Understanding Aerodynamics: Arguing from the Real Physics

4

Boundary Layers

In Section 3.6, we saw that the basic effect of viscosity is to exert shear stress, and that when that is combined with a no-slip condition at a solid surface, it leads to vorticity that originates at the surface, is convected downstream, and diffuses outward. (In Section 4.2.4, we'll look at this in detail and see that some parts of a surface act as sources of vorticity, and others act as sinks, but that the net result is that there is always some vorticity convected along next to a solid wall.) In Section 3.8.2, we saw that irrotational flow tends to remain irrotational until viscosity has had a chance to work on it. The upshot is that flows around bodies at high Reynolds numbers acquire a natural global structure: an inner vortical region where viscosity is important, consisting of the boundary layer next to the surface and the wake downstream, surrounded by an outer flow that is effectively irrotational and that behaves as if it were inviscid. This basic pattern was not generally understood until Prandtl (1904) explained it and proposed his approximate theory for the flow in the boundary layer.

In this chapter, we'll take a detailed look at the physics of the flow in the boundary layer, in preparation for a more global discussion of the whole flowfield in Chapter 5. This ordering of the discussion is convenient because it turns out that the boundary layer and the outer flow interact only through a relatively simple set of boundary conditions at their interface, ...