# Bjorn’s Corner: Engine efficiency revisited

By Bjorn Fehrm

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.

Turbofan efficiency

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.

Thermal efficiency

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.

Figure 1. Diagram of engine efficiency when pressure ratio is changed at different turbine entry temps (b) and compressor/turbine efficiencies (c). Source: N. Cumpsty’s book Jet Propulsion.

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.

### 23 Comments on “Bjorn’s Corner: Engine efficiency revisited”

1. I guess the other thing to mention is that having high pressure air in a combination chamber gives a better fuel burn. Thus you can extract more energy from a given amount of fuel than you can at a lower combustion pressure.

You need a minimum weight of air to match the weight of fuel being put in. Failing to do that produces a lot of smoke. Even if the minimum is achieved the burn is not perfect. Add yet more air improves it, liberating extra energy.

2. Bjorn, This is a good basic explanation. In the simplest terms, the thermal efficiency of an IDEAL gas turbine ( no losses ) depends only on the pressure ratio. The power produced for a given airflow is strongly dependent on the turbine inlet temperature. For the real cycle the efficiency depends on both PR and TIT. As you have shown, as TIT goes up you can go to higher PR and over the years PR has increased with better understanding of aerodynamics while TIT has increased with better materials and especially better cooling, which required major advances in blade manufacturing.
The thermal efficiency is fixed by thermodynamics, but the propulsion effy is determined by the mean jet velocity and high bypass ratio is needed . In a high BPR engine we need large flow at low exhaust velocity, also critical for low noise.
The early high BPR engines had PR of 25, BPR of 5 and TIT of 1450 K ( all numbers approx) while today we are approaching 50, 12 and 1850 K.

• Thanks Herb, good that I didn’t blow it :), always nice to have you chip in here.

• You need to add component efficiencies for a non-ideal gas turbine. That is one reason gas turbine manufacturers have gone to great lengths to increase the polytropic efficiencies. High performance CFD has helped a lot in designing and optimizing compressor and turbine stages so that maximum efficiency can be squeezed from them. So, OPR, TET and efficiencies determine the thermodynamic efficiency.

3. I use some of Cumptsy’s book in my course on Aircraft Propulsion! Nice to see those figures again here.

There is a gem of a plot from RR on turbofan efficiencies (a similar one from P&W). I don’t know how to upload them here though and I don’t want to provide a link.

This site should make provisions for not only text comments but graphics also. That would be very helpful to the audience! Bjorn? Scott?

• Kant, you can include an image by using a structure like;

• I am illiterate when it comes to things like this. Did not work. Care to e-mail me how to do it please?

• Here the graphs that Kant wanted to show. First the one from Rolls Royce:

then the same thing from PW from another angle:

4. Interesting comparison with Diesel engines, including association with higher NOx emissions.

• NOx is linked to high temps, pressure and oxygen surplus during combustion.
Diesel and Turbines run lean.
Diesels are cleaned via exhaust feed back and/or a combination of catalytic converters and some additives ( ammonia via injecting urea dissolved in water aka “AdBlue” )

5. “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.”

Volkswagen fixed that problem well, well until they got caught… 🙂

6. Of course VWs solution was to simply turn the emissions system off!

• Not quite turned off, the choice with VW diesels was lean burn/ high Nox which gave the good fuel efficiency they could promote but not pass the clean air standards. The engine performance map in the computer was altered when it detected a testing cycle to increase fuel flow and reduce performance to give the required lower Nox. Other emissions standards are still to be met including CO2

• A bit if a nit noid.

They not only turned off NOX controls for real world driving but had to have thoroughly tested the whole system to ensure it did what VW wanted it to do.

The collected tax credits while violating the set emissions Standards of the USA.

Interesting question how you test an aircraft engine (large jet) to see if they are doing the same thing.

• Much like cars, they have ground test stands which can measure every possible parameter. In addition they have special chambers to simulate high altitude conditions

• As delivered by Bosch the fadec software has hooks for detecting the emissions control run.
You need it to cope with intrinsics of a bench test
that collide with regular use behavior.

The depravity of the act is overstated.
My guess is all market participants have their personal fibs installed to pass these tests.

7. Perhaps it would be useful to add to Kant’s reference to polytropic effy. To simplify the Maths, this may be thought of as the efficiency of an individual stage and the more stages we have , the lower the overall efficiency. This gives us a rational method of predicting the variation of overall compressor efficiency with pressure ratio, and as we increase pressure ratio the overall efficiency will decrease .Polytropic efficiencies are in the region of 90%, making further increases very difficult to attain. For example, to raise from 90 to 92% would require reducing the losses in a very efficient machine by 20%. I hope this simplified explanation will be useful to non specialists.

8. Bjorn – thanks so much for this exhaustive answer to my question.

One follow-up, perhaps for another day:

Does the loss of efficiency at higher OPR partially reflect loss of propulsive efficiency in the graphs you provided? I.e. is the fan spinning too fast so that specific thrust goes up? Or, on the other hand, does the efficiency loss in the graphs only reflect thermodynamic efficiency loss?

If the graph includes propulsive efficiency loss, then perhaps a different optimization of the engine used could result in better performance at high OPR? Here I’m thinking that the RPM ratio between core and fan would be adjusted, so that revving up core RPM doesn’t make the fan spin too fast.

Beyond the books people have mentioned here, any suggestions on further reading to understand why thermodynamic efficiency would decline with higher OPR?

• Hi Eric,

yes you triggered the corner, thanks for that!

The graphs are part of an educational book, as such they handle one thing at a time, ie the propulsive side is assumed constant. In reality the fan has the same behavior as a compressor stage, it has an RPM where the efficiency is peeking. This should be for cruise with the efficiency tapering off on either side, ie TakeOff, climb or idle. As can be understood there is a lot of stuff to get right in a turbofan. Each stage of the engine has its own characteristics yet they are all asked to form a whole. They shall work over a wide range of RPMs and ambient conditions. No easy problem to crack.

Re books, I found Cumpsty’s good as it used a practical example of an A380 engine through the book’s civil engine side. The book in turn recommended GasTurb as a very good software to study things further. This was the real help for me to grasp how a turbofan worked, its graphical presentation of things is brilliant. There is a 30 day trial version of GasTurb on their site, check it out. The manuals are really good with illustrative examples: GasTurb site.

9. No one refer to Mr CARNOT famous theorem !!

200 years ago ( about the time USA became independant !!!) he demonstrated that thermal efficiency depends solely on the difference of temperature between the hot source and the cold source in °K

In our case cold source is outside the engine (Diesel or jet) Hot source is the core of the engine.
To get a temperature as high as possible , you have to burn as much fuel as possible in the smaller possible volume … to burn that fuel you need a lot of air so you better get high pressure (20 to 1 in diesel cylinders and 60 to 1 in the combustion chamber of the jet) … then it is very hot … surrondings material even if cooled must withstand these conditions.

Merry Christmas to all … start next year very smoothly and in peace

10. Geting high efficency in a turbine is much easier than in a compressor. Turine work output increases with Turbine inlet temp for the same inlet pressure. So for a given size engine you want high compressor pressure with high efficiency and a high turbine inlet temp. Both of these are hard to achive.

11. Yes increasing the peak pressure does increase the peak temperature but often overlooked is that high compression ratios allow for higher expansion ratios. The current trend in Diesel engine design is to slightly lower the compression ratio and also the inlet temperature with intercooling and also prolong the combustion with multiple injection events. I wonder if Bjorn is aware of the Bryton cycle piston engines that were produced by George Brayton?