Numerical modeling of flame acceleration and transition to detonation in narrow channels

The capabilities of an OpenFOAM solver recently developed in the detonation Team of l’Institut Pprime were tested to reproduce the behavior of the transition of reactive mix- tures to detonation in narrow channels. The process is challenging numerically as it involves the initial ignition of a flame kernel, its subsequent propagation, acceleration, formation of shock waves ahead, and finally detonation onset. Two configurations were considered: (i) channels with wavy walls (10-mm high × 1-m long) that mimic the behavior of fence- type obstacles but prevent abrupt area changes. In this case flame acceleration (FA) is strongly affected by shock-flame interactions, and detonation onset (DO) often results from the compression of the gas present between the accelerating flame front and a converging section of the channel. The effect of increasing the blockage ratio (BR) at constant initial pressure, as well as the effect of initial pressure at constant BR were investigated; the experimentally reported dependence of the run-up distance, xDDT, on the aforementioned parameters is properly captured by our numerical framework. (ii) smooth channels (1-mm high × 1-m long) in which the mechanism responsible for FA is heating due to friction, and in which the effect of flow-induced flame instabilities is suppressed due to the low Reynolds numbers characteristic of this configuration. As a result, the only way of sustaining the in- crease in burning rate is by the development of “long” finger flames that remain unchanged until DO. Boundary layer heating induced by the flow ahead of the flame makes the flame tip expand towards the walls. Upon contact, a seemingly constant volume explosion takes place that leads to the formation of a cell-less detonation. The effect of resolution on xDDT was assessed; DO occurred further downstream as resolution was increased. The flame morphologies and the DO mechanism, on the other hand, were not found to be affected by resolution. Finally, preliminary tests for a 3-D channel (5-mm × 5-mm cross section; 1-m in length) using Adaptive Mesh Refinement (AMR) are being carried out. Flame inversion and the formation of a tulip flame has been captured so far with the incipient development of asymmetries in one of the flame lobes propagating along the channel’s corners. The results so far are encouraging but a detailed analysis of mesh-induced instabilities to the flame morphology needs being done before using AMR confidently.