In our ‘Update 4’ (http://archive.swissside.com/596), we explained our CFD optimisation approach using the latest methods from Formula 1. This has been possible thanks to the insider knowledge brought to the team by Swiss Side co-founder Jean-Paul Ballard, with over 13 years of experience working in Formula 1 in the field of Aerodynamics.
Now the results are in! …
GEOMETRY AND MESH:
Each of the Hadron wheel geometries to be tested are output from our parametric CAD model and meshed using snappyHexMesh (part of OpenFOAM). The CFD mesh is prepared using the best possible resolution for the requirements, which in this particular case consists of approximately 11 million cells. Powerful computer clusters are required for computing the results which is only possible with the help of our very experienced CFD partners.
Limits are applied to the range of each of the pre-determined shape change parameters for study. From here, we use a complex mathematical process which defines groups of specific parameter variations to calculate. These particular shapes are then computed in CFD and the results analysed.
Using a mathematical interrogation process of the results together, we are able to determine how each parameter influences the trade-offs between the various performance measures. In our case, we are most interested in the Drag and Steering Moment effects. Recapping from ‘Hadron Update 4’, our performance function looks as follows:
As the cross wind (yaw) conditions occur with varying frequencies, it is important that this is correctly considered in the weighting system. This clearly varies from course to course depending on the predominant wind conditions which occur. The following graphic shows a typical cross wind frequency distribution.
The side force and steering moment response is also tied directly to the cross wind frequency, as these play a increasing role with increasing yaw angle, when the reaction forces exceed a minimum level which then begin to affect the rider.
Via the combination of CFD calculations and mathematical prediction, with numerous loops and refinements, using this process we are then able to map the frontier of the possible performance achievable within the shape parameter range.
The graph of the final results below shows the yaw (cross-wind) weighted values of drag and steering moment. A perfect design (low drag and low steering moment) would sit in the bottom left corner. The boundary of the plotted results (grey points) represents the limits of performance possible within the range of rim shape parameters.
There is a clear trade-off between drag and steering moment. The final design choice depends on the relative weighting given to these two measures as defined by the Performance Weighting System.
The final choice, (around which further detailed refinements were made), was ‘Option 34’. As can be seen, compared to ‘Option 29’ a 1% increase in drag offered a 20% decrease in steering moment. This offered the best weighted performance as per our performance function.
TYRE PROFILE SENSITIVITY:
As a part of the optimisation, a final tyre sensitivity study was made. As in Formula 1, the tyres are dominant features of the aerodynamic system and can hugely influence the flow. This is equally the case with a bike wheel.
The various extremes of tyre shapes were scanned. There were calculated in CFD together with our wheel profiles to ensure that the developed shapes behaved acceptably.
It is however important to note at this point that the flow separation (stall) point on the tyre, which occurs at higher cross-wind angles, is very difficult to predict accurately in CFD. Other real life parameters such as surface roughness and tyre mounting variation on the rim can equally play a large role. So our sensitivity study here was a rough guide for us in preparation for our more detailed tyre evaluation in the windtunnel.
FINAL RESULTS & VISUALISATION:
Our final result gave excellent performance with extremely low predicted drag for a minimal level of steering moment. Again it is important to highlight that the performance weighting method used for the Hadron optimisation, was designed to produce a wheel which gives the best all round real world aerodynamic efficiency and consequently the best overall real world performance. It might not necessarily result in the lowest drag number at a single high yaw point eg. 20 degrees, but will offer the lowest overall combined drag during a riding session.
The following, are a series of visualisations which are also used as part of the design and optimisation process, to better understand the flow fields generated by the wheel and the associated results.
Pressure contour slices vertically through the wheel at 6 degrees cross-wind angle
Flow field through wheel centre with varying cross-wind angle