18 December 2015, © Leeham Co:Part of the discussion following last week’s article around quad or twin engine airliner designs was about engine efficiency and specifically around the engine’s thermal efficiency as a function of Pressure Ratio, PR.
I got the question, if an engine working at a higher pressure ratio was therefore working at a higher thermal efficiency. I knew enough on the subject to know I did not have a good answer without doing a bit of checking; jet engines are no simple contraptions.
I have previously written about turbofan efficiency in a Corner. The article was focused around propulsive efficiency. Now we will have a look at the other part of overall engine efficiency, the thermal efficiency or the efficiency of the core.
In our Fundamentals of Aircraft performance Part 2 we covered the basics of engine efficiency. Here a short recap:
The low fuel consumption from modern turbofans comes from a high efficiency. This can be divided in the efficiency to generate shaft horse power to drive the fan from the stored energy in the fuel, thermal efficiency, and the engine’s efficiency to transfer that horse power to effective thrust driving the aircraft forward, propulsive efficiency. Thermal efficiency comes from burning the fuel under very high pressure (compression ratio in a car, pressure ratio in turbofans) and turbines that are effective in converting the gas energy into shaft energy. Propulsive efficiency comes from moving a large air mass with low overspeed, the lower the overspeed the better.
I then covered some of the fundamentals of propulsive efficiency in the previous Corner: how a low fan pressure ratio gives a low over-speed of air and that this in turn requires a High ByPass Ratio (BPR) fan to regain thrust lost when the air travels slower out the back of the engine.
To drive the large fan, we need lots of shaft horsepower and these are produced by the engine’s low pressure turbine. To generate all this horsepower (around 30,000 for the engine we looked at, the LEAP for the Boeing 737 MAX), we need a flow of air with a high pressure generated by the core. The efficiency in generating this horsepower describes the thermal efficiency of the engine and specifically the efficiency of the engine’s core.
Now to the question: Does a higher PR increase the thermal efficiency of the engine (everything else being equal)? The short answer is Yes.
The longer answer is that this depends on several other factors as well. A higher PR (caused by spinning the engine faster) can actually decrease the thermal efficiency if it increases the mismatch in the engine of component efficiencies and is past the optimum pressure ratio for the turbine entry temperature used, Figure 1.
The diagrams shows how engine efficiency changes with pressure ratio for different ratios of Turbine entry temp. (T4) to ambient air temp. (T2, all in Kelvin, diagram b) and how efficiency change with PR at a fixed T4/T2 with different compressor and turbine efficiencies (diagram c). The turbine efficiency is the effectiveness in turning gas pressure to shaft hp and compressor efficiency the reverse.
With compressor and turbine efficiencies being below 95% today, we can see that engine efficiency does not increase with PR over a certain value, dependent on turbine entry temp and compressor/turbine efficiencies. Typically an in service engine of today has a T4/T2 ratio of 5-7 at cruise and compressor/turbine efficiencies represented by the 0.90 line.
We can see that there is no point in going over a PR of 40 as we then lose efficiency. For older engines which has lower turbine entry temps (has to do with material technology and cooling sophistication) and less efficient compressor and turbine designs (no 3D fluid dynamic design tools) the optimal pressure ratio is to find more towards 30.
It shall be pointed out that the optimum pressure ratio is sought for cruise. For take-off and climb, a pressure ratio on the high side of the curves is OK, as the cruise is the phase which determines the fuel efficiency of a longer range aircraft. We can also understand why short range engines can be optimized with slightly lower cruise PR. The climb is a significant part of the overall efficiency and the whole design point is moved a bit to lower PR (everything else being equal).
The above assumes that the efficiency of the compressors and turbines are constant over the RPM range of interest. In a real engine this is not the case. A compressor/turbine designer can optimize the efficiency over a certain range of operation but then its efficiency falls off either side of this peek. This means the curves are more peaky in real life. Within margin the designer can place this peek within the RPM range. This is the adaptation of the engine to the aircraft and its operational profile; the tuning of the SFC bucket (the area of the RPM and flight conditions where the engine has its lowest SFC).
To summarize: The engine designer has for a certain generation of engines given T4 levels and compressor/turbine efficiencies that can be achieved. He then combines these with an adapted pressure range in the engine to get an overall optimum for fuel efficiency but also reliability (a higher PR increases the temperature at the end of the compressor to critical levels for the materials one wants to use). As different aircraft have different operational profiles, engines need to be adapted to the aircraft they are deployed on.
Pressure ratio and compression ratio
The jet engine’s pressure ratio and our car engine’s compression ratio are related. The gasoline engine’s compression ratio of around 10:1 is equivalent to a PR of 25 and the diesel’s 15:1 to PR 45. So everyone with a diesel car has a high PR engine under the bonnet!
The high PR diesel engine is more efficient (good mpg for diesel cars) but also share the high PR jet engine’s problems with high NOx fractions in the exhausts. Today’s turbofans goes to sophisticated combustion schemes to fix the problem, the diesel world is also applying fixes.