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Final technical report for 1993

Description: This report contains hand-written equations on the following topics: multi-phase equations in one dimension; the solid equation of state; asymptotic reduction of two-phase DDT models; characteristic analysis of the reduced models; compaction-wave computations with Prasad`s code; the six-equation equivelocity model; and the six-equation equivelocity model scaling.
Date: July 1, 1996
Creator: Kapila, A.K.
Partner: UNT Libraries Government Documents Department

Dynamic compaction of granular materials in a tube with wall friction, applied to deflagration-to-detonation transition

Description: A theoretical problem is considered in which a granular material is pushed through a tube of arbitrary cross-section by a constant velocity piston against the resistance of compaction work and wall friction. The crushing of the material is dictated by a simple yet physically reasonable compaction law. By considering two special cases - the limit of vanishing friction and the quasistatic limit - we identify the two basic compaction wave structures. We then consider the general case in which the two waves interact. Estimates suggest that for typical deflagration-to-detonation tests explosive at the wall melts on time scales short compared to the experiment.
Date: September 1, 1995
Creator: Hill, L.G. & Kapila, A.K.
Partner: UNT Libraries Government Documents Department

A Study of Detonation Diffraction in the Ignition-and-Growth Model

Description: Heterogeneous high-energy explosives are morphologically, mechanically and chemically complex. As such, their ab-initio modeling, in which well-characterized phenomena at the scale of the microstructure lead to a rationally homogenized description at the scale of observation, is a subject of active research but not yet a reality. An alternative approach is to construct phenomenological models, in which forms of constitutive behavior are postulated with an eye on the perceived picture of the micro-scale phenomena, and which are strongly linked to experimental calibration. Most prominent among these is the ignition-and-growth model conceived by Lee and Tarver. The model treats the explosive as a homogeneous mixture of two distinct constituents, the unreacted explosive and the products of reaction. To each constituent is assigned an equation of state, and a single reaction-rate law is prescribed for the conversion of the explosive to products. It is assumed that the two constituents are always in pressure and temperature equilibrium. The purpose of this paper is to investigate in detail the behavior of the model in situations where a detonation turns a corner and undergoes diffraction. A set of parameters appropriate for the explosive LX-17 is selected. The model is first examined analytically for steady, planar, 1-D solutions and the reaction-zone structure of Chapman-Jouguet detonations is determined. A computational study of two classes of problems is then undertaken. The first class corresponds to planar, 1-D initiation by an impact, and the second to corner turning and diffraction in planar and axisymmetric geometries. The 1-D initiation, although interesting in its own right, is utilized here as a means for interpretation of the 2-D results. It is found that there are two generic ways in which 1-D detonations are initiated in the model, and that these scenarios play a part in the post-diffraction evolution as well. For the parameter ...
Date: April 14, 2006
Creator: Kapila, A K; Schwendeman, D W; Bdzil, J B & Henshaw, W D
Partner: UNT Libraries Government Documents Department

A High-Resolution Godunov Method for Compressible Multi-Material Flow on Overlapping Grids

Description: A numerical method is described for inviscid, compressible, multi-material flow in two space dimensions. The flow is governed by the multi-material Euler equations with a general mixture equation of state. Composite overlapping grids are used to handle complex flow geometry and block-structured adaptive mesh refinement (AMR) is used to locally increase grid resolution near shocks and material interfaces. The discretization of the governing equations is based on a high-resolution Godunov method, but includes an energy correction designed to suppress numerical errors that develop near a material interface for standard, conservative shock-capturing schemes. The energy correction is constructed based on a uniform pressure-velocity flow and is significant only near the captured interface. A variety of two-material flows are presented to verify the accuracy of the numerical approach and to illustrate its use. These flows assume an equation of state for the mixture based on Jones-Wilkins-Lee (JWL) forms for the components. This equation of state includes a mixture of ideal gases as a special case. Flow problems considered include unsteady one-dimensional shock-interface collision, steady interaction of an planar interface and an oblique shock, planar shock interaction with a collection of gas-filled cylindrical inhomogeneities, and the impulsive motion of the two-component mixture in a rigid cylindrical vessel.
Date: February 13, 2006
Creator: Banks, J W; Schwendeman, D W; Kapila, A K & Henshaw, W D
Partner: UNT Libraries Government Documents Department