CYCLE OPERATION WITH MACHINE EFFICIENCY

1 Maximum Pressure Ratio for Maximum Specific Work

It is not possible to achieve isentropic compression and expansion in the actual Brayton cycle because of inevitable losses due to friction and turbulence in the compressor and turbine. Therefore, the temperature at the end of compression and expansion are higher than that in an ideal cycle for the same pressure ratio. The actual Brayton cycle is shown in Fig. 16.7.

Isentropic efficiency of compressor, 

Isentropic efficiency of turbine, 

Net specific work available,

w_net = w_t − w_c = c_p (T₃ − T_4′) −c_p (T_2′ − T₁)

For specific work output to be maximum for given temperature limits,

Figure 16.7 Actual Brayton cycle with machine efficiencies

2 Optimum Pressure Ratio for Maximum Cycle Thermal Efficiency

Heat supplied, q = c_p (T₃ – T_2′) = c_p (T₃ – T₂)

The thermal efficiency of the cycle is dependent only on r_p for the fixed values of T₁ and T₃. The condition for the maximum value of thermal efficiency for given temperature limits is

Let 

Taking -ve sign