Hi,

I am interested in 2-Dimensional pure rotating cylinder. I calculate the velocity field around a cylinder by the vortex particle methods.

The cylinder merged in viscous fluid has solid surface, solid body and flow around the body and they are modeled by vortex sheet, bounded vortex and free vortex respectively.

The strenth of vortex sheet is determined by their slip velocity induced by free vortex. It is difficult to calculate their strengths.

The vortex sheet's strength which is twice the slip velocity on the sheet panel is very important, because, owing to sheet's strength, no slip boundary condition is satisfied and vortex to the fluid is generated.

Let me know how to calculate the induced velocity or examples to verify the slip velocity.

Thanks.

> The strenth of vortex sheet is determined by their slip
> velocity induced by free vortex. It is difficult to
> calculate their strengths.

The field velocity in vortex methods is the sum of potential and vortical components, due to Helmholtz decomposition of vectors. The first question for you is "how do you evaluate the potential velocity? method of images, boundary element methods, etc.?" In either case the sheet strength AT the surface is quite easy to compute: it is the sum of the influences of all vortex elements and sheets on each sheet.

> Let me know how to calculate the induced velocity or
> examples to verify the slip velocity.

See above for calculating the induced velocity. As for examples, I'd suggest you try the simpler problem of boundary layer flow over a flat plate, where you can compare your results with exact solutions. Then you can worry about rotating cylinders.

I don't know which method you are thinking of (or are) using for simulating the flow near the boundary, but in any case I'd recommend you read the book (and earlier papers) by Alexander Chorin (and Marsden) for the best introduction to the method.

Adrin Gharakhani

Thanks, Adrin Gharakhani. I use the panle methods. The surface of the solid boundary modeled with panels and the slip velocity evaluated by the free vortices surrounde the solid body.

According to increasing the free vortices, the slip velocity is decreading to zero, and is very sensitive to arrangment of panels and free vortices.

This difficulties , I think, comes from enclosing panels with free vortices and eccentricity of the panle. Since the cylinder are surrounded by free vortices.

Thanks again.

>According to increasing the free vortices, the slip >velocity is decreading to zero, and is very sensitive to
>arrangment of panels and free vortices.

I don't understand! Do you mean increasing the number or the magnitude of the free vortices? If the number, then in what direction are you increasing them?

As for sensitivity of the solution... Well, assuming you don't have bugs in your code, the solution will be sensitive to panel and free vortex arrangements because this is essentially a collocation method. All collocation methods (e.g. finite difference) will exhibit sensitivity to grid distribution!

You have to be a little more specific about distribution-sensitivity. One important comment. Since you are using the panel method (by default I'm assuming you are using piecewise constant variation of the potential across each panel) then your solution, especially near the panels is consistent (and accurate) ONLY at the panel centroids. So, to be consistent you have to put your free vortices at the centroid of the panel (or along the line going through the centroid) This is VERY important. To understand what I mean, just look at the potential solution (without any free vortices) very near the body. For example, take a square shape with size unity and discretize each side using 10 panels, then look at the velocity field, say 0.001 away from one side of the aquare using 500 points (so dx=.02 for post-processing and dx=.1 for the solution) That should give you the answer why your solution is sensitive.

>This difficulties , I think, comes from enclosing panels >with free vortices and eccentricity of the panle.
>Since the cylinder are surrounded by free vortices.

I don't get it! What panel eccentricity?

Adrin Gharakhani