Strong Blast Waves in Spherical, Cylindrical, and Plane Shocks

Jones, Donald L.

doi:10.1063/1.1706468

Cited by 19 publications

(5 citation statements)

References 3 publications

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“…An approximate, analytical solution to this problem for the case where the delay time and discreteness are both taken to the limit of zero begins with the similarity solution for the planar version of the well-known point-blast problem of Taylor and Sedov [25], which was inspired by the heuristic model of a detonation cell developed by Vasiliev & Nikolaev [64] via a construction based upon the point-source blast wave solution. In this current model, the motion of the shock front x s is given by the following non-dimensionalized equation,…”

Section: A Heuristic Modelmentioning

confidence: 99%

Effect of spatial discretization of energy on detonation wave propagation

Timofeev

Higgins

2017

J. Fluid Mech.

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Detonation propagation in the limit of highly spatially discretized energy sources is investigated. The model of this problem begins with a medium consisting of a calorically perfect gas with a prescribed energy release per unit mass. The energy release is collected into sheet-like sources that are now embedded in an inert gas that fills the spaces between them. The release of energy in the first sheet results in a planar blast wave that propagates to the next source, which is triggered after a prescribed delay, generating a new blast, and so forth. The resulting wave dynamics as the front passes through hundreds of such sources is computationally simulated by numerically solving the governing one-dimensional Euler equations in the lab-fixed reference frame. Two different solvers are used: one with a fixed uniform grid and the other using an unstructured, adaptively refined grid enabling the limit of highly concentrated, spatially discrete sources to be examined. The two different solvers generate consistent results, agreeing within the accuracy of the measured wave speeds. The average wave speed for each simulation is measured once the wave propagation has reached a quasi-periodic solution. The effect of source delay time, source energy density, specific heat ratio, and the spatial discreteness of the sources on the wave speed is studied. Sources fixed in the lab reference frame versus sources that convect with the flow are compared as well. The average wave speed is compared to the ideal Chapman-Jouguet (CJ) speed of the equivalent homogenized media. Velocities in excess of the CJ speed are found as the sources are made increasingly discrete, with the deviation above CJ being as great as 15%. The deviation above the CJ value increases with decreasing values of specific heat ratio γ. The total energy release, delay time, and whether the sources remain lab-fixed or are convected with the flow do not have a significant influence on the deviation of the average wave speed away from CJ. A simple, ad hoc analytic model is proposed to treat the case of zero delay time (i.e., source energy released at the shock front) that exhibits qualitative agreement with the computational solutions and may explain why the deviation from CJ increases with decreasing γ. When the sources are sufficiently spread out so as to make the energy release of the media nearly continuous, the classic CJ solution is obtained for the average wave speed. Such continuous waves can also be shown to have a time-averaged structure consistent with the classical ZND structure of a detonation. In the limit of highly discrete sources, temporal averaging of the wave structure shows that the effective sonic surface does not correspond to an equilibrium state. The average state of the flow leaving the wave in this case does eventually reach the equilibrium Hugoniot, but only after the effective sonic surface has been crossed. Thus, the super-CJ waves observed in the limit of highly discretized sources can be understood as weak detonations due to the...

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Section: A Heuristic Modelmentioning

confidence: 99%

Effect of spatial discretization of energy on detonation wave propagation

Timofeev

Higgins

2017

J. Fluid Mech.

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“…Assuming that the original energy release is transformed into kinetic energy, which, within a constant, is the characteristic length normally used for nondimensionalization in the literature [39,40]. Following a computational study, Jones [41] finds…”

Section: Kernel Growthmentioning

confidence: 99%

Spark ignition of propane-air mixtures near the minimum ignition energy: Part II. A model development

Arpacı

Anderson

1991

Combustion and Flame

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A model is developed to simulate the kernel growth observed in the exprimental study of Part I. Kernel growth, described as a two-step process, initially involves a blast wave over a negligible short time followed by a diffusive growth with an electrical input power. The diffusive growth is formulated by an integral approach involving temperature dependent overall reaction kinetics and electrode heat loss. The model predicts the kernel growth mbly well with the measured spark power input. It predicts both ignition and nonignition kernel growth. The existence of a critical radius is also demonstrated. In addition, dimensional analyses are given to clarify the physical aspects of the critical radius and the characteristic radius of the blast wave. k/p.CpV,) Lewis number (= k/pCpDA) gas flow Mach number (u/c

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“…To that end, Janovsky et al [7] used methane and air as the tested materials to analyze the velocity and the impact on walls whose thicknesses were 14 and 29 cm thick. Mixed air has also been adopted in many experiments [8][9][10]. Xing et al [11] revealed complex influences of goaf from different cave in areas on the velocity and pressure of the air shock waves in different mining faces.…”

Section: Introductionmentioning

confidence: 99%