Example: Brayton Cycle
We assume a gas turbine operating with the compressor inlet temperature T1 = 300 K and the turbine inlet temperature T3 = 1400 K. The working medium is air under cold-air approximation, with R = 0.287 kJ and k = 1.4.
We first consider a reversible system. From (10.20) we obtain the optimum pressure ratio
We compare the above result with that for a gas turbine system with internal irreversibilities operating at the same values for p1, p2, T1, T3 but with isentropic efficiencies for compressor and turbine given as ηC = ηT = 0.9. From (9.43, 9.44) we obtain the temperatures T2 and T4 as
The thermal efficiency of the irreversible gas turbine system is
Gas Refrigeration System: Inverse Brayton Cycle
The inversion of the Brayton cycle results in a gas cooling system as depicted in Fig. 10.9. Gas is compressed adiabatically (1-2), and then cooled by heat exchange with the warm environment (2-3). The cooled gas is expanded adiabatically in a turbine, and assumes a low temperature (3-4). Finally, the gas is heated by drawing heat from the cold environment (4-1). As always, we consider a cooling system exchanging heat with reservoirs at TL, TH . Then, to have heat transfer in the proper direction, the compressor inlet temper- ature T1 must not be above TL, and the turbine inlet temperature T3 must not be smaller than TH . These temperature requirements are shown in the T-s-diagram in Fig. 10.9.
Larger pressure ratios give smaller COP, but increase the cooling power. In particular for large pressure ratios there are large external irreversibilities associated with the heat transfer over finite temperature differences between the cooling fluid and the two environments (see T-s-diagram in Fig. 10.9). Nevertheless, gas refrigeration cycles offer a relatively simple means to achieve low temperatures (∼ 130 K). Advanced gas cooling systems use internal heat exchange (regeneration) to increase the COP.