# Efficiency in a gas turbine or aircraft engine

Most modern aircraft engines, such as the one depicted below taken from Wikipedia, are composed of several compressor stages which are driven by a turbine (or several), and a combustion chamber in-between, in order to increase the temperature of the flow.

In general, manufacturers and designers focus on increasing compression ratios as well as combustion temperatures for efficiency enhancement.

My question is, under simplifying assumptions such as perfect gas, no energy losses or friction, and constant inlet temperature and velocity: How is the efficiency of this thermodynamic cycle evaluated? How can one quantify the efficiency gain from a pressure or temperature increase?

Gas turbines are modeled using Brayton cycle which in the simplest case consits of:

1. Isentropic compression (in a compressor)
2. Constant-pressure heat addition (combustion chamber)
3. Isentropic expansion (in a turbine)
4. Constant pressure heat rejection

And since efficiency is defined as Net output work / Heat input, Efficiency can be easily related to temperature of cycle states as follows:

Processes 1-2 and 3-4 are isentropic, and P2 = P3 and P4 = P1. Thus:

And finally efficiency can then be related to compression ratio as follows:

However most gas turbines do not operate on this simple theoretical ideal conditions as isentropic compression& expansion, constant pressure heat addition, single stage compression and single stage expansion. And in such cases the modeling and efficiency analysis are far more complex than the ideal cycle.

## Abbreviations:

• $w_{net}$: mechanical net work, Turbine power minus compressor power
• $q$: heat, addition or rejection. $q_{in}$ = heat addition and $q_{out}$ = heat rejection
• $k$: specific heat ratio $Cp/Cv$
• could you detail what your mathematical notations actually mean ? For instance, what is k in the last expression ? what is w or q ? – Nicolas May 22 '15 at 18:49
• @Nicolas updated – Algo May 22 '15 at 18:57
• @Nicolas I would like to recommend Yunus Cengel's book: Thermodynamics - An Engineering Approach where you can find much great detail about the brayton cycle. – Algo May 22 '15 at 19:03

One thing increased compression ratios improve upon is that it will increase the burn speed and burn completeness, reducing the percent of unburnt fuel/particles going out the exhaust.

The increased compression also allows higher expansion ratios for the exhaust turbine, which will increase power. This is similar to how compression ratios affect standard piston based engines.

• Thank you for the physical insight on the question. I was wondering if there is a "simple" way to quantify these gains. – Nicolas May 14 '15 at 14:22