Wind and Sea
Wing Shape Optimization
(click on images below to see a larger image)
Milano, Matthew Ringuette
We use Machine Learning techniques to assess from a fluid dynamics
perspective the trajectory and the shape of a flapping appendage.
We formulated a novel vortex formation parameter to help interpreting
the results of trajectory optimization for a pitching and heaving
flat plate. Our findings show that to maximize the average lift
produced, flapping appendages must generate vortices of maximal
circulation during a flap.
Shown above: three still images from an animation. DPIV
measurements taken at 50% span of the vorticity generated by
a pitching and heaving flat plate maximizing the average lift
produced: the plate turns right before the leading edge vortex
pinches off. (Click on each still to see larger graphic.)
To show that similar constraints hold for the appendage
shapes also, we consider Drosophila Melanogaster as a case study,
extending further the vortex formation parameter to account for
general shapes and flapping trajectories.
left: left graph: elliptic wing following
the trajectory of a fruit fly wing; right graph: corresponding
generalized formation parameter. Click
here or on image to view animation.
evolutionary algorithm evolves families of wing shapes that optimize
vortex formation, for a given flapping trajectory. When the flapping
trajectory is fixed to that of Drosophila melanogaster (fruit
fly), our evolutionary algorithm evolves a family of wing shapes
that correlate very closely to natural fruit fly wings.
(Picture, above right, of an actual Drosophila wing.)
shown at left: blue: digitized shape of a real fruit
fly wing; red and black: two ellipting wings belonging to
the family evolved by our evolutionary algorithm to produce
the same maximal formation parameter as the real fruit fly
larger image of graphic.