How to define boundary conditions in 3D vortex panel method
 

Hey there (=


I'm making my own custom 3D vortex panel method code (https://github.com/pedrosecchi67/LovelacePM/ if you want to check out the code I've made so far) and have some doubts.


I've read (http://heli-air.net/2016/02/19/vortex-panel-method/) that for this method the collocation points should be placed at 3/4ths of the panel's x dimension. However, I've seen other functional doublet panel method codes (http://www.3dpanelmethod.com/documen...ate%20Work.pdf and I think APAME does the same) placing the control point at the panel's midpoint. Since there's a mathematical equivalence between vortex panels and doublet panels (https://www.youtube.com/watch?v=Me9Z31d1-PE&t=410s), shouldn't the same work for vortex panel method?


My code hasn't worked so far, I've tried testing the Euler solution with a sphere (testcase_sphere.py) and it resulted in a ~0.7 peak tangential velocity to freestream velocity ratio at the surface while it should be 1.5.



If anyone can either clear the subject to me or provide me with some referrence that explains why the collocation point is placed as it is I'd be very, very thankful.

Let me point you to these posts:

https://www.cfd-online.com/Forums/ma...el-method.html
https://www.cfd-online.com/Forums/ma...lculation.html
https://www.cfd-online.com/Forums/ma...tex-rings.html

What you might be missing is the principal part of the induced velocity, that is the self-influence, which is the gradient of the surface gamma distribution.

There used to be freely available slides from Virginia Tech about this topic and this very method, but they are not anymore and I can't find my own copy of them anymore.

Besides this, if I remember correctly, the reason for the 3/4 (I actually remember 1/4) rule is that for a single vortex representing a flat plate you get the Kutta condition automatically satisfied, or something along this line. I don't know of 3D cases where this is applied.

Hi, Paolo!


http://www.dept.aoe.vt.edu/~devenpor...l%20Method.pdf


Is this the link you were looking for?


I'll post another reply as soon as I can correctly calculate the surface gradient (=


Thanks in advance!

Exactly!!! Look at slides 12-14 for the gradient part

However, refer to the work of Ashook Srivastava (I provided the links in one of the posts linked above) for the issue of rank deficiency for the vortex ring method applied to closed bodies. Basically, you have to remove one equation for each closed body (or just fix the gamma of the relative panel)

P.S. Nice hacking job :cool:

It worked!!! The tangential velocity/x coordinate curve finally reached a peak of 1.5 Uinf.


I'll make a closed cylinder my next test case and make sure to use your reference for the rank deficiency.


Thanks a lot, Paolo!! :D