2-PHASE MODELING OF DDT - STRUCTURE OF THE VELOCITY-RELAXATION ZONE

The structure of the velocity relaxation zone in a hyperbolic, noncons ervative, two-phase model is examined in the limit of large drag, and in the context of the problem of deflagration-to-detonation transition in a granular explosive. The primary motivation for the study is the desire to relate the end states across the relaxation zone, which can then be treated as a discontinuity in a reduced, equivelocity model, t hat is computationally more efficient than its parent. In contrast to a conservative system, where end states across thin zones of rapid var iation are determined principally by algebraic statements of conservat ion, the nonconservative character of the present system requires an e xplicit consideration of the structure. Starting with the minimum admi ssible wave speed, the structure is mapped out as the wave speed incre ases. Several critical wave speeds corresponding to changes in the str ucture are identified. The archetypal structure is partly dispersed, m onotonic, and involves conventional hydrodynamic shocks in one or both phases. The picture is reminiscent of, but more complex than, what is observed in such (simpler) two-phase media as a dusty gas. (C) 1997 A merican Institute of Physics. [S1070-6631(97)00312-7].