JoshTheEngineer | Vortex Panel Method: Tangential Velocity Geometric Integral [L(ij)] @JoshTheEngineer | Uploaded April 2020 | Updated October 2024, 3 hours ago.
We just finished the video for the source panel method (SPM), and saw its inherent limitations as we looked at some results for an airfoil. Now, to be able to code up the vortex panel method (VPM), we need to compute geometric integrals similar to those for the SPM. These geometric integrals come from the expressions for the normal and tangential velocity.
In this video, we derive the geometric integral from the tangential velocity expression (Lij). In the next video, we will derive the X and Y velocity expression geometric integrals needed for the streamline calculations, after which we can construct a system of equations to solve for the vortex panel strengths.
===== RELEVANT VIDEOS =====
► Panel Methods Playlist
youtube.com/watch?v=bWjo3N9COz4&list=PLxT-itJ3HGuUDVMuWKBxyoY8Dm9O9qstP
===== 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
We just finished the video for the source panel method (SPM), and saw its inherent limitations as we looked at some results for an airfoil. Now, to be able to code up the vortex panel method (VPM), we need to compute geometric integrals similar to those for the SPM. These geometric integrals come from the expressions for the normal and tangential velocity.
In this video, we derive the geometric integral from the tangential velocity expression (Lij). In the next video, we will derive the X and Y velocity expression geometric integrals needed for the streamline calculations, after which we can construct a system of equations to solve for the vortex panel strengths.
===== RELEVANT VIDEOS =====
► Panel Methods Playlist
youtube.com/watch?v=bWjo3N9COz4&list=PLxT-itJ3HGuUDVMuWKBxyoY8Dm9O9qstP
===== 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
![Vortex Panel Method: Tangential Velocity Geometric Integral [L(ij)]](https://i.ytimg.com/vi/IxWJzwIG_gY/hqdefault.jpg "Vortex Panel Method: Tangential Velocity Geometric Integral [L(ij)]
We just finished the video for the source panel method (SPM), and saw its inherent limitations as we looked at some results for an airfoil. Now, to be able to code up the vortex panel method (VPM), we need to compute geometric integrals similar to those for the SPM. These geometric integrals come from the expressions for the normal and tangential velocity.
In this video, we derive the geometric integral from the tangential velocity expression (Lij). In the next video, we will derive the X and Y velocity expression geometric integrals needed for the streamline calculations, after which we can construct a system of equations to solve for the vortex panel strengths.
RELEVANT VIDEOS
► Panel Methods Playlist
https://www.youtube.com/watch?v=bWjo3N9COz4&list=PLxT-itJ3HGuUDVMuWKBxyoY8Dm9O9qstP
NOTES
- Ill 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
https://amzn.to/3emVuXU
► Foundations of Aerodynamics, Kuethe and Chow
https://amzn.to/2yMg1Vi
► Theory of Wing Sections, Abbott and Doenhoff
https://amzn.to/2wvZyUt")
![Explained: NACA 4-Digit GUI Part 5/10 [MATLAB]](https://i.ytimg.com/vi/J0L7N7cvk80/hqdefault.jpg "Explained: NACA 4-Digit GUI Part 5/10 [MATLAB]
This is the fifth video in my 10-video series on coding a program in MATLAB to compute, display, and save a NACA 4-digit airfoil.
IN THIS VIDEO:
We code the input for the angle of attack and save file name edit text boxes. The angle of attack text box needs to be converted to a number, while the file name text box can remain a string.
IN THIS SERIES:
Part 1/10 : https://goo.gl/9UBgbo
Part 2/10 : https://goo.gl/jRRcYJ
Part 3/10 : https://goo.gl/rSVLHo
Part 4/10 : https://goo.gl/HwHB39
Part 5/10 : https://goo.gl/AlDne8
Part 6/10 : https://goo.gl/7n1QP7
Part 7/10 : https://goo.gl/nTGleR
Part 8/10 : https://goo.gl/ez247P
Part 9/10 : https://goo.gl/8mXYcc
Part 10/10: https://goo.gl/ovBlbW")
![Explained: Ghost Nodes [CFD]](https://i.ytimg.com/vi/JMP9aanQ5o0/hqdefault.jpg "Explained: Ghost Nodes [CFD]
In some finite difference/volume equations, you might need to use points that are outside of the actual grid domain. In these cases, ghost nodes can be calculated from the interior points and used for the differences (such as a central difference on a boundary node).")
![Source Panel Method: Tangential Velocity Geometric Integral [J(ij)]](https://i.ytimg.com/vi/JRHnOsueic8/hqdefault.jpg "Source Panel Method: Tangential Velocity Geometric Integral [J(ij)]
In the previous video (Geometric Integral Iij), we went through the full derivation of the geometric integral for the normal partial derivative, which was needed to solve for the source panel strengths. In this video, we will go through the (very similar) derivation of the tangential partial derivative geometric integral, which is needed to solve for the panel velocities, and thus the panel pressure coefficients.
This derivation is almost exactly the same as the normal geometric integral derivation, but there are some slight differences. Where it is exactly the same, I will refer you back to my other video (Iij) so we dont make this video longer than it needs to be.
RELEVANT VIDEOS
► Panel Methods Playlist
https://www.youtube.com/watch?v=bWjo3N9COz4&list=PLxT-itJ3HGuUDVMuWKBxyoY8Dm9O9qstP
► Panel Method Geometry
https://www.youtube.com/watch?v=kIqxbd937PI
► Building More Complex Flows
https://www.youtube.com/watch?v=EKzbwJvKcmw
► Flow Around an Airfoil
https://www.youtube.com/watch?v=cLdv1UfX1g8
► Normal Velocity Geometric Integral, Iij
https://www.youtube.com/watch?v=76vPudNET6U
NOTES
- Ill 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
https://amzn.to/3emVuXU
► Foundations of Aerodynamics, Kuethe and Chow
https://amzn.to/2yMg1Vi
► Theory of Wing Sections, Abbott and Doenhoff
https://amzn.to/2wvZyUt")
![Explained: TI-83 Linear Interpolation Program [Math]](https://i.ytimg.com/vi/KQzK5z9jkHE/hqdefault.jpg "Explained: TI-83 Linear Interpolation Program [Math]
In this video I show you how to program a linear interpolation equation into your TI-83 graphing calculator.
If you would like to see how the equation is derived, click the link below to my other video.
https://goo.gl/7OA0UU
Here is the code if you already know how to input it into your calculator:
PROGRAM:INTERP
Input X1=,A
Input X2=,D
Input X= ,I
Input Y1=,N
Input Y2=,S
Disp (((S-N)/(D-A))(I-A)+N)")
![Explained: Croccos Theorem [Taylor-Maccoll]](https://i.ytimg.com/vi/KZYHjujYpFk/hqdefault.jpg "Explained: Croccos Theorem [Taylor-Maccoll]
Croccos theorem is needed to obtain the irrotationality condition used later in the overall derivation. The equation is essentially a combination of the momentum and energy equations. The final resulting boxed equation states that the curl of the velocity field is zero, indication an irrotational flow.
The extra videos I mention in this video can be found below.
Momentum Equation: http://www.youtube.com/watch?v=ZH0fiaYGTYQ
Assumptions: http://www.youtube.com/watch?v=HIDeIZO0z-8
Total Derivative: http://www.youtube.com/watch?v=bgUDbntoXBY
TdS Equation: http://www.youtube.com/watch?v=N126SaEGuJA
Vector Identity: http://www.youtube.com/watch?v=0LO-ZcESYdE
Enthalpy: http://www.youtube.com/watch?v=yy5HQ9syrrI")
