Stability of Chapman–Jouguet detonations for a stiffened-gas model of condensed-phase explosives

Short, Mark; Bdzil, J. B.; Anguelova, Iana I.

doi:10.1017/s0022112005008347

Cited by 13 publications

(4 citation statements)

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“…His formulation of the linear stability problem made use of a Laplace transform method to determine pointwise stability. The work of Lee and Stewart [11] solved the linearized onedimensional detonation stability problem using a normal-mode approach that has been used in virtually every subsequent study, including generalizations to two dimensions [12,13], bounded cylindrical geometry [14], multi-step reaction mechanisms [15], and non-ideal equations of state [16,17].…”

Section: Introductionmentioning

confidence: 99%

Mode selection in weakly unstable two-dimensional detonations

Taylor

Kasimov

Stewart

2009

Combustion Theory and Modelling

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A formulation of the reactive Euler equations in the shock-attached frame is used to study the two-dimensional instability of weakly unstable detonation through direct numerical simulation. The results are shown to agree with the predictions of linear stability analysis. Comparisons are made with linear perturbation growth rates and oscillation frequencies as a function of transverse disturbance wavelength. The perturbation eigenfunctions predicted by linear stability analysis are directly validated through numerical simulation. Three regimes of unstable behavior -linear, weakly nonlinear, and fully nonlinear -are explored and characterized in terms of the power spectrum of the normal shock velocity for a Chapman-Jouguet detonation with weak heat release. IntroductionNumerical simulations of detonation have been conducted by many researchers over the years. The earliest simulations of one-dimensional pulsating detonation were performed by Fickett and Wood in 1966 [1]. In 1978, Taki and Fujiwara [2] performed the first two-dimensional simulations of cellular detonation. As computational capacity has grown, simulations have been made that incorporate higher grid resolution and more detailed models. Despite the significant advances made, however, many fundamental problems remain to be investigated further. In particular, the physical nature of the detonation instability, nonlinear growth of the instability, physical mechanisms of cell formation and the nature of cell dynamics demand further elucidation theoretically as well as by means of accurate numerical simulation. Our present paper is concerned primarily with the latter.Recently, methods of simulating shocks and detonations in a reference frame attached to the shock surface have been developed [3,4]. Rather than attempting to capture the evolving shock front numerically, as in conventional simulations, these shock-attached frame methods map the shock surface to a fixed location in the computational domain and solve for the shock state as part of the numerical solution. These methods allow a sharp representation of the lead shock, avoid the numerical smearing inherent in shock capturing methods, and can be much more accurate than conventional methods of simulation. These methods are ideal for the study of detonation stability since they are posed in the same frame

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Section: Introductionmentioning

confidence: 99%

Mode selection in weakly unstable two-dimensional detonations

Taylor

Kasimov

Stewart

2009

Combustion Theory and Modelling

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“…The analysis above is valid for any equation of state (EOS) and reaction rate law. We now present results for both the ideal and stiffened condensed-phase detonation models (Short, Bdzil & Anguelova 2006;Short et al 2008), whereupon the EOS model for the internal energy, e, the specific reaction enthalpy of the HE, q(=q/ũ 2 ref )…”

Section: Equation Of State and Reaction Rate Modelsmentioning

confidence: 99%

Steady detonation propagation in thin channels with strong confinement

2020

Self Cite

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“…The material derivative D/Dt = ∂/∂t +ũ •∇, wheret is time. For the HE, we use a stiffened-gas condensed-phase detonation model (Short, Bdzil & Anguelova 2006;Short et al 2008), whereupon the equation-of-state (EOS) model for the internal energy,ẽ, the specific reaction enthalpy of the HE,q, and the frozen sound speed,c HE , are given bỹ…”

Section: Modelmentioning

confidence: 99%