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

Wind tunnel — where it appears

A facility for producing a controlled stream past a stationary model, whose walls, turbulence level and size all enter the answer. Correcting for them is a computation in its own right, and the corrections are the reason tunnel data carry a facility's name.

Named by 5 essays across 4 fields — each of them below, with the objects they name alongside it.

Reynolds number: one number, four different flows. Reynolds number is inertia ÷ viscosity. It is not a property of the fluid or of the shape but of the combination, and crossing a threshold changes the physics rather than the magnitude.

The model that cannot be matched

A scale model behaves like the real thing when its dimensionless numbers agree. With one number that is a matter of choosing the tunnel speed. With two it is usually impossible, and every wind-tunnel result ever published has been obtained in spite of that.

regimes · Similarity The pressure coefficient, read off the field. The closed-form surface pressure of a cylinder, and the same quantity computed from the speeds of the solved field at the same points. The coefficient is exactly one where the flow stops and exactly minus three at the shoulder, and those two numbers are properties of the shape rather than of the tunnel.

The number that does not depend on the tunnel

A pressure measured in a wind tunnel is a fact about that tunnel on that day. Divide it by the dynamic pressure and it becomes a fact about the shape — the same at any speed, in any fluid, at any scale, and equal to exactly one where the flow comes to rest.

inviscid · Pressure 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 The wall is a boundary condition, solved for rather than reflected. A model's trailing vortices in a closed working section, with the sheet of sources that makes the wall a wall drawn as a displacement of the wall itself. The interference is an upwash — the model looks better than it is, and the correction factor comes to 0.1242 against the exact value 0.1250 that the image at the inverse point gives for a circle. The arrows are the interference velocity alone, with the model's own downwash removed, drawn to a common scale set by the longest of them.

The walls are in the answer

A wind tunnel measures a wing in a box the aeroplane will never fly in, and the box is worth a fifteenth of the induced drag. The correction is exactly an eighth for a closed circular section and exactly minus an eighth for an open jet, and the sign is the whole argument.

circulation · Tunnel interference One coefficient, two errors, two places they vanish. The two wall-interference errors against the slot parameter, in units of the tunnel's half-height. Both are positive for an open jet at the left and negative for a solid wall at the right, so each passes through zero — the blockage at 1.184 and the streamline curvature at 1.590. A wall has one coefficient and the two zeros are a third of a tunnel height apart.

One coefficient, two errors

A closed tunnel's walls push a measurement one way and an open jet's push it the other, so a wall somewhere between them should push it neither. There is such a wall, its coefficient is a length, and it nulls the blockage at 1.184 tunnel half-heights — and the streamline curvature at 1.590.

circulation · Tunnel interference

Named alongside it

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

BlockageMeasurementPotential flowBoundary conditionCorrectionDynamic similarityImagesModel limitBernoulli's equationCirculationCorrelationDimensionless

All concepts