Stability of detonations for an idealized condensed-phase model

Abstract

The stability of travelling wave Chapman–Jouguet and moderately overdriven detonations of Zeldovich–von Neumann–Döring type is formulated for a general system that incorporates the idealized gas and condensed-phase (liquid or solid) detonation models. The general model consists of a two-component mixture with a one-step irreversible reaction between reactant and product. The reaction rate has both temperature and pressure sensitivities and has a variable reaction order. The idealized condensed-phase model assumes a pressure-sensitive reaction rate, a constant-γ caloric equation of state for an ideal fluid, with the isentropic derivative γ=3, and invokes the strong shock limit. A linear stability analysis of the steady, planar, ZND detonation wave for the general model is conducted using a normal-mode approach. An asymptotic analysis of the eigenmode structure at the end of the reaction zone is conducted, and spatial boundedness (closure) conditions formally derived, whose precise form depends on the magnitude of the detonation overdrive and reaction order. A scaling analysis of the transonic flow region for Chapman–Jouguet detonations is also studied to illustrate the validity of the linearization for Chapman–Jouguet detonations. Neutral stability boundaries are calculated for the idealized condensed-phase model for one- and two-dimensional perturbations. Comparisons of the growth rates and frequencies predicted by the normal-mode analysis for an unstable detonation are made with a numerical solution of the reactive Euler equations. The numerical calculations are conducted using a new, high-order algorithm that employs a shock-fitting strategy, an approach that has significant advantages over standard shock-capturing methods for calculating unstable detonations. For the idealized condensed-phase model, nonlinear numerical solutions are also obtained to study the long-time behaviour of one- and two-dimensional unstable Chapman–Jouguet ZND waves.

A streamline approach to two-dimensional steady non-ideal detonation: the straight streamline approximation

“…In this article, we employ the standard condensed phase explosive model [14][15][16][17][18][19], consisting of a polytropic equation of state,…”

“…This model is frequently used as the foundation for development and validation of detonation theories and for providing fundamental insights [14][15][16][17][18], which are the points of interest here.…”

A study of detonation propagation and diffraction with compliant confinement

“…Such rate laws are then be fit to experimental data for a given material. Furthermore, the stability properties and the reaction-zone structure of steady planar detonations for the rate law in (12) are known and understood [23,25]. The second rate law considered here is the one used in the IG model [1,2,3].…”

“…A small value for n is chosen so that a steady planar CJ detonation is stable and the value for ν is chosen so that the reaction zone has a finite length [23,25]. The explosive in regions 1 and 2 is at rest initially with…”

Numerical simulation of detonation structures using a thermodynamically consistent and fully conservative reactive flow model for multi-component computations

“…Near the boundary, the pulsations are regular and harmonic, but become nonlinear and chaotic further away from the boundary. Richer nonlinear dynamics have also been recently observed through numerical simulations when more complex chemical kinetic mechanisms or other equations of state for condensed phase detonations are considered (Gorchkov et al 2007;Short et al 2008). A formal normal-mode linear stability analysis of planar detonations with arbitrary equations of state, such as the consideration of multi-component fluid mixtures with temperature-dependent thermo-chemical properties, has recently been formulated by Gorchkov et al (2007).…”