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Aug 12, 2019, 08:10 PM
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Actuator disk question


Hi

Can anyone please let me know the answer to the question below

https://physics.stackexchange.com/qu...of-stream-tube

Thanks
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Aug 12, 2019, 09:50 PM
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is this the sort of thing you're looking at?
https://www.e-education.psu.edu/aersp583/node/470
if not its interesting and I never knew such studies existed.

What's it for?
Mainly posted to sub and follow till my head explodes

Edit. I am thinking it can not be the same thing. the flow is reversed. Sorry for the false call.
https://web.mit.edu/16.unified/www/F...es/node86.html
https://www.researchgate.net/figure/...fig1_299645000
https://nptel.ac.in/courses/10110100...on-Lect-29.pdf
its all french to be. GL bud.
Last edited by Bryce.R; Aug 12, 2019 at 10:05 PM.
Aug 13, 2019, 01:18 AM
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ShoeDLG's Avatar
I think it’s kind of a trick question. The figure implies two things:

1) The normal velocity through the disk is uniform,

and

2) The pressure jump across the disk is uniform.

While this simplification is OK if one is only interested in what happens in the far field of the disk, it turns out that these two conditions are actually mutually exclusive.

If you want to know the shape of the stream tube, you can specify a vorticity distribution (e.g. Joukowsky actuator disk). The pressure jump profile, the velocity profile and the shape of the stream tube (area as a function of distance from the disk) all follow from a specified vorticity distribution.
Last edited by ShoeDLG; Aug 13, 2019 at 01:25 AM.
Aug 13, 2019, 11:50 AM
Registered User
.... all of which (incl. vorticity distribution) is further complicated by the propensity for multiple turbines to mutually interact, varying with wind direction and velocity

in this vid note typical interaction starting at 24 seconds >

https://www.khanacademy.org/partner-...gy/v/windpower
Aug 13, 2019, 11:28 PM
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MSelig's Avatar
You won't get the slipstream from actuator disk theory alone. But along the lines mentioned above, you can introduce into the flowfield discrete vorticity and track it. You can model the flow by dropping vortex rings into the flow (equivalent to that produced by the vortex tube in actuator disk theory) and then follow the rings. For a propeller, they will contract and give you the slipstream. For a wind turbine, you'll see the expansion of the vortex rings.
Aug 15, 2019, 04:26 AM
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Thread OP
Thanks very much for all the input.
I asked the above question actually to understand how a ducted fan stops the flow contraction aft of the fan, hence allowing an increased mass flow rate for a given power.
I will certainly try solving the stream-tube by the vortex ring method first to gain a better understanding

Thanks again for all the help
Aug 15, 2019, 05:45 AM
Registered User
Just a guess, but perhaps the duct walls tend to keep the flow near its surface due to a combination of Bernoulli and the fact that the wall prevents the ambient atmospheric pressure from constricting the flow .... (re: the infamous "blowing over the paper" demo in which the flow and paper get closer to each other)
Aug 16, 2019, 03:23 PM
Registered User
Buwa, you are talking about aft of the fan but still in the shroud?

If so then the important thing to remember is that there is still pressure inside, even though it is reduced compared to ambient outside readings.

Like Lee said "the wall prevents the ambient atmospheric pressure from constricting the flow"

Is this what you're looking at?

Edit. For some reason, I said "even though it is reduced compared to ambient outside readings"
Thinking on that, I don't know for sure if this is a given or just wrong. I am looking around to find more information on it. While Looking, I found this;
https://pdfs.semanticscholar.org/05c...15%2C000%20rpm.
Some may find it interesting because it has lots of Pretty Pictures (ME)
Last edited by Bryce.R; Aug 21, 2019 at 03:45 AM.
Aug 19, 2019, 04:23 PM
Registered User
Also, the area of the intake and that of the duct, especially as it reaches the impeller, are not usually the same. You have to subtract the diameter of the motor pod.


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