Vortex Panel Method Development Question

[Graviman]

Kind aerospace folk,

Preamble:

I'm trying to write my own aerofoil vortex panel method, but have run into some difficulties. The method is designed to work in Excel, so is limited in matrix size for reliable inversion (for vortex / velocity matrix). This means that the traditional method of a large number of panels in unrealistic. The original aerofoil data is limited to 11 points each for top and bottom surfaces and leading and trailing edge radii.

Having read Abbott & Doenhoff, I have decided to try to update the original 1940s aerofoil analysis methods. This means that i define both top and bottom surface geometries each as a polynomial, with a maximum of 10 terms. To me it seemed logical that the surface vortex distribution would also be a polynomial of similar order, with separate equations for top and bottom surfaces.

So far the method looks promising, with the surface normal velocities all meeting the no through flow boundary condition. But, i have run into difficulties with the tangential velocity distribution. Specifically how to implement the Kutta condition for no trailing edge circulation (at low AOA). Having read various papers i decided that although equal and opposite trailing edge vortices are often quoted, what is really required are equal top & bottom surface trailing edge tangential velocities. This then begs the question of how do i achieve the correct trailing edge outflow velocities (relative to free field velocity), and ensure the correct overall tangential velocity distribution.

The question(s):

Has anyone here had a go at writing their own vortex panel method?
Do any of the difficulties described here sound familiar?
Are there any techniques not documented in the literature that i am overlooking?


My plan is to compare the results i get with this code:
http://www.engapplets.vt.edu/fluids/vpm/index.html

The final step will be validation by CFD, and then some physical testing (maybe).


Thanks in advance,

Mart

 

[caslav.ilic]

Are there any techniques not documented in the literature that i am overlooking?

Do I understand you correctly: you do not want (are limited, whatever) to use methods which require "big" number of unknowns, so you are searching for a method to give you accurate results with ~20 unknowns along the airfoil contour? If so, I don't think that is possible (according to own feeling of "accurate", of course).

If I misunderstood, then why not go with run-of-the-mill method, for example, as described in the theory section of the page you linked? Having a limit at number of unknowns means that, at best and if at all, accuracy could be improved by not using the piecewise linear vortex strengts, but e.g. polynomial as you mentioned. (Though with a 10th degree polynomial I'd already be worried about roundoff problems...)

Debugging-wise, with such a low number of unknowns it is hard to tell if there is some problem in the computation, or merely a numerical inconsistency creeping in. So I'd suggest a test implementation using a tool in which you can do away with hard-coded number of unknowns, and which can handle reasonable amount of them (~100-200 ought to be just fine), and when you confirm that things work as expected, transfer it to spreedsheet under the imposed limits.

--
Chusslove Illich (Часлав Илић)

 

[caslav.ilic]

Just looked in Katz and Plotkin, if you can get a hold of it, the figure 11.27 demonstrates that using a usual first-order, piecewise linear method, with as few as 10 panels in total (5 per side) can give pressure distribution quite reminiscent of an accurate one with 90 panels.

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Chusslove Illich (Часлав Илић)

 

[Graviman]

Chusslove,

Thank you for your advice, and apologies - I've been away getting a report ready...

Yes, you have understood correctly. Rather than using Gausian elimination (with partial pivoting) i want to use matrix inversion. This works fine for say a 24x24 matrix but would likely struggle with say a 200x200 matrix. The idea is to make the maths well conditioned to the problem to keep the actual solve very simple. Most aerofoils are well represented with a polynomial for upper and lower surface, provided you allow for a leading and trailing edge radius.

I have already taken your advice and have a "floating point" to move along the aerofoil surface to check aerodynamic conditions between the points. Like your "Katz and Plotkin" reference, i have found that 10 points can be suprisingly accurate. The main problem i have now found is getting the maths right at the leading edge. Howevr, I have several ideas to solve this...

Mart

 

[manukamin]

Hi guys.I'm manu.I'm an undergraduate mechanical engineering student. i have a doubt regarding the vortex panel method.I'm trying to develop a MATLAB code of my own.But the problem is when i consider a control point on a particular panel,i add the contributions of all other panels to the stream function at that point using the formula gamma/2*pi*ln(r-r0)ds.But what's the contribution for the stream function at the control point due to the vorticity in its own panel?Because here r becomes equalto r0.someone please reply to my doubt..