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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.

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.

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.

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.

mass conservation underpins newtonian physics, and fortunately quantum mechanics is not a factor in aerodynamics today

Quick solutions to vexing problems.

A relevant consideration in lenticular blade design, and an approximation on airfoils in general.

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.

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

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.

A simple approximation of an airfoil

In this lecture we cover the Conservation Equations of aerodynamics. This is primarily a physical overview of the equations, and a helpful review for those that saw these equations in Fluid Mechanics. For those in my fluids class, this will be your first experience with the Conservation of Energy equation. As always, I take a physical perspective and try to explain each term in detail, while avoiding the time-consuming derivations (which you can find online in various places or in Anderson’s book). We detail the conservation of mass, momentum, and energy and then consider how we practically use them.

In this lecture, we discuss methods for visualizing a flow field and develop tools to better diagnose flows. Pathlines, streaklines, and streamlines are all different ways to visualize a flow, yet in a steady flow they're all the same. We mathematically define streamlines in detail, then build a new "stream function" that defines the set of streamlines based upon the velocity field.

Course Notes; https://bpb-us-w2.wpmucdn.com/sites.udel.edu/dist/5/9458/files/2019/08/Lecture-6_Streamlines-and-stream-function.pdf

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Course Notes: https://bpb-us-w2.wpmucdn.com/sites.udel.edu/dist/5/9458/files/2019/08/Lecture-7_Rotational-and-irrotational-flow.pdf

In this lecture, we go over the Bernoulli and Laplace equations, two well-known relations in Aerodynamics that work for Inviscid and Incompressible flows. We will derive the Bernoulli equation (both cursory and detailed) and then we will show how the Velocity Potential and the Stream Function satisfy the Laplace equation.

Tylers Course Notes: https://bpb-us-w2.wpmucdn.com/sites.udel.edu/dist/5/9458/files/2019/08/Lecture-10_Kutta-Joukowski-theorem.pdf

In this lecture, we take a physical approach to realistic airfoils and wings. Let's take a break from mathematics for some refreshing application. Now you will know what all the tabs, panels, and devices are on the airfoils you see when riding on a plane!

Course Notes: https://bpb-us-w2.wpmucdn.com/sites.udel.edu/dist/5/9458/files/2019/08/Lecture-13_Airfoils-and-wings.pdf

The origin of lift is complex and often questioned. Some misguided explanations include the equal transit time or air "pushing" the foil. While they are attractive, simplified explanations they do not capture the entire truth. Here, we try our best to explain the source of Lift, the "why", from fundamental principles. We will see that Lift is a balance of conservation of mass, momentum, and energy. We see flow acceleration and low pressure near the nose, the Coanda effect over the top surface curvature, and the Kutta-condition at the trailing edge.

Course Notes: https://bpb-us-w2.wpmucdn.com/sites.udel.edu/dist/5/9458/files/2019/08/Lecture-13a_What-causes-lift.pdf

In this lecture, we cover the root causes of airfoil drag. To this point, our analysis has been inviscid and ignored the main drag-causing mechanism. Specifically, we look at Viscous Drag and Pressure Drag (a.k.a. form drag). The first is due to viscous forcing, and we use flow over a flat plate to estimate the skin friction. The second is due to flow separation, and we note its characteristics and how to identify it.

In this lecture, we consider the reality that our wings are not idealized 2D foils with infinite span, and there are finite wing end effects to consider. Specifically, the pressure difference near the wing tip induces a roll-up of velocity and creates the tip vortex. This tip vortex induces a downwash velocity on the foil along the span, and locally changes the effective angle of attack and adds drag (called induced drag). We use the Biot-Savart Law to develop tools to explore the influence of theoretical semi-infinite vortices (which is what a tip vortex is) and also explore the rule of vortex filaments with the Helmholtz Vortex Theorems. Looking forward, we will use these tools to analyze the impact of the tip vortex on the wing to be able to predict downwash and change in performance.

In this lecture, we derive Prandt's famous Lifting Line Theory. Essentially, this theory models a finite-wing + wing tip vortices as a horseshoe vortex, where the wing is replaced by a vortex and the strength distribution along the vortex represents the wing's lift distribution. We go over the example for an elliptic distribution of vortex strength and why that distribution is particularly important to aerodynamics.

In this lecture, we pivot from incompressible flows and start fresh with compressible flows. Flows become compressible when you either go really fast, or really high up (low density = low speed of sound). Most of the equations we've learned past the conservation laws required incompressible flow, so they are no longer useful in this part of the course. We go over the physical aspects of compressible flow and why the Mach number is so important. Then, we review our conservation equations and refresh some thermodynamics tools that we will use moving forward.

In this lecture, we discuss the basics of shock waves and then focus on the normal shock wave, an idealized 1D case. When you go faster than the speed of sound, pressure disturbances induce shock waves. These are barriers that cause the flow to dramatically change condition, reducing the flow velocity but increasing the pressure, temperature, and density. The temperature and pressure downstream of a shock can get super-high, and that dominates the design and flight profile of high-speed aircraft.

In this video we continue our exploration of shocks by moving on to Oblique Shocks and Expansion Fans. Oblique shocks occur when the flow angles inwards which creates a shock angled to the flow. They are essentially the same as Normal Shocks, though we only worry about the normal component of velocity passing through the shock. Expansion fans are different, they have thickness to them and the changes to the flow are gradual. They occur when the flow opens, but in this case velocity increases and not decreases, as with normal/oblique shocks. We also discuss the forces on the body to the shock.

Strange things happen in this area

https://bpb-us-w2.wpmucdn.com/sites.udel.edu/dist/5/9458/files/2019/08/Lecture-10_turbulence.pdf

Occasionally, odd things happen on the fringes...

Occasionally, odd things happen on the fringes...

Lecture-1_How-we-study-aerodynamics (pdf)

DownloadLecture-2_Common-aerodynamic-variables (pdf)

DownloadLecture-3_Aerodynamic-body-forces-and-moments (pdf)

DownloadLecture-4_Nondimensional-numbers-and-Similarity (pdf)

DownloadLecture-5_conservation-laws (pdf)

DownloadLecture-6_Streamlines-and-stream-function (pdf)

DownloadLecture-7_Rotational-and-irrotational-flow (pdf)

DownloadLecture-8_Bernoulli-and-Laplace (pdf)

DownloadLecture-9_Elementary-flows (pdf)

DownloadLecture-10_Kutta-Joukowski-theorem-2 (pdf)

DownloadLecture-11_Panel-methods (pdf)

DownloadLecture-12_Thin-airfoil-theory (pdf)

DownloadLecture-13_Airfoils-and-wings (pdf)

DownloadLecture-13a_What-causes-lift-2 (pdf)

DownloadLecture-14_Drag-and-separation (pdf)

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