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Boundary layer

The boundary layer is the layer of fluid in the immediate vicinity of a bounding surface. In the atmosphere the boundary layer is air layer near the ground affected by diurnal heat, moisture or momentum transfer to or from the surface. On an aircraft wing the boundary layer is the part of the flow close to the wing.

The boundary layer is particularily important in aerodynamics because it is responsible for a considerable amount of drag. In high-performance designs, such as sailplanes and commercial transport aircraft, much attention is paid to controlling the behavior of the boundary layer to minimize drag. Two effects need to be considered. First, the boundary layer adds to the effective thickness of the body, hence increasing the pressure drag. Second, the shear forces at the surface of the wing create skin friction drag.

At high Reynolds numbers, typical of full-sized aircraft, the ideal situation is to have a laminar boundary layer. This results in the lowest skin friction due to the characteristic velocity profile of laminar flow. However, the boundary layer thickens and becomes less stable as the flow gets further along the body, and eventually even the slightest imperfection in the surface will be enough to "trip" the boundary layer into turbulence. One high-tech means of dealing with this problem is to suck the boundary layer away through a porous surface. This can result in a reduction in drag, but is usually impractical due to the complexity of the "plumbing" involved.

At lower Reynolds numbers, such as those seen with model aircraft, it is typically quite easy to maintain laminar flow. This gives low skin-friction, which is desirable. However, the same velocity profile which gives the laminar boundary layer its low skin friction also causes it to be badly affected by adverse pressure gradients. As the pressure begins to recover over the rear part of the wing chord, a laminar boundary layer tends to separate from the surface. Such separation causes a large increase in the pressure drag, since it greatly increases the effective size of the wing section. In these cases, it can be advantageous to deliberately trip the boundary layer into turbulence at a point prior to the location of laminar separation. The fuller velocity profile of the turbulent boundary layer allows it to sustain the adverse pressure gradient without separating. Thus, although the skin friction is increased, overall the drag is decreased. Special wing sections have also been designed which tailor the pressure recovery so that laminar separation is reduced or even eliminated. This gives the best of both worlds - -no extra pressure drag from the separation, and no extra skin friction from the induced turbulence.

The boundary layer approximation was one of the most important advances in the aerodynamics of wing sections. The approximation states that, for a sufficiently high Reynolds number the flow over a wing can be divided into a portion unaffected by viscosity (the majority of the flow), and a portion where viscosity is important (the boundary layer). By assuming that the boundary layer is thin, we can make the approximation that the static pressure is constant across the thickness of the boundary layer. This allows the Navier-Stokes equations within the boundary layer to be simplified. Notably, the characteristic of the PDE becomes parabolic, rather than the elliptical form of the full Navier-Stokes equations, greatly simplifying the solution of the equations. So by making the boundary layer approximation, the flow is divided into an inviscid portion (which is easy to solve by a number of methods) and the boundary layer, which is governed by an easier to solve PDE. The boundary layer approximation is widely applicable to practical flows.

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