Vortex Panel Method: Airfoil

The vortex panel method code in this video is an adaptation of the source panel method code from a few videos ago. The only change we've made between the codes is the formulation of the matrix system of equations (including the addition of the Kutta condition equation).
We'll look at a few examples of the code working like you would expect, and compare resulting lift and moment coefficients to the XFOIL results. Then we'll look at a few cases where the code seems to fall apart, which is the motivation for my next two videos, the combined source/vortex panel method.
===== WHERE ARE WE GOING? =====
→ The limitations in this video motivate the need for a more robust implementation of the VPM.
→ I will derive the combined SPM/VPM formulation and code it to show how good we can get the results for a pretty simple implementation.
→ We can finally extend the SPM/VPM formulation to multiple separate airfoil elements. This will be the last video in the series.
===== CODE =====
► My website
www.joshtheengi...
► GitHub
github.com/jte...
===== RELEVANT VIDEOS =====
► Panel Methods Playlist
• How To: Run XFoil from...
► Panel Method Geometry
• Panel Method Geometry
► Building More Complex Flows
• Building More Complex ...
► Flow Around an Airfoil
• Flow Around an Airfoil...
► Normal Velocity Geometric Integral [K(ij)]
• Vortex Panel Method: N...
► Tangential Velocity Geometric Integral [L(ij)]
• Vortex Panel Method: T...
► Streamline Geometric Integral VPM [Nx(ij) and Ny(ij)]
• Streamline Geometric I...
► Solving the System of Equations: VPM
• Vortex Panel Method: S...
► Source Panel Method: Airfoil
• Source Panel Method: A...
===== NOTES =====
→ I'll add notes here if I need to.
===== ERRORS =====
→ If you see an error in the video, please let me know and I will include it here.
===== REFERENCES =====
Note: the links are Amazon affiliate links. If you do happen to want to buy the book and use the link below, it helps me out a little.
► Fundamentals of Aerodynamics, Anderson
amzn.to/3emVuXU
► Foundations of Aerodynamics, Kuethe and Chow
amzn.to/2yMg1Vi
► Theory of Wing Sections, Abbott and Doenhoff
amzn.to/2wvZyUt

[@maxwenk4557]

Just wanted to say that these videos are extremely helpfull and well made. Thank you for helping out engineering students all over the world. Greetings from Germany!

[@geckomaniac3801]

I'm starting my Bachelor's Thesis on coupling the boundary layer equations with the airfoil panel method and your videos are a fantastic introduction to the latter. Thank you so much for putting out this content you are a phenomenal teacher. I'm excitedly waiting for future videos. You got a new sub. :)

[@JoshTheEngineer]

Thanks! Good luck with your thesis!

[@acruzp]

Has that been done before? It seems like a natural thing to do doesn't it?

[@williamsworkshop8624]

14:35 Don't tease me! These videos have been invaluable for the project I'm working on! Have you thought about exploring 3D panel methods at all?

[@JoshTheEngineer]

Hah, they're coming soon! I have so many other video topics I'd like to get to that I don't think I'm going to be doing any 3D panel methods any time soon. Maybe in the future though! Hopefully these videos provide a stepping stone for those methods though.

[@mickh7995]

Just finished watching all the videos in this series - great! I'm almost inspired to try to make a 3D version. Thanks for doing such a detailed explanation and including all the code. I have a couple of comments. 1. You say a couple of times that you can't get drag from this method. I think it might be worth clarifying a bit as you compute CN and CA and so by definition you have CL and CD. If CD is not accurate then either CN or CA or both must also be inaccurate. 2. You mostly use xfoil results as a measure of the success of your code. I think it would be very interesting to do some comparisons with experimental data. This would give an indication of how good these methods really are (including xfoil) and give a way to make your point about accepting the lift result but not the drag one. There is plenty of good data in Appendix IV of Abbott and Von Doenhoff. Perhaps there's a video number 28 in this series? Thanks again for the excellent videos.

[@rezamoradian8354]

Thank you Josh.

[@JoshTheEngineer]

You're welcome!

[@blackguardian89]

Another invaluable tutorial :) Thanks again, Josh! I'm just curious could you recommend some useful and practical sources (books, articles, lectures, videos, etc.) about the 3D panel method or the VLM?

[@JoshTheEngineer]

You're welcome! I haven't really delved into the 3D panel methods/VLM that deeply, so the best I can say is that most books with the 2D panel methods will also have sections for the VLM. For example, Anderson's book talks about those topics. I'm sure there are tutorials on here on KZbin from universities that will go into more detail, so maybe start there. Another thing you can do is Google it, and type in the search term "filetype:pdf", which generally gives some good documents. Good luck!

[@thierrydaoud3458]

Hello Josh! I wanna thank you for these videos they're extremely helpful! I just wanna ask you how can I obtain the plots of the streamlines over the airfoil using the Vortex Panel Method just like you did at 13:40? I ran the code and didn't obtain them.

[@ktprajwalprathiksh6180]

@Josh - At 7:19, when you're calculating the Lift Coefficient using the Kutta-Joukowski theorem, shouldn't there be a negative sign? Or am I missing something?

[@Bluenosecat]

Thank you Josh,I'm getting very a lot of helps from your videos. I have a question though, How could I apply this method if their are two wings like tandem or biplane?

[@JoshTheEngineer]

You're welcome! I just uploaded a multi-element panel method video, where you can have more than one airfoil, like a biplane wing for example.

[@2MilMil]

Hello Josh! I've been following your panel method video series all along and they are very helpful! Thank you! Could you please elaborate on how to obtain Cl from Cp? By running the code at various AoA, I can see that CL from your VPM matches very well with CL given by xfoil until the AoA reaches > 25 degrees. Looking back at the code, CL is indeed described by a sinusoidal function. Shouldn't we expect CL be linear if flow is inviscous?

[@JoshTheEngineer]

Hey William, sorry for taking so long to reply. If we were analyzing airfoils using thin airfoil theory, then you would expect the lift curve slope to be constant, and it would equal 2*pi. When we add thickness and camber (using the panel method), then this can change. There are two ways that I compute the lift coefficient. The first way is using the pressure coefficient, which is the way that you have noted in your comment. This is one of the ways you compute the lift coefficient for an airfoil in a wind tunnel for example (the other being force balances). You would have pressure taps around the airfoil, which would give you pressure coefficient distribution at discrete points. Then you would decompose those pressures into normal and axial forces, and then based on the angle of attack, you can decompose those into lift and drag. That's where the sine and cosine come from in my code. It's just the components of the normal and axial force coefficients. The other way I compute lift coefficient is using the Kutta-Joukowski (K-J) lift equation, where I only use the vortex panel strengths (or circulation). This means I don't need to do any decomposing of the pressure coefficient. I tend to like the K-J method better, and you can see that I primarily use that in my SPVP code. My inviscid calculations won't predict separation or stall, so the lift coefficient will presumably keep increasing. It should really only be used for low or moderate angles of attack, so anything above, say, 8 degrees is probably pushing it.

[@elpaso4765]

one of the most harsh topic i have ever seen in engineering.

[@debbyduke9932]

hey Josh, i sent you an email recently. could you please read it and get back to me