Source Panel Method: Circular Cylinder

Here we are. We finally have all the mathematical information needed to code up the source panel method. In this video, we take the code we had from the panel method geometry video, and add in the following: computation of the source panel strengths, computation of the panel tangential velocities and pressure coefficients, and computation of the grid X and Y velocities (for streamline plotting).
This video uses a circular cylinder geometry because it is a convenient test case where we can compare the pressure coefficients on the panels to an analytical solution. If your code doesn't work with a circular cylinder, it's not a good idea to move on to harder geometries.
===== WHERE ARE WE GOING? =====
→ The next video will be very similar to this one; the source panel method solution for airfoil geometries.
→ We will see some limitations in the SPM which will motivate the need for the vortex panel method (VPM).
→ 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.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 [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...
===== NOTES =====
→ I forgot to add the pop filter in front of my microphone for this video, so I apologize in advance.
===== 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

[@stuartmilam3437]

Simply an incredibly helpful compilation of tutorials. Well done.

[@JoshTheEngineer]

Thank you, much appreciated!

[@blackguardian89]

Finally! Thank you so much :) Can't wait for the next videos! Keep up the good work!

[@JoshTheEngineer]

You're welcome! They're coming soon!

[@kelvinjaramillo8007]

Thank you!! Very much.....

[@JoshTheEngineer]

You're welcome!

[@user-yx5wd5yy6h]

awesome!

[@JoshTheEngineer]

Thanks!

[@ruili9830]

Hi Josh, thanks for the awesome video. So SPM cannot be used to calculate the lift force and you can only get the pressure distribution by this method? But doublet and source panel methods can be used for lift calculations? And drag force can be calculated only in 3D cases?

[@JoshTheEngineer]

You're welcome! Correct, you can't use the SPM to get lift. To get lifting flow, you'll need a vortex in the flow. That's why in the VPM, we construct the airfoil out of vortex panels instead of source panels. You won't be able to get drag from either the SPM or the VPM. To compute drag, you'll need to introduce viscous effects, which then gets into boundary layer computations, and is the topic of a whole separate set of videos. When you start getting into 3D calculations, then things are different and more confusing, since there are different kinds of drag. This, again, is an entirely separate topic that I may get into in the future.

[@ruili9830]

​@@JoshTheEngineer Thank you Josh!

[@ruili9830]

Hi Josh, thank you for your video and codes. Hope you are well. I'm also working on coding of panel method. I found that in the seciton of calculating streamlines if you set the grid points as 30, 50, 70, etc you will get a strange plot with a straight line pointing to the circle. Do you know why this happens? Thank you very much!

[@JoshTheEngineer]

Good question Rui. That's actually the stagnation streamline, which is why it terminates on the cylinder (stagnation means there's no velocity, so it won't move anywhere once it hits the stagnation point). It just so happens that for nGridX/nGridY points of 30, 50, 70, etc., one of the streamlines hits the stagnation point and doesn't continue around the cylinder. Look at the "Ysl" variable for those grid sizes, and you'll see that one of them is zero, which means its on the centerline of the cylinder. You can use these values (30, 50, 70) if you change the slPct variable either up or down (e.g. from 0.3 to 0.35). The higher the value, the denser the streamlines. While looking at this in the code, I realized I have a bug that means you have to have square grids for the streamline computations, so I'll update that in a future version. Hope that answered your question!

[@ruili9830]

@@JoshTheEngineer Thank you Josh! It really helps!

[@calebtomes1285]

If I was given circulation values of 0,-1,-2,and -3 how would I get different streamline plots for the given values?

[@redouanehemi9693]

the number of boundary points should be equal to the number of panel

[@JoshTheEngineer]

Not the way I define the geometry.

[@hasanmutlu4304]

There is something wrong with your matlab code because it does not give the same numbers (CL,CD ,L) with python code.

[@Gabriel-oo8em]

What happens when E is not real?? I mean Iij goes to infinity ...