Detonation structure under chain-branching kinetics with small initiation rate

The structure of ZND waves under simple three step chain-branching kinetics is analyzed, assuming a slow initiation rate but arbitrary chain-branching activation energy. The analysis allows for a complete solution for the ZND wave in all cases, inside or outside the chain-branching explosion region, or close to the explosion limit. Results show that even when the von Neumann point is inside the explosion region, chain-branching effectively stops and the chain-branching radical concentration reaches a small near-steady value before all the reactant is consumed. Beyond that point, chemistry proceeds slowly, at a rate of the order of the initiation rate. For a von Neumann point relatively close to the limit, the reactant concentration is still quite significant when chain-branching stops, but diminishes for von Neumann points deeper inside the explosion region. The assumption that initiation is much slower than chain-branching is often quite accurate, in which case the length required for complete burn is orders of magnitude longer than the chain-branching length, so that as a practical matter, combustion never completes. In contrast, numerical simulation shows that under the same conditions, the cellular wave results in a more complete burn.