Draftbags

Computational fluid dynamics (CFD) is a way to model airflow. It is a numerical method of simulating the flow of air, which is influenced by drag, pressure variations, and both smooth and turbulent flows. CFD subdivides the total air volume into millions of tiny volume cubes, and solves the fluid flow equations for each volume. Each tiny cube of volume has to agree at its boundaries with all its surrounding tiny volume cubes. Not always exactly cubes, but you get the idea. The little volume elements model the behavior of real airflow. The algorithm keeps computing until the aerodynamic states of all the little volume elements agree. That's one time step. Then it increments time by an infinitesimal amount and re-calculates conditions in all the little cubes. And another time step.

Turbulence is a phenomenon which has no minimum physical scale, sort of a fractal behavior. It isn't possible to solve all flow conditions, otherwise the simulation would have to dive down to the molecular scale. There exist complicated average-value mathematical models for turbulence which help to model behavior in spite of not getting to molecular scale.

Following are exemplary videos of computational fluid dynamics (CFD) simulation of airflow around a cyclist, with and without a draftbag behind. These few are selected from a large library of simulations made in the process of refining draftbag geometry. We view the flow patterns as a sanity check, then correlate them with flow measurements. To make precise comparisons, drag data is acquired from calculated flow parameters.

Examining Vortices

The following two videos display the disturbed airflow in the wake of a rider, both with and without a draftbag. Each video represents a single instant in time. A flow slicing plane is moved incrementally rearward in the direction of flow to indicate flow components in the plane perpendicular to the cyclist movement. The arrows represent air velocity perpendicular to the bicycle direction of travel. The air was still prior to the cyclist traveling through it, Some disturbance along the direction of motion is inevitable due to drag, but disturbance perpendicular to direction of travel is particularly undesirable. Rotating flows are called trailing vortices. Trailing vortices represent energy expended by the cyclist and transferred to the air. Generation of trailing vortices is a major component of aerodynamic drag on a cyclist.

Wake Visualization of Cyclist

Wake Visualization of Cyclist with Draftbag

Examining Flow in Time

The following two videos illustrate flow progression over time. Each flow line represents the path taken by a molecule of air as the cyclist moves through the air. The flow lines move around over time. This movement indicates unstable flow, meaning the flow is constantly changing. This is turbulent, vorticular flow, which is typically found behind road vehicles. The tubes are colored with the value of k (turbulence kinetic energy), which helps visualize problems and improvements. Each vido represents 4 seconds duration, so this is a slow motion visualization. CFD requires hours of compute time to compute these 4 seconds. In the flow structure you observe dominant vortices, which also vary some over time.

You probably noticed that the cyclist's legs are stationary. Our cyclist is "coasting". It is possible for CFD to simulate moving objects, but difficult. If an object moves, mesh point locations must be transformed, which is remarkably complicated. Especially when the object is changing shape like a bending leg, not just an aircraft shifting in space. Cyclist leg position does in fact have quite an effect on the macro flow characteristics. We can't ignore this. We model the effect of rider movement by crafting individual simulations each with the legs fixed in a different position.

You probably noticed that the flow is asymmetric. The cyclist's lifted leg tends to block flow around the torso, causing the flow to be biased around the torso on the extended leg side.