Pressure distribution around an airfoil in a granular medium
This variant of the simulation • Lift and drag vs angle of attack for ... of an airfoil in a granular medium shows some additional information, namely the ratio of lift to drag, and the pressure distribution on the airfoil.
The particles in this simulation interact via a Lennard-Jones potential, and are subject to a viscous damping term, gravity directed to the right, and to a one-sided harmonic repulsion from the airfoil. There are periodic boundary conditions. The total force the particles exert on the airfoil is computed, and displayed in two ways: the figures include the two components of the total force and their ratio, and the arrow shows the total force as a vector, with drag Fx as horizontal component and lift Fy as vertical component. The force is somewhat averaged over time, to smooth out fluctuations due to the medium being composed of discrete particles. In addition, the boundary of the airfoil is colored in a way depending on the pressure it experiences, slightly averaged over time.
This simulation has two parts, showing the evolution with two different color schemes:
Averaged kinetic energy: 0:00
Initial position: 1:45
In the first part, the color of the particles depends on their kinetic energy, averaged over a time interval. Red particles move faster than blue ones. In the second part, the particles' color depends on their initial x-coordinate.
To save on computation time, particles are placed into a "hash grid", each cell of which contains between 3 and 10 particles. Then only the influence of other particles in the same or neighboring cells is taken into account for each particle.
The Lennard-Jones potential is strongly repulsive at short distance, and mildly attracting at long distance. It is widely used as a simple yet realistic model for the motion of electrically neutral molecules. The force results from the repulsion between electrons due to Pauli's exclusion principle, while the attractive part is a more subtle effect appearing in a multipole expansion. For more details, see https://en.wikipedia.org/wiki/Lennard...
Render time: 19 minutes 48 seconds
Color scheme: Part 1 - Turbo, by Anton Mikhailov
https://gist.github.com/mikhailov-wor...
Part 2 - HSL/Jet
Music: "Ether" by Silent Partner
Current version of the C code used to make these animations:
https://github.com/nilsberglund-orlea...
https://www.idpoisson.fr/berglund/sof...
Some outreach articles on mathematics:
https://images.math.cnrs.fr/_Berglund...
(in French, some with a Spanish translation)
#granular_material #airfoil #lift
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