Scaling Laws for Gas Turbine Engines (1 Viewer)

[Zipper730]

I'm curious if there's any formulas that help determine scaling for jet-engines? For example if the diameter were to double in length would the thrust increase by the square of this diameter (much like fluid going through a pipe)?

drgondog , X XBe02Drvr , W wuzak

 

[cherry blossom]

I am not one of the experts but a 0.855 scale RR Nene became the Derwent V. The Nene gave about 5,000 lb trust and the Derwent V gave 3,500 lb trust.

 

[Sergio]

I'm just a humble, forgetful, retired engineer and recall just how complex modelling factors were from my college days. I remember that you cannot always practically apply the same factor throughout to estimate a factor of a model's performance. For example, a yacht's maximum speed through the water does not change pro rata to its waterline length because of other speed-affecting rules though the 2^3 rule (2*2*2 = 8) provides a good estimate of the weight and catalogue price of similarly-specified yachts!

Assuming your factor of doubling the diameter also means you're doubling the length of the engine, I would start by expecting 8 times the thrust. It would also probably be about 8 times heavier.

You're right about the water pipe!

 

[thunderbird]

The answer is complicated.

As i understand it, the equations for predicting jet engine performance were available in the mid-fifties or early sixties. However, it takes quite a bit of explanation to describe what parameters are important. Engine diameter, for instance is tricky. Did one just upsize the whole engine or did one also change the bypass ratio? Can the two engines have the same engine pressure ratio or do materials limit one engine over another? Certainly jet engine design has seen the most change since WWII.

But to exactly address your question, other factors other than size, seem to be more important to determining engine performance. For instance, the F404 engines in F/A-18s is more powerful than J-79 engines in F-104 and F-4 among others, and more powerful than the J57 in F-101s and F-102, despite being for smaller and lighter. The F110 has about 50% more thrust than the TF30, despite being almost the same size. But some place i read that the TF30 had better supersonic performance, supposedly because of the digital controls on the F110.

But compare the J75 and J57 engines for performance change based in size. Supposedly, the J75 took the J57 and made it larger. The J75 was also a generation newer engine, so it might have benefited from internal material improvements in addition to the size increase.

 

[peceed]

I'm curious if there's any formulas that help determine scaling for jet-engines? For example if the diameter were to double in length would the thrust increase by the square of this diameter (much like fluid going through a pipe)?

Generally - yes. Engine weight is the third power of linear size, thrust is the second power. The only problem is the change in Raynold's number, which makes smaller engines less efficient and powerful - unfortunately air does not scale the same.
In a magical world with a constant Reynolds number, the engines would take the form of walls of several hundred miniature turbines placed side by side.

Assuming your factor of doubling the diameter also means you're doubling the length of the engine, I would start by expecting 8 times the thrust.

Until you consider that the turbine RPMs need to be reduced in proportion to size, just as when enlarging an internal combustion engine.
This simultaneously protects the turbine from bursting, maintaining internal stresses in the materials and maintaining the maximum linear velocity of the profiles in the gas.

Of course, there are practical engineering and economic factors that cause very small engines to maintain a constant thrust-to-weight ratio of around 10:1, even for for RC model engines: composite structures cannot be arbitrarily miniaturized, it is difficult to make precise hollow sections in miniature veins, electronic and control components do not shrink to the same degree, nor do bearings, and there is no payoff for overcoming the aforementioned challenges.

 

[peceed]

Engine diameter, for instance is tricky. Did one just upsize the whole engine or did one also change the bypass ratio?

It doesn't matter if you scale up the same geometry/construction.