Thermodynamics

538 | Thermodynamicsandh T w aw s h 3 h 4ah 3 h 4swhere states 1 and 3 are the inlet states, 2a and 4a are theactual exit states, and 2s and 4s are the isentropic exit states.In gas-turbine engines, the temperature of the exhaust gasleaving the turbine is often considerably higher than the temperatureof the air leaving the compressor. Therefore, thehigh-pressure air leaving the compressor can be heated bytransferring heat to it from the hot exhaust gases in a counterflowheat exchanger, which is also known as a regenerator.The extent to which a regenerator approaches an ideal regeneratoris called the effectiveness P and is defined asP q regen,actq regen,maxUnder cold-air-standard assumptions, the thermal efficiencyof an ideal Brayton cycle with regeneration becomesh th,regen 1 a T 1T 3b1r p 2 1k12>kwhere T 1 and T 3 are the minimum and maximum temperatures,respectively, in the cycle.The thermal efficiency of the Brayton cycle can also beincreased by utilizing multistage compression with intercooling,regeneration, and multistage expansion with reheating.The work input to the compressor is minimized when equalpressure ratios are maintained across each stage. This procedurealso maximizes the turbine work output.Gas-turbine engines are widely used to power aircraftbecause they are light and compact and have a high powerto-weightratio. The ideal jet-propulsion cycle differs fromthe simple ideal Brayton cycle in that the gases arepartially expanded in the turbine. The gases that exit theturbine at a relatively high pressure are subsequently acceleratedin a nozzle to provide the thrust needed to propel theaircraft.The net thrust developed by the engine iswhere m . is the mass flow rate of gases, V exit is the exit velocityof the exhaust gases, and V inlet is the inlet velocity of theair, both relative to the aircraft.The power developed from the thrust of the engine iscalled the propulsive power W . P , and it is given byW # P m # 1V exit V inlet 2V aircraftPropulsive efficiency is a measure of how efficiently theenergy released during the combustion process is convertedto propulsive energy, and it is defined ash P F m # 1V exit V inlet 2Propulsive powerEnergy input rate W# PQ # inFor an ideal cycle that involves heat transfer only with asource at T H and a sink at T L , the exergy destruction isx dest T 0 a q outT L q inT HbREFERENCES AND SUGGESTED READINGS1. W. Z. Black and J. G. Hartley. Thermodynamics. NewYork: Harper & Row, 1985.2. V. D. Chase. “Propfans: A New Twist for the Propeller.”Mechanical Engineering, November 1986, pp. 47–50.3. C. R. Ferguson and A. T. Kirkpatrick, InternalCombustion Engines: Applied Thermosciences, 2nd ed.,New York: Wiley, 2000.4. R. A. Harmon. “The Keys to Cogeneration and CombinedCycles.” Mechanical Engineering, February 1988,pp. 64–73.5. J. Heywood, Internal Combustion Engine Fundamentals,New York: McGraw-Hill, 1988.6. L. C. Lichty. Combustion Engine Processes. New York:McGraw-Hill, 1967.7. H. McIntosh. “Jumbo Jet.” 10 Outstanding Achievements1964–1989. Washington, D.C.: National Academy ofEngineering, 1989, pp. 30–33.8. W. Pulkrabek, Engineering Fundamentals of the InternalCombustion Engine, 2nd ed., Upper Saddle River, NJ:Prentice-Hall, 2004.9. W. Siuru. “Two-stroke Engines: Cleaner and Meaner.”Mechanical Engineering. June 1990, pp. 66–69.10. C. F. Taylor. The Internal Combustion Engine in Theoryand Practice. Cambridge, MA: M.I.T. Press, 1968.11. K. Wark and D. E. Richards. Thermodynamics. 6th ed.New York: McGraw-Hill, 1999.