This month the MIT team reports extending its fluid separation theory to three dimensions, as shown by this simulation of a fluid separating (green lines) from the surface of a spinning sphere it is flowing past. Image courtesy / Amit Surana, Gustaaf Jacobs and George Haller, MIT
MIT scientists and colleagues have reported new mathematical and experimental work for predicting where that aerodynamic separation will occur. This can lead to more efficient cars and better planes and boats.
In 1904, Ludwig Prandtl derived the exact mathematical conditions for flow separation to occur. But his work had two major restrictions: first, it applied only to steady flows, such as those around a car moving at a constant low speed. Second, it only applied to idealized two-dimensional flows.
Since 1904 there have been intense efforts to extend Prandtl’s results to real-life problems, i.e., to unsteady three-dimensional flows.
A century later, Haller led a group that did just that. In 2004 Haller published his first paper in the Journal of Fluid Mechanics explaining the mathematics behind unsteady separation in two dimensions. This month, his team reports completing the theory by extending it to three dimensions. Haller’s coauthors are Amit Surana, now at United Technologies; MIT student Oliver Grunberg; and Gustaaf Jacobs, now on the faculty at San Diego State University.
The researchers said it’s too soon to quantify the level of improvement in performance of cars and planes that might stem from the work, noting that more work must be done before it can be applied to commercial technologies