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Comparison of the temporal evolution of granular temperature in our 0D simulation with the analytic result by Haff et al. 54

Comparison of the temporal evolution of granular temperature in our 0D simulation with the analytic result by Haff et al. 54

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Article
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Even though the interaction of blast waves with dense particle distributions is ubiquitous in nature and in industry, the underlying physics of the multiphase system evolution is not clearly understood. A canonical multiphase system composed of an embedded monodisperse distribution of spherical particles in a spherical, high-energy gaseous charge i...

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... density of particles in the system. The relaxation time τ is defined as the time taken by the system of monodisperse particles of constant coefficient of restitution e n ¼ 0:8 to reach a quarter of its initial granular temperature. The temporal evolution of the system granular temperature obtained from our inelastic-DSMC simulation (shown in Fig. 2) is in good agreement with Eq. (10). The system evolves by dissipating particle kinetic energy through inelastic binary collisions and with increasing time we can see that more particles approach zero velocities in the simulation indicating homogeneous cooling as shown in Fig. 3. Journal of Applied Physics ARTICLE ...
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... incoming flows with Reynolds number 100. The flow is considered to be directed in the positive Z direction (see Fig. 5). The force experienced by each particle in the particle cloud is computed by numerically integrating the panel-wise forces corresponding to each particle. First, the forces in the lateral direction (X and Y) are considered in Fig. 20. For both the distributions, the lateral forces are equitably distributed about zero on the X-axis. Hence, as mentioned in Sec. III, the net effect of lateral forces on the distribution is negligible. Figure 21 shows the distribution of drag force (Z-direction) for the two volume fractions. The force distributions are normalized with ...

Citations

... The aforementioned macroscale gas-particle coupling that is equivalent to the coupling between the central gases and the continuum encasing shell occurs on the inner surface of shell, although the solid stresses inside the particle shell arises from the inter-grain contacts (Saurel et al. 2010;Black, Denissen & McFarland 2018;Marayikkottu & Levin 2021). The explosive dispersal of the continuum shell is predominantly governed by the macroscale coupling. ...
Article
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Explosive dispersal of granular media widely occurs in nature across various length scales, enabling engineering applications ranging from commercial or military explosive systems to the loss prevention industry. However, the correlation between the explosive dispersal behaviour and the structure of dispersal system is far from completely understood, thereby compromising the prediction of the explosive dispersal outcome resulting from a specific dispersal system. Here, we investigate the dispersal behaviours of densely packed particle rings driven by the enclosed pressurized gases using coarse-grained computational fluid dynamics–discrete parcel method. Distinct dispersal modes emerge from the dispersal systems with vastly varying sets of the macro- and micro-scale structural parameters in terms of the dispersal completeness and the spatial uniformity of the dispersed mass. Further investigation reveals the variation in the dispersal modes arises from the collective effects of multiscale gas–particle coupling relationships. Specifically, the macroscale coupling dictates the cyclic momentum/energy transfer between gases and particle ring as an entirety. The mesoscale coupling relates to the inter-pore gas filtration through the thickness of the particle ring, leading to the mass/energy reduction of the explosive source. The microscale coupling involves the individual particle dynamics influenced by the local flow parameters. A persistent macroscale coupling results in an incomplete dispersal which takes the form of an aggregated annular band, whereas the meso- and micro-scale couplings alter the macroscale coupling to a different extent. By incorporating the effects of the variety of structural parameters on the multiscale gas–particle coupling relationships, a non-dimensional parameter referred to as the modified mass ratio is constructed, which shows an explicit correlation with the dispersal mode. We proceed to establish a dispersal ring model in the continuum frame which accounts for the macro and meso-scale coupling effects. This model proves to be capable of successfully predicting the ideal and validated failed dispersal modes.
... To further enhance the capabilities of the EL code, inelastic DSMC collision modules were incorporated into the solver. This allowed the study of the evolution of a particle-laden blast wave (PLBW) system, where the e ects of inter-particulate collisions and aerodynamic interactions on the particle front were analyzed [19]. It was found that in the early stages of PLBW evolution, aerodynamic interactions tended to accelerate the particle front, while inter-particulate collisions had a decelerating e ect. ...
... The current work discusses the implementation of a two-way coupled Eulerian-Lagrangian framework using the original FLASH research code framework [13,18,19] to study compressible gas-particle multiphase flows. The Lagrangian solver considered forces such as the quasi-steady drag, pressure-gradient, added-mass, thermophoretic, gravitational, Sa man, and Magnus forces. ...
... The lift (q) and drag (p) parameters were used in a non-linear Mach number based correction factor to the Loth's [20] model for a spherical monomer to approximately model the mobility of these small fractal aggregates in the parametric space. The model was shown to be useful in large length-scale Eulerian-Lagrangian [18,19] simulations to study the transport of such particulates of complicated geometries in convoluted, complex flow regimes. The model was used to study the evolution of these particulates in a simple, canonical Rankine-vortex in a one-way coupled fashion. ...
... These interactions determine the evolution of ash dust clouds in the case of volcanic eruptions. 2,3 Such interactions are also possible in high-altitude high-speed flights, [4][5][6] and reentry flights, 4,7 dust explosions, 8,9 and plume surface interactions for inter-planetary explorations. [10][11][12] Furthermore, theoretical and numerical studies in this regime have recently gained interest with respect to explosion safety and mitigation efforts. ...
... The current work discusses the implementation of a two-way coupled Eulerian-Lagrangian framework using the original FLASH research code framework 8,19,48 to study compressible gas-particle multiphase flows. The Lagrangian solver considered forces such as the quasi-steady drag, pressure-gradient, added-mass, thermophoretic, gravitational, Saffman, and Magnus forces. ...
Article
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Although particle–laden electrostatic discharges are widely used in laboratories as well as in industrial applications, the mechanism of particle lifting for particles initially at rest in such highly unsteady systems is not well understood. A multiphase gas–particle solver is developed using the multiphase particle-in-cell (MP-PIC) approach to emulate the interaction of a compressible shock-dominated gas phase with the dense particle phase. First, the two-way coupled solver is initially used to study the interaction of a planar traveling shock with a vertical curtain of particulates. The gas and particle phase evolution was found to be in good agreement with a similar experimental study in Ling et al. [Phys. Fluids 24, 113301 (2012)]. Second, the MP-PIC code is used to study the interaction of an expanding blast wave with a thick bed of particles. The simulation considered forces such as quasi-steady drag, pressure-gradient, added-mass, Saffman, and Magnus forces. We observe that the vertical liftoff particles close to the shock impingement point in this configuration are associated with the quasi-steady drag, pressure gradient, and added-mass forces. Also, the Saffman lift and Magnus forces contribute to lifting particles located radially farther away from the shock impingement point. In addition, the study finds a decrease in particle lifting efficiency with decreasing plasma kernel length and shock strength.
... These interactions determine the evolution of ash dust clouds in the case of volcanic eruptions [4,5]. Such interactions are also possible in high-altitude high-speed flights [6], and re-entry flights [7,8], dust explosions [9,10], and plume surface interactions for inter-planetary explorations [11]. Theoretical and numerical studies in this regime are gaining interest in recent times with respect to explosion safety, and mitigation efforts [12]. ...
... The current work discusses the implementation of a two-way coupled Eulerian-Lagrangian framework using the original FLASH research code framework [1,9,21] to study compressible gas-particle multiphase flows. Inter-particle collisions are implemented using the empirical model by Harris et al. [2]. ...
Conference Paper
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For multiphase flows with dense particulate distributions, the effect of momentum and energy back coupling with the underlying gas flow and inter-particle interaction is significant. In the present work, we present our preliminary work towards developing a two-way coupled solver on the original framework of the FLASH code. Particle force models that are compatible with the underlying compressible gas flow are used in the solver. Inter-particle collisions are implemented using the empirical model by Harris et al. The developed code is used to study the canonical case of a planar shock interacting with a particle curtain. The temporal evolution of the considered force terms is discussed in detail. The evolution of gas/particle phase features is compared to the experimental results given in Ling et al.
... (4)], the viscous stress [Eq. (5)], the heat flux [Eq. (6)], and Sutherland's law [Eq. ...
Article
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Unsteady drag, unsteady lift and movement of one or two moving particles caused by the passage of a planar shock wave are investigated using particle-resolved simulations of viscous flows. The particle motion analysis is carried out based on particle-resolved simulations for one or two particles under a shock Mach number of 1.22 and a particle Reynolds number of 49, and the particle migration and fluid forces are investigated. The unsteady drag, unsteady lift, and particle behavior are investigated for different densities and particle configurations. The time evolution of the unsteady drag and lift is changed by interference by the planar shock wave, Mach stem convergence and the shock wave reflected from the other particle. They two particles become closer after the shock wave passes than in the initial state under most conditions. Two particles placed in an in-line arrangement approach most closely to each other due to the passage of a shock wave. On the other hand, two particles placed in a side-by-side arrangement are only slightly closer to each other after the shock wave passes between them. The pressure waves resulting from Mach stem convergence of the upstream particle and the reflected shock waves from the downstream particle are the main factors responsible for the force in the direction that pushes the particles apart. The wide distance between the two particles attenuates these pressure waves, and the particles reduce their motion away from each other.
... Mathematical models used to describe two-phase gas-particle mixtures can be divided into two classes. The first class of mathematical models is used to describe flows in which the volume concentration of particles c is high, c > 5% [3]. When calculating such two-phase flows, it is necessary to take into account collisions between particles [3][4][5]. ...
... The first class of mathematical models is used to describe flows in which the volume concentration of particles c is high, c > 5% [3]. When calculating such two-phase flows, it is necessary to take into account collisions between particles [3][4][5]. This is achieved by introducing the collision integral into the kinetic equation for particles [3,4]. ...
... When calculating such two-phase flows, it is necessary to take into account collisions between particles [3][4][5]. This is achieved by introducing the collision integral into the kinetic equation for particles [3,4]. In addition, when calculating the drag force acting on a particle, the constraint phenomena become significant [6]. ...
Article
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A simplified 2D model for calculating two-phase gas–particle flows in a slot space has been developed. The model can be used for fast calculation and estimation of supersonic-flow parameters in the slot space. Using this model, a numerical simulation of the flow in two-phase gas–particle supersonic jets exhausting into a submerged slot space bounded by two parallel disks was performed. The presence of particles led to the splitting of the gas jet into an internal two-phase jet and an external gas jet. In the present study, we investigated the structure of a two-phase jet as dependent on the spacing between the disks for conditions of cold spraying. A new effect was found in the flow at a small spacing between the disks (of the order of 0.2 mm) and a high-velocity internal two-phase gas–particle jet was formed. The distribution of the concentration of particles in the particle jet proved to be essentially non-uniform, with a caustic formed at the upper jet boundary.
... The laser beam is focused to a spot 29,30 via a convex lens (f ¼ 150 mm), at the center of an acrylic chamber, as shown in Fig. 1(a). Toepler's lens-type schlieren method 25,31 is applied for measuring the characteristics of the shockwave and ensuing vortex. We use a heliumneon (He-Ne) laser (22.5 mW at 632.8 nm) as the light source and a high-speed camera (Phantom V2640) for imaging. ...
Article
Focusing a laser beam to a spot within a particle-laden air flow can cause laser-induced breakdown, which generates a spherically expanding shockwave and ensuing hot gas vortex (HGV). This can cause an initially uniform spatial distribution of static particles to be scattered non-homogeneously, creating a particle void region (or cavity). High-speed schlieren imaging has been applied to investigate the propagation of this shockwave and deformation of the HGV. Evolution of the particle distribution has been captured by a high-speed camera. It has been found that the cavity evolves over three temporal phases: expansion, distortion, and separation. The cavity is first created as the shockwave expels the particles in the radial direction. Next, the cavity is distorted by the HGV and then separates into smaller cavities before finally disappearing due to mixing from the HGV. The temporal and spatial characteristics of the cavity and the mechanism by which it changes in each phase are discussed. Experiments were conducted at three different breakdown energies of 15, 49, and 103 mJ. Propagation speed of the shockwave and the size and strength of the HGV are found to be the main factors controlling this phenomenon.
... where F , F , F , F , and F ℎ are the drag [10], Saffman [11], collisional [12], Magnus [13], and thermophoretic [14] forces, respectively. Note that these forces are modeled using available surrogate models in the literature. ...
... The particle front (PF) identified by the farthest particle from the explosion core lags behind the MS due to the higher inertia associated with the particles as compared to the gas. For more details on this study, the reader is directed to Ref. [12]. ...
Conference Paper
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Two approaches for numerically modeling shock-dominated gas-particle multiphase flowsare introduced. The micron-scale simulations using the Direct Simulation Monte Carlo(DSMC) method were found to be efficient in developing mobility parameters for compli-cated particulate geometries and aerodynamically interacting particulate systems. For largelength scale systems, the Eulerian-Lagrangian approach is a viable technique to emulate theevolution of gas-particle multiphase systems with complex shocks. Relevant case studies andpreliminary results are provided for the two methods.
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In the study of gas-particulate multiphase systems, the flow of high-speed gas through a distribution of solid particulates is of utmost importance. While these aerodynamically interacting systems have been extensively studied for low-speed gas flows in the gas continuum regime, less attention has been given to high-speed systems where non-continuum effects are significant due to the high flow gradients. To address this, the flow of rarefied gas through an aerodynamically interacting monodisperse spherical particle system is studied using the Direct Simulation Monte Carlo (DSMC) gas-kinetic approach. Since the method provides the best resolution of shocks at supersonic Mach numbers it is used to classify the weak separated shocks and strong collective shocks in these systems based on particle spacing in a two-particulate system at different orientation angles. The study used the two-particle system to help analyze more complex particle distributions of volume fractions, 1%, 5%, and 15%, exposed to gas flows in the slip and transitional gas regime for a free-stream Mach number range of 0.2 < 𝑀𝑎∞ < 2.0. We observe that the weak separated shocks in the 1% distribution allow a higher degree of gas penetration and shock-particle interactions or ‘‘hypersonic-surfing ’’, exposing a major fraction of the particulates to higher force magnitudes. In contrast, the strong collective shock in the 5% and 15% distributions only generates high particulate forces on the flow-facing particles. Finally, a simple stochastic model is proposed for use in large-scale Eulerian–Lagrangian simulations that captures the non-monotonic behavior of average drag and force variability generated by the complicated gas particulate interactions in the compressible gas regime.
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Although the mobility or transport parameters, such as lift drag and pitching moments for regular-shaped particulates, are widely studied, the mobility of irregular fractal-like aggregates generated by the aggregation of monomers is not well understood. These particulates which are ubiquitous in nature, and industries have very different transport mechanisms as compared to their spherical counterpart. A high-fidelity direct simulation Monte Carlo (DSMC) study of two fractal aggregates of different shapes or dimensions is undertaken in the slip and transitional gas regime to understand the underlying mechanism of gas-particle momentum transfer that manifests as the orientation-averaged mobility parameters of the particulates. The study specifically focuses on the viscous contribution of these parameters and develops a non-linear correlation for drag and lift parameters p and q obtained from DSMC by normalizing the axial and lateral forces. The drag parameter p predicted a monotonic increase in fractal particulate drag with respect to a spherical monomer while the lift parameter q shows an initial increasing trend but a decreasing tendency toward the high Mach number or high compressibility regime. The approximate model that captures the compressibility and rarefaction effects of the fractal mobility is used to study the evolution of these particulates in a canonical Rankine vortex to illustrate the wide disparity in the trajectories of the fractal aggregate vs a spherical geometry approximation generally found in the literature.