Eric Climent

Numerical simulations of random suspensions at finite Reynolds numbers

Abstract The sedimentation of solid spherical particles in an initially quiescent fluid is investigated through numerical simulations. Under conditions of Stokes flow, the results provide good agreement with experiments for the mean settling velocity while the velocity fluctuation levels grow with the size of the system in accordance with theoretical predictions for homogeneous suspensions. New results on finite Reynolds number suspensions are presented that illustrate the role of wake-induced interactions between particles. A significant reduction in the average settling velocity is explained by an enhancement of a wake-induced scattering process. Anisotropy in the fluid flow is evident and the evolution of velocity correlations is investigated for various particulate Reynolds numbers. Increases in Reynolds number tend to decrease the integral length scale of the fluctuating flow field and reduce significantly the Lagrangian time scale of the velocity fluctuations. Analysis of the evolution of fluctuation levels when the domain width grows indicates that inertial screening dramatically reduces the divergence.

Preferential accumulation of bubbles in Couette-Taylor flow patterns

We investigate the migration of bubbles in several flow patterns occurring within the gap between a rotating inner cylinder and a concentric fixed outer cylinder. The time-dependent evolution of the two-phase flow is predicted through three-dimensional Euler-Lagrange simulations. Lagrangian tracking of spherical bubbles is coupled with direct numerical simulation of the Navier-Stokes equations. We assume that bubbles do not influence the background flow (one-way coupling simulations). The force balance on each bubble takes into account buoyancy, added-mass, viscous drag, and shear-induced lift forces. For increasing velocities of the rotating inner cylinder, the flow in the fluid gap evolves from the purely azimuthal steady Couette flow to Taylor toroidal vortices and eventually a wavy vortex flow. The migration of bubbles is highly dependent on the balance between buoyancy and centripetal forces (mostly due to the centripetal pressure gradient) directed toward the inner cylinder and the vortex cores. Dep...

The effect of neutrally buoyant finite-size particles on channel flows in the laminar-turbulent transition regime

The presence of finite-size particles in a channel flow close to the laminar-turbulent transition is simulated with the Force Coupling Method which allows two-way coupling with the flow dynamics. Spherical particles with channel height-to-particle diameter ratio of 16 are initially randomly seeded in a fluctuating flow above the critical Reynolds number corresponding to single phase flow relaminarization. When steady-state is reached, the particle volume fraction is homogeneously distributed in the channel cross-section (ϕ ≅ 5%) except in the near-wall region where it is larger due to inertia-driven migration. Turbulence statistics (intensity of velocity fluctuations, small-scale vortical structures, wall shear stress) calculated in the fully coupled two-phase flow simulations are compared to single-phase flow data in the transition regime. It is observed that particles increase the transverse r.m.s. flow velocity fluctuations and they break down the flow coherent structures into smaller, more numerous an...

Dynamics of bidisperse suspensions under Stokes flows: Linear shear flow and sedimentation

Sedimenting and sheared bidisperse homogeneous suspensions of non-Brownian particles are investigated by numerical simulations in the limit of vanishing small Reynolds number and negligible inertia of the particles. The numerical approach is based on the solution of the three-dimensional Stokes equations forced by the presence of the dispersed phase. Multibody hydrodynamic interactions are achieved by a low order multipole expansion of the velocity perturbation. The accuracy of the model is validated on analytic solutions of generic flow configurations involving a pair of particles. The first part of the paper aims at investigating the dynamics of monodisperse and bidisperse suspensions embedded in a linear shear flow. The macroscopic transport properties due to hydrodynamic and nonhydrodynamic interactions (short range repulsion force) show good agreement with previous theoretical and experimental works on homogeneous monodisperse particles. Increasing the volumetric concentration of the suspension leads...

A Lagrangian VOF tensorial penalty method for the DNS of resolved particle-laden flows

The direct numerical simulation of particle flows is investigated by a Lagrangian VOF approach and penalty methods of second order convergence in space for incompressible flows interacting with resolved particles on a fixed structured grid. A specific Eulerian volume of fluid method is developed with a Lagrangian tracking of the phase function while the solid and divergence free constraints are ensured implicitly in the motion equations thanks to fictitious domains formulations, adaptive augmented Lagrangian approaches and viscous penalty methods. A specific strategy for handling particle collisions and lubrication effects is also presented. Various dilute particle laden flows are considered for validating the models and numerical methods. Convergence studies are proposed for estimating the time and space convergence orders of the global DNS approach. Finally, two dense particle laden flows are simulated, namely the flow across a fixed array of cylinders and the fluidization of 2133 particles in a vertical pipe. The numerical solutions are compared to existing theoretical and experimental results with success.

Collision barrier effects on the bulk flow in a random suspension

Simplified models are often used for the short-range interaction of spherical particles in dilute, liquid–solid suspensions. These may range from simple collision barriers to a more detailed inclusion of viscous lubrication forces. Results are given to illustrate the sensitivity of mean particle velocity, fluctuation levels, and microstructure to different parameters and barrier models.

Numerical simulation of bubble dispersion in turbulent Taylor-Couette flow

We investigate bubble dispersion in turbulent Taylor-Couette flow. The aim of this study is to describe the main mechanisms yielding preferential bubble accumulation in near-wall structures of the flow. We first proceed to direct numerical simulation of Taylor-Couette flows for three different geometrical configurations (three radius ratios η = R 1/R 2: η = 0.5, η = 0.72, and η = 0.91 with the outer cylinder at rest) and Reynolds numbers corresponding to turbulent regime ranging from 3000 to 8000. The statistics of the flow are discussed using two different averaging procedures that permit to characterize the mean azimuthal velocity, the Taylor vortices contribution and the small-scale turbulent fluctuations. The simulations are compared and validated with experimental and numerical data from literature. The second part of this study is devoted to bubble dispersion. Bubble accumulation is analyzed by comparing the dispersion obtained with the full turbulent flow field to bubble dispersion occurring at lower Reynolds numbers in previous works. Several patterns of preferential accumulation of bubbles have been observed depending on bubble size and the effect of gravity. For the smaller size considered, bubbles disperse homogeneously throughout the gap, while for the larger size they accumulate along the inner wall for the large gap width (η = 0.5). Varying the intensity of buoyancy yields complex evolution of the bubble spatial distribution. For low gravity effect, bubble entrapment is strong leading to accumulation along the inner wall in outflow regions (streaks of low wall shear stress). When buoyancy effect dominates on vortex trapping, bubbles rise through the vortices, while spiral patterns stretched along the inner cylinder are clearly identified. Force balance is analyzed to identify dominating forces leading to this accumulation and accumulation patterns are compared with previous experiments.

Turbulent fluid acceleration generates clusters of gyrotactic microorganisms.

The motility of microorganisms is often biased by gradients in physical and chemical properties of their environment, with myriad implications on their ecology. Here we show that fluid acceleration reorients gyrotactic plankton, triggering small-scale clustering. We experimentally demonstrate this phenomenon by studying the distribution of the phytoplankton Chlamydomonas augustae within a rotating tank and find it to be in good agreement with a new, generalized model of gyrotaxis. When this model is implemented in a direct numerical simulation of turbulent flow, we find that fluid acceleration generates multifractal plankton clustering, with faster and more stable cells producing stronger clustering. By producing accumulations in high-vorticity regions, this process is fundamentally different from clustering by gravitational acceleration, expanding the range of mechanisms by which turbulent flows can impact the spatial distribution of active suspensions.

Dynamic self-assembly of spinning particles

This paper presents a numerical study of the dynamic self-assembly of neutrally buoyant particles rotating in a viscous fluid. The particles experience simultaneously a magnetic torque that drives their individual spinning motion, a magnetic attraction toward the center of the domain and flow-induced interactions. Under specific conditions, a hydrodynamic repulsion balances the centripetal attraction of the magnetized particles, which leads to the formation of an aggregate of several particles. After a short transient, an aggregate of particles is formed that then rotates with a precession velocity related to the inter-particle distance. This dynamic self-assembly is stable (but not stationary) and the morphology depends on the number of particles. The numerical simulation is based on the Navier-Stokes equations coupled with the Lagrangian tracking of each individual particle. Multi-body interactions (at low but finite Reynolds number) are achieved by a local forcing of the momentum equations of the fluid flow. The agreement with experiments of spinning disks at a liquid-air interface is not only qualitative but also quantitative. Comparisons on the evolution of the characteristic scales of the aggregate with the rotation rate of individual particles clearly show that the numerical results are consistent with the experiments.

Dynamics of a two-dimensional upflowing mixing layer seeded with bubbles: Bubble dispersion and effect of two-way coupling

The evolution and structure of a spatially evolving two-dimensional mixing layer seeded with small bubbles are numerically investigated. The one-way coupling approach is first employed to show that characteristics of bubble dispersion are dominated by the possibility for sufficiently small bubbles to be captured in the core of the vortices. A stability analysis of the ordinary differential equation system governing bubble trajectories reveals that this entrapment process is governed by the presence of stable fixed points advected by the mean flow. Two-way coupling simulations are then carried out to study how the global features of a two-dimensional flow are affected by bubble-induced disturbances. The local interaction mechanism between the two phases is first analyzed using detailed simulations of a single bubbly vortex. The stability of the corresponding fixed point is found to be altered by the collective motion of bubbles. For trapped bubbles, the interphase momentum transfer yields periodic sequence...