Pressure Ratio and Efficiency in Brayton Cycle Engines

[neutrino_cannon]

WARNING: I AM A COMPLETE N00B AT THERMODYNAMICS.

I have been reading about gas turbines lately as they are fascinating. The tolerances, materials and fluid dynamics that make these things work as well as they do work is fascinating and most impressive.

One thing I do not understand is how increasing the pressure ratio; that is, the ratio of pressure between the last stage of the compressor and atomospheric air helps to improve the efficiency of the engine. I am certain that increasing the pressure ratio does improve the efficiency of the engine, since every resource written by anyone who's actually worked on the things says so, and also because increasing pressure ratio makes the little box on the P/V chart get bigger. However, this is clearly not a scientifically rigorous explanation.

The problem, as I see it, is that if the compressor is compressing the air more then it is performing more work on the air. To perform more work on the air it needs to be provided with more power (assuming that compressor efficiency is constant). Power for the compressor in a jet engine comes from the turbine stage. The turbine works by converting some of the heat of the air flowing through the engine after it has been combusted with fuel into mechanical power. So, for the compressor to perform more work, more work needs to be taken out of the system by the turbine. Clearly, the turbine gets that work back minus leaks because the air that the compressor acts on is hotter. But at that point you're just recovering (most of) the work that you already took out of the gasses.

But how on earth does this improve efficiency?

 

[The Man]

Well you have to remember that a more efficient turbine (or any engine) gets more of the energy available from the fuel out of the fuel. So the less energy from the fuel that it takes to heat up the combustion gases the more energy from the fuel is available for mechanical use and the more efficient the cycle becomes (within some limits of course).

http://en.wikipedia.org/wiki/Compression_ratio

A high compression ratio is desirable because it allows an engine to extract more mechanical energy from a given mass of air-fuel mixture due to its higher thermal efficiency. This occurs because internal combustion engines are heat engines, and higher efficiency is created because higher compression ratios permit the same combustion temperature to be reached with less fuel, while giving a longer expansion cycle, creating more mechanical power output and lowering the exhaust temperature.

http://en.wikipedia.org/wiki/Brayton_cycle#Methods_to_improve_efficiency

http://en.wikipedia.org/wiki/Brayton_cycle#mediaviewer/File:GFImg7.png

Coming back from a trip last week my thermostat failed open. So my car (not turbine powered by the way) was running cold for the remaining 200 miles of that trip. I haven’t put the numbers into my spreadsheet yet but I expect a reduced MPG as energy that should have gone to the drive train was being dumped by the radiator.