Turbulent transport of material particles: an experimental study of finite size effects

Numerical Study on the Shear Stress Characteristics of Open-Channel Flow over Rough Beds

Bed shear stress is an important measure of benthic habitats since it is related to many ecological processes. In this study, we focused on the fluctuating characteristics of shear stress in rough-bed open-channel flows. The roughness element method was adopted to mimic natural rough beds and the Improved Delayed Detached Eddy Simulation (IDDES) model was used to obtain comprehensive information about shear stress near the rough bed. Three arrangement patterns of the roughness elements were simulated to compare their effects on flow structure and shear stresses. The arrangements of the roughness elements altered the Reynold stress and turbulent kinetic energy characteristics, due to the variance of blockage in lateral directions that led to flow detachment and changes in the flow directions. Quadrant analysis revealed the spatial variations of the instantaneous shear stress burst events at different locations in the wake. By using spectrum analysis, the accumulation of shear-stress energy from small to large vortex scales was estimated, which revealed that the instantaneous effect of the shear stress was significantly stronger than the effect of the time-averaged shear stress, especially on small scales. The results of this study suggest the significance of the fluctuation part of shear stress in further studies on ecological processes.

Two-dimensional numerical model of Marangoni surfers: From single swimmer to crystallization

We numerically study the dynamics of an ensemble of Marangoni surfers in a two-dimensional and unconfined space. The swimmers are modeled as Gaussian sources of surfactant generating surface tension gradients and are shown to follow the Marangoni flow filtered at their spatial scale in the lubrication regime, an unstable situation leading to spontaneous motion as soon as the Marangoni effect is intense enough. As the system is fully unconstrained, it is possible to study the various dynamical regimes from single swimmer, two-body interaction, to the many-particles case characterized by an efficient particle dispersion. We show that, although the present model is very simple, it reproduces the experimentally observed transition between a regime of dispersion by random agitation when the number of swimmers is moderate to the regime of crystallization with imperfect hexagonal lattice at high density.

Influence of particle-fluid density ratio on the dynamics of finite-size particles in homogeneous isotropic turbulent flows

In this paper, direct numerical simulations of particle-laden homogeneous isotropic turbulence are performed using lattice Boltzmann method incorporating interpolated bounce-back scheme. Four different particle-fluid density ratios are considered to explore how particles with different particle-fluid density ratios respond to the turbulence. Overall particle dynamics in the homogeneous isotropic turbulence such as the Lagrangian statistics of single particle and the preferential concentration of particles are investigated. Results show that particle acceleration and angular acceleration are more intermittent than velocity and angular velocity for finite-size particles with different particle-fluid density ratios. The preferential concentration of particles is investigated using radial distribution function and Voronoï tessellation, and the preferential concentration is more profound for particles with two intermediate particle-fluid density ratios. The Voronoï analysis indicates that the distribution of Voronoï cells satisfy the log-normal distribution better than the gamma distribution. The mechanism of preferential concentration is analyzed using the sweep-stick mechanism and drift mechanism. Results show that although a higher probability of having particles located near the sticky points is found, the sticky mechanism is very weak for large density ratios. The particle clustering is then found to be better qualitatively described by the drift mechanism.

Sedimentation of a suspension of paramagnetic particles in an external magnetic field

We investigate the sedimentation of initially packed paramagnetic particles in the presence of a homogeneous external magnetic field, in a Hele-Shaw cell filled with water. Although the magnetic susceptibility of the particles is small and the particle-particle-induced magnetic interactions are significantly smaller compared to the gravitational acceleration, we do observe a measurable reduction of the decompaction rate as the amplitude of the applied magnetic field is increased. While induced magnetic dipole-dipole interactions between particles can be either attractive or repulsive depending on the particles relative alignment, our observations reveal an effective overall enhancement of the cohesion of the initial pack of particles due to the induced interactions, very likely promoting internal chain forces in the initial pack of particles. The influence of the magnetic field on the particles once they disperse after being decompacted is, however, found to remain marginal.

Chain formation can enhance the vertical migration of phytoplankton through turbulence

Many species of motile phytoplankton can actively form long multicellular chains by remaining attached to one another after cell division. While chains swim more rapidly than single cells of the same species, chain formation also markedly reduces phytoplankton's ability to maintain their bearing. This suggests that turbulence, which acts to randomize swimming direction, could sharply attenuate a chain's ability to migrate between well-lit surface waters during the day and deeper nutrient-rich waters at night. Here, we use numerical models to investigate how chain formation affects the migration of phytoplankton through a turbulent water column. Unexpectedly, we find that the elongated shape of chains helps them travel through weak to moderate turbulence much more effectively than single cells, and isolate the physical processes that confer chains this ability. Our findings provide a new mechanistic understanding of how turbulence can select for phytoplankton with elongated morphologies and may help explain why turbulence triggers chain formation.

Experimental Observation of Inertial Particles through Idealized Hydroturbine Distributor Geometry

To increase and maintain existing hydropower capacity within biological performance-based regulations, predictive simulation methods are needed that can reliably estimate the risk to fish passing through flow passage routes at hydropower facilities. One of the central challenges is to validate the software capabilities for simulating the trajectories, including collisions, of inertial particles against laboratory data. In this work, neutrally buoyant spherical- and rod-shaped beads were released upstream of laboratory-scale geometries representative of the distributor of a hydroturbine. The experimental campaign involved a test matrix of 24 configurations with variations in bead geometry, collision target geometry, flow speeds, and release locations. A total of more than 10,000 beads were recorded using high-speed video cameras and analyzed using particle tracking software. Collision rates from 1–7% were observed for the cylinder geometry and rates of 1–23% were observed for the vane array over the range of test configurations.

Dispersion of Air Bubbles in Isotropic Turbulence

Bubbles play an important role in the transport of chemicals and nutrients in many natural and industrial flows. Their dispersion is crucial to understanding the mixing processes in these flows. Here we report on the dispersion of millimetric air bubbles in a homogeneous and isotropic turbulent flow with a Taylor Reynolds number from 110 to 310. We find that the mean squared displacement (MSD) of the bubbles far exceeds that of fluid tracers in turbulence. The MSD shows two regimes. At short times, it grows ballistically (∝τ^{2}), while at larger times, it approaches the diffusive regime where the MSD∝τ. Strikingly, for the bubbles, the ballistic-to-diffusive transition occurs one decade earlier than for the fluid. We reveal that both the enhanced dispersion and the early transition to the diffusive regime can be traced back to the unsteady wake-induced motion of the bubbles. Further, the diffusion transition for bubbles is not set by the integral timescale of the turbulence (as it is for fluid tracers and microbubbles), but instead, by a timescale of eddy crossing of the rising bubbles. The present findings provide a Lagrangian perspective towards understanding mixing in turbulent bubbly flows.

Binary-fluid turbulence: Signatures of multifractal droplet dynamics and dissipation reduction

We study the challenging problem of the advection of an active, deformable, finite-size droplet by a turbulent flow via a simulation of the coupled Cahn-Hilliard-Navier-Stokes (CHNS) equations. In these equations, the droplet has a natural two-way coupling to the background fluid. We show that the probability distribution function of the droplet center of mass acceleration components exhibit wide, non-Gaussian tails, which are consistent with the predictions based on pressure spectra. We also show that the droplet deformation displays multifractal dynamics. Our study reveals that the presence of the droplet enhances the energy spectrum E(k), when the wave number k is large; this enhancement leads to dissipation reduction.

Single-Particle Motion and Vortex Stretching in Three-Dimensional Turbulent Flows

Three-dimensional turbulent flows are characterized by a flux of energy from large to small scales, which breaks the time reversal symmetry. The motion of tracer particles, which tend to lose energy faster than they gain it, is also irreversible. Here, we connect the time irreversibility in the motion of single tracers with vortex stretching and thus with the generation of the smallest scales.

Stochastic dynamics of particles trapped in turbulent flows

The long-time dynamics of large particles trapped in two nonhomogeneous turbulent shear flows is studied experimentally. Both flows present a common feature, a shear region that separates two colliding circulations, but with different spatial symmetries and temporal behaviors. Because large particles are less and less sensitive to flow fluctuations as their size increases, we observe the emergence of a slow dynamics corresponding to back-and-forth motions between two attractors, and a super-slow regime synchronized with flow reversals when they exist. Such dynamics is substantially reproduced by a one-dimensional stochastic model of an overdamped particle trapped in a two-well potential, forced by a colored noise. An extended model is also proposed that reproduces observed dynamics and trapping without potential barrier: the key ingredient is the ratio between the time scales of the noise correlation and the particle dynamics. A total agreement with experiments requires the introduction of spatially nonhomogeneous fluctuations and a suited confinement strength.

Wake-Driven Dynamics of Finite-Sized Buoyant Spheres in Turbulence

Particles suspended in turbulent flows are affected by the turbulence and at the same time act back on the flow. The resulting coupling can give rise to rich variability in their dynamics. Here we report experimental results from an investigation of finite-sized buoyant spheres in turbulence. We find that even a marginal reduction in the particle's density from that of the fluid can result in strong modification of its dynamics. In contrast to classical spatial filtering arguments and predictions of particle models, we find that the particle acceleration variance increases with size. We trace this reversed trend back to the growing contribution from wake-induced forces, unaccounted for in current particle models in turbulence. Our findings highlight the need for improved multiphysics based models that account for particle wake effects for a faithful representation of buoyant-sphere dynamics in turbulence.

Visualization of two-fluid flows of superfluid helium-4

Cryogenic flow visualization techniques have been proved in recent years to be a very powerful experimental method to study superfluid turbulence. Micron-sized solid particles and metastable helium molecules are specifically being used to investigate in detail the dynamics of quantum flows. These studies belong to a well-established, interdisciplinary line of inquiry that focuses on the deeper understanding of turbulence, one of the open problem of modern physics, relevant to many research fields, ranging from fluid mechanics to cosmology. Progress made to date is discussed, to highlight its relevance to a wider scientific community, and future directions are outlined. The latter include, e.g., detailed studies of normal-fluid turbulence, dissipative mechanisms, and unsteady/oscillatory flows.

Inertial range scaling in rotations of long rods in turbulence

We derive a scaling relationship for the mean square rotation rate of rods with lengths in the inertial range in turbulence: <p(i)p(i)> ∝ l(-4/3). We present experimental measurements of the rotational statistics of neutrally buoyant rods with lengths 2.8<l/η<72.9, and find that the measurements approach the predicted scaling. The approach to inertial range scaling is shown to be more complex than anticipated with an overshoot and approach to the scaling from above. For all rod lengths, the correlation time of the Lagrangian autocorrelation of the rotation rate scales as the turnover time of the eddies of the size of the rod. Measuring rotational dynamics of single long rods provides a new way to access the spatial structure of the flow at different length scales.

Clustering of finite-size particles in turbulence

We investigate experimentally the spatial distributions of heavy and neutrally buoyant particles of finite size in a fully turbulent flow. Because their Stokes number (i.e., the ratio of the particle viscous relaxation time to a typical flow time scale) is close to unity, one may expect both classes of particles to aggregate in specific flow regions. This is not observed. Using a Voronoï analysis we show that neutrally buoyant particles sample turbulence homogeneously, whereas heavy particles do cluster. These results show that several dimensionless numbers are needed in the modeling (and understanding) of the behavior of particles entrained by turbulent motions.

Analysis of intermittency in under-resolved smoothed-particle-hydrodynamics direct numerical simulations of forced compressible turbulence

We perform three-dimensional under-resolved direct numerical simulations of forced compressible turbulence using the smoothed particle hydrodynamics (SPH) method and investigate the Lagrangian intermittency of the resulting hydrodynamic fields. The analysis presented here is motivated by the presence of typical stretched tails in the probability density function (PDF) of the particle accelerations previously observed in two-dimensional SPH simulations of uniform shear flow [Ellero et al., Phys. Rev. E 82, 046702 (2010)]. In order to produce a stationary isotropic compressible turbulent state, the real-space stochastic forcing method proposed by Kida and Orszag is applied, and the statistics of particle quantities are evaluated. We validate our scheme by checking the behavior of the energy spectrum in the supersonic case where the expected Burgers-like scaling is obtained. By discretizing the continuum equations along fluid particle trajectories, the SPH method allows us to extract Lagrangian statistics in a straightforward fashion without the need for extra tracer particles. In particular, Lagrangian PDF of the density, particle accelerations as well as their Lagrangian structure functions and local scaling exponents are analyzed. The results for low-order statistics of Lagrangian intermittency in compressible turbulence demonstrate the implicit subparticle-scale modeling of the SPH discretization scheme.

Rotational intermittency and turbulence induced lift experienced by large particles in a turbulent flow

The motion of a large, neutrally buoyant, particle freely advected by a turbulent flow is determined experimentally. We demonstrate that both the translational and angular accelerations exhibit very wide probability distributions, a manifestation of intermittency. The orientation of the angular velocity with respect to the trajectory, as well as the translational acceleration conditioned on the spinning velocity, provides evidence of a lift force acting on the particle.

Tracking the dynamics of translation and absolute orientation of a sphere in a turbulent flow

We study the six-dimensional dynamics--position and orientation--of a large sphere advected by a turbulent flow. The movement of the sphere is recorded with two high-speed cameras. Its orientation is tracked using a novel, efficient algorithm; it is based on the identification of possible orientation "candidates" at each time step, with the dynamics later obtained from maximization of a likelihood function. Analysis of the resulting linear and angular velocities and accelerations reveal a surprising intermittency for an object whose size lies in the inertial range, close to the integral scale of the underlying turbulent flow.

The Lagrangian exploration module: an apparatus for the study of statistically homogeneous and isotropic turbulence

We present an apparatus that generates statistically homogeneous and isotropic turbulence with a mean flow that is less than 10% of the fluctuating velocity in a volume of the size of the integral length scale. The apparatus is shaped as an icosahedron where at each of the 12 vertices the flow is driven by independently controlled propellers. By adjusting the driving of the different propellers the isotropy and homogeneity of the flow can be tuned, while keeping the mean flow weak.

Acceleration statistics of neutrally buoyant spherical particles in intense turbulence

We measure acceleration statistics of neutrally buoyant spherical particles with a diameter 0.4 < d/eta < 27 in intense turbulence (400 < R(lambda) < 815). High speed cameras image polystyrene tracer particles in a flow between counterrotating disks. The measurements of acceleration variance <a(2)> clearly resolve the transition from the tracer like behavior of small particles to the much smaller accelerations of large particles. Two models of this transition from small to large particle behavior are critically examined. For d > 5eta, <a(2)> decreases with the diameter as d(-2/3), in agreement with inertial range scaling arguments. Consistent with earlier work, we find that the scaled acceleration probability density function shows very little dependence on particle size.

Transport of finite-sized particles in chaotic flow

By extending traditional particle tracking techniques, we study the dynamics of neutrally buoyant finite-sized particles in a spatiotemporally chaotic flow. We simultaneously measure the flow field and the trajectories of millimeter-scale particles so that the two can be directly compared. While the single-point statistics of the particles are indistinguishable from the flow statistics, the particles often move in directions that are systematically different from the underlying flow. These differences are especially evident when Lagrangian statistics are considered.