Illustrated Physics
physics, drawn
Concept

Combustion instability — where it appears

A self-excited oscillation in which a flame's heat release, fluctuating with the pressure or flow around it, feeds an acoustic mode of the chamber that contains it. It can shake rockets and gas turbines apart and is avoided by damping the modes or changing the lag of the flame's response.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Also named here as hopf bifurcation, self excited oscillation, thermoacoustics — the same set of essays touches all of them, so they are one junction rather than several.

A whisper that grows into a note. The amplitude of the tube's lowest mode against time, in units of the time sound takes to cross the tube (a period is two), started from a small disturbance, with the gauze at a quarter of the length, at 0.12 of it, and at three-quarters; heat-transfer strength K = 1. At L/4 the disturbance grows some fortyfold over about thirty-five periods and then stops growing, at an amplitude of 0.83 in these units, where the air's to-and-fro speed at the gauze is comparable to the steady upward draught and the heat transfer, which goes as the square root of the air's speed, can no longer follow it in proportion. At 0.12 the gauze is near the edge of the singing range and the sound grows only slowly. At 3L/4 the same disturbance dies away within a few periods.

The tube that sings when heated low down

Hold a wide metal tube upright, push a red-hot wire gauze a quarter of the way up inside it, and take the flame away. The tube begins to howl — a loud, steady note at its lowest resonance, lasting until the gauze cools. Put the gauze a quarter of the way down from the top instead and the tube is silent; lay the tube on its side and it stops. Heat is driving a sound, and whether it drives or damps depends on where the heat is released and when, in a rule Lord Rayleigh stated in 1878 that now governs rocket engines and power-station turbines.

waves · Resonance A quiet resonator growing louder before it sings. The pressure in a resonator's 200 Hz mode over two and a half seconds, kicked continually by the same random noise, at three settings approaching the onset of self-sustained oscillation: the mode's natural decay rate falling from 20 to 6 to 2 per second. Each panel is on the same scale. Far from onset the noise is a faint, ragged hiss, each burst dying almost as soon as it starts. Closer, the bursts last longer and grow larger, because the mode forgets each kick more slowly and the kicks pile up; at the last setting the resonator hums in long swells of a nearly steady tone. Nothing has started oscillating on its own — every setting is below onset — but the noise has already begun to sound like the oscillation it is approaching.

The noise that warns a tube is about to sing

A resonator that is about to break into self-sustained oscillation — a combustor about to hum, a heated tube about to howl — is silent on average right up to the moment it starts. Its noise is not. As the margin of stability shrinks, the random hiss in the mode grows louder, remembers each kick for longer and narrows towards the coming tone, in proportions fixed by the margin itself. The instability can be heard before it exists, except in the case engines most often present, where noise starts the song before the warning has properly begun.

waves · Resonance

Named alongside it

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

Hopf bifurcationLimit cycleSelf excited oscillationThermoacousticsCritical slowing downFluctuation dissipationFluctuationsHeat-transferLinewidthRayleigh's criterionStanding wave

All concepts