Volume Fraction Of Particle Phase Research Articles

Pressure recovery characteristics for a dilute gas–particle suspension flowing vertically downward in a pipe with a sudden expansion: A two-fluid modeling approach

This work applies the Eulerian‒Eulerian model in conjunction with the kinetic theory of granular flow and inter-particle collisions to study the characteristics of pressure recovery for a dilute gas–particle suspension flowing through a pipe with a sudden expansion at a relatively higher solid loading. To do so, the numerical procedure was validated against experimental results for relatively small dilute phase flows in a pipe with a sudden expansion; a satisfactory agreement was obtained. Initially, the effect of the two significant numerical parameters namely, the speculairty coefficient and the coefficient of restitution for particle–particle collisions were investigated and then, for fixed combinations of these parameters the effect of particle-phase volume fraction, particle density, particle size, and inlet slip ratio were studied. It was concluded that pressure recovery diminishes as the speculairty coefficient increases and the particle–particle coefficient of restitution decreases. Pressure recovery was found to increase with increasing solid volume fraction for coarse particles whereas, for fine particles, a critical volume fraction is obtained above which pressure recovery reduces. An increase in slip ratio is found to diminish pressure recovery. Similarly, at relatively higher solid volume fractions, a critical diameter was found, above and below which pressure recovery decreases.

Dilute gas-particle flow through thin and thick orifice: a computational study through two fluid model

The present work deals with the three-dimensional computational study of dilute gas-particle suspension through thin and thick orifice. The objective of the study is to predict the two phase pressure drop across an orifice for relatively higher solid loading but within the limit of dilute phase flow situation. The study involves the investigation of effect of five pertinent parameters namely area ratio, thickness of orifice, particle phase volume fraction, particle size, and particle phase density on the two phase pressure drop across orifice. The Eulerian–Eulerian model (Two fluid model) has been used for this purpose. The numerical procedure adopted in the present work has been validated with the experimental data for gas-particle flow through a horizontal sudden expansion pipe and good agreement has been revealed. The study reveals that the two phase pressure drop across orifice increases with increases in solid volume fraction and particle density, whereas it decreases with increase in particle diameter and area ratio of the pipe. Moreover, slight increase in pressure drop across orifice is observed with increase in thickness of orifice. Thus, higher pressure drop is observed for thick orifice as compared to thin orifice.

Simulation study on chip formation mechanism in grinding particle reinforced Cu-matrix composites

Based on the coupling method of finite element method and smoothed particle hydrodynamics method, the process of single abrasive grain cutting particles reinforced Cu-matrix composites with small volume fraction of particle phase is simulated, and the chip formation mechanism of particle reinforced Cu-matrix composites was analyzed. It can be concluded that the plastic removal of the Cu-matrix is still the main removal form of the composite, but the existence of the reinforced particle phase affects the cutting deformation behavior and the chip morphology. During the cutting process, the interfaces between part of reinforced particles and the Cu-matrix are broken, and resulting in the particles falling off into chips, but most of the particles will form continuous mixed chips with copper alloy, with the plastic deformation of the Cu-matrix. The extrusion of abrasive particles leads to pile-up of dislocation producing in Cu-matrix around the reinforced particle, which interferes with the continuous plastic deformation of Cu-matrix, thus affects the cutting force and cutting temperature of the abrasive grain. The simulation results show that with the increase of cutting speed, the cutting force decreases, but the cutting temperature increases. As the cutting depth increases, the cutting force and cutting temperature increase. The increase of reinforced particle content will lead to the increase of cutting force and cutting temperature.

Strongly coupled fluid-particle flows in vertical channels. I. Reynolds-averaged two-phase turbulence statistics

Simulations of strongly coupled (i.e., high-mass-loading) fluid-particle flows in vertical channels are performed with the purpose of understanding the fundamental physics of wall-bounded multiphase turbulence. The exact Reynolds-averaged (RA) equations for high-mass-loading suspensions are presented, and the unclosed terms that are retained in the context of fully developed channel flow are evaluated in an Eulerian–Lagrangian (EL) framework for the first time. A key distinction between the RA formulation presented in the current work and previous derivations of multiphase turbulence models is the partitioning of the particle velocity fluctuations into spatially correlated and uncorrelated components, used to define the components of the particle-phase turbulent kinetic energy (TKE) and granular temperature, respectively. The adaptive spatial filtering technique developed in our previous work for homogeneous flows [J. Capecelatro, O. Desjardins, and R. O. Fox, “Numerical study of collisional particle dynamics in cluster-induced turbulence,” J. Fluid Mech. 747, R2 (2014)] is shown to accurately partition the particle velocity fluctuations at all distances from the wall. Strong segregation in the components of granular energy is observed, with the largest values of particle-phase TKE associated with clusters falling near the channel wall, while maximum granular temperature is observed at the center of the channel. The anisotropy of the Reynolds stresses both near the wall and far away is found to be a crucial component for understanding the distribution of the particle-phase volume fraction. In Part II of this paper, results from the EL simulations are used to validate a multiphase Reynolds-stress turbulence model that correctly predicts the wall-normal distribution of the two-phase turbulence statistics.

Strongly coupled fluid-particle flows in vertical channels. II. Turbulence modeling

In Part I, simulations of strongly coupled fluid-particle flow in a vertical channel were performed with the purpose of understanding, in general, the fundamental physics of wall-bounded multiphase turbulence and, in particular, the roles of the spatially correlated and uncorrelated components of the particle velocity. The exact Reynolds-averaged (RA) equations for high-mass-loading suspensions were presented, and the unclosed terms that are retained in the context of fully developed channel flow were evaluated in an Eulerian–Lagrangian (EL) framework. Here, data from the EL simulations are used to validate a multiphase Reynolds-stress model (RSM) that predicts the wall-normal distribution of the two-phase, one-point turbulence statistics up to second order. It is shown that the anisotropy of the Reynolds stresses both near the wall and far away is a crucial component for predicting the distribution of the RA particle-phase volume fraction. Moreover, the decomposition of the phase-average (PA) particle-phase fluctuating energy into the spatially correlated and uncorrelated components is necessary to account for the boundary conditions at the wall. When these factors are properly accounted for in the RSM, the agreement with the EL turbulence statistics is satisfactory at first order (e.g., PA velocities) but less so at second order (e.g., PA turbulent kinetic energy). Finally, an algebraic stress model for the PA particle-phase pressure tensor and the Reynolds stresses is derived from the RSM using the weak-equilibrium assumption.

Numerical simulation of raceway phenomena in a COREX melter–gasifier

The raceway of the COREX melter–gasifier where the interaction between gas phase and particle phase appears to be violent plays an important role in the melting process. In order to describe the behaviors of the particle phase and the gas phase in the raceway, a coupled simulation approach of discrete element method (DEM) and computational fluid dynamics (CFD) is performed at a microscopic level. The particle motion, particle phase volume fraction, velocity vector field of particles, velocity vector field of the gas phase and scalar velocity contours of particles in front of tuyere are calculated by the coupled model. In this work, as a result of considering the multiple particle–gas interaction forces (including drag force, virtual mass force, lift force and pressure gradient force) and a well-balanced computational time step, an almost stable cavity is formed in front of the tuyere, and the particles follow a rotating path in this cavity which can be defined as raceway. The scalar velocity contours of particles show that the particle velocity is greatest in the raceway central area, and it will decrease gradually with increasing distance from the raceway center. Furthermore, the calculation result is consistent with results from a physical experiment.

Numerical study of collisional particle dynamics in cluster-induced turbulence

AbstractWe present a computational study of cluster-induced turbulence (CIT), where the production of fluid-phase kinetic energy results entirely from momentum coupling with finite-size inertial particles. A separation of length scales must be established when evaluating the particle dynamics in order to distinguish between the continuous mesoscopic velocity field and the uncorrelated particle motion. To accomplish this, an adaptive spatial filter is employed on the Lagrangian data with an averaging volume that varies with the local particle-phase volume fraction. This filtering approach ensures sufficient particle sample sizes in order to obtain meaningful statistics while remaining small enough to avoid capturing variations in the mesoscopic particle field. Two-point spatial correlations are computed to assess the validity of the filter in extracting meaningful statistics. The method is used to investigate, for the first time, the properties of a statistically stationary gravity-driven particle-laden flow, where particle–particle and fluid–particle interactions control the multiphase dynamics. Results from fully developed CIT show a strong correlation between the local volume fraction and the granular temperature, with maximum values located at the upstream boundary of clusters (i.e. where maximum compressibility of the particle velocity field exists), while negligible particle agitation is observed within clusters.

On multiphase turbulence models for collisional fluid–particle flows

AbstractStarting from a kinetic theory (KT) model for monodisperse granular flow, the exact Reynolds-averaged (RA) equations are derived for the particle phase in a collisional fluid–particle flow. The corresponding equations for a constant-density fluid phase are derived from a model that includes drag and buoyancy coupling with the particle phase. The fully coupled macroscale/hydrodynamic model, rigorously derived from a kinetic equation for the particles, is written in terms of the particle-phase volume fraction, the particle-phase velocity and the granular temperature (or total granular energy). As derived from the hydrodynamic model, the RA turbulence model solves for the RA particle-phase volume fraction, the phase-averaged (PA) particle-phase velocity, the PA granular temperature and the PA turbulent kinetic energy of the particle phase. Thus, unlike in most previous derivations of macroscale turbulence models for moderately dense granular flows, a clear distinction is made between the PA granular temperature $\Theta _\textit {p}$, which appears in the KT constitutive relations, and the particle-phase turbulent kinetic energy $k_\textit {p}$, which appears in the turbulent transport coefficients. The exact RA equations contain unclosed terms due to nonlinearities in the hydrodynamic model and we briefly discuss the available closures for these terms. Finally, we demonstrate by comparing model predictions with direct numerical simulation results that even for non-collisional fluid–particle flows it is necessary to provide separate models for $\Theta _\textit {p}$ and $k_\textit {p}$ in order to correctly account for the effect of the particle Stokes number and mass loading.

Advanced continuum modelling of gas-particle flows beyond the hydrodynamic limit

The accurate prediction of dilute gas-particle flows using Euler–Euler models is challenging because particle–particle collisions are usually not dominant in such flows. In other words, in dilute flows the particle Knudsen number is not small enough to justify a Chapman–Enskog expansion about the collision-dominated near-equilibrium limit. Moreover, due to the fluid drag and inelastic collisions, the granular temperature in gas-particle flows is often small compared to the mean particle kinetic energy, implying that the particle-phase Mach number can be very large. In analogy to rarefied gas flows, it is thus not surprising that two-fluid models fail for gas-particle flows with moderate Knudsen and Mach numbers. In this work, a third-order quadrature-based moment method, valid for arbitrary Knudsen number, coupled with a fluid solver has been applied to simulate dilute gas-particle flow in a vertical channel with particle-phase volume fractions between 0.0001 and 0.01. In order to isolate the instabilities that arise due to fluid-particle coupling, a fluid mass flow rate that ensures that turbulence would not develop in a single phase flow (Re = 1380) is employed. Results are compared with the predictions of a two-fluid model with standard kinetic theory based closures for the particle phase. The effect of the particle-phase volume fraction on flow instabilities leading to particle segregation is investigated, and differences with respect to the two-fluid model predictions are examined. The influence of the discretization on the solution of both models is investigated using three different grid resolutions. Radial profiles of phase velocities and particle concentration are shown for the case with an average particle volume fraction of 0.01, showing the flow is in the core-annular regime.

A fully coupled quadrature-based moment method for dilute to moderately dilute fluid–particle flows

A third-order quadrature-based moment method for simulating dilute and moderately dilute fluid–particle flows has been implemented with full coupling in a computational fluid dynamics code. The solution algorithm for the particle phase uses a kinetic-based finite-volume technique to solve the velocity moment equations derived from kinetic theory. The procedure to couple the particle-phase volume-fraction and momentum equations with the Eulerian solver for the fluid phase is explained in detail. As an example application, simulations of a particle-laden vertical channel flow at fluid-phase Reynolds number 1379 and particle Stokes numbers 0.061 and 0.61 were carried out. The fluid and particle velocities, particle-phase volume fraction and granular temperature were observed to reach a steady state in the case of Stokes number 0.061, while instabilities that led to the formation of structures and initiated the particle segregation process were observed in the case with the higher Stokes number. These results are validated against results from a classical two-fluid model derived from the kinetic theory of granular flows in the small Knudsen number limit, and Euler–Lagrange simulations of the same flow.

Unsteady laminar hydromagnetic fluid–particle flow and heat transfer in channels and circular pipes

Abstract The problem of unsteady laminar flow and heat transfer of a particulate suspension in an electrically conducting fluid through channels and circular pipes in the presence of a uniform transverse magnetic field is formulated using a two-phase continuum model. Two different applied pressure gradient (oscillating and ramp) cases are considered. The general governing equations of motions (which include such effects as particulate phase stresses, magnetic force, and finite particle-phase volume fraction) are non-dimensionalized and solved in closed form in terms of Fourier cosine and Bessel functions and the energy equations for both phases are solved numerically since they are non-linear and are difficult to solve analytically. Numerical solutions based on the finite-difference methodology are obtained and graphical results for the fluid-phase volumetric flow rate, the particle-phase volumetric flow rate, the fluid-phase skin-friction coefficient and the particle-phase skin-friction coefficient as well as the wall heat transfer for plane and axisymmetric flows are presented and discussed. In addition, these numerical results are validated by favorable comparisons with the closed-form solutions. A comprehensive parametric study is performed to show the effects of the Hartmann magnetic number, the particle loading, the viscosity ratio, and the temperature inverse Stokes number on the solutions.

Compressible two-phase boundary-layer flow with finite particulate volume fraction

A continuum mathematical model governing compressible boundary-layer fluid-particle flow and heat transfer over a semi-infinite flat plate is developed. This model is based on separate balance laws of mass, linear momentum, and energy for both phases and allows for finite particle-phase volume fraction and viscous stresses. It is found that the volume fraction of suspended particles and, therefore, the particle-phase density is uniform in the boundary layer. Using this fact, the governing nonlinear partial differential equations are simplified and solved numerically by an iterative finite-difference method. Graphical results for flow and heat transfer properties are presented for various values of the particle-fluid viscosity ratio and the power index parameter for the viscosity-temperature relation.

Measurements of Powder Snow Avalanches- Laboratory -

Laboratory simulation of powder snow avalanches serves for the validation of numerical models and as a tool in its own right for consulting and research purposes. Two-phase gravity currents are simulated in water with quartz powder or glass spheres as the particle phase. Particle-phase velocity profiles and particle-phase volume fraction profiles are measured with an ultrasonic device. The experimental setup and the current state of the measurement technique are described and preliminary results are presented.

The Method of Calculating the Mechanical Coefficients of Fluid Mixtures : No.3 The Coefficient of Internal Friction and the Viscosity of Two-phase Fluids

The coefficient of internal friction and one of viscosity of disperse two-phase fluids are simultaneously determined by utilizing a self-consistent cell model and expressed as the functions of the volume fraction of particle phase. It is assumed that the fluid inside the cell is Stokesian and the outside fluid is Stokes-Darcian. Careful examination on the macroscopic notions is necessary to derive the conditions to determine those coefficients. the predictions obtained are satisfactory.

The Method of Calculating the Mechanical Coefficients of Fluid Mixtures : 11.The Coefficient of Internal Resistance in Two-Phase Flows

The coefficient of internal resistance in dispersive two-phase flow is considered. The method of self-consistent cell model is applied to determine the coefficient as a function of the volume fraction of particle phase. A certain spherical cell is formed around a randomly chosen particle. It is assumed that inside the cell the fluid is Stokesian while outside the fluid is Stokes-Darcian. The solutions in both sides are connected on the cell surface by suitable conditions. The condition of coincidence is considered, which is indispensable to determine the coefficient considered and supplements the boundary conditions. The numerical calculation is carried out and the prediction is reasonable.