The Effect of Curvature and Confinement on Gas-Phase Detonation Cellular Stability

We examine the evolution of cellular detonation patterns in a two-dimensional channel with yielding confinement on one side. It is shown that in a narrow channel of fixed width the number of cells first increase with decreasing level of confinement. Subsequently, with increasingly weaker confinement, the cells then grow in size and the total number of cells in the channel decreases. For sufficiently weak confinement, the flow becomes laminar with no detonation cells. We examine the relative importance of two fluid mechanisms underlying the observed evolution: global curvature of the detonation shock front due to induced flow divergence caused by the yielding confinement, and energy loss associated with transverse shock wave transmission to the confining material. In order to determine which effect is dominant, we compare two types of numerical calculations. One involves specialized calculations in which the explosive boundary, along which impermeable flow conditions are applied, is deflected through a range of specified angles upon detonation arrival. This set-up mimics the effect of yielding confinement in terms of induced flow divergence, but removes the transverse wave energy loss that would otherwise occur due to wave transmission into the confiner material. The second involves multi-material simulations which can account for transverse wave energy loss into the confining material. Shock polar theory is used to select confiner densities in the multi-material calculations that provide equivalent material interface deflection angles at the detonation shock to the angles imposed in the deflected solid wall calculations. We determine that the induced global curvature of the wave primarily drives both the evolution of the cellular pattern and eventual stabilization of the detonation front, characterized by laminar flow solutions. In wider channels, we show that the detonation front will likely remain unstable even for very weak confinement, as the mean curvature of the front only becomes significant near the edge of the explosive domain. Published by Elsevier Inc. on behalf of The Combustion Institute.