Aerodynamic wheel-wing interaction

In 2007 Martinus van den Berg published a PhD thesis on the interaction between a rotating wheel and an inverted wing. The research was sponsored by the Honda F1 team, which has, of course, evolved into the Mercedes F1 team; the same team responsible for the 2012 front-wing F-duct.

The most interesting conclusion of van den Berg's research was that the front-wheel drag is greater at high front-wing ride-heights than it is at low ride-heights.

Figure 1: High ride-height, high wheel drag

Previous research conducted by James McManus (who was snapped up by McLaren before completing his PhD) had identified that the flow field of an isolated rotating wheel contains an arch vortex in the upper region of the near wake (E and F in Figure 1), and a pair of counter-rotating vortices in the lower, ground-level region of the near wake (H and I). There is also a bow wave (D) created by the upstream side of the contact patch. 

When an inverted wing equipped with an endplate is placed in front of such a rotating wheel, van den Berg identified three further primary flow features: a vortex from the upper edge of the endplate (A); a vortex from the junction between the trailing edge of the flap and the endplate (B); and a vortex from the lower edge of the endplate (C).

With a 50% scale 580mm front wing-span (relevant to pre-2009 F1 regulations), van den Berg identified that the top edge front-wing vortex passes over the crown of the wheel at high ride-heights (Figure 1), but passes inside the wheel at low ride-heights (Figure 2). At high ride-heights this vortex over the crown keeps the flow attached for longer, increasing the lift of the wheel, and creating a zone of re-circulation (G) behind the wheel, which increases the wheel drag:

"When this vortex...passes over the wheel it starts a strong interaction with the wheel vortex originating from the top of the wheel (feature “F”), the vortex originating from the flap trailing edge (TE) junction (feature “B”) and the lower edge vortex (feature “C”), accumulating in a strong circulation," (Journal of Fluids Engineering, October 2009, Vol. 131).

Figure 2 shows the flow field at a lower front-wing ride-height, where the top-edge vortex goes inside the wheel. In addition, it can be seen that both the bow wave to the inboard side of the wheel, and the inside leg of the counter-rotating vortex pair in the wheel wake, have been replaced by the vortex generated by the bottom-edge of the front-wing, which is strengthened in ground-effect.



Figure 2: Low ride-height, low wheel drag

At first sight, this might seem to be inconsistent with the concept of the 2012 F-duct, which stalls the front-wing, and permits the front ride-height to increase, with the intention of reducing drag (and balancing front-rear downforce when the DRS is operated). One presumes, however, that the reason for this discrepancy is that the research was conducted with a narrow, pre-2009 front-wing, the endplates of which were on the inboard side of the wheel. Post-2009, with 1800mm wide front-wings, the endplates and the vortices they generate, lie upstream of the outer shoulder of the wheel. It may be that the top-edge vortex now goes outside the front-wheel at all front-wing ride-heights, and certainly the outward curvature of the front-wing endplates would achieve this.

One note of caution should be sounded here: the Figures reproduced above are obtained from steady-state simulations, whereas the actual flow in the wheel-wake tends to flap about in an unsteady manner, as close observation of the water droplets shed by the wheel in wet-weather conditions reveals. Flow features which appear to exist in a steady simulation are sometimes completely absent in the instantaneous flow fields of an unsteady simulation.