Saturday, February 18, 2012

Front-wing side-edge vortices

Aerodynamically speaking, a Formula 1 car is an interconnected system of vortices and vortex layers. The vorticity is created by viscous shear in thin boundary layers adjacent to the solid surfaces of the car; such boundary layers are attached vortex layers. The downforce (or lift) generated by a wing is often attributed to the presence of circulation in the airflow around the wing, but the circulation itself is nothing more than the net vorticity in the boundary layers above and below the wing.

When a vortex layer separates from a solid surface, it becomes a free vortex layer, and a separated vortex layer can roll-up into a volume of concentrated vorticity, called a vortex. These vortices possess a low pressure core, in some sort of balance with the centrifugal 'force' of the fluid elements spiralling around the vortex on helical trajectories. Oriented in a streamwise direction, such vortices can be particularly useful, both for the direct generation of downforce, and to act as air curtains, sealing off other low pressure areas.

Now, the front-wing of a car sees the air first, and therefore sets the conditions for the rest of the car, hence the vortices it generates are particularly important. Streamwise vortices are generated by lateral pressure gradients within the front-wing assembly, and these exist (i) across the endplate, (ii) at the transition between the wing-section and the neutral inner-section dictated by regulation, (iii) at the inner tips of the front-wing flaps, and (iv) at the arched sections in the front-wing.

To keep a vortex alive, one has to maintain the correct ratio between axial (streamwise) velocity, and the azimuthal velocity. If the azimuthal velocity gets too high, or the axial velocity gets too low, the vortex can breakdown.

For obvious reasons of commercial confidentiality, Formula 1 does a poor job at publishing its aerodynamic discoveries. Fortunately, however, there has been some academic research on the vortices generated by the front-wing endplates, conducted by Professor Zhang and colleagues at the University of Southampton. On the basis of wind-tunnel flow visualisation and measurement methods, such as Laser-Doppler Anemometry, Zhang et al (2006) claim that in the case of a simple front-wing, (without a rotating wheel in close proximity), the side-edge vortices possess "a low streamwise speed core...This feature is important as the vortex could break down or dissipate quickly further downstream," (p38, Ground effect aerodynamics of race cars, Applied Mechanics Reviews, Vol 59.).
Which brings us to Adrian Newey's Williams FW14/B of 1991/1992, which featured, at a time when the regulations permitted it, long extensions to the front-wing endplates. One might hypothesise that these extensions strengthened and stabilised the front-wing endplate vortices. One method of postponing vortex burst is to connect a vortex to a low-pressure area downstream, and these extensions may have been intended to join the front-wing vortices to the low pressure areas which exist behind the front-wheels. Certainly, on the current generation of Red Bulls, a similar trick is employed at the rear, the side-edge vortices on the diffuser being connected up to the low pressure regions behind the rear wheels.

One also presumes that those extensions were directing the front-wing vortices at a particular region downstream, perhaps the lower edges of the sidepods, both to seal off the low pressure region under the floor, and possibly also to feed the flow which is sucked under the floor in front of the rear wheels, thereby feeding the diffuser side-edge vortices, making one powerful, car-length vortex. One wonders how much such thinking still informs the design philosophy at Red Bull...

Techjury said...

Long time reader but as a physicist can you explain this:

"These vortices possess a low pressure core, in some sort of balance with the centrifugal 'force' of the fluid elements spiralling around the vortex on helical trajectories."

Centrifugal or centripetal in this case?

Gordon McCabe said...

I'd say it's centripetal in reality, hence the inverted commas around 'force'.

However, an advanced text on the subject, Vorticity and Vortex Dynamics, Wu, Ma and Zhou, Springer (2006), states that for a quasicylindrical vortex core, "the centrifugal force is entirely balanced by the radial pressure gradient," but in doing so cites the equation:

v^2/r = (1/rho) (partial p/partial r)

The term on the left is the centripetal acceleration. Although, of course, if you switched to a reference frame rotating with the vortex, then you would indeed introduce a centrifugal 'force' to balance the centripetal.