Source/Vortex Panel Method: System of Equations
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- Опубликовано: 11 сен 2024
- In this video, we will combine the source panel method and vortex panel method into a hybrid source/vortex panel method that is more robust than our previous vortex panel method implementation, and which follows the method of Hess and Smith. In the next video, we will implement the equations shown here in the MATLAB and Python code.
===== RELEVANT VIDEOS =====
► Panel Methods Playlist
• How To: Run XFoil from...
► I(ij) Geometric Integral Derivation
• Source Panel Method: N...
► J(ij) Geometric Integral Derivation
• Source Panel Method: T...
► Mx(pj) and My(pj) Geometric Integral Derivation
• Streamline Geometric I...
► K(ij) Geometric Integral Derivation
• Vortex Panel Method: N...
► L(ij) Geometric Integral Derivation
• Vortex Panel Method: T...
► Nx(pj) and Ny(pj) Geometric Integral Derivation
• Streamline Geometric I...
► Source Panel Method: Airfoil
• Source Panel Method: A...
► Vortex Panel Method: Airfoil
• Vortex Panel Method: A...
===== NOTES =====
- On the whiteboard at 13:55 (and on), the final term on the RHS (b array) has a beta_N, which for this 3-panel problem, can just be written as beta_3.
===== 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
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► Foundations of Aerodynamics, Kuethe and Chow
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► Theory of Wing Sections, Abbott and Doenhoff
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![Source Panel Method: Normal Velocity Geometric Integral [I(ij)]](http://i.ytimg.com/vi/76vPudNET6U/mqdefault.jpg)
I don't really understand this but the effort you made on your video should be appreciated. so here is your new subscriber. you doing great keep it on!
Thanks!
Well done. Thanks!
You're welcome!
Hello, Josh. I have a doubt at 14:27(pause the video there). Don't you think in the right side of the equation, inside the bracket, where sine terms are there having angle beta1 and betaN, it should be beta1 + beta 3, since for 3 panel system N=3? also same in the right hand side of '=' in the last row of the matrix?
Hello Josh. I am wondering about the accuracy of the SVPM vs the VPM with linear vortex strength variation. You have shown that the constant strength variation can fall apart in certain cases where it doesn't with the SVPM doesn't, but what about for VPM with linear strength? Which is more accurate? Thank you, your videos are very much appreciated.
I would say that the linear strength VPM is more robust than my SPVP method (and definitely better than just the constant strength VPM). The reason I didn't go through it in my series is because the derivations are more complicated, and the constant strength derivations are in-depth enough as it is. You can even go to higher order approximations of the strengths, since linear strength is also just an approximation of the actual distribution over the panel length.
Great content!I am wondering whether this method can be used in internal flow or not.How can I simulate the situation that a source with the suction effect in the end of a tube ?
Hey Josh, great video. I was able to implement all of this into code but ran into a small problem. The coordinates that I am loading in from xfoil have a blunt closed trailing edge which obviously messes with the Kutta condition as presented in the video.
The way I "fixed" this was to manually adjust the trailing edge to become sharp after loading in the coordinate files in my Matlab script.
Is there a way to immediately load in an airfoil from xfoil with a sharp trailing edge?
Thanks! Yea, that is definitely one of the issues with the way I have everything laid out here and coded. It's also something that is mentioned in books/papers regarding the panel methods; you have to make sure to be very clear about how you're dealing with the trailing edge (TE). For an introduction to panel methods (and for most of the airfoils I'll show in my next video), the way I do it here is fine. That being said, this is the most basic way to do it, and there are other better, more sophisticated ways of implementing the Kutta condition.
I've typically just been leaving the blunt TEs open (as I think I mentioned in a previous video), but technically this isn't the correct way to do it. You can also do what you did, which is just approximate a sharp TE by changing the data points, but I have actually found that this generally messes things up more than just leaving it blunt and ignoring the last "closing" panel. I've just been loading airfoils that I downloaded from the UIUC airfoil database, and that's what XFOIL uses and then spits out to me. Some have a blunt TE, and some have a sharp TE. Since my code is more of a general demonstration, I haven't fiddled around too much with it.
Hello Josh. can you please show how to calculate the stagnation point for an airfoil using vortex + source panel method and also plot it in the airfoil
The stagnation point will just be the point on the airfoil where the velocity is zero, and since the normal velocity is always zero, it's the same as saying the tangential velocity is also zero. I won't go through the full example, but one easy (approximate) way to do it is to compute the tangential velocities on the airfoil surface as I do in my code, and then find the point where it's close to zero. That gives a good starting point.