Predicting run-up distance to detonation in smooth and obstructed tubes
In plain words
In a pipe filled with a fuel-air mixture and lit at the closed end, the flame speeds up until it becomes a detonation. How far it travels before that happens decides the safety of pipelines, mines and reactors, and it cannot yet be computed reliably.
Precise statement
For a premixed mixture in a tube of diameter $D$, smooth or with obstacles of blockage ratio BR, predict the run-up distance $X_{\mathrm{DDT}}/D$ and the location and mechanism of the final transition (hot-spot ignition through a gradient of ignition delay, shock-flame interaction, boundary-layer and wall effects) as functions of mixture reactivity, expansion ratio and $D$. An answer is a validated prediction without constants fitted to the same experiments.
What would settle it
Blind predictions of $X_{\mathrm{DDT}}$ for a set of mixtures and tube geometries, compared with new experiments.
Status in the literature
Unverified note
Resolved simulations of hydrogen-air DDT in channels reproduce experiments qualitatively; no quantitative run-up prediction across mixtures as of 2026 (not re-verified for 2024-2026).