The second law efficiency of compressor in gas turbine cycle

[amir star]

hi friends,
I've used the following equation in Thermodynamics: an engineering approach(Cengel) for calculating exergy efficiency of compressor. In fact, for an adiabatic compressor with negligible kinetic
and potential energies, the second-law(exergy) efficiency becomes:

eta_ii_C=(Si_2-Si_1)/(h_2-h_1)

Si=(h-h_0)-T_0*(S-S_0)

where (Si) is flow exergy for Control volume( or various steady-flow device).
I calculated by assuming ideal gas and have temperatures inlet and outlet compressor(experimental data) and using EES software.

Now, with this formulation, exergy efficiency of compressor increase with increasing pressure ratio and inlet compressor temperature. But ,I do not know why it is!...or is it(variation of efficiency with respect to pressure ratio and inlet compressor temperature) correct?
in other word,I want to know that how to change the second law thermodynamics efficiency (exergy efficiency) of compressor with respect to compressor ratio and inlet compressor temperature?
Is it increases? or decreases?why?

Do you have any articles in this regard?

thanks for your guide and help,
amir

 

[Achy47]

Dear Amir,

Thank you for sharing your question about exergy efficiency of a compressor. It is great to see that you are using the equations from "Thermodynamics: An Engineering Approach" by Cengel for your calculations. I am a scientist in the field of thermodynamics and would be happy to provide some insights into your question.

To start, let's define exergy efficiency. Exergy efficiency is a measure of the ability of a system to perform useful work. It is a ratio of the actual work output of a system to the maximum possible work output, assuming reversible processes. In the case of a compressor, the exergy efficiency is a measure of how well the compressor can convert the available energy into useful work.

Now, let's look at the equation you have used to calculate the exergy efficiency of a compressor:

eta_ii_C=(Si_2-Si_1)/(h_2-h_1)

This equation shows that the exergy efficiency is dependent on the difference between the exergy at the outlet (Si_2) and the inlet (Si_1) of the compressor, divided by the difference between the enthalpy at the outlet (h_2) and the inlet (h_1). This means that the exergy efficiency is affected by any changes in the exergy and enthalpy of the system.

In the case of an adiabatic compressor with negligible kinetic and potential energies, the exergy efficiency can be simplified to:

eta_ii_C=(h-h_0)/(h_2-h_1)

where h is the specific enthalpy of the gas at the compressor inlet and h_0 is the specific enthalpy of the gas at the compressor inlet at ambient conditions (T_0 and S_0).

Now, let's address your question about the variation of exergy efficiency with respect to pressure ratio and inlet compressor temperature. The pressure ratio and inlet compressor temperature affect the specific enthalpy of the gas at the compressor inlet (h). As the pressure ratio and inlet compressor temperature increase, the specific enthalpy at the inlet also increases. This means that the numerator of the exergy efficiency equation increases, resulting in a higher exergy efficiency.

In other words, increasing the pressure ratio and inlet compressor temperature results in a higher exergy efficiency because there is more available energy (in the form of higher enthalpy) to be converted into useful work by the compressor.

To answer your question