TY - JOUR

T1 - Asymptotic theory of evolution and failure of self-sustained detonations

AU - Kasimov, Aslan R.

AU - Stewart, D. Scott

PY - 2005/2/25

Y1 - 2005/2/25

N2 - Based on a general theory of detonation waves with an embedded sonic locus that we have previously developed, we carry out asymptotic analysis of weakly curved slowly varying detonation waves and show that the theory predicts the phenomenon of detonation ignition and failure. The analysis is not restricted to near Chapman-Jouguet detonation speeds and is capable of predicting quasi-steady, normal detonation shock speed versus curvature (D-κ) curves with multiple turning points. An evolution equation that retains the shock acceleration, Ḋ, namely a Ḋ-D-κ relation is rationally derived which describes the dynamics of pre-existing detonation waves. The solutions of the equation for spherical detonation are shown to reproduce the ignition/failure phenomenon observed in both numerical simulations of blast wave initiation and in experiments. A single-step chemical reaction described by one progress variable is employed, but the kinetics is sufficiently general and is not restricted to Arrhenius form, although most specific calculations are performed for Arrhenius kinetics. As an example, we calculate critical energies of direct initiation for hydrogen-oxygen mixtures and find close agreement with available experimental data.

AB - Based on a general theory of detonation waves with an embedded sonic locus that we have previously developed, we carry out asymptotic analysis of weakly curved slowly varying detonation waves and show that the theory predicts the phenomenon of detonation ignition and failure. The analysis is not restricted to near Chapman-Jouguet detonation speeds and is capable of predicting quasi-steady, normal detonation shock speed versus curvature (D-κ) curves with multiple turning points. An evolution equation that retains the shock acceleration, Ḋ, namely a Ḋ-D-κ relation is rationally derived which describes the dynamics of pre-existing detonation waves. The solutions of the equation for spherical detonation are shown to reproduce the ignition/failure phenomenon observed in both numerical simulations of blast wave initiation and in experiments. A single-step chemical reaction described by one progress variable is employed, but the kinetics is sufficiently general and is not restricted to Arrhenius form, although most specific calculations are performed for Arrhenius kinetics. As an example, we calculate critical energies of direct initiation for hydrogen-oxygen mixtures and find close agreement with available experimental data.

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U2 - 10.1017/S0022112004002599

DO - 10.1017/S0022112004002599

M3 - Article

AN - SCOPUS:14844282760

SN - 0022-1120

VL - 525

SP - 161

EP - 192

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

ER -