Scaling an Axial Compressor

Let's say I have a precisely designed axial compressor, comprising of stages of rotor and stator wheels, that resembles something like this:

Such a compressor, driven by a certain torque at a certain RPM, will deliver a certain air mass per time at a certain pressure. Now, what happens if the compressor is scaled down, so that the diameter is half of what it used to be but all other angles, etc. remain the same? The RPM will be such that the speed of the blade tips is the same in both compressors, i.e. the RPM will be higher in the smaller engine.

My intuition and some quick calculations tell me that the pressure ratio will remain the same, the mass flow will be divided by 4 (since cross sectional area is divided by 4), and the torque will be divided by 8 (since I think power will be divided by 4 and RPM will be doubled). But, again, I'm not sure, and I'd like to be. Can anyone help? Thanks!

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 In axial and centrifugal compressors, you keep the peripheral speed when scaling. This keeps the gas pressure and as well the mechanical stress. So: angular speed *2 pressure *1 mass flow /4 torque /8 power /4 (consistent with the mass flow) Needless to say, some technological reasons speak against easy scaling, for instance leakage, Reynolds... The combustion chamber is also more difficult to build.

Scaling an Axial Compressor

 Quote by Enthalpy In axial and centrifugal compressors, you keep the peripheral speed when scaling. This keeps the gas pressure and as well the mechanical stress. So: angular speed *2 pressure *1 mass flow /4 torque /8 power /4 (consistent with the mass flow) Needless to say, some technological reasons speak against easy scaling, for instance leakage, Reynolds... The combustion chamber is also more difficult to build.
That makes sense, thanks. I wasn't sure if it scaled that linearly, and it probably doesn't, but that kind of simplification is probably OK for only cutting the diameter in half. Maybe it would be smart to approximate that it will need about 2% more power than predicted, and have 2% less throughput, due to gap losses etc., too. I looked at the Reynolds number a little, and it doesn't seem like it will matter that much. In the smaller engine air should be a little less turbulent.

 Happy you if you can predict flows to 2%...

 Quote by Enthalpy Happy you if you can predict flows to 2%...
I have a chart of gap loss to gap width. A .07 mm width gives a gap loss of around .7%. Relative to the compressor, then, if the gap is around .07 mm, the gap will double relative to the size of the compressor since it's difficult to get the gap smaller at this size. I made a few estimates and quick calculations, and am coming up with around a 1.3% additional loss. I just decided to round up since there will probably be some other losses from building at a smaller scale since the tolerances of manufactured parts won't scale.

 In general, when the length of the blades gets down to one inch, it is time to switch to a centrifugal stage. At that point the efficiency of the axial stage will be less than the centrifugal stage. Efficiency is not as simple as you say. It is a function of tip clearance/blade length ratio. But tip clearance is pretty constant regardless of length. The blade packing density also gets too high for the smaller disks. That can lead to surge problems. If you compare sections of real engines, you will see that the front of the flow path for an axial compre ssor looks very much like the flow path of a centrifugal compressor. That is because it is a hybrid design. That is something the engineers learned fairly recently to combine the physics of both into one for better overall efficiency.

Recognitions:
 Quote by Pkruse If you compare sections of real engines, you will see that the front of the flow path for an axial compressor looks very much like the flow path of a centrifugal compressor.
Can you give a link to a drawing of that concept?

 Probably. But not from this phone. I'll get back to my computer tonight.

 Quote by Pkruse In general, when the length of the blades gets down to one inch, it is time to switch to a centrifugal stage. At that point the efficiency of the axial stage will be less than the centrifugal stage. Efficiency is not as simple as you say. It is a function of tip clearance/blade length ratio. But tip clearance is pretty constant regardless of length. The blade packing density also gets too high for the smaller disks. That can lead to surge problems. If you compare sections of real engines, you will see that the front of the flow path for an axial compre ssor looks very much like the flow path of a centrifugal compressor. That is because it is a hybrid design. That is something the engineers learned fairly recently to combine the physics of both into one for better overall efficiency.
It actually turns out that's not really the case. It's a common misconception of the model jet engine community that axial compressors are not efficient at that size. The very best small jet engines use axial compressors. Also, you can't buy any centrifugal compressor wheels that small, and it's easier/cheaper to make an axial compressor than a centrifugal one.

 Then it is a misconception commonly held by all the engineers who design engines for real airplanes. I don't think you can name one engine currently in production in significant numbers that I can't in five minutes walk to the desk of at least one engineer who was on the design team. If I told any one of them that, then they would strongly disagree. As for engines on small model toys, I yield to your much better understanding. I don't know anything about them at all.

 Quote by Pkruse Then it is a misconception commonly held by all the engineers who design engines for real airplanes. I don't think you can name one engine currently in production in significant numbers that I can't in five minutes walk to the desk of at least one engineer who was on the design team. If I told any one of them that, then they would strongly disagree. As for engines on small model toys, I yield to your much better understanding. I don't know anything about them at all.
As for the misconception, I was talking about the model community. What about Bladon Jets? A smaller company I believe, but their engine puts out 90+ lbs of thrust with a 4.5 in diameter, and there aren't any centrifugal stages. The very best centrifugal model engines put out ~47 lbs of thrust at that size.