On what are you basing your question? Is there something in the theory of the thermodynamic cycle of a gas turbine that you are referring to? Or are you comparing the efficiencies of different size engine in produxtion?
I am not aware of thermodynamic theory stating that the size is directly proportional to the efficiency. However I believe it's what tends to happen in "real life". Maybe due to the fact that bigger gas turbines can rotate at lower speeds for the same tip blade velocities… I don’t know if this is the reason. Just an example - http://www.dg.history.vt.edu/ch5/turbines.html
Is not your question explicitly answered here in the text you reference:
The traditional gas turbine represents an 'economy of scale' system where efficiency is proportional to size. The large centralized utility grade turbines have benefited from these specific engineering solutions instead of the adapted smaller technologies. While the inlet temperatures have steadily increased, the cooling passages, materials, and compressor geometry advancements of smaller CT and MT systems have not similarly kept pace with the larger units.
But is it just a case of the higher technology development in bigger turbines?
While turbines can scale up or down in size, the stuff the drives them remains the same size.
Because of this, there will always be a sweet spot in scaling of the turbine.
Perhaps the friction and heat losses are proportional to surface area and expanding gas energy proportional to volume - and therefore increased efficiency by increased size.
There are many answers to this question, but by far the most important is tip clearance, which is a major source of lost energy. The smaller the clearance, the lowered the loss. But tip clearance cannot be scaled down as the engines get smaller. Very small axial engines become so inefficient that they switch to a centrifugal design which is much less efficient than a large axial machine.
HowlerMonkey, "While turbines can scale up or down in size, the stuff the drives them remains the same size", what do you mean?
M Grandin, "Perhaps the friction and heat losses are proportional to surface area and expanding gas energy proportional to volume - and therefore increased efficiency by increased size.", you mean because bigger gas turbines can rotate at lower speeds for the same tip blade velocities?
Pkruse, "The smaller the clearance, the lowered the loss. But tip clearance cannot be scaled down as the engines get smaller. Very small axial engines become so inefficient that they switch to a centrifugal design which is much less efficient than a large axial machine.". From wikipedia "Centrifugal compressors are often used in small gas turbine engines like APUs (auxiliary power units) and smaller aircraft gas turbines. A significant reason for this is that with current technology, the equivalent flow axial compressor will be less efficient due primarily to a combination of rotor and variable stator tip-clearance losses. Further, they offer the advantages of simplicity of manufacture and relatively low cost. This is due to requiring fewer stages to achieve the same pressure rise.". Two questions:
1) In downsizing, if tip clearance is maintained why is efficiency decreased?
2) Why centrifugal design is more appropriate/efficient for lower sizes? And why is it a less efficient design?
Thank you all
Tip clearance will be about the same in large and small engines. The problem is leakage around the tips wastes energy, so we always minimize that. But energy lost around the tips is a much larger percentage of the total in the smaller engine.
The answer to the second question is that the first only applies to axial engines. Centrifugal engines don't have blade tips to worry about.
There leakage losses between the impeller and casing in a centrifugal compressor as well, but the leaking gas still ends up being centifuged outwards to the compressor outlet. For an axial compresor, gas that leaks ober the blade tips is effectively going back "upstream" and most of the energy that was put into it is wasted.
You can get a higher pressure ratio across a signle stage centrifugal compressor than a sngle stage axial, but not enough to design an efficient large engine. Multi stage centrifugal compressors and big and heavy, because of the "plumbing" needed to get the gas from the outer diameter of one stage to the inner diameter of the next stage. The practical power limit is in the 100 kW to 1 MW range which is small compared with axial turbomachinery.
In axial turbomachinery, the basic causes of tip clearance (the deformation of flexible rotors that are not perfectly balanced, thermal expansion, creep of materials at high temperature, etc) don't scale linearly with the size of the machine. The losses are proportionately worse for small machines than for large ones.
Now I am confused. Aren`t centrifugal turbines supposed to be a "less efficient design"?
To repeat post #2, I don't think we can fix the confusion unles you tell what you mean by "efficient design" here.
Your http://www.dg.history.vt.edu/ch5/turbines.html seems to be specifically about "distributed power generation" (DG). I'm not disputing the data in that report but it doesn't cover the full range of products that is being marketed, even for that subset of the full range of applications. For example the company I work for markets a 50 MW CHP system with overall efficiency comparable to the microturbine quoted in your reference.
Pkruse - "Very small axial engines become so inefficient that they switch to a centrifugal design which is much less efficient than a large axial machine.", hence my confusion…
For small engines, centrifugal engines are more efficient. For large ones, axial is more efficient.
You can plot the efficiency curves for both as a function of size. Both will show increasing efficiency with increasing size. But at some point at about a thousand HP, the curves cross.
Confusing matters even more is that for engines near the cross point, they are often partly centrifugal and partly axial. The LPC might be centrifugal, and the rest axial. Or maybe the the LPT might also be centrifugal.
In an axial design the gas flow is much straighter, so you have less aero losses than in a centrifugal design. So if it were not for the tip loss problem, axials would always be more efficient.
Thank you for your clarification. Regards
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