RALTech | Boundary Layers

The boundary layer is one of the most important features of aerodynamics, yet it is often misunderstood or misrepresented. When air flows over a flat surface, the air directly in contact with the surface actually doesn't move relative to the surface. Some small distance away, the air is moving at the same speed as the bulk of the airflow. In between, there is a 'velocity gradient', with the speed generally increasing the further you go from the surface. This is the 'boundary layer, and a number of interesting things happen in it.

The Reynolds number is a kind of measure of 'effective speed', which takes into account density and viscosity of the fluid and the size of the object in it. By using this number it is possible to compare the type of flows between objects of different sizes at different speeds and in different fluids. For example, the way air flows around a 30mm tube at 30mph is the same as the way water flows around a 6mm tube at 10mph, since the Reynolds number works out the same. This is how we can compare scale models with their full-size counterparts.
The bigger the object or the faster it moves, the higher the Reynolds number. An object 10mm size (usually measured in direction of airflow) moving at 30mph has a Reynolds number of a little under 10,000. Remember this for later.

When the airspeed is fairly slow and the object in the stream is fairly small, the air in the boundary stays pretty well ordered. Layers of air just kind of slide over each other like fanning a pack of cards. Virtually no mixing occurs between the top and bottom of the boundary layer and speed (or momentum) is transferred only by shear. The thickness of the boundary layer grows steadily as the flow continues along the surface of the object. However, this type of flow is only stable up to a point.
This type of flow creates the lowest frictional losses, since there is no churning or swirling going on. The downside is that the boundary layer is not very 'sticky'; as the flow slows down as it tries to go around the back of an object, it is more likely to separate, as described later.

Transition from laminar to turbulent boundary layer types occurs when the Reynolds number reaches a critical value. Depending on a number of factors, this can be at Reynolds numbers of <100,000 to >2,000,000. Below the lower limit, the laminar boundary layer is quite stable and the viscosity of the fluid is enough to damp out any disturbances caused, for example, by small surface imperfections. Above the top limit, the boundary layer is highly unstable and is likely to transition to turbulent spontaneously. In between, transition can be delayed or induced to a certain extent, to suit the requirements of the designer.

At higher airspeeds, the boundary layer will become more unstable and at some point will transition to become turbulent. Now the air is no longer sliding in smooth 'layers' but is rolling, like a wave approaching the beach. Because there is now some fluid motion normal to the surface, there can be much more transfer of speed and hence energy into the boundary layer. This results in two significant features of the turbulent boundary layer: increased skin friction and increased resistance to separation. The former is not good (for us who want low drag), but the latter can be very useful, as we will discover shortly.

As air tries to flow around the back of an object, it has to curve and slow down to fill the space. This creates a pressure gradient, which tends to peel the boundary layer away from the surface. When this happens, the flow is described as separated.

What was the boundary layer is now a notional surface separating the bulk of the airflow from a region of static air in a separation 'bubble' behind the object. This bubble has a relatively low pressure and hence 'sucks' the object backwards, resulting in a large amount of drag. This is by far the greatest cause of drag created by bike or rider. In a streamlined object, where the trailing edge tapers gently, the pressure gradients are very shallow and the flow can remain attached virtually all the way to the very back of the body and this pressure drag is very low. In these cases, skin friction is the dominant drag force and attempts are often made to reduce this by maintaining laminar flow as much as possible. In contrast, a more blunt-shaped object, like most parts of a bike or rider, will have separation quite early and hence a large separation bubble, causing high drag. In this case, we need to improve matters by increasing the distance the air will flow along the body before separation. This can be done by aiming to create a turbulent boundary layer.

A useful way to illustrate the effects boundary control is to look at dimples. Golf balls have dimples. This makes them go further, right? But how does this work and, more importantly, can we use this to make bikes go faster? What the dimples do is to upset the boundary to trigger the transition from laminar to turbulent early. The turbulent boundary layer is able to remain attached to the surface much longer as the flow goes around the back of the golf ball. This creates a smaller low-pressure separation 'hole' behind the ball, reducing the drag.
The principle is described and illustrated better than I could, by aerospaceweb.org. The penalty to be paid is that the skin friction is greater with a turbulent boundary layer, but this is pretty insignificant compared to the savings in pressure drag.

A similar technique can be used for other shapes, but some thought is required to ensure the measures are effective. Firstly, is there any advantage in creating a turbulent boundary layer? A fairly bluff object like a golf ball will quite readily cause the airflow to separate as it tries to close up behind the ball. Even with high Reynolds numbers and a turbulent boundary layer there is still a small separation bubble. Creating the turbulent boundary layer is therefore quite effective at reducing the size of this bubble and reducing drag. Airflow around a very blunt object, like a square-sided box will always separate at the corners. Boundary layer control is not going to help that. Also, a very streamlined object, like an aircraft wing, allows the boundary layer to remain attached pretty much all the way to the trailing edge, even if the boundary layer is laminar. Again, forcing a transition will not help in this case, and it could well create more drag, since the skin friction part of the drag will increase.

The second thing to look at is whether the object is big enough or fast enough for transition to be possible. A golf ball is 43mm diameter and travels at up to 150mph off the club, giving it a Reynolds number of ~200,000. (The spin - around 3000rpm - may help to increase the effective Reynolds number.) This Reynolds number is low enough that the boundary layer could easily remain laminar up to the point of separation, especially as the ball slows down in flight. But we can also see that it is high enough that it is quite possible to trip the boundary layer within a quarter of its way around the ball (Re = 50,000). A frame tube, on the other hand, of 30mm diameter and travelling 30mph has Re = 30,000. Roughening of the surface is never going to be enough to trip the boundary layer here.

Finally, we should consider the technique used to trip the boundary layer. Dimples are used as an example here, because they are well known, being seen on all golf balls. However, for an object over which the air flows in a known and constant direction, a much simpler trip is more effective. At its simplest, this can be a raised ridge running across the direction of flow. The height of the trip depends on the thickness of the boundary layer at that point; a height of about a quarter of the boundary layer thickness is generally effective. A zigzag or other random variation to the straight line tends to generate small crossflow disturbances, which are very efficient at promoting early transition.