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

Wall interference — where it appears

The alteration of a model's forces by the walls of the tunnel it is tested in. It is computed from an image system and is corrected for rather than eliminated, and its sign reverses between a closed section and an open jet.

Named by 4 essays across 3 fields — each of them below, with the objects they name alongside it.

Flow net — a free vortex. Two families of curves drawn over the same flow: the streamlines, along which the streamfunction is constant, and the equipotentials, along which the velocity potential is constant. They cross at right angles at every point, because they are the two parts of a single analytic function of position.

A wall made by reflection

Imposing a boundary condition on a plane is work. Putting a mirrored copy of everything on the far side of where the plane would be is not, and the plane then appears on its own — as a consequence of the symmetry rather than as a condition anybody enforced.

inviscid · Images A wing at h/c = 0.4. A wing close to the ground, with the mirrored vortex row that makes the ground a streamline drawn faintly beneath it. The air between wing and ground is squeezed through a narrowing gap, and the wing carries more lift than it would in free air.

The wall that pushes back

A wing near the ground carries more lift than the same wing in free air, and the usual explanation — a cushion of compressed air underneath — is not what the equations say. The ground is a mirror, and what changes is not the pressure under the wing but the circulation the wing is forced to carry.

circulation · Images The tunnel makes the stream 7.4% faster. The flow past a cylinder between two walls, solved from the closed form of an infinite image row rather than from a truncated sum. The walls are streamlines exactly — that is what the images are for, and the normal velocity on them is zero to the last bit — and the flow beside the body is squeezed between the body and the wall, which is the whole of the blockage effect. The stream at the model is 7.40% faster than the speed the tunnel's own instruments report far upstream.

The instrument in the answer

A model in a wind tunnel is not a model in the sky. The walls are supplied by an infinite row of reflections, the stream at the model is faster than the tunnel's own instruments report, and the correction is not an empirical fudge — it is a series with a closed form.

applied · Metering Flow net — a stream past a cylinder. Two families of curves drawn over the same flow: the streamlines, along which the streamfunction is constant, and the equipotentials, along which the velocity potential is constant. They cross at right angles at every point, because they are the two parts of a single analytic function of position.

The mirror that is a circle

A flat wall is made by reflecting everything in it. A round one is made the same way, except that the mirror is an inversion — the image of a point at distance d sits at a²/d, and a vortex acquires a second image at the centre that nothing about the wall requires.

inviscid · Images

Named alongside it

The objects these essays reach for when they reach for this one.

Method of imagesBoundary conditionSymmetryCirculationGround effectPotential flowBlockageBound vortexCorrelationDoubletDrag coefficientImages

All concepts