2D-panelmethod, extend to lifting bodies?

[Voidses_]

I'm working on a basic 2D-"panelmethod" program. Currently it's "no-lift" but I would like to expand it to lifting bodies.

The routines I'm using are loaned from my litterature and the program is working just fine for non-lifting bodies. It uses sources distributed over the panels to calculate influence coefficients Tij,Nij (induced velocities over panel).
In the no-lift case I just need to sum these coefficients over all panels and I'm done.

The problems arise when expanding to lifting-bodies and one term of vorticity is introduced along with few more Nij and Tij.
The question is how i should implement the vorticity and extra influence coefficients to obtain the velocity at a certain panel?

 

[boneh3ad]

Is there a particular reason you are writing your own code instead of using an existing, mature code like xfoil?

 

[Voidses_]

I guess it's because I enjoy the process.

Any ideas what I might be doing wrong?

 

[RandomGuy88]

Im not sure exactly what you are having difficulty with. But you could add point vorticies in addition to your sources/sinks set up your system of equations and solve for the strengths of the vortices and sources/sinks. Then you can calculate the velocity at a point by summing the induced velocity from all of the sources and vortices. Then calculate your pressure and integrate.

An important thing to remember when applying a panel method to a lifting body is that you must satisfy the Kutta Condition. When using your sources/sinks you only needed to satisfy the condition of no flow perpendicular to the surface at your control points, this is also true for a lifting body with the addition of the Kutta Condition. It been awhile since I have done this but I believe this can be accomplished by setting the tangential velocity of the upper surface trailing edge panel equal to the tangential velocity on the lower surface trailing edge panel. To ensure an accurate answer those two panels should be relatively short and the same length.

Hope this helps some.

 

[Voidses_]

That helps a bunch. Thank you so much! The program is up and running
how's this for a NACA4412 airfoil @ 8deg?

Looks quite right imo, still a little funky at the trailing edge though. I just used midpoint aproximation to calculate the lift, not sure how accurate that is.

Now I just need to implement a boundary layer simulation ;P

 

[RandomGuy88]

You are close but I don't think that solution is quite right. The Cl for the NACA 4412 at 8 deg. is approx 1.46 according to xfoil.

What exactly are you plotting there. Its not Cp so I am assuming it is non-dimensionalized velocity. In which case your suction peak is a pretty high. You wouldn't happen to be plotting (V/Vinf)^2 would you? Because if so then it actually might be pretty close.

 

[Voidses_]

Correct, I'm plotting 1-Cp so it's basicly the same as (V/Vinf)^2. I suspect the difference in Cl is mainly because of the trailing edge panels. by changing them to a more appropiate configuration (similar length) the Cl dropped to 1.4. still not the same as X-foil but if it can change with 0.2 just by changing the trailing edge, I think the solution is correct. As a test NACA0024 was evaluated in Xfoil, the predicted Cl and Cp was in excellent agreement with my own program!
This is what I have at the moment

NACA4412@8deg

 

[RandomGuy88]

Thats great! Good job. Have you investigated if you get more accurate answers with more panels?

 

[Voidses_]

Thanks! I did try with more panels and it does improve the results to some extent (small improvement). However there's still problems close to the trailing edge. Because the rest of the Cp(x) plot look quite nice I suspect the errors are mainly due to incorrect input data (panels) at the trailing edge. Despite the errors I'm quite happy with what I have at the moment. Next step will be to add a subroutine that calculate the moment coefficient and perhaps later a boundary layer simulation.

Thank you for the help!

 

[4221371]

hello
I need to 3D potential flow based panel method for solving analysis hydrodynamics Catamaran ship, please help me, thank you.