Lesson 4 ended with a feedback loop: a slightly weaker shock means a much longer induction zone, which means weaker support, which means a still weaker shock. A flat detonation front cannot be stable. And yet detonations propagate, at almost exactly the CJ speed, for kilometres. What does a real detonation front look like?
Fish scales in the soot
In 1959, Yu. N. Denisov and Ya. K. Troshin in Moscow coated the inside wall of a detonation tube with a thin layer of soot and fired a detonation past it. When they pulled the foil out, it was covered in a pattern of fish scales: diamond-shaped cells, all much the same size, arranged as if a net had been dragged along the wall.
The pattern is made by the front itself. A real detonation is not a flat sheet but a mosaic of curved shock segments. Where a strong, bulging segment (a Mach stem) meets a weaker one (an incident shock), a third shock — a transverse wave — runs sideways along the front. The point where the three meet is a Triple pointWhere an incident shock, a Mach stem and a transverse wave meet. Triple points are the hottest spots on the front and leave tracks on a sooted foil., and it is the hottest, most violently sheared spot in the flow. Triple points race up and down the front, colliding and passing through each other, and as they go they scour tracks in the soot. The diamond between two collisions is a Detonation cellThe diamond-shaped pattern traced by triple points as transverse waves sweep across a detonation front. The cell width λ is the detonation’s fundamental length scale..
Each cell is a cycle in the life of the front. A collision of two triple points creates a burst of strong, overdriven Mach stem; it ignites the gas almost at once and pushes ahead. As the cell grows, the shock weakens and decays below CJ — the induction zone lengthens — until the next collision re-ignites it. The average speed is the CJ speed; locally, the front oscillates between about 1.6 and 0.8 within every cell.
Regular and irregular
The pattern depends on the chemistry. Mixtures with a low reduced activation energy — hydrogen–oxygen diluted with argon, for instance — make almost perfect, repeating diamonds. Mixtures with a high one, like methane–air, make chaotic patterns with cells of very different sizes, cells inside cells, and pockets of gas that escape the shock entirely and burn later as turbulent flames. Their fronts are closer to turbulence than to clockwork.
The cell size is the ruler
Whatever the regularity, a mixture has a characteristic Cell width λThe width of a detonation cell, roughly 10–50 induction lengths. About 10 mm for hydrogen–air and 300 mm for methane–air at 1 atm; it shrinks roughly as 1/p., the average distance between tracks running in the same direction. Experimentally, λ is roughly 10 to 50 times the ZND induction length — so it inherits the induction length's exponential sensitivity to temperature, and its inverse dependence on pressure.
Cell sizes have been measured for thousands of mixtures, and engineers use them as rulers. A detonation in a tube narrower than about fails: it cannot fit even one transverse wave. A detonation emerging from a tube into open space survives only if the tube is wider than about 13 λ: the critical tube diameter. And in a rotating detonation engine, as Lesson 9 will show, the layer of fresh mixture ahead of the wave must be at least about 12 λ tall.
Going deeper
Going deeper: how λ scales
Since λ is proportional to the induction length, and with , the cell width scales roughly as at fixed temperature (for most mixtures in the range that matters). Preheating raises only slightly — the CJ Mach number falls as the sound speed rises — so it shrinks λ modestly. Off-stoichiometric mixtures detonate more weakly and have colder von Neumann states, so λ grows steeply toward the detonability limits: the U-shaped curves in the plot. The proportionality constant between λ and Δ is not universal: it ranges from about 10 for regular mixtures to more than 50 for irregular ones, which is why cell sizes are measured rather than computed.
- Real detonation fronts are cellular: bulging Mach stems, weaker incident shocks and transverse waves meeting at triple points.
- Triple points carve diamond cells into soot; inside each cell the front speeds up and slows down around .
- Low-activation-energy mixtures make regular cells; high-activation-energy mixtures (hydrocarbon–air) make irregular ones.
- The cell width λ (~25 induction lengths; ~11 mm for H₂–air, ~300 mm for CH₄–air at 1 atm) scales as 1/p and sets the size of every detonation device.
Next: how to start a detonation on purpose — and why it is so hard to stop one once it has started.