A spark plug lights a car engine's mixture a hundred times a second without ever setting off a detonation. Yet a hydrogen leak in a long, cluttered pipe can turn a gentle flame into a detonation in a few metres. How do you start a detonation on purpose — and how do you stop one that has started by accident?
Route one: a big enough bang
The direct route is brute force. Set off a charge in the mixture, and its blast drives a strong shock outward. Close to the charge the shock is far faster than CJ, hot enough to ignite the gas almost instantly. As it spreads it weakens: its energy is shared over a growing sphere. The question is whether, by the time it has slowed to the CJ speed, the reaction zone has coupled to it strongly enough to keep it there.
The answer depends on the front's curvature. A small, sharply curved front loses energy sideways faster than a flat one; if its radius is not much larger than the cell size when it reaches CJ, the induction zone grows, the chemistry falls behind, and the shock and flame separate. So there is a Critical initiation energyThe minimum energy that starts a detonation directly — without a run-up — by a blast. It scales roughly with λ³ for spherical waves: grams of explosive for hydrogen–air, kilograms for methane–air., and because the critical radius scales with λ, the energy scales with λ³.
That cube is merciless. Methane–air cells are about twenty-seven times larger than hydrogen–air cells, so methane needs roughly twenty-seven cubed — some twenty thousand times — more energy to detonate directly: grams of explosive for a hydrogen cloud, tens of kilograms for natural gas. The model above, based on Lee's surface-energy argument, lands within a factor of two or three of the experiments: good enough to know which mixtures are dangerous.
Route two: a flame that cannot stay a flame
The second route starts with an ordinary spark and lets the flame do the work: DDTDeflagration-to-detonation transition: a flame accelerates by turbulence and confinement until it can form a shock strong enough to ignite the gas on its own., or DDT. In a tube closed at the ignition end, the burnt gas expands and pushes the flame forward, and it pushes the fresh gas ahead of it too. The flow becomes turbulent, the turbulent flame wrinkles and burns faster, which pushes the flow harder still. The flame accelerates.
Obstacles make it worse — or better, if a detonation is what you want. Rings, orifice plates or a coil of wire (the Shchelkin spiral, introduced by Kirill Shchelkin in 1940) stretch and fold the flame, multiplying its area. The flame races up to a few hundred metres per second, compresses the gas ahead into shocks, and eventually chokes at about the speed of sound in its products. Then, in a shock-heated pocket near a wall or an obstacle, a local explosion goes off — Antoni Oppenheim's "explosion in the explosion" — and launches a detonation.
Transition only happens if a detonation can fit. In an obstacle-filled tube, the classic criterion (Peraldi, Knystautas and Lee, 1986) is that the open orifice must be at least about one cell width across. Below that, the flame stays choked: very fast, very loud, very damaging — but not a detonation.
Stopping a detonation
The same rulers tell you how to kill a detonation. A detonation emerging from a tube into a wide space fails unless the tube is wider than the Critical tube diameterThe smallest tube from which a detonation can emerge into open space and survive: about 13 cell widths., about 13 λ: the expansion at the exit curves the front too sharply. Detonation arrestors use packed beds or fine channels, much narrower than a cell, to quench the wave. And diluting the mixture with inert gas or steam grows λ until no device in the plant is large enough to carry it.
Lighting an RDE
Rotating detonation engines start in one of two ways. Many laboratory engines use a pre-detonator: a small tube filled with a sensitive mixture such as hydrogen–oxygen, where a spark triggers DDT in a few centimetres; the detonation is fired tangentially into the annulus. Others simply put a spark plug in the chamber wall and let the flame accelerate and transition in the annulus itself, which takes longer and is less predictable, but avoids the extra hardware. Either way, the first few milliseconds of an RDE's life are a DDT experiment — and the number of waves it eventually settles into (Lesson 11) often depends on how it started.
- Direct initiation needs a blast above a critical energy that scales as λ³: about half a gram of explosive for H₂–air, around ten kilograms for CH₄–air.
- DDT: a flame accelerates through expansion, turbulence and obstacles, chokes at about the products' sound speed, and transitions through a local explosion — if the channel is at least ~λ wide.
- A detonation leaving a tube survives only if the tube exceeds the critical diameter, ~13 λ.
- RDEs are lit by a pre-detonator tube or by DDT in the annulus itself.
Next: the first engine to run on detonations — a tube fired over and over.