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Flow impinging on axisymmetric disk

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Old   March 10, 2001, 15:50
Default Flow impinging on axisymmetric disk
  #1
Chuck Leakeas
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Hello all, I am currently trying to compute the boundary layer thickness from a normally impinging flow against an axisymmetric disk, also known as Homann Flow. When looking in Schlichting's book on b.l. flows he gives the b.l. thickness as delta=2.4*sqrt(nu/a). Where delta is the b.l. thickness and nu is the kinematic viscosity of the fluid. He says that for potential flow the velocity is U=a*x, and V=-a*y where U and V are far from the plate. My question is, what is the best way to determine a? From a computed run of axisymmetric viscous flow I am very skeptical about computing a value for a. It never seems to be constant for any velocity/distance combination far from the plate. What else can I do?

Thanks, Chuck
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Old   March 12, 2001, 05:11
Default Re: Flow impinging on axisymmetric disk
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John C. Chien
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(1). In the "boundary Layer Theory" book I have, the stagnation in plane flow(Hiemanz flow) was assumed to have U=ax; V=-ay, near the stagnation point. (2). The delta for the boundary layer for this case is 2.4 SQRT(NU/a). (3). On the other hand, Stagnation in 3-D flow was assumed to have U=ar; V=-2az. This solution was given by Homann in the form of a power series. (as stated in the book) (4). It seems to me that the solution you quoted is actually the solution of 2-D plane flow, not the 3-D axisymmetric flow. Why don't you double check the solution in the book? (mine is 1960 fourth edition)
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Old   March 12, 2001, 14:17
Default Re: Flow impinging on axisymmetric disk
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Chuck Leakeas
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John,

I understand what you are saying about the 3D axisymmetric flow. Knowing this, how would you compute the value of a, given that one has the numerical solution for viscous flow impinging on a disk? I'm just interested in comparing out approaches.

Thanks, Chuck

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Old   March 12, 2001, 19:08
Default Re: Flow impinging on axisymmetric disk
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John C. Chien
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(1).At some distance from the center line, plot the U-velocity distribution normal to the wall. (2). From the profile, you should be able to identify the inviscid region, which is outside the boundary layer region next to the wall. (3). Pick a point in the inviscid region and use the computed U-velocity in the equation to derive the unknown parameter "a". (4). Use this "a" to derive the V-velocity, and compare it with the calculation. (5). You can then spot check the U,V velocity field to see whether the assumed inviscid field is consistent with your calculation. (5). You can also derive the boundary layer thickness distribution from the calculation, and check against the analytical result.
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