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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Wheel Design How-To Part 2

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).

Comparison of Wind Tunnel (left) to 2D CFD (right)

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.

Vertical velocity on wheel surface

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:90mm Rim CFD resultsThat’s enough for a single post, next post I’ll dive into some further nitty-gritty of how the CFD model was setup

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Wheel Design How-To Part 1

I think it’d be interesting to write a little bit about what all went into a wheel design for Boyd cycling this past year. The rims which are currently in production I’m super proud of because as a Pro-level racer they’re a set of wheels that I’d choose over almost any other wheels, most of this design work took place in 2014. This will probably be broken up into several manageable parts, enjoy.

Design Goals

Arguably the most important part of any design is setting out the initial design requirements. This sets the ‘ship of design’ on course and becomes very difficult to change once you have sunk costs in a given design philosophy. Working with Boyd (who has extensive feedback of what cyclist want out of their wheels) we set out a number of goals to strive for: 

  • Aerodynamics
  • Wide Rim/Tire Compatibility
  • Clincher rim brake track heat dissipation
  • Tubeless compatibility

We weighted these components in a design matrix to help evaluate different rim shapes.

The primary improvement we hoped to achieve was to design an Aerodynamic wheelset. A secondary but closely related goal was to design a wheelset to accommodate a wider tire. Traditionally road cyclists use narrow road tires measuring 21mm or 23mm, however the current trend is towards wider tires 25mm and larger. The larger tire has numerous advantages over a narrow tire: better grip, improved rolling resistance and is less prone to puncture. The two main disadvantages are weight and aerodynamics. The goal of an Aerodynamic wheelset and a wide tire are closely coupled, especially for the increasingly prevalent clincher wheelset. This means that some of the negative aerodynamic effects of a wide tire can be negated with proper design of the rim.

Composite clinchers have, in the past, had a dubious reputation. The thermal conductivity of Carbon Fiber is two orders of magnitude less than Aluminum. Low thermal conductivity coupled with the low melting point of the resin used in the some Carbon Fibers meant that under heavy braking the large heat built up through friction was not dissipated as it is with Aluminum (where heat build-up is not a concern). A two fold effect then takes place: the heat in the rim is transferred to the air in the tire, increasing the tire’s pressure and load on the rim hooks, and the material around the brake track softens allowing the rim to open up. Since braking is always heavier in the front, this leads to a catastrophic blow-out. This is a relatively rare failure, but due to its catastrophic nature (front wheel, downhill, usually at high speed), has been a fairly singular deterrent for people purchasing a carbon clincher wheelset.

The final goal is achieving improved tubeless compatibility with the rims. A tubeless rim replaces a traditional tire/tube setup with a heavier duty tire with stronger bead and latex based sealant. Nearly every Mountain Bike rim sold today is setup without tubes due to their puncture resistance, lower tire pressure that can be used, and better grip. There has been much slower adoption among road users. This can be attributed to a number of factors including but not limited to: limited tire availability, limited tubeless ready rim availability, the unproven technology factor, and difficulty of setup. There are essentially no disadvantages to producing a rim that is compatible with a tubeless and normal tube setup versus a tube setup alone.

 

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Bike Wheels and Ocean Creatures

On to part 2!!

Ground Boundary Layers

If I did not make it clear in the past post, I really enjoy new innovations in bicycling. However, there is a difference between some new kick-starter trinket that solves a problem in an innovative way, and a $4,000 wheel-set without any published data yet besides “It looks like humpback whales”.

Anyway, back to birds and whales.

The other important lesson to take from the Albatross doesn’t have to do with it’s wings, but HOW it actually fly’s 1000’s of miles without flapping:

Once over the open ocean, the albatross will perform a circular swooping flight to cheat the wind. Flying 30 or so feat above the ocean the albatross will dive down with the wind to the ocean surface gaining velocity from gravity and the wind. Once at the surface it’ll turn around right at the surface and head into the wind. Once angled towards the wind the bird then pulls up, using it’s high speed and incoming wind to climb back to it’s initial flight level. It’ll then repeat this process thousands of times to cross an ocean.  (or just watch the video below)

Albatross flight

The albatross takes advantage of the surface boundary layer to generate “free speed”. Wind speed is always lower the closer you are to the ground and this gradient is a VERY well known phenomenon. This is important because a large wind gradient close to the ground undermines the whole idea of minimizing crosswind drag. If you want a more exhaustive discussion of Atmospheric Boundary Layer check out This Post. In short , and in my humble opinion, the magical 15 degrees of cross wind that wheel and bike industry has adopted as the targeted drag angle to minimize drag for is WRONG!!!!!!!!!!!!!!!!!!!WindAngleIsTooDamnHigh

This high crosswind angle is Zipp’s ENTIRE marketing shtick. It’s fine to try to reduce drag at high angles of attack but every design choice you make when making a wheel, bike, plane, whatever represents a trade-off. Usually, high angle of attack drag reduction results in higher low angle drag, especially if you introduce drag creating turbulators, which is exactly what Zipp has done.

Now I will add, that between the testing that we did when designing our wheels we noticed that for near zero angles of attack, drag results were more insensitive to actual rim shape than at the magical 15-degree: 60mmcfd

These are results from a variety of the “best-case” 60mm rim shapes from our CFD runs along with some industry rim shapes (cough, zipp, cough). If you look closely the rims that perform best at high angles of cross wind tend to perform worse at near zero angles of attack (but results are all closer at the Zero point). I believe that in order to get a true 15-degree wind angle on your wheel you have to have near hurricane force winds and that most people would rather have a wheel that performs slightly better during the remaining 98% non-hurricane-force wind conditions. The cynic in me even would go so far as to say most bike industry has focused on 15-degrees simply because it’s the low point on the drag curve, the magical point where 90mm wheels get to the ‘negative drag’ point.

Scaling the Flow

When I posted the last post a friend brought up the important point of flow similarity between objects at different sizes and speeds. In Aerospace design its usually pretty difficult to fit a full sized aircraft or rocket into your wind tunnel. Fortunately flow is somewhat scale-able. Generally speaking if as long as Reynolds Number and Mach number of a flow is the same between say a full sized aircraft and a model in a wind tunnel.

So lets take a look at the various Re and Mach numbers for the 787, Albatross, Humpack Whale, and a Zipp 454:reynoldsnumberwheels
 What this tells us is that none of these are REALLY like any other. However it does tell us that most of the flows above are generally in the turbulent region (what this is is even highly dependent on the individual situation). If anything the bike wheelset is the one closest to the laminar region of flow.

Zipp modeled these fins off the ‘tubercles’ of a humpback whales and there’s some decent research on the topic. However, the question of the humpback whale brings up a few interesting questions and points. The paper does indeed show that flow separation on the flipper is delayed due to the tubercles. However, the tubercles are only found on the high Aspect Ratio (long) flippers of the Humpback. Faster whales like the Orca (ok litterally just learned Orca’s actually a dolphin) and dolphins have smooth contoured fins, additionally no birds that I’m familiar with have tubercles (although they do have more intricate flow control). So why do humpbacks have these features while other animals do not?figure-3-humpback-whale-megaptera-novaeangliae-flipper-leading-edge-tubercles-left

The other important question to ask about the tubercles is how it’s applied to the Zipp wheels. On the whales the tubercles are on the leading edge of the fin. With a wheelset, only a quarter of the rim is showing leading edge tubercles to the wind at any given cross-wind moment. The rest of the time, the flow that’s being turbulated by the Zipp fins is flowing off into the free-stream and not working to help flow remain attached. Also…um importantly…the humpback fins don’t rotate.

capture

So the tubercles have to provide a large benefit in that small area to offset the detriment they cause around the rest of wheel.

Most good engineering innovations have sort of an ‘ah-ha’ sense to them where the design just sort of makes sense before you even look at any data. For instance, once the Wright brothers first solved the problem of powered flight there were dozens of  other non-wright airplanes in the sky within a few years because they quickly recognized that control/balance was one of the primary problems that the wrights solved and had a bit of an ‘ah-ha’ moment.

I personally don’t get that “Oh that makes a lot of sense” feeling with the Zipp tubercles. I don’t think there’s some special magical design that’s going to cheat wind. Of course I might be very wrong since I don’t know the actual numbers, and I’m just some stupid blogger on the internet…..but I do know you don’t see airplanes that look like this:Stupid Looking Airplane

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Why Zipp Should Study the Albatross (or Oh Good Lord this….Thing)

Seriously WTF Wheelset

I’m going to break this up into a two part-er of why I think these aren’t all they’re cracked up to be. So here goes:

First off: I am a HUGE fan of biologically inspired design. Nature generally does everything better than we can. Case in point: wings. High efficiency gliders and recently developed composite passenger aircraft.

The albatross is (arguably) the most fascinating bird out there, it can fly literally 1000’s of miles without flapping it’s wings once. Half of the the equation explaining how it can do this are its wings:


Albadross WingsNow, aside from looking totally bad-ass, you’ll notice that the wings gentle curvature and tapered ends, which look remarkably similar to the new Boeing 787 Dreamliner:

boeingwing

It’s almost like a 747 and a sailplane had a baby: the 787. The reason why the 787 has such a funky wing shape is because the name of the aircraft design game is: efficiency. Now take a look at this wing you’d find on mondern-ish to old aircraft:6a4eabc2-1678-4a25-afc8-3feda38b05c0

You should notice two things: first, are the small nubs halfway down the wing, these are called ‘vortex generators’ and second, the wing sticking straight up at the end of the wing (insert Yo Dawg joke). These two devices try to accomplish the same thing: reduction of drag caused by lift (lift causes drag, which is a whole Aero chapter onto itself).

However these are not elegant solutions. The vortex generators are literally creating turbulent drag in order prevent stalls in the wing during take-off and landing, but generate a not insignificant and unwanted amount of drag during 99.999% of the rest of the flight.

The vertical wing-tip also reduces drag caused by blocking the swirling wing tip vorticies, HOWEVER the price you pay is you have to drag two of these vertical wings that don’t contribute to lift of the aircraft. Both of these devices reduce overall drag by creating more drag in a particular way, but the benefits outweigh the drag penalties of these devices.

Now comes Boeing, and more importantly the new carbon manufacturing techniques of the 21st century that allows ANY shape to be crafted with the structural integrity required for a wing. With exhaustive design and testing they came to the shape seen above which, lo and behold, looks an awfully like one of the most efficient wing designs crafted by eon’s of evolution. The wing essentially accomplishes the same goal as the wing tip and vortex generators, but without the massive drag penalty they incur.

Now, I would not say off hand that all the dimples and bumps put on a Zipp wheel make it less aerodynamic since I do not have any data to back that claim up. However, dimples and and bumps represent a trade-off: their mechanism has to benefit the design more than hurt it. Generally the trade off works like this: increased skin friction drag for lower pressure drag.

The golf ball is a great example, the dimples increase the surface roughness of the ball (increasing the skin drag), but reduces pressure drag. The reason why this works so well on a golf ball is because….it’s a ball….it has to be round. An aerodynamic rim on the other hand, has a lot more play room with regards to it’s shape, if you were to design the optimal golf ball, it’d look a lot more like a rain drop (it just wouldn’t be very hit-able).

This is why I think that things like these dimples or hump bumps (I’ve so named since the design seems to come from humpback whales), are somewhat gimmicky. Like Boeing showed, solutions can be found for complex flow problems without using these flow devices to ‘force’ the flow to do what you want it to do. I’m sure the micro-vorticies do help in the way that Zipp claims, but I’m skeptical if the improvements they generate are offset by their disturbance.

Great design in nature is elegant, smooth, and most importantly simple (because physics). We should all try to mimic it.

Stay tuned for part 2!

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