2 Literature review on gas turbine performance

Equation 15

Equation 16
On assuming constant mean C_p throughout the flow, equation 16 can take following form by substituting the equation 13:

Equation 17

Equation 18
Equation 19
Equation 20

Equation 21
Similarly,

Equation 22

Equation 23

Equation 24

Equation 25

2.4.3 Polytropic or small stage efficiency

According to the equation 21 and equation 25, the isentropic compressor efficiency and the isentropic turbine efficiency change with the pressure ratio. It is found that isentropic compressor efficiency tends to decrease and isentropic turbine efficiency tends to increase as the pressure ratio increases (Cohen, et al., 1996). Therefore it is not reasonable to define the efficiency by only considering the highest and the lowest pressures in the gas turbine. As a result of that another reasonable definition is needed when describing the efficiencies of the turbomachinary components in the gas turbine.
Apart from the two main pressure levels in the working of turbomachinary it consists of infinite numbers of small pressure levels. The pressure ratios in between those small pressure levels differ from each other. Consider the compression process in between constant pressures P₀₁ and P₀₂ in the figure 14. In between P₀₁ and P₀₂ there are infinite numbers of constant pressure levels and they can be called as P_0x1, P_0x2, P_0x3… P_0xn. By adding small stage isentropic work outputs in between, the P_0x1, P_0x2, P_0x3… P_0xn, the total flow work can be obtained;
Equation 26

Finally the polytropic efficiency for the compression is defined as follows;