Concept

Combustion — where it appears

The rapid oxidation of a fuel that releases heat, which in a flow means heat release coupled to transport. The heat expands the gas, so a flame is also a source of volume and of vorticity, and its chemistry and its fluid mechanics cannot be treated apart.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

The structure the sensitivity produces. A detonation front, schematically: a leading shock, an induction zone in which nothing measurable happens, and a reaction zone behind it. The induction zone's length is set by the shock's own strength, and because that dependence is exponential the front is unstable and breaks into cells.

A gas that has not decided to react yet

Behind a detonation's leading shock there is a zone in which nothing measurable happens. Its length is set by the temperature the shock produced, exponentially — a one per cent change in the shock shortens it by fifteen per cent — and that sensitivity is why a detonation front cannot stay flat.

compressible · Detonation

A wrinkled flame settles into arcs meeting at a cusp. The steady front of a flame in a periodic domain 5, 10 and 20 neutral wavelengths wide, from the exact pole solution of the Michelson–Sivashinsky equation, with the burnt gas below and the flame advancing upwards; each is drawn across one period, scaled to the same width. Every one is a single smooth arc bulging into the fresh gas, meeting its neighbour in a sharp cusp pointing back into the burnt gas, and in these units the three arcs nearly coincide: only the cusp sharpens as the domain widens. In physical units the arc's depth grows in proportion to the domain's width, so the three flames are the same shape at three sizes.

A wrinkled flame has one cusp and a speed limit

The linear theory of a flame says every long wrinkle grows and none is favoured. The weakly nonlinear theory — the Michelson–Sivashinsky equation — says where the growth goes: small wrinkles merge, the front settles into smooth arcs bulging into the fresh gas and meeting in sharp cusps, and in a domain of any width it ends with a single arc and a single cusp. That front is an exact solution made of poles in the complex plane, and its speed is a closed form that rises in steps as the domain admits more poles and then stops: beyond about five neutral wavelengths a wider flame is no faster, because it is the same shape at a larger size.

kinematics · Dilatation

A quiet flame has one cusp; a noisy one keeps making more. Two flame fronts twenty neutral wavelengths wide, burning upwards, drawn apart for clarity: above, the quiet front, the exact pole solution with one cusp per period and the most poles it can hold; below, the same flame with a noise of a millionth kicking its growing wavelengths. The noise keeps seeding small wrinkles on the smooth arcs; each grows as it is swept along the arc into the cusp, so the noisy front carries a train of sub-cusps the quiet one never has, and advances at 0.862 against the quiet 0.5.

A flame's speed limit holds only in silence

A quiet wrinkled flame settles into a single cusp and a speed it never exceeds, however wide it grows. Add noise and the limit is gone. A disturbance of one part in a million million already speeds the front up; one in a million makes it a third faster; and a noisy flame, unlike a quiet one, keeps getting faster as it gets wider, because every added width is room for more wrinkles to be born on its arcs and swept into its cusp. The quiet flame's speed is a property of a silence no burner has.

kinematics · Dilatation

Named alongside it

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

Instability Model limit Darrieus landau Detonation Dispersion relation Exact solution Flame front Flame speed Growth rate Induction time Measurement Memory kernel

All concepts