scholarly journals Sedimentation of a dilute suspension of rigid spheres at intermediate Galileo numbers: the effect of clustering upon the particle motion

2014 ◽  
Vol 752 ◽  
pp. 310-348 ◽  
Author(s):  
Markus Uhlmann ◽  
Todor Doychev
Keyword(s):  
Particle Velocity ◽  
Settling Velocity ◽  
Fluid Velocity ◽  
Voronoi Tessellation ◽  
Density Ratio ◽  
Fluid Motion ◽  
Finite Size ◽  
Vertical Motion ◽  
Average Particle ◽  
Rigid Spheres

AbstractDirect numerical simulation of the gravity-induced settling of finite-size particles in triply periodic domains has been performed under dilute conditions. For a single solid-to-fluid-density ratio of 1.5 we have considered two values of the Galileo number corresponding to steady vertical motion ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Ga}=121$) and to steady oblique motion ($\mathit{Ga}=178$) in the case of one isolated sphere. For the multiparticle system we observe strong particle clustering only in the latter case. The geometry and time scales related to clustering are determined from Voronoï tessellation and particle-conditioned averaging. As a consequence of clustering, the average particle settling velocity is increased by 12 % as compared with the value of an isolated sphere; such a collective effect is not observed in the non-clustering case. By defining a local (instantaneous) fluid velocity average in the vicinity of the finite-size particles it is shown that the observed enhancement of the settling velocity is due to the fact that the downward fluid motion (with respect to the global average) which is induced in the cluster regions is preferentially sampled by the particles. It is further observed that the variance of the particle velocity is strongly enhanced in the clustering case. With the aid of a decomposition of the particle velocity it is shown that this increase is due to enhanced fluid velocity fluctuations (due to clustering) in the vicinity of the particles. Finally, we discuss a possible explanation for the observation of a critical Galileo number marking the onset of clustering under dilute conditions.

scholarly journals Sedimentation of finite-size spheres in quiescent and turbulent environments

2016 ◽  
Vol 788 ◽  
pp. 640-669 ◽  
Author(s):  
Walter Fornari ◽  
Francesco Picano ◽  
Luca Brandt
Keyword(s):  
Turbulent Flow ◽  
Settling Velocity ◽  
Solid Phase ◽  
Density Ratio ◽  
Finite Size ◽  
Spherical Particles ◽  
Volume Fractions ◽  
Turbulent Environments ◽  
The Mean ◽  
Quiescent Fluid

Sedimentation of a dispersed solid phase is widely encountered in applications and environmental flows, yet little is known about the behaviour of finite-size particles in homogeneous isotropic turbulence. To fill this gap, we perform direct numerical simulations of sedimentation in quiescent and turbulent environments using an immersed boundary method to account for the dispersed rigid spherical particles. The solid volume fractions considered are ${\it\phi}=0.5{-}1\,\%$, while the solid to fluid density ratio ${\it\rho}_{p}/{\it\rho}_{f}=1.02$. The particle radius is chosen to be approximately six Kolmogorov length scales. The results show that the mean settling velocity is lower in an already turbulent flow than in a quiescent fluid. The reductions with respect to a single particle in quiescent fluid are approximately 12 % and 14 % for the two volume fractions investigated. The probability density function of the particle velocity is almost Gaussian in a turbulent flow, whereas it displays large positive tails in quiescent fluid. These tails are associated with the intermittent fast sedimentation of particle pairs in drafting–kissing–tumbling motions. The particle lateral dispersion is higher in a turbulent flow, whereas the vertical one is, surprisingly, of comparable magnitude as a consequence of the highly intermittent behaviour observed in the quiescent fluid. Using the concept of mean relative velocity we estimate the mean drag coefficient from empirical formulae and show that non-stationary effects, related to vortex shedding, explain the increased reduction in mean settling velocity in a turbulent environment.

Drag Coefficient and Settling Velocity of Particles in Non-Newtonian Suspensions

1987 ◽  
Vol 109 (3) ◽  
pp. 319-323 ◽  
Author(s):  
M. Y. Dedegil
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Drag Coefficient ◽  
Yield Stress ◽  
Particle Velocity ◽  
Settling Velocity ◽  
Fluid Velocity ◽  
Newtonian Fluids ◽  
Drag Forces ◽  
Physical Composition

Drag forces on bodies in non-Newtonian fluids which are to be described by using the Reynolds number should only contain forces which are associated with the fluid velocity or particle velocity. Forces due to the yield stress τ0 must be considered separately. According to its physical composition, the Reynolds number must be calculated by means of the fully representative shear stress including the yield stress τ0. Then the drag coefficient cD as a function of the Reynolds number can be traced back to that of Newtonian fluids.

scholarly journals Reduced particle settling speed in turbulence

2016 ◽  
Vol 808 ◽  
pp. 153-167 ◽  
Author(s):  
Walter Fornari ◽  
Francesco Picano ◽  
Gaetano Sardina ◽  
Luca Brandt
Keyword(s):  
Solid Phase ◽  
Density Ratio ◽  
Mean Square Displacement ◽  
Particle Diameter ◽  
Finite Size ◽  
Mean Square ◽  
Rigid Spheres ◽  
The Mean ◽  
Settling Speed ◽  
Quiescent Fluid

We study the settling of finite-size rigid spheres in sustained homogeneous isotropic turbulence (HIT) by direct numerical simulations using an immersed boundary method to account for the dispersed solid phase. We study semi-dilute suspensions at different Galileo numbers, $Ga$. The Galileo number is the ratio between buoyancy and viscous forces, and is here varied via the solid-to-fluid density ratio $\unicode[STIX]{x1D70C}_{p}/\unicode[STIX]{x1D70C}_{f}$. The focus is on particles that are slightly heavier than the fluid. We find that in HIT, the mean settling speed is less than that in quiescent fluid; in particular, it reduces by 6 %–60 % with respect to the terminal velocity of an isolated sphere in quiescent fluid as the ratio between the latter and the turbulent velocity fluctuations $u^{\prime }$ is decreased. Analysing the fluid–particle relative motion, we find that the mean settling speed is progressively reduced while reducing $\unicode[STIX]{x1D70C}_{p}/\unicode[STIX]{x1D70C}_{f}$ due to the increase of the vertical drag induced by the particle cross-flow velocity. Unsteady effects contribute to the mean overall drag by about 6 %–10 %. The probability density functions of particle velocities and accelerations reveal that these are closely related to the features of the turbulent flow. The particle mean-square displacement in the settling direction is found to be similar for all $Ga$ if time is scaled by $(2a)/u^{\prime }$ (where $2a$ is the particle diameter and $u^{\prime }$ is the turbulence velocity root mean square).

Transport and Capture of Colloidal Particles in Single Fractures

1984 ◽  
Vol 44 ◽  
Author(s):  
E. J. Bonano ◽  
W. E. Beyeler
Keyword(s):  
Particle Velocity ◽  
Colloidal Particles ◽  
Particle Production ◽  
Dynamic Balance ◽  
Fluid Velocity ◽  
Single Fracture ◽  
Average Particle ◽  
Particle Capture ◽  
External Forces ◽  
Plate Channel

AbstractIn this study, the transport and capture rates of colloidal particles were calculated for a parallel-plate channel simulating a single fracture. The steady-state convective diffusion equation was solved with the particle velocity normal to the walls of the channel being the sum of the external forces acting on the particles. The forces considered were the gravitational, London-van der Waals and electric-double layer forces. The effects of parameters governing these forces and particle production mechanism on the rates of particle capture and transport are determined. The dynamic balance between particle production and capture has a significant effect on the concentration of particles leaving the fracture. The average particle velocity, though higher than the average fluid velocity, seems to be insensitive to phenomena governing particle capture.

Shear waves from a nuclear explosion in a salt cavity

1968 ◽  
Vol 58 (6) ◽  
pp. 2043-2051
Author(s):  
William R. Perret
Keyword(s):  
Particle Velocity ◽  
Nuclear Explosion ◽  
Shear Waves ◽  
Vertical Motion ◽  
Salt Dome ◽  
Explosive Source ◽  
Level Plane ◽  
Stable Cavity

ABSTRACT Shear waves have been resolved in records of acceleration and particle velocity resulting from the Sterling event which was a nuclear explosion (380 tons) within the stable cavity left by the Salmon detonation in the Tatum salt dome. These shear waves were strongest in records of vertical motion at stations in the shot-level plane, but were detectable in records from both vertical and horizontal radial gages above and below that elevation. No appreciable shear waves could be identified in records from shot-level gages oriented horizontally. All instruments involved in this study were situated within the salt dome at ranges between 166 and 660 meters from the explosive source. Shear waves carried over 95 per cent of the energy in vertical shot-level records, but they represented less than 11 per cent of the energy in horizontal radial shot-level records. Cause of the vertically polarized shear waves is considered to be vertical asymmetry at the source.

scholarly journals Heat Induction by Viscous Dissipation Subjected to Symmetric and Asymmetric Boundary Conditions on a Small Oscillating Flow in a Microchannel

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 499 ◽  
Author(s):  
Chih Tso ◽  
Chee Hor ◽  
Gooi Chen ◽  
Chee Kok
Keyword(s):  
Temperature Field ◽  
Prandtl Number ◽  
Boundary Conditions ◽  
Viscous Dissipation ◽  
Fluid Velocity ◽  
Fluid Motion ◽  
Lower Plate ◽  
Brinkman Number ◽  
Energy Equations ◽  
Oscillation Rate

The heat induced by viscous dissipation in a microchannel fluid, due to a small oscillating motion of the lower plate, is investigated for the first time. The methodology is by applying the momentum and energy equations and solving them for three cases of standard thermal boundary conditions. The first two cases involve symmetric boundary conditions of constant surface temperature on both plates and both plates insulated, respectively. The third case has the asymmetric conditions that the lower plate is insulated while the upper plate is maintained at constant temperature. Results reveal that, although the fluid velocity is only depending on the oscillation rate of the plate, the temperature field for all three cases show that the induced heating is dependent on the oscillation rate of the plate, but strongly dependent on the parameters Brinkman number and Prandtl number. All three cases prove that the increasing oscillation rate or Brinkman number and decreasing Prandtl number, when it is less than unity, will significantly increase the temperature field. The present model is applied to the synovial fluid motion in artificial hip implant and results in heat induced by viscous dissipation for the second case shows remarkably close agreement with the experimental literature.

scholarly journals Closed-Form Non-Stationary Solutionsfor Thermo and Chemovibrational Viscous Flows

Fluids ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 175 ◽  
Author(s):  
Dmitry Bratsun ◽  
Vladimir Vyatkin
Keyword(s):  
Viscous Flow ◽  
Closed Form ◽  
General Procedure ◽  
Fluid Velocity ◽  
Fluid Motion ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Chemical Transformations ◽  
Navier Stokes Equation ◽  
Harmonic Vibrations

A class of closed-form exact solutions for the Navier–Stokes equation written in the Boussinesq approximation is discussed. Solutions describe the motion of a non-homogeneous reacting fluid subjected to harmonic vibrations of low or finite frequency. Inhomogeneity of the medium arises due to the transversal density gradient which appears as a result of the exothermicity and chemical transformations due to a reaction. Ultimately, the physical mechanism of fluid motion is the unequal effect of a variable inertial field on laminar sublayers of different densities. We derive the solutions for several problems for thermo- and chemovibrational convections including the viscous flow of heat-generating fluid either in a plain layer or in a closed pipe and the viscous flow of fluid reacting according to a first-order chemical scheme under harmonic vibrations. Closed-form analytical expressions for fluid velocity, pressure, temperature, and reagent concentration are derived for each case. A general procedure to derive the exact solution is discussed.

Analysis of Dispersion of Small Spherical Particles in a Random Velocity Field

1990 ◽  
Vol 112 (1) ◽  
pp. 114-120 ◽  
Author(s):  
H. Ounis ◽  
G. Ahmadi
Keyword(s):  
Particle Velocity ◽  
Digital Simulation ◽  
Density Ratio ◽  
Spherical Particles ◽  
Theoretical Predictions ◽  
The Mean ◽  
Analysis Of Dispersion ◽  
Gradient Effects ◽  
Analytical Expressions ◽  
Good Agreement

The equation of motion of a small spherical rigid particle in a turbulent flow field, including the Stokes drag, the Basset force, and the virtual mass effects, is considered. For an isotropic field, the lift force and the velocity gradient effects are neglected. Using the spectral method, responses of the resulting constant coefficient stochastic integrao-differential equation are studied. Analytical expressions relating the Lagrangian energy spectra of particle velocity to that of the fluid are developed and the results are used to evaluate various response statistics. Variations of the mean-square particle velocity and particle diffusivity with size, density ratio and response time are studied. The theoretical predictions are compared with the digital simulation results and the available data and good agreement is observed.

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