Shock-Induced Multiphase Instability in a High Volume Fraction Finite-Thickness Particle Layer

2021 ◽  
Author(s):  
Bertrand Rollin ◽  
Frederick Ouellet ◽  
Bradford Durant ◽  
Rahul Babu Koneru ◽  
S. Balachandar
Keyword(s):  
Shock Tube ◽  
Volume Fraction ◽  
Solid Phase ◽  
Particle Volume Fraction ◽  
Finite Thickness ◽  
Spherical Particles ◽  
Shock Strength ◽  
Particle Volume ◽  
Particle Cloud ◽  
Particle Layer

Abstract We study the interaction of a planar air shock with a perturbed, monodispersed, particle curtain using point-particle simulations. In this Eulerian-Lagrangian approach, equations of motion are solved to track the position, momentum, and energy of the computational particles while the carrier fluid flow is computed in the Eulerian frame of reference. In contrast with many Shock-Driven Multiphase Instability (SDMI) studies, we investigate a configuration with an initially high particle volume fraction, which produces a strongly two-way coupled flow in the early moments following the shock-solid phase interaction. In the present study, the curtain is about 4 mm in thickness and has a peak volume fraction of about 26%. It is composed of spherical particles of d = 115μm in diameter and a density of 2500 kg.m−3, thus replicating glass particles commonly used in multiphase shock tube experiments or multiphase explosive experiments. We characterize both the evolution of the perturbed particle curtain and the gas initially trapped inside the particle curtain in our planar three-dimensional numerical shock tube. Control parameters such as the shock strength, the particle curtain perturbation wavelength and particle volume fraction peak-to-trough amplitude are varied to quantify their influence on the evolution of the particle cloud and the initially trapped gas. We also analyze the vortical motion in the flow field. Our results indicate that the shock strength is the primary contributor to the cloud particle width. Also, a classic Richtmyer-Meshkov instability mixes the gas initially trapped in the particle curtain and the surrounding gas. Finally, we observe that the particle cloud contribute to the formation of longitudinal vortices in the downstream flow.

Computer Simulation Model for Spherical Particle Filled Composite Materials

2011 ◽  
Vol 474-476 ◽  
pp. 7-10 ◽  
Author(s):  
Zhuo Chen ◽  
Zhi Xiong Huang ◽  
Ming Zhang ◽  
Min Xian Shi ◽  
Yan Qin ◽  
...  
Keyword(s):  
Computer Simulation ◽  
Composite Materials ◽  
Simulation Model ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Spherical Particles ◽  
Computer Simulation Model ◽  
Particle Volume ◽  
Minimal Sphere ◽  
Center Density

This paper introduced a computer simulation model for composite materials which was reinforced by spherical particles. We introduced its algorithm and visualize the model with different particle volume fraction. In order to evaluate the uniformity of the particle distribution, we estimated Particle Center Density and standard deviation of minimal sphere distance.

Effects of Particle Concentration on the Partitioning of Suspensions at Small Divergent Bifurcations

1996 ◽  
Vol 118 (3) ◽  
pp. 287-294 ◽  
Author(s):  
R. Ditchfield ◽  
W. L. Olbricht
Keyword(s):  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Particle Diameter ◽  
Circular Cross Section ◽  
Experimental Results ◽  
Hydrodynamic Interactions ◽  
Spherical Particles ◽  
Straight Tube ◽  
Particle Volume ◽  
Reynolds Number Flow

Experimental results are reported for the low Reynolds number flow of a suspension of spherical particles through a divergent capillary bifurcation consisting of a straight tube of circular cross-section that splits to form two tubes of equal diameter. The partitioning of particles between the downstream branches of the bifurcation is measured as a function of the partitioning of total volume (particles + suspending fluid) between the branches. Two bifurcation geometries are examined: a symmetric Y-shaped bifurcation and a nonsymmetric T-shaped bifurcation. This experiment focuses on the role of hydrodynamic interactions between particles on the partitioning of particles at the bifurcation. The particle diameter, made dimensionless with respect to the diameter of the branch tubes, ranges from 0.4 to 0.8. Results show that hydrodynamic interactions among the particles are significant at the bifurcation, even for conditions where interactions are unimportant in the straight branches away from the bifurcation. As a result of hydrodynamic interactions among particles at the bifurcation, the partitioning of particles between the branches is affected for particle volume fractions as small as 2 percent. The experimental results show that the effect of particle volume fraction is to diminish the inhomogeneity of particle partitioning at the bifurcation. However, the magnitude of this effect depends strongly on the overall shape of the bifurcation geometry, and, in particular on the angles between the branches.

Radiative Transfer With Dependent Scattering by Particles: Part 1—Theoretical Investigation

1986 ◽  
Vol 108 (3) ◽  
pp. 608-613 ◽  
Author(s):  
J. D. Cartigny ◽  
Y. Yamada ◽  
C. L. Tien
Keyword(s):  
Radiative Transfer ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Spherical Particles ◽  
Sphere Model ◽  
Radiation Scattering ◽  
Particle Volume ◽  
Scattering Approximation ◽  
Regime Map ◽  
Packed Sphere

Dependent radiation scattering for which the independent scattering theory fails to predict the scattering properties is important in analyzing radiative transfer in packed and fluidized beds. In this paper the dependent scattering properties have been derived assuming the Rayleigh–Debye scattering approximation for two cases: two identical spheres and a cloud of spherical particles. The two-sphere calculated results compare well with the exact solutions in the literature, giving confidence in the present analytical approach. The gas model and packed-sphere model have been employed to calculate dependent scattering properties for a cloud of particles of small and large particle volume fraction, respectively. The calculated dependent scattering efficiencies for a cloud of particles are smaller than the independent scattering efficiencies and decrease with increasing particle volume fraction. A regime map for independent and dependent scattering has been constructed and compared with existing empirical criteria.

scholarly journals Rheology of mobile sediment beds in laminar shear flow: effects of creep and polydispersity

2021 ◽  
Vol 932 ◽  
Author(s):  
Christoph Rettinger ◽  
Sebastian Eibl ◽  
Ulrich Rüde ◽  
Bernhard Vowinckel
Keyword(s):  
Friction Coefficient ◽  
Shear Flow ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Rheological Behaviour ◽  
Spherical Particles ◽  
Particle Volume ◽  
Two Phase ◽  
Transport Modelling ◽  
Static State

Classical scaling relationships for rheological quantities such as the $\mu (J)$ -rheology have become increasingly popular for closures of two-phase flow modelling. However, these frameworks have been derived for monodisperse particles. We aim to extend these considerations to sediment transport modelling by using a more realistic sediment composition. We investigate the rheological behaviour of sheared sediment beds composed of polydisperse spherical particles in a laminar Couette-type shear flow. The sediment beds consist of particles with a diameter size ratio of up to 10, which corresponds to grains ranging from fine to coarse sand. The data was generated using fully coupled, grain resolved direct numerical simulations using a combined lattice Boltzmann–discrete element method. These highly resolved data yield detailed depth-resolved profiles of the relevant physical quantities that determine the rheology, i.e. the local shear rate of the fluid, particle volume fraction, total shear and granular pressure. A comparison against experimental data shows excellent agreement for the monodisperse case. We improve upon the parameterization of the $\mu (J)$ -rheology by expressing its empirically derived parameters as a function of the maximum particle volume fraction. Furthermore, we extend these considerations by exploring the creeping regime for viscous numbers much lower than used by previous studies to calibrate these correlations. Considering the low viscous numbers of our data, we found that the friction coefficient governing the quasi-static state in the creeping regime tends to a finite value for vanishing shear, which decreases the critical friction coefficient by a factor of three for all cases investigated.

scholarly journals On the Effective Elastic Properties of Macroscopically Isotropic Media Containing Randomly Dispersed Spherical Particles

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
D. Cojocaru ◽  
A. M. Karlsson
Keyword(s):  
Elastic Properties ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
3D Structure ◽  
Area Fraction ◽  
Spherical Particles ◽  
Particle Volume ◽  
Effective Elastic Properties ◽  
Isotropic Media ◽  
Equivalent Area

A computational scheme for estimating the effective elastic properties of a particle reinforced matrix is investigated. The randomly distributed same-sized spherical particles are assumed to result in a composite material that is macroscopically isotropic. The scheme results in a computational efficient method to establish the correct bulk and shear moduli by representing the three-dimensional (3D) structure in a two-dimensional configuration. To this end, the statistically equivalent area fraction is defined in this work, which depends on two parameters: the particle volume fraction and the number of particles in the 3D volume element. We suggest that using the statistically equivalent area fraction, introduced and defined in this work, is an efficient way to obtain the effective elastic properties of an isotropic media containing randomly dispersed same-size spherical particles.

Two-Way Coupling Effects in Dilute Gas-Particle Flows

1982 ◽  
Vol 104 (3) ◽  
pp. 304-311 ◽  
Author(s):  
M. Di Giacinto ◽  
F. Sabetta ◽  
R. Piva
Keyword(s):  
Stokes Equations ◽  
Volume Fraction ◽  
Solid Phase ◽  
Coupling Effect ◽  
Particle Volume Fraction ◽  
Stokes Number ◽  
Particle Volume ◽  
Fluid Field ◽  
Particle Flows ◽  
Energy Dissipated

A general analysis of gas-particle flows, under the hypotheses of number of particles large enough to consider the solid phase as a continuum and of volume fraction small enough to consider the suspension as dilute, is presented. The Stokes number Sk and the particle loading ratio β are shown to be the basic parameters governing the flow. Depending on the values of these two parameters, in one case the reciprocal interaction of the fluid and solid phases must be considered (two-way coupling), in the second case only the effect of the fluid field on the particle motion is relevant (one-way coupling). In the more general case of two-way coupling, the flow is governed by two sets of Navier-Stokes equations, one for each phase, which are coupled together through the particle volume fraction and the momentum interchange forces. The two systems of equations, expressed in the variables velocity, pressure, and particle volume fraction, are solved numerically by a finite difference scheme. The model has been applied to a duct with a sudden restriction, simulating a flow metering device. The coupling effect both on fluid and solid phase fields, the increase of pressure drop, and the energy dissipated in the fluid-solid interaction have been determined as functions of the governing parameters, Sk and β. The parametric study also indicates the ranges of β and Sk in which simplified formulations may be assumed.

scholarly journals Lattice Boltzmann simulations of low-Reynolds-number flows past fluidized spheres: effect of inhomogeneities on the drag force

2017 ◽  
Vol 833 ◽  
pp. 599-630 ◽  
Author(s):  
Gregory J. Rubinstein ◽  
Ali Ozel ◽  
Xiaolong Yin ◽  
J. J. Derksen ◽  
Sankaran Sundaresan
Keyword(s):  
Reynolds Number ◽  
Drag Force ◽  
Lattice Boltzmann ◽  
Volume Fraction ◽  
Low Reynolds Number ◽  
Particle Volume Fraction ◽  
Spherical Particles ◽  
Particle Volume ◽  
Lattice Boltzmann Simulations ◽  
Low Reynolds

The formation of inhomogeneities within fluidized beds, both in terms of the particle configurations and flow structures, have a pronounced effect on the interaction force between the fluid and particles. While recent numerical studies have begun to probe the effects of inhomogeneities on the drag force at the particle scale, the applicability of prior microscale constitutive drag relations is still limited to random, homogeneous distributions of particles. Since an accurate model for the drag force is needed to predict the fluidization behaviour, the current study utilizes the lessons of prior inhomogeneity studies in order to derive a robust drag relation that is both able to account for the effect of inhomogeneities and applicable as a constitutive closure to larger-scale fluidization simulations. Using fully resolved lattice Boltzmann simulations of systems composed of fluid and monodisperse spherical particles in the low-Reynolds-number (Re) regime, the fluid–particle drag force, normalized by the ideal Stokes drag force, is found to significantly decrease, over a range of length scales, as the extent of inhomogeneities increases. The extent of inhomogeneities is found to most effectively be quantified through one of two subgrid-scale quantities: the scalar variance of the particle volume fraction or the drift flux, which is the correlation between the particle volume fraction and slip velocity. Scale-similar models are developed to estimate these two subgrid measures over a wide range of system properties. Two new drag constitutive models are proposed that are not only functions of the particle volume fraction and the Stokes number ($St$), but also dependent on one of these subgrid measures for the extent of inhomogeneities. Based on the observed, appreciable effect of inhomogeneities on drag, these new low-Re drag models represent a significant advancement over prior constitutive relations.

Simulation on the aggregation process of spherical particle confined in a spherical shell

2016 ◽  
Vol 30 (11) ◽  
pp. 1650065
Author(s):  
J. Wang ◽  
J. J. Xu ◽  
L. Zhang
Keyword(s):  
Spherical Shell ◽  
Density Distribution ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Porous Polymer ◽  
Spherical Particles ◽  
Aggregation Kinetics ◽  
Aggregation Process ◽  
Particle Volume ◽  
Aggregate Structure

The aggregation process of spherical particles confined in a spherical shell was studied by using a diffusion-limited cluster–cluster aggregation (DLCA) model. The influence of geometrical confinement and wetting-like properties of the spherical shell walls on the particle concentration profile, aggregate structure and aggregation kinetics had been explored. The results show that there will be either depletion or absorption particles near the shell walls depending on the wall properties. It is observed that there are four different types of density distribution which can be realized by modifying the property of the inner or outer spherical shell wall. In addition, the aggregate structure will become more compact in the confined spherical shell comparing to bulk system with the same particle volume fraction. The analysis on the aggregation kinetics indicates that geometrical confinement will promote the aggregation process by reducing the invalid movement of the small aggregates and by constraining the movement of those large aggregates. Due to the concave geometrical characteristic of the outer wall of the spherical shell, its effects on the aggregating kinetics and the structure of the formed aggregates are more evident than those of the inner wall. This study will provide some instructive information of controlling the density distribution of low-density porous polymer hollow spherical shells and helps to predict gel structures developed in confined geometries.

scholarly journals The rheology of three-phase suspensions at low bubble capillary number

2015 ◽  
Vol 471 (2173) ◽  
pp. 20140557 ◽  
Author(s):  
J. M. Truby ◽  
S. P. Mueller ◽  
E. W. Llewellin ◽  
H. M. Mader
Keyword(s):  
Capillary Number ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Spherical Particles ◽  
Bubbly Liquid ◽  
Particle Suspension ◽  
Suspension Rheology ◽  
Particle Volume ◽  
Two Phase ◽  
Three Phase

We develop a model for the rheology of a three-phase suspension of bubbles and particles in a Newtonian liquid undergoing steady flow. We adopt an ‘effective-medium’ approach in which the bubbly liquid is treated as a continuous medium which suspends the particles. The resulting three-phase model combines separate two-phase models for bubble suspension rheology and particle suspension rheology, which are taken from the literature. The model is validated against new experimental data for three-phase suspensions of bubbles and spherical particles, collected in the low bubble capillary number regime. Good agreement is found across the experimental range of particle volume fraction ( 0 ≤ ϕ p ≲ 0.5 ) and bubble volume fraction ( 0 ≤ ϕ b ≲ 0.3 ). Consistent with model predictions, experimental results demonstrate that adding bubbles to a dilute particle suspension at low capillarity increases its viscosity, while adding bubbles to a concentrated particle suspension decreases its viscosity. The model accounts for particle anisometry and is easily extended to account for variable capillarity, but has not been experimentally validated for these cases.

Thermal Stresses in SiC-Si3N4 Cubic-Cell-Divided Multi-Particle-Matrix System

2005 ◽  
Vol 290 ◽  
pp. 320-323
Author(s):  
L. Ceniga
Keyword(s):  
Thermal Stresses ◽  
Crack Formation ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Spherical Particles ◽  
Formation Condition ◽  
Infinite Matrix ◽  
Matrix System ◽  
Particle Volume ◽  
Thermal Expansion Coefficients

The paper deals with crack formation of thermal stresses in an isotropic multi-particle-matrix system of homogeneously distributed spherical particles in an infinite matrix divided to cubic cells containing a central particle. Originating during a cooling process as a consequence of the difference in thermal expansion coefficients between a matrix and a particle, the thermal stresses are thus investigated within the cubic cell and extreme at the critical particle volume fraction. Resulting from the derived crack formation condition related to an ideal-brittle particle, the critical particle radius considering the critical particle volume fraction is presented along with an application to the thermalstress- strengthened SiC-Si3N4 ceramics.

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