas turbine, \(\dot{m}_{\mathrm{air}}\left[\mathrm{e}_{\mathrm{f} 3}-\mathrm{e}_{\mathrm{f} 2}\right]\), in Btu/h.

Discuss. Let \(T_{0}=520^{\circ} \mathrm{R}, \ p_{0}=14.7 \mathrm{\ lbf} / \mathrm{in}^{2}\)

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