If someone asked you to mathematically describe the flow of air in this picture, you would probably just blink a lot and smile winningly - or run as fast as possible in the other direction. Even aerodynamicists are intimidated by the challenge of understanding what happens in the boundary layers around airfoils, cars, and golf balls. That's why George Haller and Thomas Peacock of MIT are feeling good this week: They've developed, and tested experimentally, a new mathematical theory that can predict exactly where the separation of flow occurs in unsteady, three-dimensional, real-life conditions.You can try all you want to hose dust off of a car, but it's not going to work. The reason for that is that the velocity of a fluid — like air or water — at a surface — like a car or a wing — is zero. At the exact point where fluid flow touches a solid, it's technically not moving. As you observe the flow as it moves away from the surface, however, the velocity steadily increases, until it matches the surrounding freestream velocity. What this means is that moving cars, planes, or golf balls all have boundary layers, areas around their surfaces where the velocity of the fluid flow has not quite reached that of the freestream. In the graphic below, the green arrows represent increasing velocity, and the blue-purple-red area is the boundary layer.
Where things begin to get wild is when the flow in the boundary layer separates and becomes turbulent. Think of the wing of a plane: Necessarily, the air pressure on the top of the wing must be lower than the pressure on the bottom of the wing, because that's what keeps the plane flying. At the same time, then, the air pressure at the top of the wing must increase until it reaches the trailing edge and the higher pressure of the freestream. The airflow reacts to this increase in pressure; if the pressure reaches a high enough level, the flow will actually turn back on itself before it leaves the wing. Suddenly, you've got eddies, vortices, and a frightening cornucopia of turbulent behavior, just like you see around the airfoil at the top of this page. Naturally, predicting when this flow separation occurs is a very large concern for fluid dynamicists everywhere. Until recently, the bulk of our understanding came from a 1904 breakthrough by Ludwig Prandtl, who derived mathematical relations to describe the phenomenon. Unfortunately — though unsurprisingly — his work was applicable only to steady (or time-invariant), two-dimensional flows. Though Prandtl certainly provided invaluable insight with his equations, the fact is that real-life flows are unsteady and three-dimensional. Fluid dynamicists longed for mathematics that could reliably predict flow separation in those conditions. And now, they have it. Two research groups, led by MIT professors and with members hailing from San Diego State and the Université Libre in Brussels, have published both mathematical and experimental investigations of their kinematic theory of unsteady separation. What's remarkable about the kinematic theory of unsteady separation is that it does not rely on point quantities, properties of the flow at a specific time and place. Instead, this kinematic theory uses time averages of the fluid flow properties to find separation points. Under many different flow conditions in their experiments, these research teams were able to confirm their mathematical derivations. The kinematic theory of unsteady separation has been around for several months now, but this experimental validation seals the deal. This is a fantastic discovery, and not least because it is a triumph for the laws of physics to predict complicated conditions in real life. Haller and Peacock's research will have important applications for vehicle fuel efficiency — and that's just the most urgent example. Flow separation may look bizarre, but it is a mystery no longer. Images from Wikipedia. MIT solves 100-year-old engineering problem [MIT News Office] Experimental and numerical investigation of the kinematic theory of unsteady separation [Journal of Fluid Mechanics] Unsteady flow separation on slip boundaries [Physics of Fluids]