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Rotating Disc in a Volume of Air

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Old   August 24, 2009, 13:54
Default Rotating Disc in a Volume of Air
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Daniel McGregor
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Hello All-

I am new to CFD solvers therefore would like benefit from the knowledge base this forum represents. Can FLOW-3D solve the following test case?

Physical Problem Description/Definition:

a) Define a disc in a volume of air. The disc would of negligible thickness, but rigid. Since I intend to spin the disc about its central axis, I am thinking that it would be a good idea to take advantage of symmetry and define both the volume of air and the disc in a cylindrical coordinate system (not a requirement, but it would make pre- and post-processing easier, so software that makes this easy would be desirable).

Initial Conditions:

a) Assign a rotational velocity to the disc, i.e., assign a tangential (to the axis of rotation) surface velocity to the individual mesh elements of the disc. once again a preprocessor that would use a cylindrical coordinate system would be desirable...

b) the air in the volume (the cylindrical "can") is initially at rest and, if need be, the air in contact with the boundary of the volume would be zero.

Solving:

a) solve for a steady state solution. the spinning disc should cause the air in the volume to spin as well. the steady state solution should be where the rotation of the air reaches equilibrium with the spinning disc. (At least this what I think should happen!!)

Post Processing:

a) have a look at the normal forces on the surface of the disc (induced by the Bernoulli effect) as a function of radius

b) have a look at how the air in the volume rotates as a function of the rotating
disc

That's It! Can FLOW-3D do the above?

Any help in narrowing my search for a solver (and pre- and post-processor) is appreciated!!
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Old   August 24, 2009, 16:25
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I'm pretty sure that flow-3d can solve the equations with the bc's you specify - at least it could when I was using it. But give flow science a call and ask. Maybe get a demo if you don't have access to the code.

Selecting the proper bc's may be a lot of 'fun' for you. That's not a code problem. But figuring out how you want to decouple your problem region from the (in theory) infinite region about and to the sides of the disk will require some thought. There are results for infinite and finite disk solutions in early versions of Schlichting. If I recall correctly, there's also some data for the finite disk version.

Good luck with this!
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Old   August 24, 2009, 20:30
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Hi Otd
just curious on the term "it could when i was using it" so can you advice any reason you are not using it now?
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Old   August 25, 2009, 09:11
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Well, I retired 10 years ago so don't have any access to the code. Actually we leased it for (perhaps) a year in the late 80's for a project that had funding cancelled, so the lease was not renewed.

Full disclosure: I knew Tony Hirt, who invented the code. I don't have (and have never had) any relationship with Flow Science except as a customer.

As to your problem, I can't imagine that they would REMOVE capability that the code used to have. But, if you're a potential customer, you should ask for a demonstration on a problem similar to the one you need to solve.

To repeat: your challenge won't be the code but to decide what bc's you need to apply.
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Old   August 28, 2009, 16:45
Default Rotating Disc treatment by Schlichting
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Hello otd-

Thanks for your input. I am very interested in your comment about a solutions published for the infinite and finite disc problems. I have found the following versions of Schlichting (Hermann) available from my local library as follows:

Boundary-layer Thoery, 8th ed. publ. 2000
Boundary-layer Thoery, 7th ed. publ. 1979
Boundary-layer Thoery, 6th ed. publ. 1968
Boundary-layer Thoery, 4th ed. publ. 1960
Boundary-layer Thoery, 1st ed. publ. 1955

Any further refinement as to which editions may have a treatment of the rotating disc problem??
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Old   August 28, 2009, 17:04
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I have the English translation of the 4th edition, published in 1960. The full solution for an infinite disk starts on page 83. It appears you have access to that. The 3rd edition, in German, was evidently published in 1958.

What I was remembering as a second solution is on pp. 86-87, and is just an approximation for a disk of "large but finite" radius.

I recall the mathematical fluids (whatever that is) literature in the 60's & 70's had many attempts to solve the problem.

Pages 83 to 89 will give you a bit to chew on.
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