Other Gas Power System Applications Air enters

Chapter 9, Problem 95P

(choose chapter or problem)

Air enters the compressor of a combined gas turbine–vapor power plant (Fig. 9.22) at 1 bar, \(25^{\circ} \mathrm{C}\). The isentropic compressor efficiency is 85% and the compressor pressure ratio is 14. The air passing through the combustor receives energy by heat transfer at a rate of 50 MW with no significant decrease in pressure. At the inlet to the turbine the air is at \(1250^{\circ} \mathrm{C}\). The air expands through the turbine, which has an isentropic efficiency of 87%, to a pressure of 1 bar. Then, the air passes through the interconnecting heat exchanger and is finally discharged at \(200^{\circ} \mathrm{C}\), 1 bar. Steam enters the turbine of the vapor cycle at 12.5 MPa, \(500^{\circ} \mathrm{C}\), and expands to a condenser pressure of 0.1 bar. Water enters the pump as a saturated liquid at 0.1 bar. The turbine and pump have isentropic efficiencies of 90 and 100%, respectively. Cooling water enters the condenser at \(20^{\circ} \mathrm{C}\) and exits at \(35^{\circ} \mathrm{C}\). Determine

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

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

(c) the thermal efficiency of the combined cycle.

(d) the net rate at which exergy is carried out with the exhaust air, \(\dot{m}_{\mathrm{air}}\left[\mathrm{e}_{\mathrm{f} 5}-\mathrm{e}_{\mathrm{f} 1}\right]\), in MW.

(e) the net rate at which exergy is carried out with the cooling water, in MW.

Let \(T_{0}=20^{\circ} \mathrm{C}, \ p_{0}=1\) bar.