Thermodynamics

Chapter 9 | 517Discussion Note that the thermal efficiency of the gas turbine has gone upfrom 26.6 to 36.9 percent as a result of installing a regenerator that helpsto recuperate some of the thermal energy of the exhaust gases.9–10 ■ THE BRAYTON CYCLE WITHINTERCOOLING, REHEATING,AND REGENERATIONThe net work of a gas-turbine cycle is the difference between the turbinework output and the compressor work input, and it can be increased byeither decreasing the compressor work or increasing the turbine work, orboth. It was shown in Chap. 7 that the work required to compress a gasbetween two specified pressures can be decreased by carrying out the compressionprocess in stages and cooling the gas in between (Fig. 9–42)—thatis, using multistage compression with intercooling. As the number of stagesis increased, the compression process becomes nearly isothermal at thecompressor inlet temperature, and the compression work decreases.Likewise, the work output of a turbine operating between two pressurelevels can be increased by expanding the gas in stages and reheating it inbetween—that is, utilizing multistage expansion with reheating. This isaccomplished without raising the maximum temperature in the cycle. As thenumber of stages is increased, the expansion process becomes nearlyisothermal. The foregoing argument is based on a simple principle: Thesteady-flow compression or expansion work is proportional to the specificvolume of the fluid. Therefore, the specific volume of the working fluidshould be as low as possible during a compression process and as high aspossible during an expansion process. This is precisely what intercoolingand reheating accomplish.Combustion in gas turbines typically occurs at four times the amount ofair needed for complete combustion to avoid excessive temperatures. Therefore,the exhaust gases are rich in oxygen, and reheating can be accomplishedby simply spraying additional fuel into the exhaust gases betweentwo expansion states.The working fluid leaves the compressor at a lower temperature, and theturbine at a higher temperature, when intercooling and reheating are utilized.This makes regeneration more attractive since a greater potential forregeneration exists. Also, the gases leaving the compressor can be heated toa higher temperature before they enter the combustion chamber because ofthe higher temperature of the turbine exhaust.A schematic of the physical arrangement and the T-s diagram of an idealtwo-stage gas-turbine cycle with intercooling, reheating, and regeneration areshown in Figs. 9–43 and 9–44. The gas enters the first stage of the compressorat state 1, is compressed isentropically to an intermediate pressure P 2 ,iscooled at constant pressure to state 3 (T 3 T 1 ), and is compressed in the secondstage isentropically to the final pressure P 4 . At state 4 the gas enters theregenerator, where it is heated to T 5 at constant pressure. In an ideal regenerator,the gas leaves the regenerator at the temperature of the turbine exhaust,that is, T 5 T 9 . The primary heat addition (or combustion) process takesPPolytropicprocess pathsD CP 2BIsothermalprocess pathsP 1INTERACTIVETUTORIALSEE TUTORIAL CH. 9, SEC. 5 ON THE DVD.Work savedas a result ofintercoolingAIntercoolingFIGURE 9–42Comparison of work inputs to asingle-stage compressor (1AC) and atwo-stage compressor withintercooling (1ABD).1v