It is of great importance for fields such as implosion dynamics and fusion research to understand the dynamics of ejecta transport in converging gases. In this paper, the evolution of particulate flow within a cylindrically imploding system is investigated experimentally and numerically. The ejecta particles are emitted from the inner surface of a roughened Sn liner into vacuum, He and Ar gases. Dynamic images of liner implosion and ejecta transport are obtained with X-ray radiographs and multi-frame optical schlieren images. The transport of ejecta particles is simulated with a four-way coupled multiphase flow model, including modelling of gas-particle coupling and inter-particle collisions. Results reveal that the ejecta transport in shock-induced converging gases differs significantly from that in planar systems, primarily due to features such as interaction with the rebounding gas shock wave and continuous compression by the imploding liner. After being generated from the inner surface, the ejecta width undergoes an 'expansion-compression' variation. According to mechanisms governing ejecta-gas coupling, three distinct stages of ejecta evolution are identified: (i) post-shock transport dominated by drag and particle breakup; (ii) shock-particle interaction leading to quick reduction in particle size and rapid deceleration of the ejecta front; and (iii) dense ejecta compression governed by inter-particle collisions. Leveraging particle motion and size predictions at the ejecta front, combined with the self-similar converging shock solution, a theoretical model is established to estimate the three-stage evolution of ejecta width in a cylindrically converging system.

Photon Doppler velocimetry (PDV) for high-speed particles has gained significant attention due to its non-contact real-time diagnostic advantage and wide range of applications. This study establishes a theoretical framework linking PDV spectra to optical thickness distributions in high-speed particle fields. Through powder impact experiments with known particle states and Monte Carlo light transport simulations, we demonstrate that PDV spectral distributions are governed by particle optical thickness. The proposed model incorporates multiple scattering effects, resolving spectral underestimation issues in prior Simple Diffusion Model. A direct inversion method enables optical thickness retrieval via spectral intensity integration, validated against Asay foil diagnostics with ±30% error for time-averaged spectra and -58% to +42% error for instantaneous spectra. Compared to conventional fitting strategies exhibiting higher uncertainty (-40% to +322% error) and failure on instantaneous spectra, the inversion method shows superior robustness. The framework advances real-time diagnostics for high-speed particle scenarios including impact damage, spray combustion, space debris monitoring, and extreme ultraviolet lithography.

The effects of initial conditions on the mixing layer in two-dimensional multimode stratified compressible Rayleigh–Taylor instability (RTI) are investigated through direct numerical simulations with five wave amplitudes (10−2 to 10−6) and five wave numbers (1–30 to 121–150) at a high Atwood number of 0.9. In contrast to the quadratic growth observed in incompressible RTI, the bubble mixing layer in stratified compressible RTI exhibits additional growth due to the mean flow induced by compressibility. The growth width hb, caused by both the mean and fluctuating flows, is sensitive to the initial conditions. The growth width, induced by the fluctuating flow, remains in quadratic growth and exhibits a strong dependence on the initial amplitude and wave number. The bubble growth width, induced by the mean flow, is sensitive to both the initial amplitude and the flow compressibility, and can be rescaled by its total width hb. The bubble growth width, induced by the mean flow, is sensitive to long-wave perturbations but not to short-wave perturbations. Furthermore, the mixing characteristics, including mixedness, mixed mass, and normalized mixing mass, are also analyzed under different initial conditions.

Experimental study on the instability at a V-shaped interface accelerated by a strong shock wave with a Mach number exceeding 3.0 is performed in a shock-tube facility. To highlight the effect of initial amplitude on flow evolution, five V-shaped interfaces with various initial amplitudes are considered. Several interface evolution features differing significantly from those under weak shock conditions are observed, such as the secondary vortices on the spike stem and reverse jets at the spike root. For the linear evolution period, existing models exhibit limited predictive capability because they cannot effectively describe the strong flow compressibility and the intricate coupling between interface-geometry, shock-proximity, and secondary-compression effects. To overcome this limitation, we propose a modified model that combines a compressible linear theory to cover strong compressibility and a reduction factor to describe the coupling of the three effects. This model is applicable under both weak and strong shock conditions. In the nonlinear period, the amplitude evolution law is positively correlated with the initial amplitude due to the enhanced Mach-reflection effect under higher initial-amplitude conditions. None of the nonlinear models is effective under all initial-amplitude conditions, as they fail to account for the coupling influences of the Mach-reflection effect, geometric effect, shock-proximity effect, secondary-compression effect, and Kelvin-Helmholtz instability on nonlinear evolution. To bridge this gap, we propose parametrizing the composite mechanism through correction factors explicitly expressed as functions of initial amplitude and Mach number and develop an empirical nonlinear model that achieves favorable predictive performance across a broad range of initial-amplitude conditions.

Shock-tube experiments are conducted to investigate the Atwood-number dependence of hydrodynamic instability induced by a strong shock with a Mach number exceeding 3.0. The compressible linear theory performs reliably under varying compressibility conditions. In contrast, the impulsive model significantly loses predictive accuracy at high shock intensities and Atwood numbers ( $A_t$ ), particularly when specific heat ratio differences across the interface are pronounced. To address this limitation, we propose a modified impulsive model that offers favourable predictions over a wide range of compressibility conditions while retaining practical simplicity. In the nonlinear regime, increasing $A_t$ enhances both the shock-proximity and secondary-compression effects, which suppress bubble growth at early and late stages, respectively. Meanwhile, spike growth is promoted by the spike-acceleration and shock-proximity mechanisms. Several models reproduce spike growth across a wide range of $A_t$ , whether physical or incidental. In contrast, no models reliably describe bubble evolution under all $A_t$ conditions, primarily due to neglecting compressibility effects that persist into the nonlinear regime. Building on these insights, we develop an empirical model that effectively captures bubble evolution over a wide $A_t$ range. Modal evolution is further shown to be strongly affected by compressibility-induced variations in interface morphology. The effect is particularly pronounced at moderate to high $A_t$ , where it suppresses the fundamental mode growth while promoting higher-order harmonic generation.

The interaction between shock waves and multiple cylinders, referred to as shock-cylinder interaction (SCI), is an important phenomenon in science and engineering. However, its underlying physical mechanisms remain unclear. This study entailed the numerical simulation of the aerobreakup of two tandem water columns subjected to a high-speed gas flow by using an adaptive mesh refinement (AMR)-based diffusion-interface model. The objective was to elucidate the changes in water-column deformation patterns over a wide range of Weber numbers. Statistical analysis was performed to examine the deformation of the water columns in vertical directions. Results reveal distinct deformation patterns between the two columns as the Weber number increases. Additionally, an extended exponential stretching law model was devised, and its improved capability to predict the deformation patterns was demonstrated.

In this study, we investigate high-accuracy three-dimensional surface detection in smoothed particle hydrodynamics for free-surface flows. A new geometrical method is first developed to enhance the accuracy of free-surface particle detection in complex flows. This method detects free-surface particles via continuous global scanning inside the sphere of a particle through a cone region whose vertex corresponds to the particle position. The particle is identified as a free-surface particle if there exists a cone region with no neighboring particles. Next, an efficient semi-geometrical method is proposed based on the geometrical method to reduce the computational cost. It consists of finding particles near the free surface via position divergence and then accurately detecting these particles using the geometrical method to identify free-surface particles. The accuracy and robustness of the proposed method are demonstrated by performing tests on several model problems. In particular, the test demonstrating the surface detection of the free surface with periodic perturbations shows that the detection accuracy of the proposed method is improved compared with the traditional methods because the detection capability for concave surfaces is enhanced and the detection accuracy is independent of the estimation of the normal vector of particles.

This paper analyzes the oxidation law of metal particles and proposes a new oxidation reaction rate model, based on measurements of thermogravimetric-mass spectrometer (TG-MS), X-ray diffractometer (XRD) and scanning electron microscope (SEM). The model is named EBM (egg broken model) with a formula of exponential law. According to the model, the aluminum particles do not react in a spherical shape, but crack and the melted metal inside flows out to form a new nonspherical surface and the reaction rate is still determined by the surface area. The model is verified with heating rates of 5°C/min, 10°C/min and 25°C/min, and with particle size of 1–2 µm, 8–9 µm and 20–22 µm. Many models are based on spherical hypothesis and the new model gives a different physical illustration to explain oxidation progress of metal particles. The new model gives an exponential law, which fits the experimental data well, and it may be useful to understand oxidation mechanism of metal particles.

This paper presents an Eulerian diffuse-interface method using a high-order compact difference scheme for simulating elastic-plastic flows with the Mie-Gru center dot neisen (MG) equation of state (EoS). For simulations of multimaterial problems, numerical errors were generated in the material discontinuities owing to inconsistent treatment of the convective terms. Based on the normal-stress-based mechanical equilibrium assumption for elastic-plastic solids, we introduce an improved form of the consistent localized artificial diffusivity (LAD) method to ensure an oscillation-free interface for velocity and normal stress. The proposed algorithm uses a hyperelastic model. A mixture type of the model system was formed by combining the conservation equations for the basic conserved variables, an equation of a unified deviatoric tensor describing solid deformation, and an additional set of equations for solving the material quantities in the MG EoS. Several one-and two-dimensional problems with various discontinuities, including the elastic-plastic Richtmyer-Meshkov instability, were considered for testing the proposed method.

When a shock wave impacts a roughened metal/gas interface, metal ejecta particles emit and transport in the gas. The exchanges of momentum and energy between ejecta particles and the gas occur. If active metal particles transport in the reactive gas, the heat released by a chemical reaction could change these exchanges. In this paper, we use numerical simulations to study solid cerium ejecta transporting in a vacuum, and in non-reactive and reactive gases. In vacuum, the emitted ejecta could self-similarly expand neglecting the particle interaction. In the non-reactive gas (He), ejecta particles slow down by the gas resistance and have the exchanges of momentum and energy with the gas. In the reactive gas ( D-2), the ejecta particles also slow down. The exothermic reaction could induce the temperature rise of the ejecta and the gas, which could induce changes in physical property values of the gas after the shock wave and the velocity of the shock wave. The numerical result shows that the maximum temperature of the ejecta may appear in the middle of the mixture zone, which may result from the ejecta temperature being controlled by two competitive effects. Furthermore, the maximum ejecta temperature increases rapidly in the beginning and then becomes steady. Finally, the ejecta with a different initial size distribution is investigated. The ejecta with a smaller maximum size has a larger maximum particle temperature, a larger gas temperature after the shock wave, and a larger chemical reaction function of the ejecta at the same moment.

This work studied the rheological properties and magnetorheological (MR) mechanism of dry magnetorheological fluid (MRF) under various working modes. A novel simulation method combining the discrete element method and computational fluid dynamics was developed, in which the bilateral coupling between particles and the flow field of the matrix (air) was considered. The microstructures and mechanical properties in the redispersion process, shear mode, and valve mode were systematically simulated for the first time. The results indicated that dry MRF presented superior redispersion property and response time (several μs) than liquid-based MRFs. In shear mode, the magnetic dipolar force and friction force dominated the evolution of microstructures. In valve mode, the magnetic dipolar force and viscous drag force of air became the main interactions. Magnetic particles aggregated into sturdy chain structures and hindered the airflow. The MR effect in valve mode was the pressure gradient of the matrix, which increased up to 1.08 × 105 Pa m−1 with the increasing particle volume fractions and decreased under a large inflow velocity. The best MR effect in valve mode was achieved under a magnetic field of B = 63 mT. Simulations revealed the influence of dimensionless Mn and Re number on the MR effect. The pressure gradient of the matrix was controlled by the external field and can be utilized to design a dry MRF valve for precious and transient vibration control. Simulated dimensionless shear stress in shear mode agreed well with experiments. This work will promote the development and applications of novel high-performance MRFs.

In this paper, a novel high-order numerical method is proposed for the simulation of compressible multimaterial solid–fluid problems involving elastic–plastic solid behaviors. The solid, liquid, and gas behaviors are described by an Eulerian interface-capturing model derived from hyperelasticity theory. The deformations in each component of the solids are tracked using a single deviatoric strain tensor. The numerical algorithm employs a tenth-order compact finite difference scheme and a fourth-order Runge–Kutta time-stepping scheme. To prevent numerical oscillations near the material interface, a mechanical equilibrium assumption is introduced for the elastic–plastic problems, and a localized artificial diffusivity method satisfying this assumption is designed and applied in the numerical algorithm. Numerical tests in one and two dimensions are shown to demonstrate the accuracy and feasibility of the proposed approach. In particular, the accuracy and numerical resolution of the method are verified using problems with analytical solutions. Numerical tests of interface advection problems demonstrate that our method preserves the velocity, pressure, and elastic stress equilibria at the material interface and prevents overshoots in the rest of the domain. The two-dimensional Richtmyer–Meshkov instabilities between two elastic or two elastic–plastic solids are simulated to verify the suitability of the numerical method for solving problems involving large deformations. Impact of a 2D Taylor bar to a rigid wall is also simulated to test the robustness of the numerical method.

The photon Doppler velocimetry (PDV) spectrum is investigated in an attempt to reveal the particle parameters of ejecta from shock-loaded samples in a vacuum. A GPU-accelerated Monte–Carlo algorithm, which considers the multiple-scattering effects of light, is applied to reconstruct the light field of the ejecta and simulate the corresponding PDV spectrum. The influence of the velocity profile, total area mass, and particle size of the ejecta on the simulated spectra is discussed qualitatively. To facilitate a quantitative discussion, a novel theoretical optical model is proposed in which the single-scattering assumption is applied. With this model, the relationships between the particle parameters of ejecta and the peak information of the PDV spectrum are derived, enabling direct extraction of the particle parameters from the PDV spectrum. The values of the ejecta parameters estimated from the experimental spectrum are in good agreement with those measured by a piezoelectric probe.

Linear stability analysis is a useful tool for the exploration of the initial evolution of flow motions in mixing layers. A real fluid mixing layer exhibits strong property variations and, thus, may present stability behaviors distinct from its ideal gas counterpart. The present study carries out spatial and temporal stability analyses of nitrogen mixing layers at supercritical conditions, with special attention to the density stratification induced by the temperature and velocity gradients across the mixing layer. The differences between the ideal gas and real fluid approaches are discussed. The maximum spatial growth rate and the most unstable frequency evaluated based on the real fluid density profile are found to be substantially lower than their ideal gas counterparts near the critical point, where an inflection of the density distribution occurs in the mixing layer. Across the inflection point, the strong density stratification arising from the real fluid effect tends to stabilize the mixing layer. The maximum growth rate and the most unstable frequency do not show a monotonic trend with the ratios of temperature and density. In the absence of the inflection point, however, the mixing layer is destabilized and features a substantially higher maximum spatial growth rate at lower ratios of density and temperature. The most unstable frequency and the maximum spatial growth rate increase with increasing pressure. The real fluid effect diminishes when the pressure is away from the critical value or when there is no inflection point in the density profile. The temporal stability analysis also indicates that a detailed density distribution plays a key role in dictating the stability characteristics of mixing layers at supercritical pressures.

Ejecta of micrometer-sized particles from a shocked damaged metal surface into a gas environment are widely observed in the engineering fields. Investigating the transport of ejecta particles in the converging geometries is a challenging scientific issue. Rousculp et al. [“Damaged surface hydrodynamics (DSH) flash report,” Report No. LA-UR-15-22889, 2015] have studied the transport of shock-launched tungsten powders from a cylindrical metal surface into an inert gas. In the so-called damaged surface hydrodynamic experiments, the effect of gas species on powder transport was investigated. Distinctive phenomena were observed in all cases in which particles aggregated into radial spikes or stripes with an azimuthal modulation of n > 20, though the initial powder coating was highly controlled and the shock loading was believed to be azimuthally uniform. In this work, discrete element method coupling with magneto-hydrodynamic simulations was employed to explore the mechanism behind the experimental phenomena. Results showed that stripes may be originated from the non-uniform initial distribution and small velocity difference of particles. The intense particle collision during the shock launching caused the microstripe-like structures, which merged into macroscopic ones observed in the subsequent particle transport process. Lagrange tracking revealed the stripes at different moments consisted of different particles. Oblique collisions played an important role in the long-term transport of ejecta particles in the convergence geometries, while the drag force of gas showed little influence. This work will promote the understanding of dense particle–gas flow in converging geometries.

When the surface tension force acts on the multi-layer particles near the free surface, the integral of the previous surface delta function through the free surface is less than 1 because of the boundary truncation and kernel truncation, which leads to the problem that the numerical results cannot converge to the theoretical solution. Although a few studies have recognized this problem, it has not been completely solved. In the present work, a new formulation of the continuum surface force (CSF) model in smoothed particle hydrodynamics (SPH) is developed for free-surface flows, in which two measures are taken to correct the shortcomings of the commonly used formulations. In the first measure, a new surface delta function that meets the normalization requirement is proposed to solve the problem that the integral of the previous surface delta function through the free surface is less than 1 when the surface tension force acts on the multi-layer particles near the free surface. This normalization measure is key to make the numerical results with surface tension converge to the theoretical solution. In the second measure, the normal vector and curvature of the free surface are derived by the finite particle method (FPM) to improve their calculation accuracy. Through the one-dimensional tests, the new surface delta function is analyzed and compared with existing formulations. Through the two-dimensional tests on a unit circle, the new normal vector and curvature of the particles near the free surface are implemented and also compared with previous formulations. Finally, the proposed formulation is validated using eight two-dimensional and three-dimensional numerical cases with surface tension. The results show that the proposed formulation solves the problem that the numerical results of the previous formulation cannot converge to the theoretical solution, and it is accurate and robust in calculating the free-surface flows with surface tension. (C) 2021 Elsevier Inc. All rights reserved.

Droplet impingement is a widespread phenomenon in nature and industrial production. Different from the problem of light drop/wall impact, which has been investigated early and sufficiently, few researches are found on the dynamic behavior and modeling of heavy drop impingement, which is widely existed in the field of plasma spray, 3D printing and ejecta mixing caused by detonation, etc. In this paper, the behavior of different metal drops impinging on dry smooth wall is studied based on Smoothed Particle Hydrodynamics (SPH) method. A newly splash threshold is proposed for heavy drop impact, and the difference of splash criteria between light drop and heavy drop is analyzed. The results show that incident kinetic energy is an important factor to determine the outcomes of heavy droplet impact. When the incident kinetic energy is relatively low, the metal droplet would spread, and the maximum spreading radius increases with the increase of kinetic energy. With higher incident kinetic energy, the droplet would splash, and the proportion of secondary droplets increases with the increase of incident kinetic energy. Higher droplet viscosity will hinder its spreading, but when splash occurs, it will promote the increase of secondary droplet. The increase of surface tension would suppress droplet spreading rate, but it has little effect on the maximum spreading radius. The splash criteria of heavy droplet impinging on dry smooth wall is proposed as K=Oh⋅Re1.5346=3341.95. The splash threshold of heavy droplet is higher than that of light droplet within the range of Re < 4000, owing to the higher surface tension of heavy droplet. When Re > 4000, the outcomes of light droplet impact show strong randomness, thus no uniform splash threshold can be found, while the metal droplet has a uniform splash threshold within the range of Re <100000.

Multiple steady solutions and hysteresis phenomenon in the square cavity flows driven by the surface with antisymmetric velocity profile are investigated by numerical simulation and bifurcation analysis. A high order spectral element method with the matrix-free pseudo-arclength technique is used for the steady-state solution and numerical continuation. The complex flow patterns beyond the symmetry-breaking at Re ≃ 320 are presented by a bifurcation diagram for Re < 2500. The results of stable symmetric and asymmetric solutions are consistent with those reported in literature, and a new unstable asymmetric branch is obtained besides the stable branches. A novel hysteresis phenomenon is observed in the range of 2208 < Re < 2262, where two pairs of stable and two pairs of unstable asymmetric steady solutions beyond the stable symmetric state coexist. The vortices near the sidewall appear when the Reynolds number increases, which correspond to the bifurcation of topology structure, but not the bifurcation of Navier–Stokes equations. The hysteresis is proposed to be the result of the combined mechanisms of the competition and coalescence of secondary vortices.

The early-time dynamics of Rayleigh-Taylor instability with a premixed density gradient layer was investigated by three-dimensional implicit large eddy simulation. Compared with the classic Rayleigh-Taylor instability, it was found that the mixing layer undergoes an inactive stage when the mixing width of the layer is nearly unchanged. The development of hydrodynamic instability with a premixed layer was studied. Energy transfer and vortex generation at the early time show that span-wise vortices predominate at this stage. Afterwards, initial conditions including the parameters of initial perturbations and the mixing width of premixed layer were investigated in detail. In our study, it was found that the amplitude of initial perturbations and the width of premixed layer are important for determining the characteristic time scale of the inactive stage while the wave number has less effect. The influence of initial conditions on the early-time dynamics of mixing layer was also analysed.

A high order unstructured spectral element method with a domain decomposition Stokes solver is presented for the hydrodynamic instability and bifurcation analysis. A Jacobian-Free Inexact-Newton-Krylov algorithm with a Stokes time-stepping preconditioning technique is introduced for the steady-state solution of incompressible flow. A matrix-free arc-length approach with Householder transformation is used for the numerical continuation near a turning point. An Arnoldi method is utilized to calculate the leading eigenvalues and their corresponding eigenvectors for the big system of linearized incompressible Navier-Stokes equations, which are responsible for initiating the hydrodynamic instability. The new method can do the steady and unsteady simulations in the similar way without time-splitting divergence error, it do not form the Jacobian matrix, which can reduce the memory allocation, decrease the computation cost, and speed up the convergence rate. The symmetric-breaking Hopf and Pitchfork bifurcations are considered in the flow passed a circular cylinder between two parallel plates. An antisymmetric sinusoidal velocity driven cavity problem is considered and the stable and unstable patterns are analyzed by checking the leading eigenvalues of their steady states. Besides the stable patterns of steady symmetric and steady asymmetric solutions a pound new pair of unsteady asymmetric solutions are found depending on the different initial conditions.