Application of an Arbitrary Lagrangian Eulerian Method to Describe High Velocity Gas-Particle Flow Behavior

Novel computational and small-scale experimental investigations were performed in order to better understand the high velocity flow behavior of gas-particle mixtures. The motion of solid objects impacted by the flow of the mixtures was measured by use of high-speed digital video photography. Computations were performed by use of an arbitrary Lagrangian Eulerian (ALE) treatment in a nonlinear finite element code. Constitutive models for description of the solid component of the gas-particle blend were developed based on quasi-statically determined test results. It was observed that there was very close agreement between experimental and computational results and that it was possible to accurately predict the high velocity flow behavior of the gas-particle mixture using quasi-statically determined constitutive models. INTRODUCTION Full-scale vehicle blast tests are relatively expensive. However, computational and small-scale experimental methods can be employed to gain deeper insight into the mechanics of phenomena that involve the interactions between explosives, geomaterials, and solid bodies that are excited by such multicomponent systems. Many experimental techniques, analytical methods, and correlations for the description of blast events and for the prediction of structural response to blast inputs have been developed over the years. Baker [1] assembled an excellent review of experimental and theoretical results relating to air blast. Kinney and Graham [2] collected and compiled air blast data from various sources. Based on these data, they showed empirical formulations for the prediction of air blast phenomena. Westine et al. [3] performed tests with measurement of impulse imparted to flat plates from explosives buried in soil and, based on the results, developed an empirical correlation for the prediction of structural excitation from blasts from shallow buried explosives. It has been shown that small-scale experimental results can closely match those for full-scale tests [4-6]. Genson [7] performed small-scale blast tests on rigid aluminum plates. Various researchers have applied computational techniques for treatment of the behavior of explosive, soil, and target in mine blast situations. Laine and Sandvik [8] developed a constitutive model that has been used as the basis for definition of the behavior of sand. Szymzcak [9] applied a viscoplastic model for soil and used a generalized hydrodynamic numerical formulation in order to predict the response of flat plates to excitation from explosives buried in wet sand. It was observed that this computational approach matched experimental results very well as long as the ratio of target height above the ground to depth of burial was three or less. Grujicik et al. [10-11] have investigated the use of various soil constitutive models with incorporation of porosity effects. More recently, Deshpande et. al. [12] have proposed a novel approach to modeling the soil that takes into account various regimes of soil behavior that evolve during the course of the detonation event. Neuberger et al. [13] examined the scaling of flat plate deformation with excitation from large explosive charges flush buried in dry sand, by means of a combination of experiment and computation. The computation agreed well with experiment and was performed using an arbitrary Lagrangian-Eulerian technique with the dry sand modeled by means of a generalized Mohr-Coulomb model. Finally, Williams et al. [14] used a Lagrangian method, with soil and explosive modeled with a particle technique and soil behavior prescribed using a hybrid elastic plastic model, to predict the response of a flat target to the blast from a shallow buried explosive. Three types of soil were modeled – dry sand, a mix of clay and sand, and a wet clay – and although direct correlations to experiment were not presented, computational results followed the expected trend, viz., the impulse imparted to the target increased with decreasing soil compressibility and yield strength. In the present work, experimental results from small-scale tests performed by Fourney et. al. [15] are compared with computational investigations in order to gain deeper insight into the physics behind the excitation of rigid targets. The targets used for this work were disk-shaped, relatively rigid, aluminum targets and were excited by explosive buried in water, wet sand, or dry sand. EXPERIMENTAL PROCEDURES Figure 1 illustrates the experimental setup used by Fourney et. al. [15] to measure the response of the rigid aluminum plates to the excitation of shallow buried explosive. The 4.4 g explosive charges used for this work were constructed using Detasheet C and an RP-87 detonator. The cylindrical charges were inserted into a bed of water, wet sand, or dry sand so that their top faces were 9.9 mm below the top surface of the bed. The bottom face of the aluminum target plate was located 40.1 mm above the top surface of the bed. The plate was constructed of aluminum alloy 6061 with mass 10.05 kg and behaved essentially as a rigid body in its response to the loading from the buried explosive. Impulse on target was measured by tracking the motion of the target using high-speed video. COMPUTATIONAL PROCEDURES Often, it is considered that computations involving solid mechanics are best performed using a Lagrangian description of the problem with a computational mesh that moves with the solid material. Computations involving fluids are most often performed using an Eulerian description with a mesh that is fixed in space. As a result of the nature of the current problem, which involves coupling between fluid and solid constituents, computations were here performed using an ALE approach for the fluids coupled with a Lagrangian approach for the solid target. If a purely Lagrangian finite element approach had been used, this would have been an appropriate choice for the solid mechanics part of the problem, but mesh distortion resulting from large displacements caused by the explosive and fluid motions would have caused the calculations to become unstable. An Eulerian approach would have been a good choice of continuum treatment for the explosive and the fluid components but the accuracy of the treatment of the solid target would have been sacrificed. The ALE approach used here offers the advantages of the moving mesh for handling the transport of mass, momentum, and energy for the fluid constituents and can be easily coupled, via a penalty coupling algorithm, to the solid target, which is given a purely Lagrangian treatment. Given a moving mesh such as the one that is used for the ALE computations, the conservation equations, neglecting thermal effects, for the transport of mass, momentum, and energy, respectively, are