Two-phase modeling of DDT: Structure of the velocity-relaxation zone

Abstract

The structure of the velocity relaxation zone in a hyperbolic, nonconservative, 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, that is computationally more efficient than its parent. In contrast to a conservative system, where end states across thin zones of rapid variation are determined principally by algebraic statements of conservation, the nonconservative character of the present system requires an explicit consideration of the structure. Starting with the minimum admissible wave speed, the structure is mapped out as the wave speed increases. Several critical wave speeds corresponding to changes in the structure are identified. The archetypal structure is partly dispersed, monotonic, and involves conventional hydrodynamic shocks in one or both phases. The picture is reminiscent of, but more complex than, what is observed in such ͑simpler͒ two-phase media as a dusty gas.

A hybrid scheme to compute contact discontinuities in one-dimensional Euler systems

“…Note for instance that Tamman EOS and single component perfect gas EOS belong to the first class. It also includes EOS such as Tait EOS for solid material (see for instance [28]), since this one reads:…”

“…whereP n i is given in (28), and h stands for the mean mesh size. For given EOS in T 1 P n i =P n i , thus the choice α(h) has no influence.…”

The Riemann problem and a high-resolution Godunov method for a model of compressible two-phase flow

“…The authors observe that this degeneracy is analogous to choked flow in a duct, and provides a constraint on the admissible states for the Riemann problem. Modeling issues, certain physicallymotivated reductions and numerical solutions were presented in a series of papers by Bdzil, Kapila, Menikoff, Son and Stewart [10][11][12]. These papers built upon an analysis of a simpler approach described earlier by Bdzil and Son [13] and Asay, Son and Bdzil [14].…”

A Godunov-type method for the seven-equation model of compressible two-phase flow

“…Then, the model (and related ones, see among others Stewart & Wendroff [41], Abgrall & Saurel [37], [38]...) has gained interest for the modelling and computation of two phase flows. See for instance, in a non-exhaustive way, Kapila et al [29], Glimm et al [23], Abgrall & Saurel [37], Gavrilyuk & Saurel [22], Gallouët, Hérard & Seguin [21], Coquel, Gallouët, Hérard & Seguin [13], and more recently Ambroso, Chalons, Coquel & Galié [1], Tokareva & Toro [42], and the references therein. One of the main features of this model is to involve two distinct velocities u 1 and u 2 and two pressures p 1 and p 2 associated with the two phases.…”