Source Panel Method: Airfoil

Flows over a circular cylinder are a bit boring, so here we apply the same code (with a couple minor tweaks) to the flow over an airfoil. In this video, we add two code blocks: the first is for loading and creating the airfoil, and the second is to compute the circulation around an ellipse that encompasses the airfoil. Everything else from the previous video (Source Panel Method: Circular Cylinder) is the same. The results we get in this video motivate the need for the vortex panel method.
===== WHERE ARE WE GOING? =====
→ I will need to go through the derivations for the geometric integrals for the VPM (which are similar to the SPM derivations).
→ We will then implement the VPM and see some of its limitations. These limitations will 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.joshtheengineer.com/2020/0...
► GitHub
github.com/jte0419/Panel_Methods
===== 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 [I(ij)]
• Source Panel Method: N...
► Tangential Velocity Geometric Integral [J(ij)]
• Source Panel Method: T...
► Streamline Geometric Integral SPM [Mx(ij) and My(ij)]
• Streamline Geometric I...
► Solving the System of Equations
• Source Panel Method: S...
► Source Panel Method: Circular Cylinder
• Source Panel Method: C...
===== 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

[@blackguardian89]

Thanks again, Josh! Looking forward to your next videos about VPM :)

[@JoshTheEngineer]

No problem! Trying to film them this weekend.

[@Dani-ox6yw]

Love your videos. Your hard work is really appreciated bro.
Thanks alot :)

[@JoshTheEngineer]

That's really nice of you, thanks!

[@carlosmaldonado8600]

Thanks mate!

[@JoshTheEngineer]

You're welcome!

[@StandforTr00th]

You are the best Josh! Fsr, I'm getting errors in line 81, and line 103 and idk how to fix it.

[@JoshTheEngineer]

Thanks! I would need you to post the exact error message you're getting, otherwise I'm not sure I can help.

[@SangJin-Nick]

thank you :)
I have a question, how to change the length of cord ?

[@saberhaghgooyeshafagh1693]

hi josh, why didn't you calculate the source strength in this video?

[@JoshTheEngineer]

I'm not sure what you mean. At 1:21, you can see the code block where I calculate the source strengths, and at 7:03 I go through that code block. The source strengths are calculated on line 173.

[@ramibarbar5]

Hey josh, I have some questions about a fluid mechanics project, just wondered if u could kindly answer some questions!

[@JoshTheEngineer]

I'm not sure how much I can help, but you can always email me.

[@nickname6363]

Bug report: Run "clarkysm.dat", error occurs because of atan2 when solving the second term in Mx equation.

[@nickname6363]

Changing the default 170 panel nodes is able to skip this "bug" of finite discretization.

[@JoshTheEngineer]

Thanks for pointing this out! I updated the STREAMLINE_SPM.m file to set E to zero when it is imaginary or a NaN. This way you don't need to change the number of panel nodes.

[@nickname6363]

@@JoshTheEngineer Thank you! By the way, when will be the next video ready for updating? Looking forward to it. Again, many thanks.

[@nickname6363]

@@JoshTheEngineer Small correction: legend([pXu,pXl,pSl,pSu] instead of legend([pXu,pXl,pSu,pSl] at line 374, to make same color denote same boundary, if I read the codes correctly.