In this article we present a numerical study of the dynamics of two disks settling in a narrow vertical channel filled with Oldroyd-B fluid. Two kinds of particle dynamics are obtained: (i) periodic interaction between two disks and (ii) the chain formation of two disks. For the periodic interaction of two disks, two different motions are obtained: (a) two disks stay far apart and interact periodically and (b) two disks interact closely and then far apart in a periodic way, like the drafting, kissing and tumbling of two disks sedimenting in Newtonian fluid, due to the lack of strong enough elastic force. For the formation of two disk chain occurred at higher values of the elasticity number, it is either a tilted chain or a vertical chain. The tilted chain can be obtained for either that the elasticity number is less than the critical value for having the vertical chain or that the Mach number is greater than the critical value for a long body to fall broadside-on. Hence the values of the elasticity number and the Mach number determine whether the the chain can be formed and the orientation of the chain.
We present a novel distributed Lagrange multiplier/fictitious domain (DLM/FD) method for simulating fluid-particle interaction in Oldroyd-B fluids under creeping conditions. The results concerning two ball interaction in a three dimensional (3D) bounded shear flow are obtained for Weissenberg numbers up to 1 . The pass and return trajectories of the two ball mass centers are similar to those in a Newtonian fluid; but they lose the symmetry due to the effect of elastic force arising from viscoelastic fluids. A tumbling chain of two balls (a dipole) may occur, depending on the value of the Weiss…
We use theory and Direct Numerical Simulations (DNS) to explore the average vertical velocities and spatial distributions of inertial particles settling in a wall-bounded turbulent flow. The theory is based on the exact phase-space equation for the Probability Density Function describing particle positions and velocities. This allowed us to identify the distinct physical mechanisms governing the particle transport. We then examined the asymptotic behavior of the particle motion near the wall, revealing the fundamental differences to the near wall behavior that is produced when incorporating gr…
Using Direct Numerical Simulations (DNS), we examine the effects of Taylor Reynolds number, $R_λ$, and Froude number, $Fr$, on the motion of settling, bidisperse inertial particles in isotropic turbulence. Particle accelerations play a key role in the relative motion of bidisperse particles, and we find that reducing $Fr$ leads to an enhancement of the accelerations, but a suppression of their intermittency. For Stokes numbers $St>1$, the effect of $R_λ$ on the accelerations is enhanced by gravity, since settling causes the particle accelerations to be affected by a larger range of flow scales…
The settling of heavy spherical particles in a column of quiescent fluid is investigated. The performed experiments cover a range of Galileo numbers ($110 \leq \text{Ga} \leq 310$) for a fixed density ratio of $Γ= ρ_p/ρ_f = 2.5$. In this regime the particles are known (M. Jenny, J. Dušek and G. Bouchet, Journal of Fluid Mechanics 508, 201 (2004).) to show a variety of motions. It is known that the wake undergoes several transitions for increasing $\text{Ga}$ resulting in particle motions that are successively: vertical, oblique, oblique oscillating, and finally chaotic. Not only does this chan…
The evolution of suspension drops sedimenting under gravity in a viscous fluid close to a vertical wall was studied experimentally and numerically with the use of the point-force model, in the Stokes flow regime. The fluid inside and outside the drop was identical. The initial distribution of the suspended solid heavy particles was uniform inside a spherical volume. In the experiments and in the simulations, the suspension drops evolved qualitatively in the same way as in an unbounded fluid. However, it was observed, both experimentally and numerically that, on the average, the destabilization…
We have performed spectral/spectral-element simulations of a single oblate spheroid with small geometrical aspect ratio settling in an unbounded ambient fluid, for a range of Galileo numbers covering the various regimes of motion (steady vertical, steady oblique, vertical periodic and chaotic). The high-fidelity data provided includes particle quantities (statistics in the chaotic case), as well as flow profiles and pressure maps. The reference data can be used as an additional benchmark for other numerical approaches, where a careful grid convergence study for a specific target parameter poin…
In this article we present a numerical method for simulating the sedimentation of circular particles in two-dimensional channel filled with a viscoelastic fluid of FENE-CR type, which is generalized from a domain/distributed Lagrange multiplier method with a factorization approach for Oldroyd-B fluids developed in [J. Non-Newtonian Fluid Mech. 156 (2009) 95]. Numerical results suggest that the polymer extension limit L for the FENE-CR fluid has no effect on the final formation of vertical chain for the cases of two disks and three disks in two-dimensional narrow channel, at least for the value…
We study the settling of rigid oblates in quiescent fluid using interface-resolved Direct Numerical Simulations. In particular, an immersed boundary method is used to account for the dispersed solid phase together with lubrication correction and collision models to account for short-range particle-particle interactions. We consider semi-dilute suspensions of oblate particles with aspect ratio AR=1/3 and solid volume fractions $ϕ=0.5\%-10\%$. The solid-to-fluid density ratio $R=1.5$ and the Galileo number (i.e. the ratio between buoyancy and viscous forces) based on the diameter of a sphere wit…
The effect of turbulence on snow precipitation is not incorporated into present weather forecasting models. Here we show evidence that turbulence is in fact a key influence on both fall speed and spatial distribution of settling snow. We consider three snowfall events under vastly different levels of atmospheric turbulence. We characterize the size and morphology of the snow particles, and we simultaneously image their velocity, acceleration, and relative concentration over vertical planes about 30 m2 in area. We find that turbulence-driven settling enhancement explains otherwise contradictory…
A study on the spatial organization and velocity fluctuations of non Brownian spherical particles settling at low Reynolds number in a vertical Hele-Shaw cell is reported. The particle volume fraction ranged from 0.005 to 0.05, while the distance between cell plates ranged from 5 to 15 times the particle radius. Particle tracking revealed that particles were not uniformly distributed in space but assembled in transient settling clusters. The population distribution of these clusters followed an exponential law. The measured velocity fluctuations are in agreement with that predicted theoretical…
We use Direct Numerical Simulations (DNS) to investigate the dynamics of settling, bidisperse particles in isotropic turbulence. In agreement with previous studies, we find that without gravity (i.e. $Fr=\infty$, where $Fr$ is the Froude number), bidispersity leads to an enhancement of the relative velocities, and a suppression of their spatial clustering. For $Fr<1$, the relative velocities in the direction of gravity are enhanced by the differential settling velocities of the bidisperse particles, as expected. However, we also find that gravity can strongly enhance the relative velocities in…
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. 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 resp…
We investigate regular configurations of a small number of particles settling under gravity in a viscous fluid. The particles do not touch each other and can move relative to each other. The dynamics is analyzed in the point-particle approximation. A family of regular configurations is found with periodic oscillations of all the settling particles. The oscillations are shown to be robust under some out-of-phase rearrangements of the particles. In the presence of an additional particle above such a regular configuration, the particle periodic trajectories are horizontally repelled from the symm…
We develop a physical and computational model for performing fully coupled, particle-resolved Direct Numerical Simulations of cohesive sediment, based on the Immersed Boundary Method. The model distributes the cohesive forces over a thin shell surrounding each particle, thereby allowing for the spatial and temporal resolution of the cohesive forces during particle-particle interactions. The influence of the cohesive forces is captured by a single dimensionless parameter in the form of a cohesion number, which represents the ratio of cohesive and gravitational forces acting on a particle. We te…
Using Direct Numerical Simulations (DNS), we investigate how gravity modifies the multiscale dispersion of bidisperse inertial particles in isotropic turbulence. The DNS has a Taylor Reynolds number $R_λ=398$, and we simulate Stokes numbers (based on the Kolmogorov timescale) in the range $St\leq 3$ , and consider Froude numbers $Fr = 0.052$ and $\infty$, corresponding to strong gravity and no gravity, respectively. The degree of bidispersity is quantified by the difference in the Stokes number of the particles $|ΔSt|$. We first consider the mean-square separation of bidisperse particle-pairs …
We present experimental and computational results for the orientation distributions of slender fibers and ramified particles settling in an isotropic turbulent flow. The rotational dynamics of the particles is modeled using a slender-body theory that includes the inertial torque due to sedimentation that tends to rotate the particles toward a broadside orientation. The particles are assumed to rotate due to viscous forces associated with the turbulent velocity gradients occurring on the particle length scale. In the simulations, the turbulence is obtained from a stochastic model of the velocit…
The dynamics of dense finite-size particles in vertical channel flows of Newtonian and viscoelastic carrier fluids are examined using particle resolved simulations. Comparison to neutrally buoyant particles in the same configuration highlights the effect of settling. The particle volume fraction is $5\%$, and a gravity field acts counter to the flow direction. Despite a modest density ratio ($ρ_r = 1.15$), qualitative changes arise due to the relative velocity between the particle and fluid phases. While dense particles are homogeneously distributed in the core of the channel, the mean concent…
Direct 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 (Ga=121) and to steady oblique motion (Ga=178) in the case of one isolated sphere. For the multi-particle system we observe strong particle clustering only in the latter case. The geometry and time scales related to clustering are determined from Voronoi tesselation and particle-conditioned averaging. …
The gravity-driven motion of rigid particles in a viscous fluid is relevant in many natural and industrial processes, yet this has mainly been investigated for spherical particles. We therefore consider the sedimentation of non-spherical (spheroidal) isolated and particle pairs in a viscous fluid via numerical simulations using the Immersed Boundary Method. The simulations performed here show that the critical Galileo number for the onset of secondary motions decreases as the spheroid aspect ratio departs from 1. Above this critical threshold, oblate particles perform a zigzagging motion where…
Detailed data describing the motion of a rigid sphere settling in unperturbed fluid is generated by means of highly-accurate spectral/spectral-element simulations with the purpose of serving as a future benchmark case. A single solid-to-fluid density ratio of 1.5 is chosen, while the value of the Galileo number is varied from 144 to 250 such as to cover the four basic regimes of particle motion (steady vertical, steady oblique, oscillating oblique, chaotic). This corresponds to a range of the particle Reynolds number from 185 to 365. In addition to the particle velocity data, extracts of the f…
Hydrodynamic interactions between two identical elastic dumbbells settling under gravity in a viscous fluid at low-Reynolds-number are investigated within the point-particle model. Evolution of a benchmark initial configuration is studied, in which the dumbbells are vertical and their centres are aligned horizontally. Rigid dumbbells and pairs of separate beads starting from the same positions tumble periodically while settling down. We find that elasticity (which breaks time-reversal symmetry of the motion) significantly affects the system's dynamics. This is remarkable taking into account th…
