How Magic happens
0. Tutorials
These tutorials are provided by Associate Professor Tyler Van Buren, of the faculty at Princeton University, and a graduate and postgrad of Rensselaer Polytech, an institute with a notable. body of work in aerodynamic and fluid mechanics research.
Tyler provides clear explanations on what is often a complex subject matter. The following are links to his YouTube channel where additional information may be found.
1. Fluid Mechanics, Basics
The recipe starts with basic thermodynamics, which are pretty much inviolate. We then make fluid, air water, etc move by design, the general concept of which is taught to teenagers, the physically correct is a little bit more involved.
2. Common flow variables
3. Aerodynamic body forces and moments
Tyler discusses the common variables we encounter and how they're related to producing force on an object. It may seem very basic, but it's important we are all on the same level when it comes to the fluid properties we work with. We will dive deeply into the physical meaning of each variable, some of which require considerations at the molecular level.
3. Aerodynamic body forces and moments
3. Aerodynamic body forces and moments
3. Aerodynamic body forces and moments
This module covers forces and moments on an aerodynamic body. There are two primary ways for a fluid to force a surface: Pressure, which acts normal to a surface; and Shear, which acts tangential. We will discuss common pressure/shear distributions over bodies and calculate the resulting body forces/moments due to their distributions. Last, we cover the Center of Pressure, the central point at which the forces act on the body.
2. Conservation of Mass
3. Aerodynamic body forces and moments
2. Conservation of Mass
mass conservation underpins newtonian physics, and fortunately quantum mechanics is not a factor in aerodynamics today
4. Common Assumptions
3. Aerodynamic body forces and moments
2. Conservation of Mass
Quick solutions to vexing problems.
Thin Airfoil Theory
10 Kutta Joukowski Theorem
10 Kutta Joukowski Theorem
A relevant consideration in lenticular blade design, and an approximation on airfoils in general.
10 Kutta Joukowski Theorem
10 Kutta Joukowski Theorem
10 Kutta Joukowski Theorem
In this lecture, Tyler formally introduce the Kutta-Joukowski theorem. This is a powerful equation in aerodynamics that can provide the lift on a body from the flow circulation, density, and velocity. By taking a deep-dive into the rotating cylinder elementary flow, we derive the Kutta-Joukowski theorem through example.
11. Panel methods
10 Kutta Joukowski Theorem
4. Nondimensional numbers and Similarity
how we apply the elemental flow concepts to realistic aerodynamic shapes. It requires discretization of our body surface, and applying elemental flows to individual segments on the surface. Specifically, we look at the Source Panel Method and the Vortex Panel Method. By enforcing the "no penetration" boundary condition (normal velocity at the surface is zero), we can find the strength distributions of the sources or vortices to recreate the aerodynamic shape with streamlines.
https://bpb-us-w2.wpmucdn.com/sites.udel.edu/dist/5/9458/files/2019/08/Lecture-11_Panel-methods.pdf
4. Nondimensional numbers and Similarity
4. Nondimensional numbers and Similarity
4. Nondimensional numbers and Similarity
In this lecture, Tyler introduces non-dimensional numbers and similarity. Non-dimensionlization in aerodynamics and fluid mechanics is a way of thinking relatively, and we continuously compare forces, lengths, etc. to other relevant problem parameters. These non-dimensional numbers continue into Similarity, which is a way of scaling problems and ensuring things stay consistent.
Lifting Line Theory
4. Nondimensional numbers and Similarity
Lifting Line Theory
A simple approximation of an airfoil