JoshTheEngineer | Normal Shock Example Problem @JoshTheEngineer | Uploaded January 2018 | Updated October 2024, 1 hour ago.
Let's work through a normal shock problem together! In this video, we will be using four different ways of solving a simple normal shock problem. The four different methods we will be using can be found below (along with links which can be found in the RELEVANT LINKS section)
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
Let's work through a normal shock problem together! In this video, we will be using four different ways of solving a simple normal shock problem. The four different methods we will be using can be found below (along with links which can be found in the RELEVANT LINKS section)
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
![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")
![Explained: TdS Equation [Taylor-Maccoll]](https://i.ytimg.com/vi/N126SaEGuJA/hqdefault.jpg "Explained: TdS Equation [Taylor-Maccoll]
The TdS equation is a combined statement of the first and second law of thermodynamics. It relates the entropy, enthalpy, and pressure changes in a system (for the form that we need for Croccos theorem). To keep the big picture in mind, recall that I mentioned that Croccos theorem is a combination of the thermodynamics and kinematics of a flow. This equation gives us the thermodynamics part.")
