A simple investigation into the effects on Lift/Drag efficiency of a formula-car style two element rear wing when endplate details commonly seen in Formula 1 are applied.
A wing efficiency increase of 12.7% from 2.25 L/D baseline to 2.53 L/D.
Potential for an estimated 5% increase in efficiency through further investigation.
Figure 1 – Original wing design with plane through wing centre and streamlines demonstrating flow regimes
A model of a two element rear wing, typical of that seen on many open wheel and prototype race cars was created. From this, several schemes were created focusing on the wing endplate design. The schemes incorporated design cues from current and previous Formula 1 cars with the intention of examining the downforce and drag figures, the downforce to drag ratio (efficiency) of the resultant designs and also visually examine the flow regime changes caused by the changes in wing endplate designs.
The scheme models were imported into meshing software where mesh density was carefully applied to areas of the model where the most complex flow was expected to occur. The mesh density was at its greatest close to the surfaces of the wing and endplates and reduced in density with increasing distance from the surfaces. Greater mesh density was maintained rearwards of the wing and endplate to capture wing-initiated vortex behaviour and other types of drag-inducing flows.
The model meshes were simulated at a nominal wind speed of 44.7 m/s (100mph). A no-slip condition was applied on all walls other than the wing itself to ensure the wing and its endplates were the only elements influencing airflow. All meshes were subject to identical simulation variables. Prior to commencing the simulations, the wing and endplate surfaces were selected for force measurement. Force measurements are taken in three axes for every iteration of the analysis via integrating the pressure distribution across the wing surfaces. These can be live monitored to gain an appreciation of the steadiness and reliability of the results.
A two element wing with endplate. The most forward point of the cutaway featured on the upper edge of the endplate is coincident with the trailing edge of the second wing element.
Figure 2- Standard rear wing
Wing with a 50mm cutaway
The cutaway is extended 50mm along the z-axis.
Figure 3 - 50mm cutaway
Wing with Gills
Three horizontal gills are added forwards of the second element. These allow high pressure air from above the wing to flow out through the gills and mix with the relatively lower pressure air flowing past the endplates.
Figure 4 - Gills added above high pressure surface
Figure 5 - Close-up of gill detail
Wing with Slats
A large cutaway is added to the lower edge of the endplate and four highly-cambered airfoil profiles are added.
Figure 6 - Endplate slats
Figure 7 - Endplate slats, reverse view
Wing with Gills and Slats
In this scheme, both the gills and slats are incorporated. When analysing combinations of schemes, there is an amount of uncertainty as to whether the flow regimes set up by individual elements may complement each other, cancel each other out, or fall somewhere on the spectrum between those two extremes.
Figure 8 - Gills and slats
Wings with Slats, Gills and 50mm cutaway
In this scheme, all the individual components making up the previous schemes are combined.
Figure 9 - Gills, slats and extended cutaway
In addition to the net gains it is pertinent to observe the differences in air flow around the wing created by the changes in wing geometry. This allows us to develop an understanding of why these changes in lift and drag have occurred and can influence the direction of future development.
In the images below, the pressure profile above and below the wing can be seen. There is a good distribution of high pressure above the wing and low below the wing. This is true even to the trailing edge of the second element, showing a stable, attached flow. This provides a good base upon which to test wing endplate treatments and their effects.
The particle streamline demonstrations in these images show the general behaviour of air flowing either side of the endplates at two different heights. A wingtip vortex can be seen developing at the cutaway where the higher pressure freestream air meets with the lower pressure air flowing off the trailing edge of the second element.
In figure 11 the streamlines flowing off the trailing edge of the outer surface of the wing endplate can be seen to turn upwards sharply as it comes into contact with the lower pressure, faster moving air that has flowed under the suction surface of the wing. The suction surface flow has changed direction significantly and the combination of the differences between the two flow leads to a vorticity, visible but weaker and separate to the wingtip vortex which is much more intense.
Figure 10 – Base wing. Streamlines around endplate
Figure 11 - Base wing. Streamlines showing wingtip and endplate vortex
50mm Cutaway Scheme
The most interesting change in the flow behaviour has been highlighted in the images below, lowering the cutaway allows more air flowing by the outside of the endplate to be drawn into the low pressure area directly behind the second element. This has the effect of intensifying the wingtip vortex. This vortex has its origin at the outer, trailing edges of the wing and has a very low pressure core. It is possible that the drag reduction seen through analysing this scheme is caused by the more favourable layout for both high and low pressure air fed into this vortex.
he cutaway creates an intense shear boundary which sets up an intense vortex. The high pressure flow above the wing feeds into the top of this vortex this can be seen in image . This has the effect of increasing the pressure in this area, reducing the downforce (as seen in the overall force-based results) but the net lift-drag balance is improved.
This scheme reduced the efficiency of the wing. Pictured below are some streamline plots showing the wingtip vortex to be weaker yet larger in diameter. It is possible that the gills have diminished the suction on the trailing edge of the wing caused by the previous small, intense vortex there. This in particular is a scheme that should be analysed at multiple velocities. It’s a possibility that this scheme is more efficient at higher speeds.
Figure 15 - Gills. General flow by wing shows wingtip vortex to be weaker
By observing the streamline plots below we can see that the introduction of the slats add some turbulence to the flow curling over the lower edge of the endplate. This turbulence results in the many small vortices formed rolling up into the upward-turned low pressure air under the wing. This in turn wraps into the wingtip vortex and appears to be an efficient flow regime.
Figure 16 - Slats. Streamlines show vortices from slats rapidly join with wingtip vortex
Figure 17 – Regular wing.. Streamlines show lower endplate flow takes considerable distance to join vortex flow
Figure 18. Slats. Comparatively the flow past the slats shows the streamlines fed into the wingtip vortex much sooner.
Figure 19 - Base Wing. Looking streamwise down the flow, some rotational flow is observed
Figure 20 - Slats. The rotational flow is much more organised and feeds directly into the wingtip vortex
Slats and Gills Scheme
In these next two streamline analyses, the particles are injected into the flow at exactly the same point to highlight the difference in the flow regimes created by the 50mm cutaway when all other geometry is maintained. The most obvious difference is the behaviour of the wingtip vortex. The same streamlines are seen to rotate at a much higher angular velocity when the cutaway is employed. This more intense, faster rotating vortex contains a lower pressure core and draws flow from its surroundings into it more quickly. This organisation of flow could be responsible for the reduction in drag seen in the results.
Figure 21 - Slats and Gills. Streamlines showing general flow characteristics
Slats, Gills and Cutaway Scheme
Figure 22 - Slats, Gills and Cutaway. Streamlines showing general flow characteristics
Following these observations the next logical step would be to analyse the combination of schemes which provided the greatest gains in terms of wing efficiency. This would be the 50mm cutaway and the vertical slats.
Also of interest would be the efficiency of these schemes at various air velocities. A weakness of this investigation is that the results presented are essentially a snapshot of the flow behaviour at a single airspeed. To gain a full appreciation of the most appropriate endplate treatments, all schemes should be analysed at higher and lower velocities to ensure consistency across the range of airspeeds that the wing would be likely to encounter in operation. It is possible that certain schemes could become dramatically more or less efficient at higher velocities.
Finally, for completeness the wing would be analysed as part of the vehicle it is intended to be used on. Airflow disruptions upstream of the wing are likely to affect the performance of the wing and should be something the end user should be aware of before selecting a particular wing design for their use.