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 Jerome July 26, 1999 05:17

Core size in VEM

I am using a regularized vortex element method to study wakes behind aircrafts but I have a problem with the choice of the core size of regularization: the cores of particles have to overlap and is then of the order of the mean inter-particles distance but my vortex sheet is likely to be torn between flaps, but the method cannot foresee that, and so to my mind, I can't take into account directly the mean inter-particles distance.

Can anybody help me?

 olus boratav July 26, 1999 09:51

Re: Core size in VEM

Hi,

The following references might help.

Knio and Ghoniem (1990)

Numerical study of a 3D vortex method

J. Comput. Phys, 86, pp.75-106

Fernandez, Zabusky, Gryanik (1995)

Vortex intensification and collapse.....

JFM 229, pp.289-331

Pelz (1997)

Locally Self-similar, finite-time collapse in a high-symmetry model

Phys. Rev. E. 55(2), 1617-1626

Olus Boratav

 Adrin Gharakhani July 26, 1999 14:22

Re: Core size in VEM

I don't see a significant problem with the vortex sheet spliting around the flaps. That is if you use discrete (disjoint) elements and not the vortex filament model (where the elements are assumed connected).

The core overlap condition is really a confusing criterion! Basically you'd want the core of an element to overlap the core of the nearest neighbors. If a stream of elements reach a "bifurfaction" such as the flap, then the particles within each stream would have to maintain their respective core overlap. In practice, and unless you have significant vorticity stretch, you hardly have to worry about core overlap if you have small enough of a timestep (as overlap would generally be satisfied if it was satisfied initially). You can check the validity of the above statement by post-processing the relative positions of the elements. As for the case with stretch, there are issues just as important as core overlap that you need to consider and worry about (and it is beyond the scope here)

 Jerome July 27, 1999 03:42

Re: Core size in VEM

I understand what you mean but my aim was to fix the value of the core size in order not to give it arbitrarily so that I can find the same results as experiments. That's why I wanted to use the core overlap condition. In the main part of the computation, the core overlap is satisfied elsewhere but not between flaps where the stretch remains to high, hence my question: I have to give a value of the core size but how?

Hopping that I was clear,

Jerome

 Adrin Gharakhani July 27, 1999 15:29

Re: Core size in VEM

Well, the core size is an arbitrary variable (no ifs or buts about it) - in a sense it's similar to (but not exactly the same as) grid size in grid-based computations. Larger core sizes will give you more diffuse results, and convergence occurs (presumably) in the limit of zero core size (much like grid size).

I still don't see why you should worry (too much) about the flap region. You should just make sure that the cores don't cross the flap (that will lead to a misrepresentation of vorticity). Thus, so long as the cores don't cut through the flap and you have core overlap you're safe. If the cores do cut the flap, say at a sharp leading edge, I'd say the effect of this is similar to rounding the sharp edge. The rest is a matter of "convergence study"

Check out the JFM paper by Marshall et al (within the last 3 years or so) which is a vortex simulation of a 3D vortex ring cutting through a blade. This is quite similar to what you're doing - the difference is that in the JFM paper the blade does not generate vorticity (flow about it is inviscid)