Fluid Flow & Aerodynamics
why things fly, and why the usual explanation is wrong
Series

Separation — the series

4 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. Flow past a cylinder at Re 100. A real fluid past a circular cylinder. At low Reynolds number the flow closes up behind the body much as the ideal theory says; as it rises the flow separates and a region of reversed flow appears behind, which is where drag comes from.

    When the flow lets go

    Every body asks the air behind it to slow down and climb back up to the pressure it started at. Sometimes the air cannot, and the moment it refuses is separation — the source of most drag, the cause of stall, and the reason a golf ball has dimples.

    part 1 · viscous
  2. The wall slope against pressure gradient, and where it runs out. How steeply the flow leaves the wall, plotted against the pressure gradient the layer is running into. A favourable gradient presses the profile against the surface and steepens it; an adverse one hollows it out. The curve reaches zero at a definite value, and beyond that there is no attached solution at all.

    How much uphill a layer can take

    A boundary layer running into rising pressure is climbing a hill on the last of its momentum. There is a definite steepness at which it can no longer do it, and the number is not a rule of thumb — it is where a family of solutions stops existing.

    part 2 · viscous
  3. Pressure recovery along the upper surface at 6°. Surface speed and the local Falkner–Skan pressure-gradient parameter, plotted along the upper surface from the nose. The speed peaks near the leading edge and then falls, which is the layer climbing back up to the pressure it started at, and the parameter crosses the separation value where that climb becomes too steep.

    Where the straight line stops

    Ideal flow will report a lift coefficient at forty degrees of incidence without complaint. What ends the lift curve is the boundary layer refusing to follow the surface, and the estimate of when that happens joins two solvers that have nothing else in common.

    part 3 · viscous
  4. Every wavelength grows, and the shortest grows fastest. Growth rate against wavenumber for a vortex sheet of zero thickness and for a layer of thickness δ. The sheet's curve rises without limit, which is the model announcing that it has no shortest scale in it; the layer's turns over and dies at kδ = 1, the neutral wavenumber computed from Rayleigh's equation rather than fitted.

    The gradient that does both

    One line of the boundary-layer equations at the wall says the profile's curvature there equals the pressure gradient. That single sign causes separation and causes instability, and it causes the instability a long way before it causes the separation.

    part 4 · viscous

All series