Wheel Design How-To Part 3

Detailed CFD procedures

Going to go over some details in setting up our computer model for running simulations.

As requested in a previous comment here is the Bontrager white paper that provided some resource in our initial research phase of development.

Mesh Definition

The initial 3D mesh was fraught with convergence and generation issues:InitialQuadMesh

Instead we decided to use a Polyhedral mesh type for simulation. The main concerns were limited computational resources and ease/automation with which we could mesh the components. Polyhedral meshes have a few advantages over more traditional Hex and Tet mesh procedures. Mainly in a comparison of element count and time to convergence is much improved with a poly mesh. This is a result of poly meshes having a higher number of interfaces with other elements per element, thus making the mesh more efficient and robust in resolving to a solution. 

This allowed us to create a script to run several flow cases in sequence for different angles, each of which required a new mesh to be created.

Turbulence Modeling

Given limited time frame and computational resources the run was done as a steady state simulation. It was found by Defraeye that a RANS k-w model provided the most accurate results for a cyclist in a wind tunnel without using a more computationally expensive turbulence model.

Wheel Boundary Layer Mesh

Wheel Boundary Layer Mesh

Overall Wheel Mesh

Overall Wheel Mesh

Boundary Layer Thickness

A boundary layer height of 5 mm was used for wheel

Boundary Layer Thickness estimation

Boundary Layer Thickness estimation

 

Where x is set as depth of rim to obtain a rough general estimation of propagation length (without having to spend excessive time creating BL mesh areas). This 5mm thickness was applied as a 10 element thick BL mesh (expansion ratio set to 1.2).

Speed Selection

CFD domain run speeds were set at 30 mph (13.4 m/s). This was chosen to provide some spread between wheelsets. Reynolds numbers for bicycle wheels range from 11,000-650,000 (20mm rim @ 20mph and Full Disc at 30mph). This is sufficiently high to place wheel aerodynamics in the fully developed turbulent region of air flow (i.e. Re>4000). This means that flow structures remain relatively constant throughout interested flow speeds and Drag will scale directly with a square relation to velocity. It was found at low speeds drag differences between manufacturers only vary slightly, meaning experimental or computational error would make it difficult to determine which wheel design is in fact better. A higher wind speed amplifies This further lent itself to our design theory of creating a wheel based on multiple factors instead of just Aero Performance.

Wheel rotation

Many existing CFD studies neglect rotational effects of the wheel. It is computationally easier to solve for a stationary solution. While we don’t have a lot of computational power on hand, we still achieve rotational modeling by eliminating our spokes. This allows us to set the wheel boundary surfaces with a rotation condition. Eliminating spokes is a safe assumption since their requirement is largely dependent on structural and governing body concerns. Additionally eliminating them will not greatly affect the drag results of a particular rim design. 

Disc Wheel Streamlines

Disc Wheel Streamlines

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