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.

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).

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.

Modulation of isotropic turbulence by particles of Taylor length-scale size

2010 ◽  
Vol 650 ◽  
pp. 5-55 ◽  
Author(s):  
FRANCESCO LUCCI ◽  
ANTONINO FERRANTE ◽  
SAID ELGHOBASHI
Keyword(s):  
Isotropic Turbulence ◽  
Volume Fraction ◽  
Density Ratio ◽  
Particle Diameter ◽  
Finite Size ◽  
Rate Of Change ◽  
Spherical Particles ◽  
Length Scale ◽  
Frequency Spectra ◽  
Scale Size

This study investigates the two-way coupling effects of finite-size solid spherical particles on decaying isotropic turbulence using direct numerical simulation with an immersed boundary method. We fully resolve all the relevant scales of turbulence around freely moving particles of the Taylor length-scale size, 1.2≤d/λ≤2.6. The particle diameter and Stokes number in terms of Kolmogorov length- and time scales are 16≤d/η≤35 and 38≤τp/τk≤178, respectively, at the time the particles are released in the flow. The particles mass fraction range is 0.026≤φm≤1.0, corresponding to a volume fraction of 0.01≤φv≤0.1 and density ratio of 2.56≤ρp/ρf≤10. The maximum number of dispersed particles is 6400 for φv=0.1. The typical particle Reynolds number is of O(10). The effects of the particles on the temporal development of turbulence kinetic energy E(t), its dissipation rate (t), its two-way coupling rate of change Ψp(t) and frequency spectra E(ω) are discussed.In contrast to particles with d < η, the effect of the particles in this study, with d > η, is that E(t) is always smaller than that of the single-phase flow. In addition, Ψp(t) is always positive for particles with d > η, whereas it can be positive or negative for particles with d < η.

Computational Study of Slurry Flow in Pipes to Determine Profiles Sensed in Near Infrared Slurry Measurements

2011 ◽  
Author(s):  
V. Pasangulapati ◽  
N. R. Kesana ◽  
G. Sharma ◽  
F. W. Chambers ◽  
M. E. McNally ◽  
...  
Keyword(s):  
Near Infrared ◽  
Volume Fraction ◽  
Solid Phase ◽  
Computational Study ◽  
Solid Volume Fraction ◽  
Density Ratio ◽  
Optical Measurements ◽  
Concentration Profiles ◽  
Horizontal Pipe ◽  
Volume Fractions

It is desired to perform accurate Near Infrared sensor measurements of slurries flowing in pipes leaving large batch reactors. A concern with these measurements is the degree to which the slurry sensed is representative of the material in the reactor and flowing through the pipe. Computational Fluid Dynamics (CFD) has been applied to the flow in the pipe to determine the flow fields and the concentration profiles seen by the sensors. The slurry was comprised of a xylene liquid phase and an ADP (2-amino-4, 6-dimethylpyrimidine) solid phase with a density ratio of 1.7. Computations were performed for a horizontal pipe with diameter 50.8 mm, length 2.032 m, and 1.76 m/s and 3.26 m/s mixture velocities. The corresponding pipe Reynolds numbers were 1.19E+05 and 2.21E+05. The flow through a slotted cylindrical probe inserted radially in the pipe also was considered. Spherical slurry particles with diameters from 10 μm to 1000 μm were considered with solid volume fractions of 12%, 24%, and 35%. Computations were performed with ANSYS FLUENT 12 software using the Realizable k-ε turbulence model and the enhanced wall treatment function. Comparisons of computed vertical profiles of solid volume fraction to results in the literature showed good agreement. Symmetric, nearly flat solid volume fraction profiles were observed for 38 μm particles for all three initial solid volume fractions. Asymmetric solid volume fraction profiles with greater values toward the bottom were observed for the larger particles. Changes in the profiles of turbulent kinetic energy also were observed. These changes are important for optical measurements which depend upon the mean concentration profiles as well as the turbulent motion of the slurry particles.

scholarly journals Propagation of a strong shock over a random bed of spherical particles

2018 ◽  
Vol 839 ◽  
pp. 157-197 ◽  
Author(s):  
Y. Mehta ◽  
C. Neal ◽  
K. Salari ◽  
T. L. Jackson ◽  
S. Balachandar ◽  
...  
Keyword(s):  
Mach Number ◽  
Numerical Simulations ◽  
Volume Fraction ◽  
Spherical Particles ◽  
Wave Dynamics ◽  
Volume Fractions ◽  
Reflected Shock ◽  
Complex Wave ◽  
The Mean ◽  
Particle Bed

Propagation of a strong incident shock through a bed of particles results in complex wave dynamics such as a reflected shock, a transmitted shock, and highly unsteady flow inside the particle bed. In this paper we present three-dimensional numerical simulations of shock propagation in air over a random bed of particles. We assume the flow is inviscid and governed by the Euler equations of gas dynamics. Simulations are carried out by varying the volume fraction of the particle bed at a fixed shock Mach number. We compute the unsteady inviscid streamwise and transverse drag coefficients as a function of time for each particle in the random bed for different volume fractions. We show that (i) there are significant variations in the peak drag for the particles in the bed, (ii) the mean peak drag as a function of streamwise distance through the bed decreases with a slope that increases as the volume fraction increases, and (iii) the deviation from the mean peak drag does not correlate with local volume fraction. We also present the local Mach number and pressure contours for the different volume fractions to explain the various observed complex physical mechanisms occurring during the shock–particle interactions. Since the shock interaction with the random bed of particles leads to transmitted and reflected waves, we compute the average flow properties to characterize the strength of the transmitted and reflected shock waves and quantify the energy dissipation inside the particle bed. Finally, to better understand the complex wave dynamics in a random bed, we consider a simpler approximation of a planar shock propagating in a duct with a sudden area change. We obtain Riemann solutions to this problem, which are used to compare with fully resolved numerical simulations.

scholarly journals Turbulent channel flow of dense suspensions of neutrally buoyant spheres

2015 ◽  
Vol 764 ◽  
pp. 463-487 ◽  
Author(s):  
Francesco Picano ◽  
Wim-Paul Breugem ◽  
Luca Brandt
Keyword(s):  
Volume Fraction ◽  
Solid Phase ◽  
Reynolds Shear Stress ◽  
Plane Channel ◽  
Laminar Flows ◽  
Momentum Balance ◽  
Mean Velocity ◽  
Volume Fractions ◽  
The Mean ◽  
Neutrally Buoyant

AbstractDense particle suspensions are widely encountered in many applications and in environmental flows. While many previous studies investigate their rheological properties in laminar flows, little is known on the behaviour of these suspensions in the turbulent/inertial regime. The present study aims to fill this gap by investigating the turbulent flow of a Newtonian fluid laden with solid neutrally-buoyant spheres at relatively high volume fractions in a plane channel. Direct numerical simulation (DNS) are performed in the range of volume fractions ${\it\Phi}=0{-}0.2$ with an immersed boundary method (IBM) used to account for the dispersed phase. The results show that the mean velocity profiles are significantly altered by the presence of a solid phase with a decrease of the von Kármán constant in the log-law. The overall drag is found to increase with the volume fraction, more than one would expect if just considering the increase of the system viscosity due to the presence of the particles. At the highest volume fraction investigated here, ${\it\Phi}=0.2$, the velocity fluctuation intensities and the Reynolds shear stress are found to decrease. The analysis of the mean momentum balance shows that the particle-induced stresses govern the dynamics at high ${\it\Phi}$ and are the main responsible of the overall drag increase. In the dense limit, we therefore find a decrease of the turbulence activity and a growth of the particle induced stress, where the latter dominates for the Reynolds numbers considered here.

Saltation and incipient suspension above a flat particle bed below a turbulent boundary layer

2000 ◽  
Vol 417 ◽  
pp. 77-102 ◽  
Author(s):  
K. NISHIMURA ◽  
J. C. R. HUNT
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Settling Velocity ◽  
Particle Density ◽  
Surface Wind ◽  
Spherical Particles ◽  
Flux Profile ◽  
Horizontal Flux ◽  
The Mean ◽  
The Impact

Experiments were conducted in a wind tunnel in which a turbulent boundary layer was naturally grown over flat beds of three types of nearly mono-disperse spherical particles with different diameters, densities and coefficient of restitution (r) (snow, 0.48 mm, 910 kg m−3; mustard seeds, 1.82 mm, 1670 kg m−3, r = 0.7; ice particles, 2.80 mm, 910 kg m−3, r = 0.8–0.9). The surface wind speeds (defined by the friction velocity u∗) were varied between 1.0 and 1.9 times the threshold surface wind speed (defined by u∗t). The trajectories, and ejection and impact velocities of the particles were recorded and analysed, even those that were raised only about one diameter into the flow.Measurements of the average horizontal flux of saltating particles per unit area, f(z), at each level z above the surface showed that, for u∗/u∗t [les ] 1.5, f(z) is approximately independent of the particle density and decreases exponentially over a vertical scale length lf, that is about 3 to 4 times the estimated mean height of the particle trajectories 〈h〉. Numerical simulations of saltating grains were computed using the measured probabilities of ejection velocities and the mean velocity profile of the air flow, but neglecting the direct effect of the turbulence. The calculated mean values of the impact velocities and the trajectory dimensions were found to agree with the measurements in the saltation range, where u∗/u∗t < 1.5. Similarly, in this range the simulations of the horizontal flux profile and integral are also consistent with the measurements and with Bagnold's u∗3 formula, respectively.When u∗/u∗t [ges ] 1.5, and u∗/VT [ges ] 1/10, where VT is the settling velocity, a transition from saltation to suspension occurs. This is indicated by the change in the mean mass flux profile which effectively becomes uniform with height (z) up to the top of the boundary layer. An explanation is provided for this low value of turbulence at transition relative to the settling velocity in terms of the random motion of the particles under the action of the turbulence when they reach the tops of their parabolic trajectories. The experiments show that, as u∗/u∗t increases from 1.0 to 1.9 the normalized mean vertical impact velocity 〈V3I〉/u∗ decreases by nearly 60% to about 0.6, which is less than 50% of the value for fluid particles. There is also a decrease in the vertical and horizontal component of the ejection velocity to values of 0.8 and 2.3, which are much less than their values in the saltation regime. We hypothesize that at the transition from saltation to suspension the ejection process changes quite sharply from being determined by impact collisions to being the result of aerodynamic lift forces and upward eddy motions.

scholarly journals Finite-size effects in the dynamics of neutrally buoyant particles in turbulent flow

2010 ◽  
Vol 651 ◽  
pp. 81-91 ◽  
Author(s):  
HOLGER HOMANN ◽  
JÉRÉMIE BEC
Keyword(s):  
Turbulent Flow ◽  
Size Effects ◽  
Finite Size ◽  
Point Particle ◽  
Spherical Particles ◽  
Finite Size Effects ◽  
Kolmogorov Scale ◽  
Neutrally Buoyant ◽  
Numer Math ◽  
Dynamics Of Particles

The dynamics of neutrally buoyant particles transported by a turbulent flow is investigated for spherical particles with radii of the order of the Kolmogorov dissipative scale or larger. The pseudo-penalization spectral method that has been proposed by Pasquetti et al. (Appl. Numer. Math., vol. 58, 2008, pp. 946–954) is adapted to integrate numerically the simultaneous dynamics of the particle and of the fluid. Such a method gives a unique handle on the limit of validity of point-particle approximations, which are generally used in applicative situations. Analytical predictions based on such models are compared to result of very well-resolved direct numerical simulations. Evidence is obtained that Faxén corrections reproduce dominant finite-size effects on velocity and acceleration fluctuations for particle diameters up to four times the Kolmogorov scale. The dynamics of particles with larger diameters is consistent with predictions obtained from dimensional analysis.

scholarly journals Clustering and preferential concentration of finite-size particles in forced homogeneous-isotropic turbulence

2017 ◽  
Vol 812 ◽  
pp. 991-1023 ◽  
Author(s):  
Markus Uhlmann ◽  
Agathe Chouippe
Keyword(s):  
Isotropic Turbulence ◽  
Density Ratio ◽  
Finite Size ◽  
Statistical Correlation ◽  
Point Particle ◽  
Vortical Flow ◽  
Spherical Particles ◽  
Moderate Intensity ◽  
Homogeneous Isotropic Turbulence ◽  
Acceleration Field

We have performed interface-resolved direct numerical simulations of forced homogeneous-isotropic turbulence in a dilute suspension of spherical particles in the Reynolds number range $Re_{\unicode[STIX]{x1D706}}=115{-}140$. The solid–fluid density ratio was set to $1.5$, gravity was set to zero and two particle diameters were investigated corresponding to approximately $5$ and $11$ Kolmogorov lengths. Note that these particle sizes are clearly outside the range of validity of the point-particle approximation, as has been shown by Homann & Bec (J. Fluid Mech., vol. 651, 2010, pp. 81–91). At the present parameter points the global effect of the particles upon the fluid flow is weak. We observe that the dispersed phase exhibits clustering with moderate intensity. The tendency to cluster, which was quantified in terms of the standard deviation of Voronoï cell volumes, decreases with the particle diameter. We have analysed the relation between particle locations and the location of intense vortical flow structures. The results do not reveal any significant statistical correlation. Contrarily, we have detected a small but statistically significant preferential location of particles with respect to the ‘sticky points’ proposed by Goto & Vassilicos (Phys. Rev. Lett., vol. 100 (5), 2008, 054503), i.e. points where the fluid acceleration field is acting such as to increase the local particle concentration in one-way coupled point-particle models under Stokes drag. The presently found statistical correlation between the ‘sticky points’ and the particle locations further increases when focusing on regions with high local concentration. Our results suggest that small finite-size particles can be brought together along the expansive directions of the fluid acceleration field, as previously observed only for the simplest model for sub-Kolmogorov particles. We further discuss the effect of density ratio and collective particle motion upon the basic Eulerian and Lagrangian statistics.

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.

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