## Saturday, May 14, 2011

Ferrari reportedly used riblets on the undersurface of its front-wing at the Turkish Grand Prix last week. These are finely-spaced, V-shaped grooves, typically separated by something of the order of 10-100 microns, which are used on aircraft and yachts to reduce skin friction drag. They have also naturally evolved on sharks, where they are referred to as denticles. Riblets work by reducing the amount of friction created by a turbulent boundary layer.

Now, recall that the boundary layer is a very thin layer, adjacent to a solid surface, in which the airflow is subjected to shear stresses, and Bernoulli's theorem no longer applies. In a laminar boundary layer, the velocity decreases from the freestream velocity, down to zero at the surface of the solid object, yet the pressure remains fairly constant. (In a direction normal to the surface of the solid object, the pressure inside a laminar boundary layer is basically equal to the pressure at that point on the outside of the boundary layer).

The presence of a boundary layer is necessary for a wing to induce lift or downforce. However, the pressure increases towards the trailing edge of a wing, and at some point this causes the airflow velocity at the surface of the wing to become negative, pointing in a direction opposite to the freestream velocity outside the boundary layer. This is the point at which the boundary layer separates, creating wake vortices as it does so.

To generate the maximum amount of lift (or downforce), it is necessary to push the point of separation as far back on the wing as possible. Slightly perversely, one of the mechanisms which facilitates this is the creation of a turbulent boundary layer. This arises when the freestream velocity rises above a certain critical speed, with the consequence that the boundary layer divides into three sublayers: a laminar layer at the bottom, a turbulent zone at the top, and a buffer zone in-between. The turbulent boundary layer is subject to a fluctuating flow, in which coherent structures are constantly created and then dissipated. At the point where the boundary layer transitions from laminar to turbulent flow, pairs of counter-rotating longitudinal vortices are constantly created. These vortices survive for a brief period of time before bursting, whence they release their kinetic energy. A lot of this vortex burst energy sweeps down to the surface of the solid object, causing a peak in the shear stress, and thereby contributing to the average skin friction drag.

The effect of the turbulent boundary layer can be represented as an extra type of viscosity. Particles from a turbulent boundary layer will be more likely than those from a laminar boundary layer, to wander upwards into the faster freestream flow, where they will get deflected, and returned to the boundary layer with extra velocity. A turbulent boundary layer will therefore get dragged further along before it separates. Turbulent viscosity therefore increases lift or downforce.

Famously, golf-balls are manufactured with dimples, with the purpose of inducing a turbulent boundary layer at a freestream velocity where one would not otherwise occur. However, in the case of golf-balls, the primary advantage of delaying the separation of the boundary layer is that the wake turbulence, and hence the drag, is reduced.

Riblets are slightly different, in the sense that they reduce the skin friction drag by influencing the vortex burst process within the turbulent boundary layer. The precise mechanism by which this occurs is not completely understood, but there seem to be two hypotheses: either (i) the riblets raise the height of the vortex bursts within the boundary layer, thereby reducing the downwash onto the solid surface; or (ii) the riblets reduce the duration and/or intensity of the vortex bursts.

However, if Ferrari were using riblets purely for the purpose of reducing skin friction drag, it is difficult to understand why they would only use them on the undersurface of the front-wings. Gary Anderson remarks in Autosport that "this coating works by creating small vortices on the surface that will reduce the airflow-separation problems and make the wing work more consistently." This makes them sound a lot more like the dimples on a golf ball, delaying the separation of the boundary layer rather than merely reducing skin friction drag...