## General Aerodynamic Design Methodology:

From the start it was desired to implement Computational Fluid Dynamics in the design process of the rim shapes. CFD breaks a fluid (in our case air) into small computational blocks that we can setup around various shapes and configurations. We decided to stage the design process of the various rim depths. This would make it possible to iterate between CFD and wind tunnel results. While CFD has advanced tremendously over the past years, the amount of non-linear flow systems involved in a bicycle wheels will not be fully modeled by CFD for some time. This means that the wind tunnel is a crucial stopping point in not only design of the wheel, but in verification and refinement of the CFD modeling, this means that as we went through different wheelsets, we arrived at each desired wheelset configuration with less computational time required .

Early on several research papers were taken as a point of reference for completing CFD analysis of Wheels. The knowledge leveraged from these papers helped set up some basic parameters for the model.

Initially for the 44mm depth rim a 2D model was used for rapid runs and design iterations to setup a design space of possible shapes. The 2D model has smaller mesh and computational requirements meaning we can run through a large number of rim designs relatively quickly.

Many companies follow this 2D methodology. Bontrager, for instance, has a great white paper on their design methodology. However in order to extrapolate the 2D results to 3D they use an empirically determined factor. I decided not to try to artificially fit the 2D results into 3D numbers for reasons I’ll explain shortly.

With this CFD setup we aimed for a relatively wide rim, 28 mm, that was wide, while just as if not more Aerodynamic as leading industry competitors (Zipp, Enve, Bontrager, etc).

After the first trip to the wind tunnel with 44mm prototypes (which will be detailed later), it was decided that the results obtained with the 2D models were not getting enough separation in results between the top performing rim shapes in order to determine which rim shapes were actually more aerodynamic. However in the wind tunnel we were seeing significant variation between rims especially at higher angles of attack. This means that the 2D model was significantly missing something that could likely be attributed to the overly simplified 2D model. There are several factors this can be attributed to: spokes, hub, rotational effects, ground interactions, and other 3D effects.

In order to increase the fidelity of our runs and capture the differences between the rims, the domain was expanded to encompass the entire wheel/tire system. The mesh used increased in size to ~3.5M elements. The total number of elements was kept from increasing too much (and impeding run time) by using some very basic local mesh refinement around the rim where the flow is most complex.

Rotational effects were also captured in the 3D modeling. Commonly rotating components are modeled with over-set mesh domains. This essentially overlays a rotating set of mesh elements that encompasses the rotating component and iterates between the stationary mesh and rotating/translating mesh. This technique is the most accurate and would allow for the modeling of spoke elements. However due to the complex nature of the mesh, this technique would be too computationally exhaustive for our limited computing resources. Instead we decided to ignore spokes since their effect would be largely secondary to any changes made to the actual wheel shape. Since spokes were ignored the wheel surface could remain stationary, but with a rotational surface velocity assigned to each individual mesh surface. This technique is a variation of the no-slip condition. Instead of the wheel surface having a zero velocity assigned to it (no-slip), each element was assigned a rotational velocity based on its location relative to a central point of rotation.

This accomplishes modeling a rotating wheel, without the high computational costs associated with an over-set mesh.

The final aspect that was added into the model for 3D analysis was a floor or road interface with the wheel. Since the entire domain was a wind-tunnel setup, the floor boundary condition was set to a slip boundary condition. This meant that the velocity along the floor of the domain was the same as the free-stream velocity. The reasoning for this is to mimic real world situations. When a wheel is riding outdoors, the wheel itself sees non-zero airspeed, but the airspeed relative to the ground is zero (except in windy conditions). If this slip condition was NOT applied to the floor the flow in the domain would be zero and near-zero near the floor of the model. This would result in the rotating wheel essentially pushing against the stationary air at the floor, artificially reducing total drag on the wheel.

These small changes to the model setup not only gave a larger spread of wheel drag results, but it also gave drag profiles that actually matched real world conditions:That’s enough for a single post, next post I’ll dive into some further nitty-gritty of how the CFD model was setup

Would you have a link to the Bontrager white paper or the other ones?. .. Just another curious engr interested in CFD wanted something to read over.