Simulation Of Shock Wave Propagation Research Articles

Image-based processing simulation of shock wave propagation through the area of ionization instability

A partially automatic method of digital processing images (photographs, shadow and Schlieren pictures) for the analysis of experimental data is proposed. The method is utilized to investigate the effect of the region of ionization instability created by a glow gas discharge on the front of an initially flat shock wave. The proposed method is based on a composition of simple image processing operations and makes it possible to perform simulations taking into account the real geometry of the ionization strata and the shape of the front of a shock wave based on the obtained experimental images. First, as a result of digital processing the geometry of experimental objects is extracted from the images. This information is then embedded in the Navier-Stokes code for conducting simulations. New results for the real geometry of ionization strata of different scales are presented which confirmed the previous ones obtained for the density homogeneously stratified source model.

Molecular dynamics simulation of shock wave propagation and spall failure in single crystal copper under cylindrical impact

The shock premelting and spallation of single crystal copper under cylindrical converging impact are studied using molecular dynamics simulations. For the axis of a cylindrical potential wall along the [001] crystallographic direction, the anisotropy of shock response is very obvious at the shock strength 1.4 km s−1. Premelting occurs at the wavefront in the 〈110〉 direction, but not in the 〈100〉 direction. As a result of the converging effect, the requisite shock strength for generating premelting decreases in comparison with planar shock. Under the interaction of reflected wave and unloaded wave, the nucleation of spallation occurs in premelting tensile regions.

Molecular Dynamics Simulations of Shock Propagation and Spallation in Amorphous Polymers

Abstract We conducted large-scale molecular dynamics (MD) simulations of shock wave propagation and spallation in amorphous polyurethane and polyurea. First, we computed the shock Hugoniot of the polymers using the multiscale shock technique and compared them with available experimental data to establish the upper limit of the shock pressure that can be accurately modeled using a non-reactive interatomic force field. Subsequently, we simulated shock wave propagation in the polymers, varying the shock particle velocity from 0.125 km/s to 2 km/s. A remarkable similarity in the shock behavior of polyurethane and polyurea was observed. The spall strength of each sample was computed by two methods: (a) the indirect method (based on the free surface velocity history)—accessible in experiments and (b) a direct method (based on the atomic stresses in the region of spallation)—accessible only through MD. The results reveal that the tensile strength computed from the indirect method is consistently smaller than the value obtained from the direct method. Moreover, the strength computed from the indirect method shows a noticeable agreement with the fracture nucleation stress. Our results provide novel molecular-level insights into the spallation mechanisms of amorphous polymers, which could facilitate the design of polymers for structural barrier applications.

Three-Dimensional Cartesian Grid Method for the Simulations of Flows with Shock Waves in the Domains with Varying Boundaries

This paper is devoted to the development and quantitative evaluation of the properties of the numerical algorithm of the Cartesian grid method for three-dimensional (3D) simulation of shock-wave propagation in areas of varying shape. The detailed description of the algorithm is presented. The algorithm is relatively simple to implement and does not require solving the problem of determination of the shape of the body’s boundary intersection with regular computational cell. The accuracy of the algorithm is demonstrated by comparing the simulated and experimental data in the problems of the interaction of a shock wave (SW) with a nonmoving sphere and a moving particle.

Application of the Spectral Element Method in a Surface Ship Far-Field UNDEX Problem

The prediction of surface ship response to a far-field underwater explosion (UNDEX) requires the simulation of shock wave propagation in the fluid, cavitation, fluid-structure interaction, and structural response. Effective approaches to model the fluid include cavitating acoustic finite element (CAFE) and cavitating acoustic spectral element (CASE) methods. Although the spectral element method offers the potential for greater accuracy at lower computational cost, it also generates more spurious oscillations around discontinuities which are difficult to avoid in shock-related problems. Thus, the advantage of CASE remains unproven. In this paper, we present a 3D-partitioned FSI framework and investigate the application of CAFE and CASE to a surface ship early-time far-field UNDEX problem to determine which method has the best computational efficiency for this problem. We also associate the accuracy of the structural response with the modeling of cavitation distribution. A further contribution of this work is the examination of different nonmatching mesh information exchange schemes to demonstrate how they affect the structural response and improve the CAFE/CASE methodologies.

Influence of plasma channel impedance model on electrohydraulic shockwave simulation

The simulation of electrohydraulic shockwaves is the key technology for their application and device design. The analytical approach of underwater pulsed discharge is described using the dimensionless analysis method, which combines energy based hydrodynamic equations and the electrical differential equation describing the discharge characteristics of the circuit. A constant plasma channel impedance model based on the experimental results and an improved time-varying plasma channel impedance model based on the Braginskii equation are proposed and presented. The plasma channel impedance has a great influence on the deposited energy into the plasma channel and then affects the calculation and analysis of the shockwave propagation. The electrical characteristics and fluid physical properties are taken into consideration, and the results are compared. The application range of different impedance models is summarized, and the time-varying impedance model can provide a more accurate result in the simulation of shockwave propagation. The dimensionless analysis method, together with a time-varying impedance model, could be a useful tool for evaluation of the electrohydraulic shockwave in practical applications and applied physics research of underwater spark discharge.

Numerical simulation of shock wave propagation in 2-D channels with obstacles filled with chemically reacting gas suspensions

Modification of the serial Fortran code for solving unsteady 2-D Euler equations for the mixture of compressible gas and polydisperse particles was carried out using OpenMP technology. Modified code was verified and parallel speed-up was measured. Analysis showed that the data on parallel efficiency is in a good agreement with the Amdahls law, which gives the estimate for serial code fraction about 30%. Parallel code was used for the numerical simulation of two test-cases, namely shock wave propagation in 2-D channel with obstacles filled with reactive Al-O2 gas particle mixture and heterogeneous detonation propagation in polydisperse suspensions. For the first test-case the data on particles distribution in the flow was obtained, the existense of particle free zones inside the vortices was demonstrated and the attenuation of a shock wave was studied. In the second test, numerical simulation of detonation shock wave propagation in plain 2-D channel for the three polydisperse mixtures was carried out and data on detonation regimes was also obtained.

Numerical simulation on high speed impact behavior of Al-W and Al-Ni mixture

Multi-functional energetic structural material (MESM) is a mixture of metals, metal oxides and binders, which improves the insensitivity and maintains explosion power of the explosives. MESM during explosion reaction undergoes various changes in thermal, mechanical, and chemical characteristics caused by shock wave propagation in time scale of nanoseconds. It is hard to study impact characteristics of MESM through various experiments due to short impact reaction, high cost and safety problem. Therefore, analysis using mesoscale simulation is important in studying impact characteristics such as Hugoniot relation and pressure data. In this study, meso-scale simulations of shock wave propagation were conducted for Al, Ni, W, Al-W and Al-Ni mixture, under the conditions of impact velocities ranging from 0.5 km/s to 5 km/s. Simulation data of Al, W and Ni using Mie-Gruneisen EOS were used to confirm the accuracy of analysis, and the results correlated reasonably well with the corresponding data (Los Alamos explosive experiment). Based on this single metal simulation results, simulations for Al-W and Al-Ni mixture were performed at various volume fractions and propagation distances of shock. The results of these simulations could be useful information to predict impact characteristics of mixtures.

Numerical simulation of shock wave propagation in dry sand based on a 3D mesoscopic model

Mesoscopic modelling has been an effective approach in predicting the averaged dynamic states of dry sand under intense dynamic events, such as impact, blast and penetration. Many previous studies are limited to two-dimensional (2D) formulations due to computational cost. This paper develops a three-dimensional (3D) mesoscopic model of dry sand particulate system to get insight into a shock wave propagation under blast. The sand particle is modelled using a polyhedron with a random shape. The deformation, elastic or permanent deformation, of single particle is considered in simulation. It resolves explicitly the particle to particle contact and friction effects based on the mesoscopic model. In simulation, averaging is used to perform a macroscale analysis of the quantities and the distributions on shock variables. It simulates the shock wave propagation and the attenuation effects of dry sand particles on the peak pressure of the transmitted shock wave. The wave propagation in the dry sand is calculated and discussed numerically. The dependence of peak pressure and propagation velocity on the incident shock is presented. The variations in the dry sand configurations and the correlations to pressure are as well as discussed under shock events. Mesoscopic observation reveals that the permanent deformation and contact and friction effects are the origin of energy absorption capability. It leads to the attenuation on the shock wave.

Experimental impact cratering: A summary of the major results of the MEMIN research unit

AbstractThis paper reviews major findings of the Multidisciplinary Experimental and Modeling Impact Crater Research Network (MEMIN). MEMIN is a consortium, funded from 2009 till 2017 by the German Research Foundation, and is aimed at investigating impact cratering processes by experimental and modeling approaches. The vision of this network has been to comprehensively quantify impact processes by conducting a strictly controlled experimental campaign at the laboratory scale, together with a multidisciplinary analytical approach. Central to MEMIN has been the use of powerful two‐stage light‐gas accelerators capable of producing impact craters in the decimeter size range in solid rocks that allowed detailed spatial analyses of petrophysical, structural, and geochemical changes in target rocks and ejecta. In addition, explosive setups, membrane‐driven diamond anvil cells, as well as laser irradiation and split Hopkinson pressure bar technologies have been used to study the response of minerals and rocks to shock and dynamic loading as well as high‐temperature conditions. We used Seeberger sandstone, Taunus quartzite, Carrara marble, and Weibern tuff as major target rock types. In concert with the experiments we conducted mesoscale numerical simulations of shock wave propagation in heterogeneous rocks resolving the complex response of grains and pores to compressive, shear, and tensile loading and macroscale modeling of crater formation and fracturing. Major results comprise (1) projectile–target interaction, (2) various aspects of shock metamorphism with special focus on low shock pressures and effects of target porosity and water saturation, (3) crater morphologies and cratering efficiencies in various nonporous and porous lithologies, (4) in situ target damage, (5) ejecta dynamics, and (6) geophysical survey of experimental craters.

Simulation of shock-wave propagation in the argon plasma of a positive column discharge

The computer simulation of shock-wave propagation in the argon plasma of positive column discharge was performed. A one-dimensional model of the gas-discharge plasma is used, which comprises the continuity equations for the electron and ion plasma components and the equation of electrostatics with allowance for initial and boundary conditions. The distribution of plasma parameters in the shock wave was obtained; the effect of its intensity was evaluated. The simulation results were compared with experimental data.

Molecular Dynamics Simulations of Shock Wave Propagation through the Crystal–Melt Interface of (100)-Oriented Nitromethane

Molecular dynamics (MD) simulations were used to study shock wave passage with normal incidence through the equilibrium interface between (100)-oriented nitromethane and the melt. The simulations were performed using the fully flexible, nonreactive SRT force field (Sorescu, D. C.; Rice, B. M.; Thompson, D. L. The Journal of Physical Chemistry B 2000, 104, 8406–8419). The local kinetic energies (intermolecular, intramolecular, and total) and stress states differ significantly in the liquid and crystal regions, and depend on whether the shock is initiated in the crystal or liquid. The number and spatial distributions of shock-induced molecular disorientations in the crystal for shocks initiated in the crystal are similar to those obtained for analogous simulations for a completely crystalline sample; however, substantial differences in the extent and distribution of shock-induced molecular disorientations in the crystal region were observed when the shock was initiated in the liquid. All three measures of k...

On the determination of the mesh size for numerical simulations of shock wave propagation in near field underwater explosion

It is well known that the accuracy of mesh-based numerical simulations of underwater explosion strongly relies on the mesh size adopted in the analyses. Although a numerical analysis of underwater explosion can be performed with enough accuracy by using considerably fine meshes, such fine meshes may lead to substantially increase in the CPU time and the usage of computer memory. Thus, how to determine a suitable mesh size in numerical simulations is always a problem confronted when attempting to study the shock wave propagation resulting from underwater explosion and the subsequent response of structures. Considering that there is currently no universally accepted method for resolving this problem, this paper aims to propose a simple method to determine the mesh size for numerical simulations of near field underwater explosion. To this end, the mesh size effects on the shock wave propagation of underwater explosion are carefully investigated for different charge weights, through which the correlation between mesh sizes and charge weights is identified. Based on the numerical study, a dimensionless variable (λ), defined as the ratio of the radius of charge to the side length of element, is introduced to be the criterion for determining the mesh size in simulations. It is interesting to note that the presented method is suitable for various charge weights. By using the proposed meshing rule, adequate balance between solution accuracy and computational efficiency can be achieved for different blast scenarios in numerical simulations of underwater explosion.

Simulation of shock wave propagation in single crystal and polycrystalline aluminum

A thermoelastic–viscoplastic constitutive model has been developed to model high strain rate deformation in single crystal metals. The thermoelastic formulation employs a material Eulerian strain measure, which has recently been shown to converge more rapidly than traditional Lagrangian strain measures for material undergoing large compression. The viscoplastic formulation is based on the physics of dislocation glide and generation as well as their interaction. This model has been implemented into a one-dimensional, extended finite-difference formulation for anisotropic materials and is used to model shock wave propagation in aluminum single crystals, polycrystals, and pre-textured polycrystals for peak shock pressures ranging from 2 to 110GPa. The model was able to reproduce experimentally measured particle velocity profiles from both plate impact and laser shock experiments performed on single crystals and polycrystals. Simulations showed that the orientation distribution in vapor-deposited polycrystalline samples can affect the observed elastic precursor decay by a factor of two, as well as change the observed response in laser shock experiments from a dual to single-wave shock structure. Simulations performed on cold rolled aluminum samples showed that an increase in the cold rolling reduction caused a decrease in the number of active slip systems, as well as a decrease in the heterogeneity of total accumulated slip. Finally, a coarse-grained analytical model was developed from results of plane wave simulations and was shown to effectively reproduce plastic heterogeneity induced by single crystal orientations. Simulations in this work showed that single crystal effects play a key role in dictating the macroscopically observed response, which suggests high strain rate experiments that omit detailed initial microstructural characterization do not provide sufficient information for complete mechanistic understanding or model validation.

Simulation of shock wave propagation in a duct with a side branch

Experimental studies conducted during the 70s and 80s of the previous century are numerically simulated. We examine a horizontal duct with a vertical branch having a circular cross section whose diameter is 5 cm. These experiments were conducted by the late Dr Heilig in the Ernst-Mach-Institute (private communication). In both segments of the branched duct pressure transducers were installed. They were used for recording the pressure histories and for deducing the traveling shock wave speed. These results were compared with the present numerical simulation. The numerical simulations were conducted using the commercial code Fluent with the density-based AUSM solver. The solver is second order in both space and time. It is apparent from the results obtained that good agreement exists between the recorded pressure histories and their simulations. Based on the good agreement between recorded and simulated pressures a numerical study was conducted by comparison between two similar branched ducts, one having a circular cross section while the other has a rectangular cross section. Also, the effect that changes in the branched segment orientation have on the resulting flow field were investigated.

Modeling the effect of orientation on the shock response of a damageable composite material

A carbon fiber-epoxy composite (CFEC) shock response in the through thickness orientation and in one of the fiber directions is significantly different. The hydrostatic pressure inside anisotropic materials depends on deviatoric strain components as well as volumetric strain. Non-linear effects, such as shock effects, can be incorporated through the volumetric straining in the material. Thus, a new basis is required to couple the anisotropic material stiffness and strength with anisotropic shock effects, associated energy dependence, and damage softening process. This article presents these constitutive equations for shock wave modeling of a damageable carbon fiber-epoxy composite. Modeling the effect of fiber orientation on the shock response of a CFEC has been performed using a generalized decomposition of the stress tensor [A. A. Lukyanov, Int. J. Plast. 24, 140 (2008)] and Mie-Grüneisen's extrapolation of high-pressure shock Hugoniot states to other thermodynamics states for shocked CFEC materials. The three-wave structure (non-linear anisotropic, fracture, and isotropic elastic waves) that accompanies damage softening process is also proposed in this work for describing CFEC behavior under shock loading which allows to remove any discontinuities observed in the linear case for relation between shock velocities and particle velocities [A. A. Lukyanov, Eur. Phys. J. B 74, 35 (2010)]. Different Hugoniot stress levels are obtained when the material is impacted in different directions; their good agreement with the experiment demonstrates that the anisotropic equation of state, strength, and damage model are adequate for the simulation of shock wave propagation within damageable CFEC material. Remarkably, in the through thickness orientation, the material behaves similar to a simple polymer whereas in the fiber direction, the proposed in this paper model explains an initial ramp, before at sufficiently high stresses, and a much faster rising shock above it. The numerical results for shock wave modeling using proposed constitutive equations are presented, discussed, and future studies are outlined.

Mesoscale simulation of shock wave propagation in discrete Ni/Al powder mixtures

A numerical model is developed to simulate shock wave propagation in discrete Ni/Al powder mixtures. The model is used to investigate the particle-level deformation, heating, and mixing of two distinct Ni/Al powders, as mixing intensity dictates whether or not shock ignition is achieved in these reactive material systems. The main innovations of this work are (1) use of a rate-dependent, dislocation-based model of particle flow stress in the shock simulations and (2) quantitative analysis of the Ni/Al interfaces that are formed during wave propagation. An experimental powder, which is composed of micron-scale spherical Ni and Al particles, is simulated to validate the numerical model. An additional powder, composed of smaller particles, is simulated to investigate the effects of particle size on constituent deformation and mixing under shock wave loading. The simulations indicate that a reduction in particle size leads to increased Ni/Al interface temperature and dislocation density, as well as increased stress-sensitivity of Ni/Al interface formation. Finally, it is shown that accounting for the rate-dependence of particle flow stress likely yields improved accuracy in predicted flow morphologies, especially at intermediate stress wave amplitudes.

Two-fluid simulations of shock wave propagation and shock-bubble interaction in collisionless plasma

The propagation of collisionless shock waves and the influence of the space-charge field on the development of fluid instabilities induced by a collisionless shock wave are investigated by solving the two-fluid plasma equations numerically in two space-dimensions. A second-order accurate Riemann solver is employed to sharply capture the shock wave and contact discontinuity. First, a series of shock-tube problems is solved to verify the method. The shock structure similar to that obtained in a previous particle-in-cell (PIC) simulation is reproduced. However, it is found that the shock wave propagates at speeds higher than the PIC results for high initial density ratios at the shock tube diaphragm. Second, the interactions between a collisionless shock wave of Mach number 1.6 and an isolated cylindrical bubble of Atwood number 0.81 are investigated. It is found that in addition to the well-known Richtmyer-Meshkov instability, filamentary fluid-instability is induced at the bubble interface introducing turbulence in the region ahead of the shock wave.

Initiation of detonation in a tube with a profiled central body

Numerical simulation of shock wave propagation in a tube with a central body proved the possibility of significant facilitation of the deflagrationtodetona� tion transition in a methane-air mixture. It was shown that the central body should meet some requirements: it should block approximately 60% of the tube cross section, and should have a parabolic forebody profile with an angle of attack of ~40° and a parabolic or ellip� tic afterbody profile with an angle of convergence of no more than 7°. In this case, detonation can be initi� ated by a shock wave with a Mach number of 3.5 over a length of ~0.5 m for a time of ~0.2 ms.

Elastic anisotropy of shocked aluminum single crystals: Use of molecular dynamics simulations

Molecular dynamics (MD) calculations were used to examine shock wave propagation along [100], [111], and [110] directions in aluminum single crystals. Four different embedded-atom method (EAM) potentials were used to obtain wave profiles in ideal (defect-free) crystals shocked to peak longitudinal stresses approaching 13 GPa. Due to the lack of defects in the simulated crystals, the peak stresses considered, and the short time scales examined, inelastic deformation was not observed in the MD simulations. Time-averaged and spatially averaged continuum variables were determined from the MD simulations to compare results from different potentials and to provide a direct comparison with results from nonlinear elastic continuum calculations that incorporated elastic constants up to fourth order. These comparisons provide a basis for selecting the optimal potential from among the four potentials examined. MD results for shocks along the [100] direction show significant differences for stresses and densities determined from simulations using different EAM potentials. In contrast, the continuum variables for shocks along the [111] and [110] directions show smaller differences for three of the four potentials examined. Comparisons with the continuum calculations show that the potential developed recently by Winey, Kubota, and Gupta [Modell. Simul. Mater. Sci. Eng. 17, 055004 (2009)] provides the best overall agreement between the MD simulations and the continuum calculations. As such, this potential is recommended for MD simulations of shock wave propagation in aluminum single crystals. Extending the current findings to elastic-plastic deformation would be desirable. More generally, our work demonstrates that MD simulations of elastic shock waves in defect-free single crystals, in combination with nonlinear elastic continuum calculations, constitute an important step in establishing the applicability of classical MD potentials for simulations involving dynamic compression.