2 Literature review on gas turbine performance

2.2 Pressure ratio

The amount of compressibility of the compressor can be considered as the pressure ratio. In similar manner it can be defined as the ratio between the exit pressure and the inlet pressure of the compressor. In an ideal open gas turbine cycle both the compressor inlet pressure and the turbine exit pressure is equal and it is same as ambient pressure. Both the points are in the same isobar line with different enthalpy and entropy values (1 and 4 points in the figure 6). The compressor exit pressure and the turbine inlet pressure are equal and those points are also in the same isobar line with different enthalpy and entropy values (2 and 3 points in the figure 6). However in practically the compressor exit pressure and the turbine inlet pressure are different due to pressure loss in the combustion chamber.
Consider an ideal open gas turbine cycle and the relative TS diagram. Suppose W and Q are the work and heat transfer per unit mass.

By applying the energy balance to the ideal Brayton cycle, following equations can be derived; assume that the C_p is constant for the process.
During the state 1 to 2 the air under goes isentropic compression process in the compressor and work input is given by,

Equation 1
From the state 2 to 3 the compressed air under goes isobaric heat addition in the combustion chamber.
This heat addition comes from the fuel.

Equation 2
From the state 3 to 4 the combust air goes through isentropic expansion inside the turbine. The work output of the turbine is given by,

Equation 3
For the complete cycle the net-work output is given by;

Equation 4
Heat supplied for the cycle is given by;

Equation 5
Hence the efficiency of the open ideal gas turbine cycle can be derived as;

Equation 6
From the isentropic temperature and pressure relation;