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## Joukowski Airfoil Performance

The Joukowski transformation is a great way to study basic airfoils using potential flow. It gives a nice way to derive the Kutta condition, as well as the classic lift slope . But in all those demonstrations, I never saw the lift and drag curves of the Joukowski airfoil! Luckily, I have XFOIL to remedy […]

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## The Sleekest Airfoil

What does a minimum force airfoil look like? I basically want to make a fairing that minimizes the total force over the range of 0-5 degrees. This mostly means reducing the lift generated at non-zero angles of attack, while keeping the drag manageable. Minimizing lift on an airfoil feels oddly perverse. I suppose that’s why […]

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## Improving the NACA 0015 Airfoil

The four-digit NACA airfoil is perfectly decent, which is a bit surprising considering it was first published way back in 1933. Since it was designed before computers, I’m sure that it could be improved. The general form of the thickness equation is: This does not provide the proper thickness, but ensures a rounded leading edge […]

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## Airfoils with Circular Leading Edges

Airfoils are generally thickest somewhere around the middle. The classic NACA four-digit airfoils are thickest at 30% of the chord, and laminar flow airfoils are thicker around the 50% mark. Let’s throw out the received wisdom and make some airfoils that are thickest close to the front. Rather than working with a lifting body, let’s […]

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## Conformal Mapping: Point Vortex Near a Corner

I wanted to know what a point vortex would do near a corner with an arbitrary angle. Time to dust off the complex analysis! A really useful summary of using complex analysis to model potential flow is here. I will use the method of images to ensure that there is no flow through the wall, […]

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I want to have the ink on a photo clump together, leading to a black and white image. This is a sort of flow, so my first thought is to take a look at the advection-diffusion equation. Let’s say that the ink distribution across an image is , the diffusion factor is , and the […]

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## Line Integral Convolution

Line integral convolution, or LIC, is a nice way to get a sense of the directions of a flow field. By averaging a noisy image along sections of streamlines, you get some nice streaks. Look at this example, applied to the flow around a spinning cylinder: There are a couple main parameters to tweak: the […]

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## Evenly Spaced Streamlines

There’s a whole body of literature out there for illustrating vector fields. One topic is ‘evenly spaced streamlines’: lines that follow a direction field, and don’t get too close to each other. How do we do this? From a starting point, use the midpoint method to figure out the position of the next point. If […]

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## Ph.D. Research: Problem Solving

A PhD is an exercise in learning to define and solve problems. This post will describe some of those problems and how I addressed them. I would have liked to see this sort of post back then, and hopefully this will give some idea of the process. This is, of course, very focused on experimental […]

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## Proper Orthogonal Decomposition

Time for some competing acronyms. Fluids people like to call this technique Proper Orthogonal Decomposition (POD), statisticians call it Principal Component Analysis (PCA), and so on and so on. Whatever you want to call it, it’s basically an eigenvector decomposition of the data you toss into it. That means that it optimally splits the data […]