Thermodynamics

tion on the thermal efficiency is an increase of 63 percent. As the number ofcompression and expansion stages is increased, the cycle will approach theEricsson cycle, and the thermal efficiency will approachh th,Ericsson h th,Carnot 1 T LT H 1 300 K1300 K 0.769 TurbineAdding a second stage increases the thermal efficiency from 42.6 to 69.6percent, an increase of 27 percentage points. This is a significant increasein efficiency, and usually it is well worth the extra cost associated with thesecond stage. Adding more stages, however (no matter how many), canincrease the efficiency an additional 7.3 percentage points at most, andusually cannot be justified economically.Chapter 9 | 5219–11 ■ IDEAL JET-PROPULSION CYCLESGas-turbine engines are widely used to power aircraft because they are lightand compact and have a high power-to-weight ratio. Aircraft gas turbinesoperate on an open cycle called a jet-propulsion cycle. The ideal jetpropulsioncycle differs from the simple ideal Brayton cycle in that thegases are not expanded to the ambient pressure in the turbine. Instead, theyare expanded to a pressure such that the power produced by the turbine isjust sufficient to drive the compressor and the auxiliary equipment, such asa small generator and hydraulic pumps. That is, the net work output of a jetpropulsioncycle is zero. The gases that exit the turbine at a relatively highpressure are subsequently accelerated in a nozzle to provide the thrust topropel the aircraft (Fig. 9–47). Also, aircraft gas turbines operate at higherpressure ratios (typically between 10 and 25), and the fluid passes through adiffuser first, where it is decelerated and its pressure is increased before itenters the compressor.Aircraft are propelled by accelerating a fluid in the opposite direction tomotion. This is accomplished by either slightly accelerating a large mass offluid ( propeller-driven engine) or greatly accelerating a small mass of fluid( jet or turbojet engine) or both (turboprop engine).A schematic of a turbojet engine and the T-s diagram of the ideal turbojetcycle are shown in Fig. 9–48. The pressure of air rises slightly as it is deceleratedin the diffuser. Air is compressed by the compressor. It is mixed withfuel in the combustion chamber, where the mixture is burned at constantpressure. The high-pressure and high-temperature combustion gases partiallyexpand in the turbine, producing enough power to drive the compressor andother equipment. Finally, the gases expand in a nozzle to the ambient pressureand leave the engine at a high velocity.In the ideal case, the turbine work is assumed to equal the compressorwork. Also, the processes in the diffuser, the compressor, the turbine, andthe nozzle are assumed to be isentropic. In the analysis of actual cycles,however, the irreversibilities associated with these devices should be considered.The effect of the irreversibilities is to reduce the thrust that can beobtained from a turbojet engine.The thrust developed in a turbojet engine is the unbalanced force that iscaused by the difference in the momentum of the low-velocity air enteringthe engine and the high-velocity exhaust gases leaving the engine, and it isNozzleHigh T and PV exitFIGURE 9–47In jet engines, the high-temperatureand high-pressure gases leaving theturbine are accelerated in a nozzle toprovide thrust.