Computation of Cellular Detonation

Brian Taylor, University of Illinois

A detonation is a region of rapid chemical reaction in which a very strong shock wave is sustained by the reaction heat release. Detonations can occur in explosives that are premixed gases, liquids and solids. The nominal speed of a steady detonation wave is experimentally found to be close to the Chapman-Jouguet (CJ) detonation wave speed, which corresponds to a case where the state at the end of the reaction zone is sonic relative to the steady frame. Typically, the lead shock dynamics are influenced only by a finite region, mostly in the reaction zone.

Detonations are subject to strong multidimensional, cellular and chaotic instabilities associated with shock-shock dynamics. Shock collisions may generate disturbances in the reaction zone. Typically, two portions of a detonation shock that collide will generate an oblique shock interaction. The oblique shock can generate reflected shocks and slip lines, which induce short-lived Kelvin-Helmholtz instabilities in the region near the detonation front. Detonation flows are inherently multi-scale and their resolved dynamics and spatial structures are exceedingly difficult to compute.

We have begun an investigation of cellular detonation as a test bed for understanding the convergence properties of adaptive mesh refinement schemes as compared to the properties of uniform mesh codes. To do this, we have defined a base case by computing 2D cellular detonation on a uniform mesh. The base test problem is taken from the classical theory of detonation instability. We demonstrate the effect of uniform grid refinement for a standard 4th order space, 3rd order time TVD method. We also discuss plans to carry out similar testing using AMR schemes in collaboration with researchers at LLNL and Rensselaer Polytechnic Institute.

Abstract Author(s): Brian Taylor and D. S. Stewart