Advanced9 min read6 / 9

Viscosity, boundary layers & stall

Everything so far assumed an inviscid (frictionless) fluid — the same assumption our panel solver makes. It is astonishingly good for lift, but it hides two real effects: drag and stall. Both live in a paper-thin layer of air right against the skin.

The no-slip condition and the boundary layer

Real air sticks to a surface: the layer of molecules touching the skin moves with the skin (zero relative velocity). This is the no-slip condition. Just above, the speed climbs from zero up to the full external value over a very thin region — the boundary layer, often less than a millimetre thick near the nose. Inside it, velocity gradients are enormous and viscosity rules; Bernoulli does not apply there.

Fig. 1. The boundary layer grows from the leading edge, transitions from laminar to turbulent, and — against a rising pressure — can separate, reversing near the wall.

Laminar vs turbulent

Near the leading edge the boundary layer is usually smooth and orderly — laminar — with low friction. Downstream it typically trips into a chaotic turbulent layer: more friction, but more resistant to separation because turbulent mixing drags high-momentum air down toward the wall. Where this transition happens is set by the Reynolds number $Re$ — which is exactly why it is such a central parameter.

Separation and stall

Over the rear of the wing the pressure rises again (an adverse pressure gradient): the flow is being asked to decelerate. The already-slow boundary-layer air may run out of momentum, stop, and reverse — the flow separates from the surface, leaving a turbulent wake. When you raise the angle of attack too far the separation point jumps forward and the upper-surface suction collapses. That is stall: lift falls even as the angle increases.

D’Alembert’s paradox

There is a second, famous consequence of dropping viscosity. Integrate the pressure around a closed body in steady inviscid flow and the net drag comes out exactly zero:

D_{\text{inviscid}} = 0

(1)

This is d’Alembert’s paradox — obviously wrong for real bodies, and the historical clue that viscosity is essential. Our solver inherits it: it reports essentially zero pressure drag, so the drag number in the demo is a separate empirical estimate (next article), layered on top of the inviscid solution.