JoshTheEngineer
Curl of the Gradient of a Scalar Field is Zero
updated
00:00 - Introduction
00:20 - Background
00:49 - Notebook types
01:49 - Writing utensils
02:22 - General content structure
02:47 - Page numbering
03:11 - Dates and highlighting
04:33 - Referencing pages and notebooks
05:10 - Adding figures
05:22 - Extra notes, corrections
06:05 - Finishing up
===== NOTES =====
- This is how I do it. There is no right answer here. Do what you want.
===== LINKS =====
Note: These are Amazon affiliate links. If you use these links to purchase any of the items, it helps me out a little bit.
► Oxford Composition Notebook (100 sheets, quad ruled), $4.49 at this moment
amzn.to/3wTIZLV
► National Laboratory Notebook (96 sheets, quad ruled), $10.79 at this moment
amzn.to/3yXHYEb
► Adams Record Ledger (300 pages, my preference), $34.11 at this moment
amzn.to/2S0aaFO
► Pilot G2 0.7mm (five-color pack: black, blue, red, green, purple), $6.79 at the moment
amzn.to/3uH76vI
► Pilot G2 0.7mm (5 black, 5 blue), $15.97 at the moment
amzn.to/3vGYExX
► BIC Brite Liner Grip Highlighter (five-color pack: pink, blue, green, orange, yellow), $4.89 at the moment
amzn.to/34AiZcl
1) How does the mirror reflect the light when the incident rays are collimated (parallel)?
2) How does the mirror reflect the light when the incident rays emanate from the 2f point?
We'll see why the spherical mirror is ideal for the double-pass system, while the parabolic mirror is ideal for the Z-type system, but also why you can use either mirror in both systems without much loss in quality.
===== RELEVANT VIDEOS =====
► How To: Build Your Own Schlieren Setup
youtube.com/watch?v=IZ0bYi9UFv8
===== NOTES =====
- All simulations assume on-axis performance, even though in the schematics I show, the light source is located off-axis. If you want to use a beamsplitter for the double-pass system, then you would have on-axis light through the system.
- I'm aware the spherical mirror focusing issue is called spherical aberration. Sometimes I deliberately choose not to include terminology depending on the intended audience of the video.
===== RELEVANT REFERENCES =====
- Any optics book
00:00 - Motivation
00:36 - PowerPoint: Getting ready
01:01 - PowerPoint: Create schematic
02:48 - PowerPoint: Save as PDF
03:22 - PowerPoint: Resize slides
06:18 - PowerPoint: Viewing PNG vs. PDF in LaTeX
06:53 - PowerPoint: Multiple schematics
09:06 - Inkscape: Getting ready
10:06 - Inkscape: Create some text
10:43 - Inkscape: Keys and mouse clicks
11:19 - Inkscape: Create schematic
13:18 - Inkscape: Create duplicate schematic
14:10 - Inkscape: Unicode symbols
14:56 - Inkscape: Larger equations
16:22 - Inkscape: Exporting PDF
19:12 - Inkscape: Viewing two PDFs in LaTeX
19:39 - Inkscape: Multiple schematics in one document
===== LINKS =====
► Inkscape download
inkscape.org
► Introduction to LaTeX
youtube.com/watch?v=qjLqM1YYNN4
===== THUMBNAIL =====
► PowerPoint Logo
UT Dallas, CC BY-SA 4.0 creativecommons.org/licenses/by-sa/4.0, via Wikimedia Commons
► Inkscape Logo
Inkscape Community (original logo), This vector image was created with Inkscape by Speck-Made, and then manually replaced by sarang., CC0, via Wikimedia Commons
00:00 - Introduction
00:31- Dark theme
00:53 - Creating a library
01:14 - When to create new libraries
03:36 - Citation keys
04:57 - Importing citations and editing entries (e.g. AIAA)
10:36 - Importing citations and editing entries (e.g. Applied Optics)
12:22 - Importing using DOI
13:18 - Importing using ISBN
13:53 - Special table columns
14:40 - "Read status" column
15:00 - "Quality" column
15:55 - "Linked files" column
17:34 - "Linked identifiers" column
18:18 - Using groups and "Groups" column
20:54 - Updating references in Texmaker
22:08 - Final thoughts
===== VIDEOS =====
►Introduction to Latex
youtube.com/watch?v=qjLqM1YYNN4
===== TEMPLATES =====
►Download from my GitHub
github.com/jte0419/LaTeX_Templates
===== USEFUL REFERENCES =====
JabRef: docs.jabref.org
Wikibook: en.wikibooks.org/wiki/LaTeX
Overleaf: overleaf.com
Stack Exchange: tex.stackexchange.com
===== PROGRAMS FOR LATEX =====
Texmaker: xm1math.net/texmaker
MiKTeX: miktex.org
JabRef: jabref.org
Sumatra PDF: sumatrapdfreader.org/free-pdf-reader.html
===== NOTES =====
- There are a bunch of options and customization features I didn't cover in the video.
===== ERRORS =====
Please let me know if you find any errors in my video, or in the template files provided.
00:00 - Who should use LaTeX?
01:03 - Useful references
01:22 - Programs you'll need
01:49 - Texmaker download
02:06 - MiKTeX download
02:27 - JabRef download
02:45 - Sumatra PDF download
04:00 - Texmaker settings
05:38 - Starting a document
07:40 - Adding references
11:27 - Adding figures
14:12 - Adding equations
16:24 - Templates
===== TEMPLATES =====
►Download from my GitHub
github.com/jte0419/LaTeX_Templates
===== PROGRAMS =====
Texmaker: xm1math.net/texmaker
MiKTeX: miktex.org
JabRef: jabref.org
Sumatra PDF: sumatrapdfreader.org/free-pdf-reader.html
===== USEFUL REFERENCES =====
Wikibook: en.wikibooks.org/wiki/LaTeX
Overleaf: overleaf.com
Stack Exchange: tex.stackexchange.com
===== NOTES =====
- There are so many ways to accomplish the same thing with LaTeX, so if you see something I did and you do it a different way, that's great.
- I'm deliberately not going into a bunch of details and explanation in this video.
===== ERRORS =====
Please let me know if you find any errors in my video, or in the template files provided.
The motivation for this video was to show how to add the BOS_Save_Sequence_v2.ijm file to the Plugins → Macros menu for use with my Background Oriented Schlieren code/video (see links below).
===== LINKS =====
►DIY Background Oriented Schlieren Video
youtube.com/watch?v=VCUN59x0LF4
►Updated ImageJ Macro for DIY BOS
youtube.com/watch?v=GXapOtBf52o&t=5s
►GitHub Code
github.com/jte0419/Background_Oriented_Schlieren
►My Website Code
http://www.joshtheengineer.com/2019/10/20/how-to-take-pictures-like-nasa-using-background-oriented-schlieren-bos
===== LINKS =====
GitHub (download version 2 of the .ijm macro)
►github.com/jte0419/Background_Oriented_Schlieren
My website (download version 2 of the .ijm macro)
►http://www.joshtheengineer.com/2019/10/20/how-to-take-pictures-like-nasa-using-background-oriented-schlieren-bos
DIY BOS YouTube Video
►youtube.com/watch?v=VCUN59x0LF4
===== CODE =====
► My website
http://www.joshtheengineer.com/2020/07/12/multi-airfoil-source-vortex-panel-method
► GitHub
github.com/jte0419/Panel_Methods
===== RELEVANT VIDEOS =====
► Panel Methods Playlist
youtube.com/watch?v=bWjo3N9COz4&list=PLxT-itJ3HGuUDVMuWKBxyoY8Dm9O9qstP
► Source Panel Method: Airfoil
youtube.com/watch?v=fdNOYdwY9Bw
► Vortex Panel Method: Airfoil
youtube.com/watch?v=JL2fz-xTTT0
► Source/Vortex Panel Method: System of Equations
youtube.com/watch?v=bc_pkKGEypU
► Source/Vortex Panel Methods: Airfoil
youtube.com/watch?v=V77QTAgZuqw
===== NOTES =====
→ I haven't coded this particular script in Python, and I'm not sure if I'm going to. You can download my single-airfoil SPVP code and update it based on my MATLAB code if you want to.
→ More airfoils and more panels per airfoil will cause the streamline calculations to take longer.
→ The grid for the streamline has to have equal X and Y points at the moment. I know there's an error since it doesn't work for irregular grids, but I'm not planning on fixing it at the moment.
===== 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
In this penultimate video of my Panel Methods series, we will look at how to populate the matrix system to obtain the solution of the source and vortex strengths. Then we'll go through a bunch of examples of different airfoils to see how well this method works. Comparisons of the lift coefficient, moment coefficient, and pressure coefficient to XFOIL will be made.
In the next (and last) video of this series, we will update this code to be able to work with any number of airfoils.
===== CODE =====
► My website
http://www.joshtheengineer.com/2020/06/22/source-vortex-panel-method-airfoil
► GitHub
github.com/jte0419/Panel_Methods
===== RELEVANT VIDEOS =====
► Panel Methods Playlist
youtube.com/watch?v=bWjo3N9COz4&list=PLxT-itJ3HGuUDVMuWKBxyoY8Dm9O9qstP
► Source Panel Method: Airfoil
youtube.com/watch?v=fdNOYdwY9Bw
► Vortex Panel Method: Airfoil
youtube.com/watch?v=JL2fz-xTTT0
► Source/Vortex Panel Method: System of Equations
youtube.com/watch?v=bc_pkKGEypU
===== NOTES =====
→ The code is also available in Python, but I didn't include it in this video.
→ The streamline computation section in the Python code takes a really long time to run in comparison to the same MATLAB code. I'm assuming it has to do with the external function calls taking longer, but if you have any suggestions on speeding up that aspect of the code, please let me know.
===== 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
===== RELEVANT VIDEOS =====
► Panel Methods Playlist
youtube.com/watch?v=bWjo3N9COz4&list=PLxT-itJ3HGuUDVMuWKBxyoY8Dm9O9qstP
► I(ij) Geometric Integral Derivation
youtube.com/watch?v=76vPudNET6U
► J(ij) Geometric Integral Derivation
youtube.com/watch?v=JRHnOsueic8
► Mx(pj) and My(pj) Geometric Integral Derivation
youtube.com/watch?v=BnPZjGCatcg
► K(ij) Geometric Integral Derivation
youtube.com/watch?v=5lmIv2CUpoc
► L(ij) Geometric Integral Derivation
youtube.com/watch?v=IxWJzwIG_gY
► Nx(pj) and Ny(pj) Geometric Integral Derivation
youtube.com/watch?v=TBwBnW87hso
► Source Panel Method: Airfoil
youtube.com/watch?v=fdNOYdwY9Bw
► Vortex Panel Method: Airfoil
youtube.com/watch?v=JL2fz-xTTT0
===== 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
amzn.to/3emVuXU
► Foundations of Aerodynamics, Kuethe and Chow
amzn.to/2yMg1Vi
► Theory of Wing Sections, Abbott and Doenhoff
amzn.to/2wvZyUt
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
http://www.joshtheengineer.com/2020/06/21/vortex-panel-method-airfoil
► GitHub
github.com/jte0419/Panel_Methods
===== RELEVANT VIDEOS =====
► Panel Methods Playlist
youtube.com/watch?v=bWjo3N9COz4&list=PLxT-itJ3HGuUDVMuWKBxyoY8Dm9O9qstP
► Panel Method Geometry
youtube.com/watch?v=kIqxbd937PI
► Building More Complex Flows
youtube.com/watch?v=EKzbwJvKcmw
► Flow Around an Airfoil
youtube.com/watch?v=cLdv1UfX1g8
► Normal Velocity Geometric Integral [K(ij)]
youtube.com/watch?v=5lmIv2CUpoc
► Tangential Velocity Geometric Integral [L(ij)]
youtube.com/watch?v=IxWJzwIG_gY
► Streamline Geometric Integral VPM [Nx(ij) and Ny(ij)]
youtube.com/watch?v=TBwBnW87hso
► Solving the System of Equations: VPM
youtube.com/watch?v=j3ETHFBiYOg
► Source Panel Method: Airfoil
youtube.com/watch?v=fdNOYdwY9Bw
===== 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
In the next video, we will adapt my SPM code into the VPM code, look at some results, compare to the Kuethe and Chow implementation, and motivate the need for my combined SP/VP implementation.
===== RELEVANT VIDEOS =====
► Panel Methods Playlist
youtube.com/watch?v=bWjo3N9COz4&list=PLxT-itJ3HGuUDVMuWKBxyoY8Dm9O9qstP
► Source Panel Method: System of Equations
youtube.com/watch?v=ep7vPzGYsbw
► K(ij) Geometric Integral Derivation
youtube.com/watch?v=5lmIv2CUpoc
► L(ij) Geometric Integral Derivation
youtube.com/watch?v=IxWJzwIG_gY
► Nx(pj) and Ny(pj) Geometric Integral Derivation
youtube.com/watch?v=TBwBnW87hso
===== NOTES =====
- At 2:56, I show a screenshot from the Kuethe and Chow book (1976), and this expression does not have a negative sign. In their book, they generally take the negative sign out of the summation and move it to the uniform flow term immediately, hence the missing negative sign. The focus of that screenshot is actually the text below the equation.
===== 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
===== 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
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
In this video, we derive the geometric integral from the normal velocity expression (Kij). In the next video, we will derive the geometric integral from the tangential velocity expression (Lij). Finally, 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
===== 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
http://www.joshtheengineer.com/2020/03/05/source-panel-method-airfoil
► GitHub
github.com/jte0419/Panel_Methods
===== RELEVANT VIDEOS =====
► Panel Methods Playlist
youtube.com/watch?v=bWjo3N9COz4&list=PLxT-itJ3HGuUDVMuWKBxyoY8Dm9O9qstP
► Panel Method Geometry
youtube.com/watch?v=kIqxbd937PI
► Building More Complex Flows
youtube.com/watch?v=EKzbwJvKcmw
► Flow Around an Airfoil
youtube.com/watch?v=cLdv1UfX1g8
► Normal Velocity Geometric Integral [I(ij)]
youtube.com/watch?v=76vPudNET6U
► Tangential Velocity Geometric Integral [J(ij)]
youtube.com/watch?v=JRHnOsueic8
► Streamline Geometric Integral SPM [Mx(ij) and My(ij)]
youtube.com/watch?v=BnPZjGCatcg
► Solving the System of Equations
youtube.com/watch?v=ep7vPzGYsbw
► Source Panel Method: Circular Cylinder
youtube.com/watch?v=zIrDfEz-5mc
===== 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
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
http://www.joshtheengineer.com/2020/02/29/source-panel-method-circular-cylinder
► GitHub
github.com/jte0419/Panel_Methods
===== RELEVANT VIDEOS =====
► Panel Methods Playlist
youtube.com/watch?v=bWjo3N9COz4&list=PLxT-itJ3HGuUDVMuWKBxyoY8Dm9O9qstP
► Panel Method Geometry
youtube.com/watch?v=kIqxbd937PI
► Building More Complex Flows
youtube.com/watch?v=EKzbwJvKcmw
► Flow Around an Airfoil
youtube.com/watch?v=cLdv1UfX1g8
► Normal Velocity Geometric Integral [I(ij)]
youtube.com/watch?v=76vPudNET6U
► Tangential Velocity Geometric Integral [J(ij)]
youtube.com/watch?v=JRHnOsueic8
► Streamline Geometric Integral SPM [Mx(ij) and My(ij)]
youtube.com/watch?v=BnPZjGCatcg
► Solving the System of Equations
youtube.com/watch?v=ep7vPzGYsbw
===== 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
This video goes through how to set up the system of equations that needs to be solved in order to obtain each panel's source strength.
===== RELEVANT VIDEOS =====
► Panel Methods Playlist
youtube.com/watch?v=bWjo3N9COz4&list=PLxT-itJ3HGuUDVMuWKBxyoY8Dm9O9qstP
► Panel Method Geometry
youtube.com/watch?v=kIqxbd937PI
► Building More Complex Flows
youtube.com/watch?v=EKzbwJvKcmw
► Flow Around an Airfoil
youtube.com/watch?v=cLdv1UfX1g8
► Normal Velocity Geometric Integral [I(ij)]
youtube.com/watch?v=76vPudNET6U
► Tangential Velocity Geometric Integral [J(ij)]
youtube.com/watch?v=JRHnOsueic8
► Streamline Geometric Integral SPM [Mx(ij) and My(ij)]
youtube.com/watch?v=BnPZjGCatcg
===== NOTES =====
→ To solve the system of equations, I'm using the programmatic function (x = A\b). This takes care of the solution method for you, but you can also use your own Gaussian elimination solver, for instance. Here is a link to the MATLAB documentation for the solver:
mathworks.com/help/matlab/ref/mldivide.html
===== 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
In this video, we go through the derivation of the X and Y velocity geometric integrals (Mx(ij) and My(ij)). These will allow us to compute the flowfield pressure coefficients and the streamlines around the airfoil. Much of this derivation is exactly the same as the Iij derivation, so I will refer you to that video for those details.
===== RELEVANT VIDEOS =====
► Panel Methods Playlist
youtube.com/watch?v=bWjo3N9COz4&list=PLxT-itJ3HGuUDVMuWKBxyoY8Dm9O9qstP
► Panel Method Geometry
youtube.com/watch?v=kIqxbd937PI
► Building More Complex Flows
youtube.com/watch?v=EKzbwJvKcmw
► Flow Around an Airfoil
youtube.com/watch?v=cLdv1UfX1g8
► Normal Velocity Geometric Integral [I(ij)]
youtube.com/watch?v=76vPudNET6U
► Tangential Velocity Geometric Integral [J(ij)]
youtube.com/watch?v=JRHnOsueic8
===== 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
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 don't make this video longer than it needs to be.
===== RELEVANT VIDEOS =====
► Panel Methods Playlist
youtube.com/watch?v=bWjo3N9COz4&list=PLxT-itJ3HGuUDVMuWKBxyoY8Dm9O9qstP
► Panel Method Geometry
youtube.com/watch?v=kIqxbd937PI
► Building More Complex Flows
youtube.com/watch?v=EKzbwJvKcmw
► Flow Around an Airfoil
youtube.com/watch?v=cLdv1UfX1g8
► Normal Velocity Geometric Integral, Iij
youtube.com/watch?v=76vPudNET6U
===== 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
Don't worry, we're almost ready to code our panel method. The next video is about creating the system of equations and solving it.
===== RELEVANT VIDEOS =====
► Panel Methods Playlist
youtube.com/watch?v=bWjo3N9COz4&list=PLxT-itJ3HGuUDVMuWKBxyoY8Dm9O9qstP
► Panel Method Geometry
youtube.com/watch?v=kIqxbd937PI
► Building More Complex Flows
youtube.com/watch?v=EKzbwJvKcmw
► Flow Around an Airfoil
youtube.com/watch?v=cLdv1UfX1g8
===== 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
In this video, we dictate a boundary condition that forces the airfoil to be a streamline of the flow, allowing us to solve for the unknowns in the velocity potential equation (all the source panel strengths). We also dictate the other boundary condition that will allow us to calculate the velocity (and thus pressure coefficient) on the airfoil surface.
===== RELEVANT VIDEOS =====
► Panel Methods Playlist
youtube.com/watch?v=bWjo3N9COz4&list=PLxT-itJ3HGuUDVMuWKBxyoY8Dm9O9qstP
► Panel Method Geometry
youtube.com/watch?v=kIqxbd937PI
► Building More Complex Flows
youtube.com/watch?v=EKzbwJvKcmw
===== NOTES =====
- As shown in the text in my video at 12:32, the boundary point indices (k and k+1) are reversed. This has no implication on the derivation, but just note that the tangential vector always points from point k to point k+1.
===== 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
The final equation in this video shows the velocity potential induced at an arbitrary point P in the flowfield due to a uniform flow and N source panels. The next video will go through how we can use this equation to solve for the source panel strengths that will result in a physical flow around our airfoil.
===== RELEVANT VIDEOS =====
► Panel Methods Playlist
youtube.com/watch?v=bWjo3N9COz4&list=PLxT-itJ3HGuUDVMuWKBxyoY8Dm9O9qstP
► Source/Sink Flow
youtube.com/watch?v=eLDI_jV3yo0
► Uniform Flow
youtube.com/watch?v=jCTTDclJZEk
► Uniform + Source/Sink Flow
youtube.com/watch?v=zIvpN9f9dAA
===== NOTES =====
- Notes will be included here.
===== ERRORS =====
- Let me know if you see any errors and I will include them 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
UPDATED: Please use the second version (v2) of my ImageJ macro so you don't run into any issues. Here is my update YouTube video: youtube.com/watch?v=GXapOtBf52o
==== TIME-STAMPS ====
00:00 - Introduction
01:25 - Outline
02:32 - Programs you will need
03:08 - FFmpeg
05:28 - ImageJ/Fiji
13:42 - ImageJ macros
16:39 - Python code (images)
23:38 - MATLAB code (images and videos)
36:05 - DIY at home
==== NOTES ====
► This is a long video, I know. But I would rather upload a long, comprehensive video than skimp on the details. But if you're a regular to my channel, you probably know that already.
► My programs are not completely fool-proof. If you do something horribly wrong, you might get an error. But, if you use it the way I walk you through in the video, you shouldn't have any issues. If you do get an error, it might be best to just restart the program.
► I will probably be adding the video capability to the Python GUI at some point. Or better yet, you can fork the repository on GitHub and practice your Python coding by adding it in yourself.
► Not every video you download from YouTube will work when trying to convert it like I did with FFmpeg. Most of the ones I tried worked, but if yours doesn't, I'm not the best person to ask how to fix it. Google is helpful here.
► The NASA data obviously looks really nice. My processing of their data doesn't look as nice. There are many reasons for this, including (but not limited to) the high quality of their raw images, averaging multiple images together, using a more sophisticated code, and using a different analysis technique (optical flow).
==== RELEVANT VIDEOS ====
Schlieren YouTube Playlist
► youtube.com/watch?v=GEImPtOM-d4&list=PLxT-itJ3HGuWift1-NXVhSCzGd9uqDJv1
==== RELEVANT LINKS ====
My website with code and PDF document
► http://www.joshtheengineer.com/2019/10/20/how-to-take-pictures-like-nasa-using-background-oriented-schlieren-bos
My GitHub with code
► github.com/jte0419/Background_Oriented_Schlieren
==== REFERENCES ====
Python's "normxcorr2" function from GitHub user Sabrewarrior
→ github.com/Sabrewarrior/normxcorr2-python
NASA AirBOS Shock Wave Video
→ youtube.com/watch?v=443RLEnu_UI
Find all the rest of my references in my PDF document
In this video, I'll go through the panel method geometry in detail. We will use the simplest geometry, a circle approximated with 8 points (octagon), to define the variables. Then we will look at the Python code I wrote for both the circle and an airfoil. You can find the links to my Python and MATLAB programs in the CODE section below.
==== CODE =====
Panel Method Blog Post and Code (Python and MATLAB)
- Code can be downloaded at the bottom of the post
► http://www.joshtheengineer.com/2019/10/09/panel-method-geometry
GitHub: Panel Methods
► github.com/jte0419/Panel_Methods
==== RELATED VIDEOS/PLAYLISTS ====
Panel Methods YouTube Playlist
► youtube.com/playlist?list=PLxT-itJ3HGuUDVMuWKBxyoY8Dm9O9qstP
Panel Methods Overview Launch Page
► http://www.joshtheengineer.com/panel-methods
==== ERRORS ====
- If you find errors in the video, let me know and I'll add them 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
==== RELEVANT VIDEOS ====
Incompressible Potential Flow
- youtube.com/watch?v=Zo5XIcX8s2Q
Uniform Flow
- youtube.com/watch?v=jCTTDclJZEk
Source/Sink Flow
- youtube.com/watch?v=eLDI_jV3yo0
Uniform + Source/Sink Flow
- youtube.com/watch?v=zIvpN9f9dAA
Vortex Flow
- youtube.com/watch?v=61jvr3rtmLE
==== RELEVANT LINKS ====
Blog post about incompressible potential flow
► http://www.joshtheengineer.com/2019/05/05/introduction-to-incompressible-potential-flow
Blog and code for combined uniform and vortex flow
► http://www.joshtheengineer.com/2019/08/25/combined-flow-uniform-and-vortex-flow
GitHub: Panel Methods
► github.com/jte0419/Panel_Methods
===== 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
► Fundamental Mechanics of Fluids, Currie
amzn.to/2RpX2q4
► Elements of Gasdynamics, Liepmann and Roshko
amzn.to/2XrZjoo
==== ERRORS ====
- On the whiteboard from 6:16 to 6:58, the "V_theta" partial derivative should have a "del theta" in the denominator instead of a "del r". This is incorrect in the first and second expressions, but correct in the third expression (right before the boxed equation).
==== RELEVANT VIDEOS ====
Incompressible Potential Flow
- youtube.com/watch?v=Zo5XIcX8s2Q
Uniform Flow
- youtube.com/watch?v=jCTTDclJZEk
Source/Sink Flow
- youtube.com/watch?v=eLDI_jV3yo0
Uniform + Source/Sink Flow
- youtube.com/watch?v=zIvpN9f9dAA
Uniform + Vortex Flow
- youtube.com/watch?v=SoMuRp5v16w
==== RELEVANT LINKS ====
Blog post about incompressible potential flow
► http://www.joshtheengineer.com/2019/05/05/introduction-to-incompressible-potential-flow
Blog and code for combined uniform and vortex flow
► http://www.joshtheengineer.com/2019/08/25/elementary-flow-vortex-flow
GitHub: Panel Methods
► github.com/jte0419/Panel_Methods
===== 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
► Fundamental Mechanics of Fluids, Currie
amzn.to/2RpX2q4
► Elements of Gasdynamics, Liepmann and Roshko
amzn.to/2XrZjoo
==== RELEVANT VIDEOS ====
Incompressible Potential Flow
- youtube.com/watch?v=Zo5XIcX8s2Q
Uniform Flow
- youtube.com/watch?v=jCTTDclJZEk
Source/Sink Flow
- youtube.com/watch?v=eLDI_jV3yo0
Vortex Flow
- youtube.com/watch?v=61jvr3rtmLE
Uniform + Vortex Flow
- youtube.com/watch?v=SoMuRp5v16w
==== RELEVANT LINKS ====
Blog post about incompressible potential flow
► http://www.joshtheengineer.com/2019/05/05/introduction-to-incompressible-potential-flow
Blog and code for combined uniform and source/sink flow
► http://www.joshtheengineer.com/2019/08/25/combined-flow-uniform-and-source-flow
GitHub: Panel Methods
► github.com/jte0419/Panel_Methods
===== 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
► Fundamental Mechanics of Fluids, Currie
amzn.to/2RpX2q4
► Elements of Gasdynamics, Liepmann and Roshko
amzn.to/2XrZjoo
==== RELEVANT VIDEOS ====
Incompressible Potential Flow
- youtube.com/watch?v=Zo5XIcX8s2Q
Uniform Flow
- youtube.com/watch?v=jCTTDclJZEk
Uniform + Source/Sink Flow
- youtube.com/watch?v=zIvpN9f9dAA
Vortex Flow
- youtube.com/watch?v=61jvr3rtmLE
Uniform + Vortex Flow
- youtube.com/watch?v=SoMuRp5v16w
==== RELEVANT LINKS ====
Blog post about incompressible potential flow
► http://www.joshtheengineer.com/2019/05/05/introduction-to-incompressible-potential-flow
Blog and code for source/sink flow
► http://www.joshtheengineer.com/2019/08/25/elementary-flow-source-sink-flow
GitHub: Panel Methods
► github.com/jte0419/Panel_Methods
===== 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
► Fundamental Mechanics of Fluids, Currie
amzn.to/2RpX2q4
► Elements of Gasdynamics, Liepmann and Roshko
amzn.to/2XrZjoo
==== RELEVANT VIDEOS ====
Incompressible Potential Flow
- youtube.com/watch?v=Zo5XIcX8s2Q
Source/Sink Flow
- youtube.com/watch?v=eLDI_jV3yo0
Uniform + Source/Sink Flow
- youtube.com/watch?v=zIvpN9f9dAA
Vortex Flow
- youtube.com/watch?v=61jvr3rtmLE
Uniform + Vortex Flow
- youtube.com/watch?v=SoMuRp5v16w
==== RELEVANT LINKS ====
Blog post about incompressible potential flow
► http://www.joshtheengineer.com/2019/05/05/introduction-to-incompressible-potential-flow
Blog and code for uniform flow
► http://www.joshtheengineer.com/2019/08/25/elementary-flow-uniform-flow
GitHub: Panel Methods
► github.com/jte0419/Panel_Methods
===== 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
► Fundamental Mechanics of Fluids, Currie
amzn.to/2RpX2q4
► Elements of Gasdynamics, Liepmann and Roshko
amzn.to/2XrZjoo
Because Laplace's equation is linear, the sum of solutions to the equation is still a solution. The power of this result will become clearer when we start to build more complicated flows from what are called "elementary flows", which I will go through in the next video.
==== RELEVANT VIDEOS ====
Curl of the Gradient of a Scalar Field is Zero
- youtube.com/watch?v=A5WYHY8qhe8
Coming soon: elementary flow videos including
- Uniform Flow
- Source/Sink Flow
- Combined Uniform + Source/Sink Flow
- Vortex Flow
- Combined Uniform + Vortex Flow
==== RELEVANT LINKS ====
Blog post about incompressible potential flow
- http://www.joshtheengineer.com/2019/05/05/introduction-to-incompressible-potential-flow
GitHub: Panel Methods
► github.com/jte0419/Panel_Methods
==== REFERENCES ====
Fundamentals of Aerodynamics, Anderson
► Chapter 2.15+ (5th edition), Chapter 3.6+
Fundamental Mechanics of Fluids, Currie
► Pg. 63+ (2nd edition), works with complex variables
Foundations of Aerodynamics, Kuethe and Chow
►Chapter 2.11+ for incompressible, Chapter 7.3 for compressible (3rd edition)
Elements of Gasdynamics, Liepmann and Roshko
►Pg. 196+, works in index notation
Theory of Wing Sections, Abbott and Doenhoff
►Chapter 2 (pg. 31+)
The purpose of this code is to be able to compute the circulation, and thus the lift per unit span, of an airfoil in my future vortex panel method video/code. I will also be using it in my potential flow elementary solutions videos.
===== ERRORS =====
► The angle definitions in the MATLAB code shown in the video are incorrect. The Python version was always correct, but I was using an old version of the MATLAB code in the video by accident. The code available on my website has been updated as of 08/19/19, and both Python and MATLAB functions are correct now.
► The error is that you do in fact need a duplicate angle in order to finish the line integral around the ellipse. Without the duplicate angle, it leaves the integrated ellipse open. Including the duplicate angle ensures that the entire ellipse is integrated over (i.e. a closed curve).
===== RELEVANT LINKS =====
MATLAB and Python code from my website
► http://www.joshtheengineer.com/2019/04/01/compute-circulation-of-a-vector-field-in-matlab-and-python
GitHub: Panel Methods
► github.com/jte0419/Panel_Methods
===== NOTES =====
► I'm using the circulation defined in Anderson's "Fundamentals of Aerodynamics".
► You can use any other shape you want for the closed curve, but the ellipse is useful for my purposes.
===== RELEVANT LINKS =====
► MATLAB script and functions from this video
http://www.joshtheengineer.com/2019/03/30/load-airfoil-data-into-matlab
► Python code to download UIUC airfoil database
http://www.joshtheengineer.com/2019/01/30/uiuc-airfoil-database-file-download
GitHub: Panel Methods
► github.com/jte0419/Panel_Methods
===== RELEVANT VIDEOS =====
UIUC Airfoil Database Download Python Code
→ http://bit.ly/2I0zvIl
===== NOTES =====
► There are other ways to load these airfoil data files, this is just my take on it.
https://m-selig.ae.illinois.edu/ads/coord_database.html
I'll be using these airfoil files in my future Source Panel Method and Vortex Panel Method videos. I'm using Python because it's easy to scrape data from websites. Once you get all the files once, you won't need to do it again.
===== RELEVANT LINKS =====
► You can download the Python code from my website
http://www.joshtheengineer.com/2019/01/30/uiuc-airfoil-database-file-download
► Anaconda Navigator Download
anaconda.com/distribution
GitHub: Panel Methods
► github.com/jte0419/Panel_Methods
===== RELEVANT VIDEOS =====
How To: Run XFoil from MATLAB
→ youtube.com/watch?v=bWjo3N9COz4
Load Airfoil Coordinates from UIUC Files into MATLAB
→ Coming soon!
Panel Method Motivation and Introduction
→ Coming soon!
Panel Method Geometry Definitions
→ Coming soon!
Source Panel Derivation and Coding
→ Coming soon!
Vortex Panel Derivation and Coding
→ Coming soon!
===== NOTES =====
► This code used in this video downloads all the files from the main page of the database. In my next video on how to load these airfoil files in MATLAB, I show how it might be easier to download all the Selig file formats instead. The code for that can also be found at the link above for the Python code.
► I'm not an expert at Python. I'm still learning. The code might not be the most efficient way to do something, but it works, and that's all I care about for now.
► Thanks to Dr. Selig for giving me permission to scrape the database for every airfoil data file.
1) Run XFoil and output the files we need (airfoil coordinates and pressure coefficient)
2) Load saved files from XFoil into MATLAB and view plots
3) Run XFoil from the MATLAB script itself, and view plots
===== RELEVANT LINKS =====
► You can download the MATLAB script from my website
http://www.joshtheengineer.com/2019/01/30/running-xfoil-from-matlab
► Do you want to run XFoil from Python instead? Download the script from my website
http://www.joshtheengineer.com/2019/02/06/running-xfoil-from-python
► Download XFoil
https://web.mit.edu/drela/Public/web/xfoil/
GitHub: Panel Methods
► github.com/jte0419/Panel_Methods
===== RELEVANT VIDEOS =====
UIUC Airfoil Database Download Python Code
→ youtube.com/watch?v=nILo18DlqAo
Load Airfoil Coordinates from UIUC Files into MATLAB
→ youtube.com/watch?v=xJYxMfGFrk8
Panel Method Motivation and Introduction
→ Coming soon!
Panel Method Geometry Definitions
→ Coming soon!
Source Panel Derivation and Coding
→ Coming soon!
Vortex Panel Derivation and Coding
→ Coming soon!
===== NOTES =====
► This is not a comprehensive XFoil user guide video. I'm only running the commands I need for my future Vortex Panel Method video.
► If you just want the NACA 4-digit airfoil coordinates, you can also use my NACA 4-Digit Airfoil MATLAB code to generate them.
===== NOTES =====
► The sizes of NPT fittings don't correspond to actual dimensions, so you'll note the 1/8 NPT doesn't have a diameter of 1/8". Keep that in mind when purchasing parts.
► The clamp I used can also be purchased at Harbor Freight for a couple bucks.
► As mentioned in the video, you can try printing the threads into your part, but I did it this way instead. The higher the threads-per-inch, the harder it will be to print the threads into your part.
===== RELEVANT VIDEOS =====
→ Monoprice MP Select Mini Intro/Review
http://bit.ly/MPSelectMini
→ How To: Level Your Printing Bed
http://bit.ly/LevelTheBed
===== RELEVANT LINKS =====
►McMaster-Carr
mcmaster.com/#
► Harbor-Freight Tap and Die Set
harborfreight.com/hand-tools/tap-die/40-pc-carbon-steel-sae-tap-and-die-set-62831.html
► Carbide Depot: Tap Chart/Pipe Threads
http://www.carbidedepot.com/formulas-tap-pipe.htm
► Carbide Depot: Drill Size Chart
http://www.carbidedepot.com/formulas-drillsize.htm
===== NOTES =====
► I'm using the MARKER_FAR boundary condition to set the throat, or inlet, values. You can also use the MARKER_SUPERSONIC_INLET boundary condition and get the same results.
► I'm not quite sure why the throat values are slightly off even though the solutions converged. Part of me thinks it has to do with the Mach number being set to 1 (or close to 1, since I've tried it with it slightly above 1 as well with the same results). The way that problems are solved when they are subsonic vs. supersonic changes, and since it's straddling that line, it might be difficult. Without looking at the numerics and spending too much time on this, it's hard for me to say. If you figure it out or have any comments/suggestions, let me know.
===== RELEVANT LINKS =====
► CFG and SU2 files used in this video
http://www.joshtheengineer.com/2018/04/16/cfd-with-su2-normal-shock-in-cd-nozzle
► NSN MATLAB code
http://www.joshtheengineer.com/2018/01/24/normal-shock-in-converging-diverging-nozzle
===== RELEVANT VIDEOS =====
→ Converging-Diverging Nozzle Explained
http://bit.ly/CDNozzleExplained
→ Pressure Ratio Delineations
http://bit.ly/PressureDelineations
→ Calculating Normal Shock in Nozzle
http://bit.ly/CalculatingNSN
→ Isentropic Supersonic CFD Simulation
http://bit.ly/IsentropicSupersonic
→ GMSH: Rocket Nozzle Mesh
http://bit.ly/GMSHRocketNozzle
→ How To: Install SU2
http://bit.ly/InstallSU2
→ CFD Example in SU2
http://bit.ly/SU2Example
===== FREE SOFTWARE =====
► SU2 Download
su2code.github.io/download.html
► GMSH Download
http://gmsh.info
► Paraview Download
paraview.org/download
===== NOTES =====
→ You can also skip the masking step and just vector validate afterwards, and that works pretty well too.
→ If you do want to mask, make sure to mask both the A and B images, and you probably won't need to do any vector validation afterwards if you're careful. I went through it again doing this, and I got some nice results.
→ I tried to see if there was a way to get rid of the mask when outputting the video, but I wasn't able to find a way to do this. If you figure it out, let me know. If that's not a feature, I might try to go into the code and put that option in myself.
- Thanks again to Jenna and Wayne for their help, which took time away from our coveted Wednesday Ninja Warrior night.
===== PIVLAB =====
→ MATLAB File Exchange
mathworks.com/matlabcentral/fileexchange/27659-pivlab-particle-image-velocimetry--piv--tool
→ PIVLab Website
http://pivlab.blogspot.com
→ William's YouTube video
youtube.com/watch?v=Sp3Ounq07Qc&t=26s
→ Citations
Thielicke, W. and Stamhuis, E.J. (2014): PIVlab – Towards User-friendly, Affordable and Accurate Digital Particle Image Velocimetry in MATLAB. Journal of Open Research Software 2(1):e30, DOI: http://dx.doi.org/10.5334/jors.bl
Thielicke, W. and Stamhuis, E. J. (2014): PIVlab - Time-Resolved Digital Particle Image Velocimetry Tool for MATLAB (version: X.XX modify this). http://dx.doi.org/10.6084/m9.figshare.1092508
Thielicke, W. (2014): The Flapping Flight of Birds - Analysis and Application. Phd thesis, Rijksuniversiteit Groningen. http://irs.ub.rug.nl/ppn/382783069
===== ATTRIBUTION =====
► Force India image
Artes Max, Flickr
flickr.com/photos/105731165@N07
flickr.com/photos/105731165@N07/25768805927
License: creativecommons.org/licenses/by-sa/2.0
► Red Bull Racing promotional video
Aston Martin Red Bull Racing
youtube.com/watch?v=0tEHQJn_hxo
Time: ~3:16 to 3:18
Links to all the necessary videos and files can be found in the sections below.
===== FILES TO DOWNLOAD =====
► Mesh File and Configuration File
http://www.joshtheengineer.com/2018/04/01/cfd-with-su2-isentropic-supersonic-nozzle-flow
===== RELEVANT VIDEOS =====
► Download and Install SU2
goo.gl/MxeL3X
► How to Run SU2
goo.gl/z5NDsh
► Nozzle Mesh in GMSH
http://bit.ly/RocketGMSHSU2
I will be using this exact mesh in some rocket nozzle simulations in my future videos, so stay tuned for those!
If you don't have MATLAB, you can simply download the mesh (.su2 file) from the link below.
===== NOTES =====
The boundary condition marker names for this mesh are the following:
- Inlet
- Nozzle
- Outlet
- Symmetry
===== RELEVANT VIDEOS =====
→ How To: Install SU2
goo.gl/U8xYM2
→ How To: Run SU2 Code Start to Finish
goo.gl/z5NDsh
→ More GMSH Tutorials
goo.gl/BL8Fzn
→ Isentropic Supersonic Nozzle Simulation
Posting soon!
===== RELEVANT LINKS =====
► My GitHub Repository
github.com/jte0419/Rocket_Nozzle_Design
► GEO and SU2 Files for Rocket Nozzle
http://www.joshtheengineer.com/2018/04/01/cfd-with-su2-isentropic-supersonic-nozzle-flow
===== TOO LONG DIDN'T WATCH =====
► What they do:
The document divides the exit velocity of the gases coming out of the nozzle by the ambient speed of sound at sea level.
► Why it's misleading:
When you compare a velocity to a speed of sound, it is generally taken as a Mach number, which relates the local velocity to the local speed of sound. The local speed of sound in this case would be the speed of sound at the exit plane of the nozzle, which is much higher than the speed of sound at sea level standard.
► Why it's not incorrect:
They don't actually say anything about a Mach number in the document. They also don't mention what speed of sound they're talking about. It's vague enough to be correct.
► Why did I make a video about this?
I'm not quite sure.
===== NOTES =====
→ I actually emailed Aerojet Rocketdyne asking where this number came from when I first read this document. To their credit, they emailed back very quickly and asked for more information about my question, but by that time I had already figured out where it came from. I ended up forgetting to email them back, but it was nice that they responded so quickly.
===== RELEVANT LINKS =====
► RS-25 Incredible Facts Document
http://www.rocket.com/files/aerojet/documents/Capabilities/PDFs/RS-25_incred_facts_update_3-25-16_cropped.pdf
► VT Calculator
http://www.dept.aoe.vt.edu/~devenpor/aoe3114/calc.html
► CEA Online
cearun.grc.nasa.gov
===== THUMBNAIL CREDIT =====
NASA Image Gallery
images-assets.nasa.gov/image/9400164/9400164~orig.jpg
NASA ID: 9400164
"Space Shuttle Project"
===== NOTES =====
► You can mess around with the settings in the configuration file to see how it changes the solution. For example, you can get more well-defined shock by changing the way the convective fluxes are evaluated.
===== FILES TO DOWNLOAD =====
► Mesh File (.su2) and Configuration File (.cfg)
http://www.joshtheengineer.com/2018/02/28/how-to-run-su2-start-to-finish
===== RELEVANT VIDEOS =====
→ Download and Install SU2
goo.gl/KmkUgD
→ Oblique Shock Example
goo.gl/8yjUvy
===== RELEVANT LINKS =====
► SU2 Oblique Shock Test Case
su2code.github.io/tutorials/Inviscid_Wedge
===== PROGRAMS I USE (ALL FREE) =====
► SU2
su2code.github.io
► GMSH
http://gmsh.info
► Paraview
paraview.org
► VirtualBox
virtualbox.org/wiki/Downloads
► Notepad++
notepad-plus-plus.org
===== REFERENCES =====
→ The SU2 GitHub and website
→ Matt MacLean for introducing me to SU2 along with his GMSH tutorial
===== NOTES =====
► There are multiple ways to do what I do in the video. This video just shows you one of the methods.
► The newest version of SU2 is now at 6.0 (Falcon).
► I use version 4 for the video tutorials I'm making since I ran these simulations before version 5 or 6 were out. If you want to follow along with the exact same configuration files, download version 4. Configuration files might need to be slightly changed if you want to run in 5 or 6, since some options have been added or removed.
► I don't think you actually need to add the "SU2_CFD" line in the .bashrc file, as I do in this video.
► Apparently I like the word "currently".
===== LINKS =====
→ SU2 Main GitHub Site
su2code.github.io
→ SU2 Releases Page
github.com/su2code/SU2/releases
→ Other SU2 Stuff
github.com/su2code
→ VirtualBox
virtualbox.org/wiki/Downloads
→ Paraview
paraview.org/download
→ GMSH
http://gmsh.info
===== ALIASES =====
► Add the following to your alias file, which is called .bash_aliases in my case
n. = nautilus.
lsl = ls -l
lsla = ls -la
maxwindow = resize -s 1000 1000
===== KEYBOARD SHORTCUTS =====
Alt + Tab → Switch between windows
Win + S → Open workspace view
Arrow + Enter → Switch to other workspace
===== LINUX TERMINAL COMMANDS =====
cd = Change directory
ls = List files
ls -l = List files in an ordered list
ls -a = List files including hidden files
nano = Text editing program without leaving terminal (can also use gedit, nedit, etc.)
1) Derived equations
2) Compressible flow tables (NACA 1135)
3) VT calculator
4) MATLAB functions
===== RELEVANT VIDEOS =====
→ Oblique Shock Derivation
goo.gl/xLYYYP
→ Normal Shock Relations Derivation
goo.gl/Unvjey
→ Normal Shock Example
goo.gl/RBJtgV
===== RELEVANT LINKS =====
► VT Calculator
http://www.dept.aoe.vt.edu/~devenpor/aoe3114/calc.html
► MATLAB Functions
github.com/jte0419/Compressible_Flow_Relations
===== THUMBNAIL CREDIT =====
By Settles1 (Own work) [CC BY-SA 4.0 (creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons
===== RELEVANT VIDEOS =====
→ Oblique Shock Example
goo.gl/77hjcb
→ Normal Shock Relations Derivation
goo.gl/Unvjey
→ Normal Shock Example
goo.gl/RBJtgV
===== RELEVANT LINKS =====
► Surface (Double) Integrals Explanation
http://www.joshtheengineer.com/2017/01/02/surface-double-integrals
► VT Calculator
http://www.dept.aoe.vt.edu/~devenpor/aoe3114/calc.html
► MATLAB Functions
github.com/jte0419/Compressible_Flow_Relations
===== THUMBNAIL CREDIT =====
By Settles1 (Own work) [CC BY-SA 4.0 (creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons
After watching Destin's recent SmarterEveryDay video titled "The Incredible Sounds of the Falcon Heavy Launch", I thought it would be a fun little example problem to calculate how far away the photographer was from the rocket using the sound from the video. We can also check this value using Google maps, since we know where he was standing and where the rocket was launched from.
===== NOTES =====
→ At 3:12 in my video, I say 12,000 to 13,000 kilometers, when obviously I mean meters (so 12 to 13 kilometers)
===== TIMING FROM VIDEO =====
Here's what I think the timing is from the video:
► Launch start = 3:22
► First sound = 3:37
As mentioned at the end of my video, here are the times that I was using for my calculation for the boosters on the way down to land. Let me know if you think they are actually something different!
► See first ignition = 6:13
► Done landing = 6:31
► Sonic booms = 6:47 or 6:48
The difference between seeing the first ignition and the sonic booms would be the time used in the calculation.
===== RELEVANT VIDEOS =====
→ SmarterEveryDay Video
goo.gl/Ra9mdB
→ Photographer Trevor Mahlmann
http://photos.tmahlmann.com
→ Speed of Sound Equation Derivation
goo.gl/txELT2
===== THUMBNAIL CREDIT =====
By SpaceX (Falcon Heavy Demo Mission) [CC0 or CC0], via Wikimedia Commons
For the code used at the end of the video, check out the link below in the RELEVANT LINKS section.
===== RELEVANT VIDEOS =====
→ Converging-Diverging Nozzle
goo.gl/nC5hzb
→ CD Nozzle Pressure Delineations
goo.gl/rQEA6S
→ Normal Shock Relations
goo.gl/8BaJDH
→ Normal Shock Example
goo.gl/HJfH3B
===== RELEVANT LINKS =====
► Solving the Area-Mach Number Relation
http://www.joshtheengineer.com/2016/11/16/solving-the-area-mach-number-relation
► CD Nozzle Pressure Delineations
http://www.joshtheengineer.com/2017/12/17/converging-diverging-nozzle-pressure-delineations
► MATLAB Code
http://www.joshtheengineer.com/2018/01/24/normal-shock-in-converging-diverging-nozzle
===== REFERENCES =====
→ Modern Compressible Flow, John D. Anderson (goo.gl/tBPr9n)
→ Elements of Gasdynamics, Lipemann and Roshko (goo.gl/7mUFEi)
→ Gas Dynamics, Zucrow and Hoffman (goo.gl/cVAa2G)
1) Equations derived in my Normal Shock Relations video
2) Compressible flow tables (only valid when gamma = 1.4)
3) Online VT Calculator
4) MATLAB functions based on VT Calculator
===== NOTES =====
► At around 5:54, I point to 1.4 in the Mach number column when I'm talking about the fact that the tables only work for gamma equal to 1.4. That's just where my finger happened to land on the page, and has nothing to do with what I'm talking about at the moment.
► I happened to pick a Mach number that had an entry in the table (method 2). If your Mach number isn't listed in the table, you'll have to interpolate between the two bounding Mach numbers. Check out my linear interpolation video in the links below. I also have a video on programming a linear interpolation solver on your graphing calculator, also in the links below.
===== RELEVANT LINKS =====
→ Normal Shock Relations
goo.gl/8BaJDH
→ Online VT Calculator
http://www.dept.aoe.vt.edu/~devenpor/aoe3114/calc.html
→ MATLAB Functions
github.com/jte0419/Compressible_Flow_Relations
→ Linear Interpolation Explained
goo.gl/WACknt
→ TI-83 Linear Interpolation Program
goo.gl/i6PoeN
===== ATTRIBUTION =====
For VT Calculator:
Javascript by William J. Devenport, Department of Aerospace and Ocean Engineering, Virginia Tech.
Last update 5th January 2014. Please send comments, questions, or suggestions to: William Devenport
http://www.dept.aoe.vt.edu/~devenpor/aoe3114/calc.html
I'm aware that there are other functions already out there that can do these calculations, but I didn't see a MATLAB function on the VT Calculator site. It's nice to have MATLAB functions so you can code up some more interesting problems, and you won't need to worry about always hard-coding normal shock relations, etc.
The format of these functions should be pretty easy to understand. If not, don't hesitate to ask. If you find any errors, let me know and I'll fix them.
===== RELEVANT LINKS =====
→ GitHub
github.com/jte0419/Compressible_Flow_Relations
→ My Website
Post coming soon.
===== ATTRIBUTION =====
From the bottom of the website:
Javascript by William J. Devenport, Department of Aerospace and Ocean Engineering, Virginia Tech.
Last update 5th January 2014. Please send comments, questions, or suggestions to: William Devenport
Fanno Flow and Rayleigh Flow calculators by Adam Ford, included 7th February 2008.
Conical flow calculator by Stephen Krauss, included 5th January 2014.
1) Choked Isentropic Subsonic
2) Normal Shock at Nozzle Exit
3) Choked Isentropic Supersonic
In this video, we will compute the pressure ratios needed to obtain the three states listed above for a given nozzle area ratio (Ae/At).
===== NOTES =====
→ In this video, we can say that At = A* for each case because the flow is choked, and we do have sonic flow at the throat.
→ We generally know the exit-to-reservoir pressure ratio that our engine is operating at. For instance, if we are analyzing the Space Shuttle Main Engine (RS-25) on the launchpad, then we know the exit pressure is approximately 101.325 kPa. We also know from the engine's specifications that the reservoir (or chamber) pressure is approximately 20.64 MPa. Dividing the two appropriately gives the pressure ratio we are looking for.
===== RELEVANT LINKS=====
→ Blog Post - Converging-Diverging Nozzle Pressure Delineations
http://www.joshtheengineer.com/2017/12/17/converging-diverging-nozzle-pressure-delineations
→ Solving the Area-Mach Number Relation
http://www.joshtheengineer.com/2016/11/16/solving-the-area-mach-number-relation
→ CD Nozzle MATLAB Code - GitHub
github.com/jte0419/Converging_Diverging_Nozzle
→ Compressible Flow Relations Code - GitHub
github.com/jte0419/Compressible_Flow_Relations
===== RELEVANT VIDEOS =====
→ Explained: Converging Diverging Nozzle
goo.gl/7MBSck
→ Area-Mach Number Relation [CPG]
goo.gl/t8QE9T
→ Normal Shock Relations
goo.gl/Bvv2jj
→ Stagnation Relations
goo.gl/yrT9D4
===== REFERENCES =====
► Modern Compressible Flow, Anderson
► Gas Dynamics, Volume 1, Zucrow and Hoffman
► Elements of Gasdynamics, Liepmann and Roshko