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Numerical anomalies mimicking physical effects

Description: Numerical simulations of flows with shock waves typically use finite-difference shock-capturing algorithms. These algorithms give a shock a numerical width in order to generate the entropy increase that must occur across a shock wave. For algorithms in conservation form, steady-state shock waves are insensitive to the numerical dissipation because of the Hugoniot jump conditions. However, localized numerical errors occur when shock waves interact. Examples are the ``excess wall heating`` in the Noh problem (shock reflected from rigid wall), errors when a shock impacts a material interface or an abrupt change in mesh spacing, and the start-up error from initializing a shock as a discontinuity. This class of anomalies can be explained by the entropy generation that occurs in the transient flow when a shock profile is formed or changed. The entropy error is localized spatially but under mesh refinement does not decrease in magnitude. Similar effects have been observed in shock tube experiments with partly dispersed shock waves. In this case, the shock has a physical width due to a relaxation process. An entropy anomaly from a transient shock interaction is inherent in the structure of the conservation equations for fluid flow. The anomaly can be expected to occur whenever heat conduction can be neglected and a shock wave has a non-zero width, whether the width is physical or numerical. Thus, the numerical anomaly from an artificial shock width mimics a real physical effect.
Date: September 1, 1995
Creator: Menikoff, R.
Partner: UNT Libraries Government Documents Department

MESO-SCALE SIMULATIONS OF COMPACTION WAVES IN A GRANULAR BED

Description: A granular bed provides an extreme example of a heterogeneous material. Behind a moderate strength wave, the shock compression in a granular material is due to squeezing out pore space rather than an increase in the density of individual grains. This type of shock is known as a compaction wave. The key properties of compaction waves are displayed in mesomechanics simulations--continuum mechanics calculations in which individual grains are resolved. Fluctuations in hydrodynamic quantities occur behind the wave front due to stress concentrations at the contact between grains exceeding the yield strength and leading to localized plastic flow. Nevertheless, average wave profiles have the appearance of a dispersed shock wave, and for the most part the fluid mechanics equations, with the addition of a porosity variable, can be used as a homogenized model to describe the behavior of a granular bed. However, some aspects of the wave structure are not accounted for by the homogenized model. These include dispersion of weak waves and an elastic precursor for intermediate strength waves.
Date: May 1, 2001
Creator: MENIKOFF, R.
Partner: UNT Libraries Government Documents Department

COMPACTION WAVE PROFILES IN GRANULAR HMX

Description: Meso-scale simulations of a compaction wave in a granular bed of HMX have been performed. The grains are fully resolved in order that the change in porosity across the wave front is determined by the elastic-plastic response of the grains rather than an empirical law for the porosity as a function of pressure. Numerical wave profiles of the pressure and velocity are compared with data from a gas gun experiment. The experiment used an initial porosity of 36%, and the wave had a pressure comparable to the yield strength of the grains. The profiles are measured at the front and back of the granular bed. The transit time for the wave to travel between the gauges together with the Hugoniot jump conditions determines the porosity behind the wave front. In the simulations the porosity is determined by the yield strength and stress concentrations at the contact between grains. The value of the yield strength needed to match the experiment is discussed. Analysis of the impedance match of the wave at the back gauge indicates that the compaction wave triggers a small amount of burn, less than 1% mass fraction, on the micro-second time scale of the experiment.
Date: June 1, 2001
Creator: MENIKOFF, R.
Partner: UNT Libraries Government Documents Department

Anomalous physical effects from artificial numerical length scales

Description: Shock capturing algorithms are widely used for simulations of compressible fluid flow. Though these algorithms resolve a shock wave within a couple of grid points, the artificial length scale from the numerical shock profile can have side effects. The side effects are similar to physical effects that occur when a relaxation process gives rise to fully or partly dispersed shock waves. Two anomalies due to a non-zero shock width are discussed: (1) in one-dimension, a non-decaying entropy spike results from a transient when a shock profile is formed or changed; (2) in multi-dimensions, front curvature affects the propagation of a shock wave. The authors show that both the entropy anomaly and the curvature effect are a natural consequence of the conservation laws. The same analysis applies both to the continuum equations and to their finite difference approximations in conservation form. Consequently, the artificial length scale inherent in a shock capturing algorithm can mimic real physical effects that are associated with partly dispersed shock waves.
Date: September 1, 1995
Creator: Menikoff, R. & Lackner, K.S.
Partner: UNT Libraries Government Documents Department

EQUATION OF STATE AND HUGONIOT LOCUS FOR POROUS MATERIALS: P-ALPHA MODEL REVISITED

Description: Foams, porous solids and granular materials have a characteristic Hugoniot locus that for weak shocks is concave in the (particle velocity, shock velocity)-plane. An equation of state (EOS) that has this property can be constructed implicitly from a Helmholtz free energy of the form {Psi}{sub s}(V,T,{phi}) = {Psi}{sub s}(V,T)+B({phi}) where the equilibrium volume fraction {phi}{sub eq} is determined by minimizing {Psi}, i.e., the condition {partial_derivative}{sub {psi}} {Psi} = 0. For many cases, a Hayes EOS for the pure solid {Psi}{sub s}(V,T) is adequate. This provides a thermodynamically consistent framework for the P-{alpha} model. For this form of EOS the volume fraction has a similar effect to an endothermic reaction in that the partial Hugoniot loci with fixed {psi} are shifted to the left in the (V,P)-plane with increasing f. The equilibrium volume fraction can then be chosen to match the concavity of the principal Hugoniot locus. An example is presented for the polymer estane. A small porosity of only 1.4 percent is required to match the experimental concavity in the Hugoniot data. This type of EOS can also be used to obtain the so-called ''universal'' Hugoniot for liquids.
Date: August 1, 1999
Creator: MENIKOFF, R. & AL, ET
Partner: UNT Libraries Government Documents Department

Modeling energy dissipation induced by quasi-static compaction of granular HMX

Description: A simple extension of a conventional two-phase (inert gas and reactive solid) continuum model of Deflagration-to-Detonation Transition (DDT) in energetic granular material is given to account for energy dissipation induced by quasi-static compaction. To this end, the conventional model equations,, valid in the limit of negligible gas phase effects, are supplemented by a relaxation equation governing irreversible changes in solid volume fraction due to intergranular friction, plastic deformation of granules, and granule fracture. The proposed model constitutes a non-strictly hyperbolic system of equations, and is consistent with the Second Law of Thermodynamics for a two-phase mixture. The model predicts stress relaxation and substantial dissipation induced by quasi-static compaction; such phenomena are commonly observed in quasi-static compaction experiments for granular HMX. Predicted intergranular stress histories compare well with experimental data.
Date: November 1, 1997
Creator: Gonthier, K.A.; Menikoff, R.; Son, S.F. & Asay, B.W.
Partner: UNT Libraries Government Documents Department

Modeling compaction-induced energy dissipation of granular HMX

Description: A thermodynamically consistent model is developed for the compaction of granular solids. The model is an extension of the single phase limit of two-phase continuum models used to describe Deflagration-to-Detonation Transition (DDT) experiments. The focus is on the energetics and dissipation of the compaction process. Changes in volume fraction are partitioned into reversible and irreversible components. Unlike conventional DDT models, the model is applicable from the quasi-static to dynamic compaction regimes for elastic, plastic, or brittle materials. When applied to the compaction of granular HMX (a brittle material), the model predicts results commensurate with experiments including stress relaxation, hysteresis, and energy dissipation. The model provides a suitable starting point for the development of thermal energy localization sub-scale models based on compaction-induced dissipation.
Date: December 31, 1998
Creator: Gonthier, K.A.; Menikoff, R.; Son, S.F. & Asay, B.W.
Partner: UNT Libraries Government Documents Department

Compaction Waves in Granular HMX

Description: Piston driven compaction waves in granular HMX are simulated with a two-dimensional continuum mechanics code in which individual grains are resolved. The constitutive properties of the grains are modeled with a hydrostatic pressure and a simple elastic-plastic model for the shear stress. Parameters are chosen to correspond to inert HMX. For a tightly packed random grain distribution (with initial porosity of 19%) we varied the piston velocity to obtain weak partly compacted waves and stronger fully compacted waves. The average stress and wave speed are compatible with the porous Hugoniot locus for uni- axial strain. However, the heterogeneities give rise to stress concentrations, which lead to localized plastic flow. For weak waves, plastic deformation is the dominant dissipative mechanism and leads to dispersed waves that spread out in time. In addition to dispersion, the granular heterogeneities give rise to subgrain spatial variation in the thermodynamic variables. The peaks in the temperature fluctuations, known as hot spots, are in the range such that they are the critical factor for initiation sensitivity.
Date: January 1, 1999
Creator: Kober, E. & Menikoff, R.
Partner: UNT Libraries Government Documents Department