# Calculating pressure coeff. in triangular panel method

1. Mar 3, 2004

### pjmab101

hi,

i am currently writing a 3D panel method program which uses triangular panels. i have written the part that calculates the doublet strengths on each panel and these seem to be correct. however i am having trouble determining the pressure coefficients from the doublet strengths.

now, for a four-sided panel method the local velocity tangential to the wing panel is the derivative of the doublet strength with respect to distance. this is done using a finite difference approach, by finding the change in doublet strength across adjacent panels and dividing by distance between panel control points. this is done in the spanwise and chordwise directions and then the cp is calculated as follows:

cp=1.0-((qinf+ql)^2+qm^2)/(vt^2)

where qinf is the local freestream vel, ql is local chordwise vel, qm is local spanwise vel. and vt is the freestream vel.

my problem is, how can i adapt this so that it works for triangular panels that may not be regular in shape, size or orientation?

2. Apr 7, 2007

### smarras

Triangular panel methods

Hi there, I saw thata you wrote a code for triangular patches for a panel method. I wanted to ask you if your problem is for a lifting surface problem and/or multi-components body

I can't help you with your question you posted, but ifyou could tell me a little more of what you are doing, that could help because im trying to actually modify a code for sails that is currently using quadrangular patches,

Thanks a lot,

Simone (simone.marras@gmail.com)

3. Apr 8, 2007

### caslav.ilic

I had a similar concern once when I wanted to implement a 3D panel method, but never got to actually do it.

Note that pressure coefficient in potential flow at certain point depends only on local velocity at that point. The term $$(q_\infty + q_l)^2 + q_m^2$$ in the formula for $$c_p$$ that you give is the local velocity squared.

So, I thought that to find $$c_p$$ at the control point of a triangular panel, one could do like this. First, compute FD at each of three sides, using this and neigboring panel doublet strength. This should give local disturbance velocity at each side middle point (and that would be a vector -- doublet-FD provides magnitude, and side normal in the plane of the panel provides direction). To this free stream velocity vector should be added, to obtain total local velocity.

Now, there are three points (panel side middle points), and three values in them (local velocity vectors). This is enough to define linear velocity distribution over the panel (ie. velocity-plane), so that velocity vector at the control point can be interpolated.

Admittedly, to work out all the vector stuff may be a bit ugly. It would certainly ease the derivation if you have vector algebra facilities in your code.

Whatever you do, please report how it turned out. May save me some time in the future, too :)

--
Chusslove Illich (Часлав Илић)

Last edited: Apr 8, 2007
4. Apr 8, 2007

### smarras

RE: triangular panels

Hi there, thanks so much for replying so quickly. Look, are you considering constant strength doublets on each panel? Also, what does FD mean?
Ill surely let you have all the results I come across with once I am done (might take long though cause Im working on it only in weekends!)

Thank you

s.

5. Apr 8, 2007

### caslav.ilic

Finite differrence.

Yes, I guessed it so. That's why I said to take FDs at panel sides, as these are the only places where there are potential jumps.

Also note that by "add free stream velocity vector", I ment the component of this vector in the plane of the panel. There is no point considering panel normal direction anyway, as that component of velocity should always sum to zero -- but it won't, due to various (expected) errors.

--
Chusslove Illich (Часлав Илић)

6. Apr 9, 2007

### smarras

DFs

Thanks for replying, i just don´t understand the achronym DF that you are using
What does it mean?

thanks a lot

s.

7. Sep 1, 2009