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Using DNS-based Eulerian-Lagrangian simulations, we investigate the dynamics of small gyrotactic swimmers in free-surface turbulence. We consider open channel flow turbulence in which bottom-heavy swimmers are dispersed. Swimmers are characterized by different vertical stability, so that some realign to swim upward with a characteristic time smaller than the Kolmogorov time scale, while others possess a re-orientation time longer than the Kolmogorov time scale. We cover one order of magnitude in the flow Reynolds number, and two orders of magnitude in the stability number, which is a measure of bottom heaviness. We observe that large-scale advection dominates vertical motion when the stability number, scaled on the local Kolmogorov time scale of the flow, is larger than unity: This condition is associated to enhanced migration towards the surface, particularly at low Reynolds number, when swimmers can rise through surface renewal motions that originate directly from the bottom-boundary turbulent bursts. Conversely, small-scale effects become more important when the Kolmogorov-based stability number is below unity: Under this condition, migration towards the surface is hindered, particularly at high Reynolds, when bottom-boundary bursts are less effective in bringing bulk fluid to the surface. In an effort to provide scaling arguments to improve predictions of models for motile micro-organisms in turbulent water bodies, we demonstrate that a Kolmogorov-based stability number around unity represents a threshold beyond which swimmer capability to reach the free surface and form clusters saturates.

The motion of particles settling in turbulence is an intriguing problem, which is relevant to an in-depth understanding of planktons in marine flows or the design of photobioreactors. This work studies the motion, orientation and distribution of inertia-less spheroidal particles settling in vertical channel flows by direct numerical simulations. We show that, compared to spherical tracers, the settling velocity of spheroidal tracers is enhanced due to preferential orientation and local clustering (not due to particle inertia, in the present case). Prolate spheroids tend to align their symmetry axes in the direction of gravity while oblate ones align perpendicular to it. Both kinds of particles attain a larger slip velocity in the direction of gravity and, therefore, settle faster. We also show that particles sample preferentially regions of high fluid velocity in downward flow and regions of low fluid velocity in upward flow. Such preferential sampling, which also contributes to the enhancement of settling, is the result of clustering. Besides, tracer particles are observed to accumulate in the channel center in downward flow and near the wall in upward flow: We show that tracer transport in the wall-normal direction is controlled by the particle-to-fluid slip velocity and by clustering. The slip velocity dominates the transport initially, but tracers increasingly cluster in regions with opposite flow direction as they accumulate either in the channel center or near the wall. Clustering appears to be associate with the coherent structures that characterize wall turbulence, and tracer distribution in the wall-normal direction is found to reach a steady state when the two qualitatively different mechanisms balance each other.

We examine the effect of wind-induced shear on the orientation and distribution of motile micro-swimmers in free-surface turbulence. Winds blowing above the air–water interface can influence the distribution and productivity of motile organisms via the shear generated just below the surface. Swimmer dynamics depend not only on the advection of the fluid but also on external stimuli like nutrient concentration, light, gravity, which are in turn coupled to and influenced by the distribution of the swimmers. Here we focus on gyrotaxis, resulting from the gravitational torque generated by an asymmetric mass distribution within the organism. The combination of such torque with the viscous torque due to shear can reorient swimmers, reducing their vertical migration and causing entrapment in horizontal fluid layers. Through DNS-based Euler–Lagrangian simulations we investigate the effect of wind-induced shear on the motion of gyrotactic swimmers in turbulent open channel flow. We consider different wind forcing and swimmers with different reorientation time (reflecting the ability to react to turbulent fluctuations). We show that only stable (high-gyrotaxis) swimmers may reach the surface and form densely concentrated filaments, the topology of which depends on the wind direction. Otherwise swimmers exhibit weaker vertical fluxes and loose segregation at the surface.

In this article, we examine the effect of shear on scalar transport in double diffusive convection (DDC). DDC results from the competing action of a stably stratified, rapidly diffusing scalar (temperature) and an unstably stratified, slowly diffusing scalar (salinity), which is characterized by fingering instabilities. We investigate, for the first time, the effect of shear on the diffusive and convective contributions to the total scalar transport flux within a confined fluid layer, examining also the associated fingering dynamics and flow structure. We base our analysis on fully resolved numerical simulations under the Oberbeck–Boussinesq condition. The problem has five governing parameters: The salinity Prandtl number, Prs (momentum-to-salinity diffusivity ratio); the salinity Rayleigh number, Ras (measure of the fluid instability due to salinity differences); the Lewis number, Le (thermal-to-salinity diffusivity ratio); the density ratio, Λ (measure of the effective flow stratification), and the shear rate, Γ. Simulations are performed at fixed Prs, Ras, Le, and Λ, while the effect of shear is accounted for by considering different values of Γ. Preliminary results show that shear tends to damp the growth of fingering instability, leading to highly anisotropic DDC dynamics associated with the formation of regular salinity sheets. These dynamics result in significant modifications of the vertical transport rates, giving rise to negative diffusive fluxes of salinity and significant reduction of the total scalar transport, particularly of its convective part.

Non-spherical particles suspended in fluid flows are subject to hydrodynamic torques generated by fluid velocity gradients. For small axisymmetric particles, the most popular formulation of hydrodynamic torques is that given by Jeffery (Proc R Soc Lond A 102:161–179, 1922), which is valid for uniform shear flow in the viscous Stokes regime. In the lack of simple alternative formulations outside the Stokes regime, the Jeffery formulation has been widely applied to inertial particles in turbulent flows, where it is bound to produce inaccurate results. In this paper we quantify the statistical error incurred when the Jeffery formulation is used to study the motion of elongated axisymmetric particles under nonlinear shear flow conditions. Considering the archetypical case of prolate ellipsoidal particles in turbulent channel flow, we show that error for ellipsoids of the same length, l, as the Kolmogorov scale of the flow, $$\eta _K$$ , is indeed small (order $$1\%$$ ) but increases exponentially up to $$l \simeq 10 \eta _K$$ before becoming almost independent of elongation.

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In this paper, we investigate the dynamics of flexible fibers in turbulent channel flow. Fibers are longer than the Kolmogorov length scale of the carrier flow, and their velocity relative to the surrounding fluid is non-negligible. Our aim is to examine the effect of local shear and turbulence anisotropy on the translational and rotational behavior of the fibers, considering different elongation (parameterized by the aspect ratio, $$\lambda $$ ) and inertia (parameterized by the Stokes number, St). To these aims, we use a Eulerian–Lagrangian approach based on direct numerical simulation of turbulence in the dilute regime. Fibers are modeled as chains of sub-Kolmogorov rods (referred to as elements hereinafter) connected through ball-and-socket joints that enable bending and twisting under the action of the local fluid velocity gradients. Velocity, orientation, and concentration statistics, extracted from simulations at shear Reynolds number $$Re_{\tau }=150$$ (based on the channel half height), are presented to give insights into the complex fiber–turbulence interactions that arise when non-sphericity and deformability add to inertial bias. These statistical observables are examined at varying aspect ratios (namely $$\lambda _{r}=l_{r}/a=2$$ and 5, with $$l_{r}$$ the semi-length of each rod-like element r composing the fiber and a its cross-sectional radius) and varying fiber inertia (considering values of the element Stokes number, $$St_{r}=1$$ , 5, 30). To highlight the effect of flexibility, statistics are compared with those obtained for fibers of equal mass that translate and rotate as rigid bodies relative to the surrounding fluid. Flexible fibers exhibit a stronger tendency to accumulate in the very-near-wall region, where they appear to be trapped by the same inertia-driven mechanisms that govern the preferential concentration of spherical particles and rigid fibers in bounded flows. In such region, the bending of flexible fibers increases as inertia decreases, and fiber deformation appears to be controlled by mean shear and turbulent Reynolds stresses. Preferential segregation into low-speed streaks and preferential orientation in the mean flow direction is also observed.

In this paper, we examine from a statistical point of view the deformation of flexible fibers in turbulent channel flow. Fibers are longer than the Kolmogorov length scale of the carrier flow and have finite inertia. Our aim is to examine the effect of local shear and turbulence anisotropy on fiber twisting and bending, when shape effects add to the inertial bias. To these aims, we use an Eulerian–Lagrangian approach based on direct numerical simulation of turbulence in dilute flow conditions. Fibers are modelled as chains of sub-Kolmogorov rods (referred to as elements hereinafter) interconnected by holonomic constraints that enable relative rotation of neighbouring elements. Statistics are computed from simulations at shear Reynolds number $${\text{Re}}_{\tau }=150$$, based on the channel half height, for fibers with different aspect ratio, $$\lambda _r$$ (defined as the ratio between the length $$l_r$$ of each element r composing the fiber and its cross-sectional radius, a), and different inertia, parameterized by the Stokes number of the element, $$St_r$$. We show that bending of flexible fibers is in general stronger in the bulk of the flow, where they are subject to turbulent velocity fluctuations only. Near the wall, fibers are more easily stretched by the mean shear, especially for large-enough inertia ($$St_r > 5$$ in our simulations). In spite of this different dynamics, which is connected to the anisotropy of the flow, we find that the fiber end-to-end distance reaches a steady state regardless of fiber location with respect to the wall.

When hovering over sandy terrain, the rotor of helicopters generates a downward jet that induces resuspension of dust and debris. We investigate the mechanisms that govern particle resuspension in such flow using an Eulerian–Lagrangian approach based on large-eddy simulation of turbulence. The wake generated by the helicopter is modelled as a vertical impinging jet, to which a sequence of periodically forced azimuthal vortices is superposed. The resulting flow field provides a unique range of flow scales with which the particles can interact. Downstream of the impingement region, layers of negative azimuthal vorticity (secondary vortices) form on the upwash side of the primary azimuthal (large-scale) vortices. These layers then detach from the surface together with the near-wall (small-scale) vortices populating the wall-jet region. We show how the dynamics of sediments is governed by its interaction with these structures. After initial lift off from the impingement surface, particles accumulate in regions where near-wall vortices roll around the impinging azimuthal vortex, forming rib-like structures that either propel particles away from the azimuthal vortex or entrap them in the shear layer between the azimuthal and secondary vortices. We demonstrate that these trapped particles are more likely to reach the outer flow region and generate a persistent cloud of airborne particles. We also show that, in a time-averaged sense, particle resuspension and deposition fluxes balance each other near the impingement surface.

The effect on heat transfer produced by injection of solid microparticles with high thermal capacity in turbulent channel flow is analyzed. Convection is forced by letting the fluid flow between a hot plate and a cold plate under zero-gravity conditions. An Eulerian–Lagrangian approach based on direct numerical simulation of turbulence (shear Reynolds number Re* = 150 and molecular Prandtl number Pr = 3) and on point-particle tracking is used. Full momentum and energy coupling between fluid and particles is considered. Different particle sizes and different particle concentrations are examined.

Deposition and entrainment of particles in turbulent flows are crucial in a number of technological applications and environmental processes. We present a review of recent results from our previous works, which led to physical insights on these phenomena. These results were obtained from a systematic numerical study based on the accurate resolution – Direct Numerical Simulation via a pseudo-spectral approach – of the turbulent flow field, and on Lagrangian tracking of particles under different modelling assumptions. We underline the multiscale aspect of wall turbulence, which has challenged scientists to devise simple theoretical models adequate to fit experimental data, and we show that a sound rendering of wall turbulence mechanisms is required to produce a physical understanding of particle deposition and re-entrainment. This physical understanding can be implemented in more applied simulation techniques, such as Large-Eddy Simulation. Our arguments are based also on the phenomenology of coherent structures and on the examination of flow topology in connection with particle preferential distribution. Starting from these concepts, reasons why theoretical predictions may fail are examined together with the requirements which must be fulfilled by suitable predictive models.

The Eulerian-Lagrangian approach based on Large-Eddy Simulation (LES) is one of the most promising and viable numerical tools to study particle-laden turbulent flows, when the computational cost of Direct Numerical Simulation (DNS) becomes too expensive. The applicability of this approach is however limited if the effects of the Sub-Grid Scales (SGSs) of the flow on particle dynamics are neglected. In this paper, we propose to take these effects into account by means of a Lagrangian stochastic SGS model for the equations of particle motion. The model extends to particle-laden flows the velocity-filtered density function method originally developed for reactive flows. The underlying filtered density function is simulated through a Lagrangian Monte Carlo procedure that solves a set of Stochastic Differential Equations (SDEs) along individual particle trajectories. The resulting model is tested for the reference case of turbulent channel flow, using a hybrid algorithm in which the fluid velocity field is provided by LES and then used to advance the SDEs in time. The model consistency is assessed in the limit of particles with zero inertia, when “duplicate fields” are available from both the Eulerian LES and the Lagrangian tracking. Tests with inertial particles were performed to examine the capability of the model to capture the particle preferential concentration and near-wall segregation. Upon comparison with DNS-based statistics, our results show improved accuracy and considerably reduced errors with respect to the case in which no SGS model is used in the equations of particle motion.

In this paper we study breakage rate statistics of small colloidal aggregates in non-homogeneous anisotropic turbulence. We use pseudo-spectral direct numerical simulation of turbulent channel flow and Lagrangian tracking to follow the motion of the aggregates, modelled as sub-Kolmogorov massless particles. We focus specifically on the effects produced by ductile rupture: This rupture is initially activated when fluctuating hydrodynamic stresses exceed a critical value, $\sigma>\sigma_{cr}$, and is brought to completion when the energy absorbed by the aggregate meets the critical breakage value. We show that ductile rupture breakage rates are significantly reduced with respect to the case of instantaneous brittle rupture (i.e. breakage occurs as soon as $\sigma>\sigma_{cr}$). These discrepancies are due to the different energy values at play as well as to the statistical features of energy distribution in the anisotropic turbulence case examined., Comment: Accepted for publication in Phys. Rev. E (April 2015)

The distribution of inertial particles in turbulent flows is strongly non-homogeneous and is driven by the structure of the underlying carrier flow field. In this work, we use DNS combined with Lagrangian particle tracking to characterize the effect of inertia on particle preferential accumulation. We compare the Eulerian statistics computed for fluid and particles of different size, and observe differences in terms of distribution patterns and deposition rates which depend on particle inertia. Specifically, different statistics are related to the selective interaction occurring between particles and coherent flow structures. This selective response causes a preferential sampling of the flow field by the particles and eventually leads to the well-known phenomenon of long-term particle accumulation in the boundary layer. We try to measure particle preferential accumulation with a Lagrangian parameter related to the rate of deformation of an elemental volume of the particle phase along a particle trajectory. In the frame of the Lagrangian approach, this parameter is mathematically defined as the particle position Jacobian, J ( t ) , computed along a particle path. This quantity is related to the local compressibility/divergence of the particle velocity field. Lagrangian statistics of J ( t ) show that compressibility increases for increasing particle response times τ p + (up to τ p + = 25 and within the time span covered by the simulation).

Particle transfer in the wall region of turbulent boundary layers is dominated by the coherent structures which control the turbulence regeneration cycle. Coherent structures bring particles toward and away from the wall and favour particle segregation in the viscous region, giving rise to non-uniform particle distribution profiles which peak close to the wall. The object of this work is to understand the reasons for higher particle concentration in the wall region by examining turbulent transfer of heavy particles to and away from the wall in connection with the coherent structures of the boundary layer. We will examine the behaviour of a dilute dispersion of heavy particles – flyashes in air – in a vertical channel flow, using pseudo-spectral direct numerical simulation to calculate the turbulent flow field at a shear Reynolds number Reτ = 150, and Lagrangian tracking to describe the dynamics of particles. Drag force, gravity and Saffman lift are used in the equation of motion for the particles, which are assumed to have no influence on the flow field. Particle interaction with the wall is fully elastic. As reported in several previous investigations, we found that particles are transferred by sweeps – Q2 type events – in the wall region, where they preferentially accumulate in the low-speed streak environments, whereas ejections – Q4 type events – transfer particles from the wall region to the outer flow. We quantify the efficiency of the instantaneous realizations of the Reynolds stresses events in transferring different size particles to the wall and away from the wall, respectively. Our findings confirm that sweeps and ejections are efficient transfer mechanisms for particles. In particular, we find that only those sweep and ejection events with substantial spatial coherence are effective in transferring particles. However, the efficiency of the transfer mechanisms is conditioned by the presence of particles to be transferred. In the case of ejections, particles are more rarely available since, when in the viscous wall layer, they are concentrated under the low-speed streaks. Even though the low-speed streaks are ejection-like environments, particles remain trapped for a long time. This phenomenon, which causes accumulation of particles in the near-wall region, can be interpreted in terms of overall fluxes toward and away from the wall by the theory of turbophoresis. This theory, proposed initially by Caporaloni et al. (1975) and re-examined later by Reeks (1983), can help to explain the existence of net particle fluxes toward the wall as a manifestation of the skewness in the velocity distribution of the particles (Reeks 1983). To understand the local and instantaneous mechanisms which give rise to the phenomenon of turbophoresis, we focus on the near-wall region of the turbulent boundary layer. We examine the role of the rear-end of a quasistreamwise vortex very near to the wall in preventing particles in the proximity of the wall from being re-entrained by the pumping action of the large, farther from the wall, forward-end of a following quasi-streamwise vortex. We examine several mechanisms for turbulence structures near the wall and we find that the mechanism based on the archetypal quasi-streamwise structures identified by Schoppa & Hussain (1997), the parent–offspring regeneration cycle for near-wall quasi-streamwise vortices discussed by Brooke & Hanratty (1993), and the mechanism based on coherent packets of hairpin vortices, the fundamental super-structure characterized by Adrian, Meinhart & Tomkins (2000), all depict the same characteristic pattern which is responsible for particle trapping very near to the wall.

The dispersion of small inertial particles in inhomogeneous turbulent flows is important in a number of industrial applications and environmental phenomena, such as, for instance, mixing, combustion, depulveration, spray dynamics, pollutant dispersion or cloud dynamics. Direct Numerical Simulations (DNS) of turbulence coupled with Lagrangian Particle Tracking (LPT) have demonstrated their capability to capture the mechanisms characterizing particle dynamics in turbulent flows (see e.g. [1]). Due to the computational requirements of DNS, however, analysis of problems characterized by complex geometries and high Reynolds numbers demands alternative approaches; Large-Eddy Simulation (LES) is increasingly gaining in popularity, especially for cases where the large flow scales control particle motion. LES is based on a filtering approach of the fluid phase governing equations, in which the unresolved Sub-Grid Scales (SGS) of turbulence are modeled.

We study the dispersion of light particles floating on a flat shear-free surface of an open channel in which the flow is turbulent. This configuration mimics the motion of buoyant matter (e.g., phytoplankton, pollutants, or nutrients) in water bodies when surface waves and ripples are smooth or absent. We perform direct numerical simulation of turbulence coupled with Lagrangian particle tracking, considering different values of the shear Reynolds number (${\mathrm{Re}}_{\ensuremath{\tau}}=171$ and 509) and of the Stokes number ($0.06l\mathrm{St}l1$ in viscous units). Results show that particle buoyancy induces clusters that evolve towards a long-term fractal distribution in a time much longer than the Lagrangian integral fluid time scale, indicating that such clusters overlive the surface turbulent structures which produced them. We quantify cluster dynamics, crucial when modeling dispersion in free-surface flow turbulence, via the time evolution of the cluster correlation dimension.

In this work we study deposition of particles and droplets in non-rotating swirled turbulent pipe flow. We aim at verifying whether the capability of swirl to enhance particle separation from the core flow and the capability of turbulence to efficiently trap particles at the wall can co-exist to optimize collection efficiency in axial separators. We perform an Eulerian–Lagrangian study based on Direct Numerical Simulation (DNS) of turbulence, considering the effect of different swirl intensities on turbulence structures and on particle transfer at varying particle inertia. We show that, for suitably-chosen flow parameters, swirl may be superimposed to the base flow without disrupting near-wall turbulent structures and their regeneration mechanisms. We also quantify collection efficiency demonstrating for the first time that an optimal synergy between swirl and wall turbulence can be identified to promote separation of particles and droplets.

In this paper, the rotation of rigid fibers is investigated for the reference case of turbulent channel flow. The aim of the study is to examine the effect of local shear and turbulence anisotropy on the rotational dynamics of fibers with different elongation and inertia. To this aim, statistics of the fiber angular velocity, Ω, are extracted from direct numerical simulation of turbulence at shear Reynolds number Reτ = 150 coupled with Lagrangian tracking of prolate ellipsoidal fibers with Stokes number, St, ranging from 3 to 100 and aspect ratio, λ, ranging from 1 to 50. Accordingly, the fiber-to-fluid density ratio ranges from \({S \simeq 7}\) (for St = 1, λ = 50) to \({S \simeq 3, 470}\) (for St = 100, λ = 1). Statistics are compared one to one with those obtained for spherical particles to highlight effects due to elongation. Results for mean and fluctuating angular velocities show that elongation is important for fibers with small inertia (St ≤ 5 in the present flow-fiber combination). For fibers with larger inertia, elongation has an impact on fiber rotation only in the streamwise and wall-normal directions, where mean values of Ω are zero. It is also shown that, in the center of the channel, the Lagrangian autocorrelation coefficients of Ω and corresponding rotational turbulent diffusivities match the exponential behavior predicted by the theory of homogeneous dispersion. In this region of the channel, the probability density function of fiber angular velocities is generally close to Gaussian, indicating that particle rotation away from solid walls can be modeled as a diffusion process of the Ornstein–Uhlenbeck type at stationary state. In the strong shear region (comprised within a distance of 50 viscous units from the wall in the present simulations), fiber anisotropy adds to flow anisotropy to induce strong deviations on fiber rotational dynamics with respect to spherical particles. The database produced in this study is available to all interested users at https://www.fp1005.cism.it.

Large-Eddy Simulations (LES) of two-phase turbulent flows exhibit quantitative differences in particle statistics if compared to Direct Numerical Simulations (DNS) which, in the context of the present study, is considered the exact reference case. Differences are primarily due to filtering, a fundamental intrinsic feature of LES. Filtering the fluid velocity field yields approximate computation of the forces acting on particles and, in turn, trajectories that are inaccurate when compared to those of DNS. In this paper, we focus precisely on the filtering error for which we quantify a lower bound. To this aim, we use a DNS database of inertial particle dispersion in turbulent channel flow and we perform a-priori tests in which the error purely due to filtering is singled out removing error accumulation effects, which would otherwise lead to progressive divergence between DNS and LES particle trajectories. By applying filters of different type and width at varying particle inertia, we characterize the statistical properties of the filtering error as a function of the wall distance. Results show that filtering error is stochastic and has a non-Gaussian distribution. In addition, the distribution of the filtering error depends strongly on the wall-normal coordinate being maximum in the buffer region. Our findings provide insight on the effect of subgrid-scale velocity field on the force driving the particles, and establish the requirements which a LES model must satisfy to predict correctly the velocity and the trajectory of inertial particles., 39 pages, 1 table, 12 figures, submitted to Physics of Fluids

In this work, we run a numerical experiment to study the behaviour of incompressible Newtonian fluids with anisotropic temperature-dependent viscosity in forced convection turbulence. We present a systematic analysis of variable-viscosity effects, isolated from gravity, with relevance for aerospace cooling/heating applications. We performed an extensive campaign based on pseudo-spectral direct numerical simulations of turbulent water channel flow in the Reynolds number parameter space. We considered constant temperature boundary conditions and different temperature gradients between the channel walls. Results indicate that average and turbulent fields undergo significant variations. Compared with isothermal flow with constant viscosity, we observe that turbulence is promoted in the cold side of the channel, characterized by viscosity locally higher than the mean: in the range of the examined Reynolds numbers and in absence of gravity, higher values of viscosity determine an increase of turbulent kinetic energy, whereas a decrease of turbulent kinetic energy is determined at the hot wall. Examining in detail the turbulent kinetic energy budget, we find that turbulence modifications are associated with changes in the rate at which energy is produced and dissipated near the walls: specifically, at the hot wall (respectively cold wall) production decreases (respectively increases) while dissipation increases (respectively decreases).

In this paper we examine the mutual interactions between microbubbles and turbulence in vertical channel flow. An Eulerian–Lagrangian approach based on pseudo-spectral direct numerical simulation is used: bubbles are momentum coupled with the fluid and are treated as pointwise spheres subject to gravity, drag, added mass, pressure gradient, Basset and lift forces. Two different flow configurations (upward and downward channel flow of water at shear Reynolds number Re τ = 150) and four different bubble diameters are considered, assuming that bubbles are non-deformable (i.e. small Eotvos number) and contaminated by surfactants (i.e. no-slip condition applies at bubble surface). Confirming previous knowledge, we find macroscopically different bubble distribution in the two flow configurations, with lift segregating bubbles at the wall in upflow and preventing bubbles from reaching the near-wall region in downflow. Due to local momentum exchange with the carrier fluid and to the differences in bubble distribution, we also observe significant increase (resp. decrease) of both wall shear and liquid flowrate in upflow (resp. downflow). We propose a novel force scaling to examine results in vertical turbulent bubbly flows, which can help to judge differences in the turbulence features due to bubble presence. By examining two-phase flow energy spectra, we show that bubbles determine an enhancement (resp. attenuation) of energy at small (resp. large) flow scales, a feature already observed in homogeneous isotropic turbulence. Bubble-induced flow field modifications, in turn, alter significantly the dynamics of the bubbles and lead to different trends in preferential concentration and wall deposition. In this picture, a crucial role is played by the lift force, which is a delicate issue when accurate models of shear flows with bubbles are sought. We analyze and discuss all the observed trends emphasizing the impact that the lift force model has on the simulations.

The rate at which two particles separate in turbulent flows is of central importance to predict the inhomogeneities of particle spatial distribution and to characterize mixing. Pair separation is analyzed for the specific case of small, inertial particles in turbulent channel flow to examine the role of mean shear and small-scale turbulent velocity fluctuations. To this aim an Eulerian-Lagrangian approach based on pseudo-spectral direct numerical simulation (DNS) of fully developed gas-solid flow at shear Reynolds number Ret = 150 is used. Pair separation statistics have been computed for particles with different inertia (and for inertialess tracers) released from different regions of the channel. Results confirm that shear-induced effects predominate when the pair separation distance becomes comparable to the largest scale of the flow. Results also reveal the fundamental role played by particles-turbulence interaction at the small scales in triggering separation during the initial stages of pair dispersion. These findings are discussed examining Lagrangian observables, including the mean square separation, which provide prima facie evidence that pair dispersion in non-homogeneous anisotropic turbulence has a superdiffusive nature and may generate non-Gaussian number density distributions of both particles and tracers. These features appear to persist even when the effects of shear dispersion are filtered out, and exhibit strong dependency on particle inertia. Application of present results is discussed in the context of modelling approaches for particle dispersion in wall-bounded turbulent flows.

In this paper, we discuss the applicability of the Eulerian–Lagrangian point-particle approach to predict sedimentation and resuspension phenomena in solid–liquid flows. We start from results obtained for dilute systems and we examine to which degree such results can be applied to sedimentation phenomena, in which higher concentration values will be at some point relevant. We examine critical issues in state-of-the-art direct and large-eddy simulations of sediment dynamics in turbulence, starting from concepts and ideas that were derived from a systematic study of particle transport in turbulent boundary layer and applied to several canonical flow configurations (closed/open channel with flat/wavy bottom). We focus on issues related to high sediment concentration near the boundary and we examine critically results from original modelling strategies specifically aimed at dealing with boundary conditions where concentration peaks, with inter-particle collisions and with subgrid scale models in higher Reynolds number simulations employing LES.

Current capabilities of Large-Eddy Simulation (LES) in Eulerian-Lagrangian studies of dispersed flows are limited by the modeling of the Sub-Grid Scale (SGS) turbulence effects on particle dynamics. In this paper, the possibility is examined to account explicitly for SGS effects by incorporating ad-hoc closure models in the Lagrangian equations of particle motion. Specifically, a candidate model based on approximate deconvolution is considered and applied to particle-laden turbulent channel flow. Results show that, even if the fraction of SGS turbulent kinetic energy for the fluid velocity field (not resolved in LES) is recovered, quantitative prediction of local segregation and, in turn, of near-wall accumulation may still be inaccurate. This failure indicates that reconstructing the correct amount of fluid and particle velocity fluctuations is not enough to reproduce the effect of SGS turbulence on particles and that further information on the flow structure at the sub-grid scales must be incorporated.

One issue associated with the use of Large-Eddy Simulation (LES) to investigate the dispersion of small inertial particles in turbulent flows is the accuracy with which particle statistics and concentration can be reproduced. The motion of particles in LES fields may differ significantly from that observed in experiments or direct numerical simulation (DNS) because the force acting on the particles is not accurately estimated, due to the availability of the only filtered fluid velocity, and because errors accumulate in time leading to a progressive divergence of the trajectories. This may lead to different degrees of inaccuracy in the prediction of statistics and concentration. We identify herein an ideal subgrid correction of the a-priori LES fluid velocity seen by the particles in turbulent channel flow. This correction is computed by imposing that the trajectories of individual particles moving in filtered DNS fields exactly coincide with the particle trajectories in a DNS. In this way the errors introduced by filtering into the particle motion equations can be singled out and analyzed separately from those due to the progressive divergence of the trajectories. The subgrid correction term, and therefore the filtering error, is characterized in the present paper in terms of statistical moments. The effects of the particle inertia and of the filter type and width on the properties of the correction term are investigated., Comment: 15 pages,24 figures. Submitted to Journal of Physics: Conference Series

Particle dispersion in turbulent channel flow is investigated through Lagrangian tracking of inertial pointwise particles one-way coupled to the fluid. First, the results obtained in direct numerical simulations at two different shear Reynolds numbers, \(Re^l_{\tau}\) = 150 and \(Re^h_{\tau}\) = 300, for particles having different inertia are briefly summarized and the Reynolds number effects are discussed. Then, particle dispersion in LES flow fields at \(Re^h_{\tau}\) is compared to reference DNS data. Comparison is made with and without approximate deconvolution of the LES fluid velocity field in the particle motion equations. It is found that particle segregation and, consequently, near wall accumulation are underestimated in LES, although approximate deconvolution improves the agreement with DNS. These findings confirm those of analogous previous studies at \(Re^l_{\tau}\).

International audience; In this paper the results of an international collaborative test case relative to the production of a direct numerical simulation and Lagrangian particle tracking database for turbulent particle dispersion in channel flow at low Reynolds number are presented. The objective of this test case is to establish a homogeneous source of data relevant to the general problem of particle dispersion in wall-bounded turbulence. Different numerical approaches and computational codes have been used to simulate the particle-laden flow and calculations have been carried on long enough to achieve a statistically steady condition for particle distribution. In such stationary regime, a comprehensive database including both post-processed statistics and raw data for the fluid and for the particles has been obtained. The complete datasets can be downloaded from the web at http://cfd.cineca.it/cfd/repository/. In this paper the most relevant velocity statistics (for both phases) and particle distribution statistics are discussed and benchmarked by direct comparison between the different numerical predictions.

The problem of accurate Eulerian-Lagrangian modeling of inertial particle dispersion in large-eddy simulation (LES) of turbulent wall-bounded flows is addressed. We run direct numerical simulation (DNS) of turbulent channel flow at shear Reynolds number Re-tau=150 and corresponding a priori and a posteriori LES on two coarser grids. For each flow field, we tracked swarms of particles with different inertia to examine the behavior of particle statistics, specifically focusing on particle preferential segregation and accumulation at the wall. Our object is to discuss the necessity of a closure model for the particle equations when using LES and we verify if the influence of the subgrid turbulence filtered by LES is an important effect on particle motion according to particle size. The results show that well-resolved LES gives particle velocity statistics in satisfactory agreement with DNS. However, independent of the grid, quantitatively inaccurate predictions are obtained for local particle preferential segregation, particularly in the near-wall region. Inaccuracies are observed for the entire range of particle size considered in this study, even when the particle response time is much larger than the flow time scales not resolved in LES. The satisfactory behavior of LES in reproducing particle velocity statistics is thus counterbalanced by the inaccurate representation of local segregation phenomena, indicating that closure models supplying the particle motion equation with an adequate rendering of the flow field might be needed. Finally, we remark that recovering the level of fluid and particle velocity fluctuations in the particle equations does not ensure a quantitative replica of the subgrid turbulence effects, thus implying that accurate subgrid closure models for particles may require information also proportional to the higher-order moments of the velocity fluctuations. (c) 2008 American Institute of Physics.

Current capabilities of Large-Eddy Simulation (LES) in Eulerian-Lagrangian studies of dispersed flows are limited by the modeling of the Sub-Grid Scale (SGS) turbulence effects on particle dynamics. These effects should be taken into account in order to reproduce accurately the physics of particle dispersion since the LES cut-off filter removes both energy and flow structures from the turbulent flow field. In this paper, we examine the possibility of including explicitly SGS effects by incorporating ad hoc closure models in the Lagrangian equations of particle motion. Specifically, we consider candidate models based on fractal interpolation and approximate deconvolution techniques. Results show that, even when closure models are able to recover the fraction of SGS turbulent kinetic energy for the fluid velocity field ( not resolved in LES), prediction of local segregation and, in turn, of near-wall accumulation may still be inaccurate. This failure indicates that reconstructing the correct amount of fluid and particle velocity fluctuations is not enough to reproduce the effect of SGS turbulence on particle near-wall accumulation.

In this study, the rotation of small rigid fibers relative to the surrounding fluid in wall-bounded turbulence is examined by means of direct numerical simulations coupled with Lagrangian tracking. Statistics of the relative (fiber-to-fluid) angular velocity, referred to as slip spin in the present study, are evaluated by modelling fibers as prolate spheroidal particles with Stokes number, St, ranging from 1 to 100 and aspect ratio, λ, ranging from 3 to 50. Results are compared one-to-one with those obtained for spherical particles (λ = 1) to highlight effects due to fiber length. The statistical moments of the slip spin show that differences in the rotation rate of fibers and fluid are influenced by inertia, but depend strongly also on fiber length: Departures from the spherical shape, even when small, are associated with an increase of rotational inertia and prevent fibers from passively following the surrounding fluid. An increase of fiber length, in addition, decouples the rotational dynamics of a fiber from its translational dynamics suggesting that the two motions can be modelled independently only for long enough fibers (e.g., for aspect ratios of order ten or higher in the present simulations).

Turbulent dispersed flows over boundary layers are crucial in a number of industrial and environmental applications. In most applications, the key information is the spatial distribution of inertial particles, which is known to be highly non-homogeneous and may exhibit a complex pattern driven by the structures of the turbulent flow field. Theoretical and experimental evidence shows that fluid motions in turbulent boundary layers are intermittent and have a strongly organized and coherent nature represented by the large scale structures. These structures control the transport of the dispersed species in such a way that the overall distribution will resemble not at all those given by methods in which these motions are ignored.

The present study reports detailed statistics for velocity and transfer rates of heavy particles dispersed in turbulent boundary layers. Statistics have been extracted from a homogeneous source of data covering a large target parameter space and are used here to analyze the effects of gravity and lift on particle dispersion and deposition in a systematic way. Datasets were obtained performing Direct Numerical Simulation (DNS) of particle-laden turbulent upward/downward flow in a vertical channel. Six values for the particle timescale (the particle Stokes number, St) ranging three orders of magnitude were considered to analyze the deposition process as the controlling mechanism was shifting from turbulent diffusion to inertia-moderated crossing trajectories. For the particle timescales examined, gravity and lift do not influence the qualitative behavior of particles even though velocity profiles and deposition coefficients are modified in a non-monotonic fashion, reaching an optimum for St P 15. Physical mechanisms for the different behavior are discussed. Raw data and statistics obtained from the present DNS are made available at http://cfd.cineca.it (mirror site: http://158.110.32.35/download/database) and can be used to test simple models and closure equations for multiphase RANS and Large Eddy simulations.

In this Brief Communication, we examine in detail the motion of light particles—or dense gas bubbles—rising under gravity in a cellular flow. We follow the methodology of Maxey [Phys. Fluids 30, 1915 (1987)], and we examine a range of parameters not fully discussed in the past, corresponding to particles lighter and yet more inertial than the surrounding fluid if the added mass effect is considered. We observe a nonmonotonic behavior of the particle rise velocity, which exhibits a maximum for density of the particles only slightly smaller than the density of the fluid. The maximum value of the average rise velocity corresponding to the “optimum” density is several times (more than 40) higher than those obtained for small density changes around the optimum. The occurrence of this maximum is due to the combined effects of particle inertia and fluid added mass, which segregate the rising particles into specific, fast pathlines where the local fluid velocity adds to the particle gravitational velocity. A plot...

It has been long recognized that turbulent flow over steep waves can produce coherent flow structures of different temporal and spatial scales. In particular, quasistreamwise vortices grow up on the upslope side of the wave and interact with geometry-dependent vortical structures, aligned spanwise and located within the recirculation bubble in the wave trough, thus creating the conditions for the development of a three-dimensional highly turbulent flow field. In this work, we have analyzed the trajectories of O(105) small dense particles (either in solid form or in the form of liquid droplets) released into a turbulent air flow over waves precisely to clarify the role of coherent vortical structures in controlling particle deposition and resuspension. The three-dimensional time-dependent flow field at Reτ=170 is calculated using large-eddy simulation, and the dynamics of individual different-sized particles is described using a Lagrangian approach. Drag, gravity, and lift are used in the equation of motio...

In this work, we study the dispersion of inertial particles in fully-developed turbulent channel flow to evaluate the relationship between particle and fluid time scales, and to identify suitable scales for parametrization of near-wall particle behavior. Direct Numerical Simulation (DNS) and Lagrangian particle tracking are used to build a complete and homogeneous dataset which covers a large target parameter space and includes statistics of particle velocity and particle concentration at steady state. Our results show that the Lagrangian integral time scale of the fluid is adequate to characterize particle wall deposition and that such fluid time scale will be different when sampled at the position of either fluid particles or inertial particles. Differences become particularly evident in the range 5 < St < 25. These observations can be crucial to improve the accuracy of engineering models for particle deposition.

Particle transfer in the wall region of turbulent boundary layers is dominated by the coherent structures which control the turbulence regeneration cycle. Coherent structures bring particles toward the wall and away from the wall and favour particle segregation in the viscous region giving rise to nonuniform particle distribution profiles which peak close to the wall. In this work, we focus on the transfer mechanism of different size particles and on the influence of gravity on particles deposition. By tracking O(105 ) particles in Direct Numerical Simulation (DNS) of a turbulent channel flow at Reτ = 150, we find that particles may reach the wall directly or may accumulate in the wall region, under the low-speed streaks. Even though low-speed streaks are ejection-like environments, particles are not re-entrained into the outer region. Particles segregated very near the wall by the trapping mechanisms we investigated in a previous work [1] are slowly driven to the wall. We find that gravity plays a role on particle distribution but, for small particles (τp + < 3), the controlling transfer mechanism is related to near-wall turbulence structure.Copyright © 2003 by ASME

Particle transfer in the wall region of turbulent boundary layers is dominated by the coherent structures which control the turbulence regeneration cycle. Coherent structures bring particles toward the wall and away from the wall and favour particle segregation in the viscous region. In this work we examine turbulent transfer of heavy particles to the wall and away from the wall in connection with the coherent structures of the boundary layer. First, a detailed analysis of wall turbulence phenomena in a boundary layer will be provided. We will focus on the evolutionary dynamics of the structures populating the boundary layer: according to Schoppa & Hussain (1996, 1997), we will identify the following turbulence regeneration cycle: (i) low-speed streaks generate quasi-streamwise vortices, (ii) quasi-streamwise vortices generate sweeps and ejections, (iii) sweeps and ejections contribute to maintain the low-speed streaks.

Transfer and deposition of inertial particles or droplets in turbulent pipe flow are crucial processes in a number of industrial and environmental applications. In this work, we use direct numerical simulation (DNS) and Lagrangian tracking to study turbulent transfer and deposition of inertial particles in vertical upward circular pipe flow. Our objects are: (i) to quantify turbulent transfer of heavy particles to the wall and away from the wall; (ii) to examine the connection between particle transfer mechanisms and turbulence structure in the boundary layer. We use a finite difference DNS to compute the three-dimensional time dependent turbulent flow field (Res ¼ 337) and Lagrangian tracking of a dilute dispersion of heavy particles––flyashes in air––to simulate the dynamics of particles. Drag, lift and gravity are used in the equation of motion for the particles, which are assumed to have no influence on the flow field. Particle interaction with the wall is fully elastic. Results on preferential distribution of particles in the boundary layer, particle fluxes to and off the wall and particle deposition mechanisms are shown. Our findings confirm: (i) the specific tendency of particles to segregate in the near-wall region; (ii) the crucial role of the instantaneous realizations of the Reynolds stresses in determining particle fluxes toward and away from the wall; (iii) the relative importance of free-flight and diffusion deposition mechanisms. 2003 Elsevier Science Ltd. All rights reserved.

In this study, the slip velocity between rigid fibers and a viscous carrier fluid is investigated for the reference case of turbulent channel flow. The statistical moments of the slip velocity are evaluated modelling fibers as prolate spheroids with Stokes number, St, ranging from 1 to 100 and aspect ratio, λ, ranging from 3 to 50. Statistics are compared one-to-one with those obtained for spherical particles (λ = 1) to highlight effects due to fiber elongation. Comparison is also made at different Reynolds numbers (Reτ =150, 180, and 300 based on the fluid shear velocity) to discuss effects due to an increase of turbulent fluctuations. Results show that elongation has a quantitative effect on slip velocity statistics, particularly evident for fibers with small St. As St increases, differences due to the aspect ratio tend to vanish and the relative translational motion between individual fibers and surrounding fluid is controlled by fiber inertia through preferential concentration. A clear manifestation o...

The particle slip velocity is adopted as an indicator of the behavior of heavy particles in turbulent channel flow. The statistical moments of the slip velocity are evaluated considering particles with Stokes number, defined as the ratio between the particle response time and the viscous time scale of the flow, in the range 1 < St < 100. The slip velocity fluctuations exhibit a monotonic increase with increasing particle inertia, whereas the fluid-particle velocity covariance is gradually reduced for St ⩾ 5. Even if this covariance equals the particle turbulence intensity, a substantial amount of particle slip may occur. Relevant to two-fluid modeling of particle-laden flows is the finding that the standard deviation of the slip velocity fluctuations is significantly larger than the corresponding mean slip velocity.

In this paper, the dispersion of rigid, highly elongated fibers in a turbulent channel flow is investigated. Fibers are treated as prolate ellipsoidal particles which move according to their inertia and to hydrodynamic drag and rotate according to hydrodynamic torques. The orientational behavior of fibers is examined together with their preferential distribution, near-wall accumulation, and wall deposition: all these phenomena are interpreted in connection with turbulence dynamics near the wall. In this work a wide range of fiber classes, characterized by different elongation (quantified by the fiber aspect ratio, λ) and different inertia (quantified by a suitably defined fiber response time, τp) is considered. A parametric study in the (λ,τp)-space confirms that, in the vicinity of the wall, fibers tend to align with the mean streamwise flow direction. However, this aligned configuration is unstable, particularly for higher inertia of the fiber, and can be maintained for rather short times before fibers ...

Theoretical models for particle dispersion in turbulent wall layers are based on closure assumptions for particle-turbulence correlations which strongly depend on the wall-normal coordinate. This paper presents new data for the near-wall dispersion of inertial particles in fully developed turbulent channel flow, obtained using direct numerical simulation (DNS) with a one-way point-particle approach. The link between wall-dependent flow time scales and particle time scales is discussed addressing further the issue of using integral flow time scales to parametrize particle behavior. This is fundamental to validate closure relations in theoretical local-equilibrium models for particle dispersion in wall-bounded flows, where the reduction of the fluid velocity fluctuation in the wall-normal direction is not accompanied by an equivalent reduction of the particle velocity fluctuation.

In this paper, we examine particle distribution in the wall region of turbulent boundary layers, considering specific flow conditions (Reτ=150) and spanning two orders of magnitude of particle inertial parameter—the particle timescale. First, we identify the flow timescales that govern particle distribution, examining the degree of particle preferential concentration and determining the optimum in connection with particle timescale. Second, we identify which of the flow variables may be used to control particle distribution. These are the streamwise and spanwise shear stress components at the wall, which correspond to the only nonvanishing elements of the fluctuating fluid velocity gradient tensor.

Thermal stratification in water bodies influences the exchange of heat, momentum, and chemical species across the air-water interface by modifying the sub-surface turbulence characteristics. Turbulence modifications may in turn prevent small motile algae (phytoplankton, in particular) from reaching the heated surface. We examine how different regimes of stable thermal stratification affect the motion of these microscopic organisms (modelled as gyrotactic self-propelling cells) in a free-surface turbulent channel flow. This archetypal setup mimics an environmentally plausible situation that can be found in lakes and oceans. Results from direct numerical simulations of turbulence coupled with Lagrangian tracking reveal that rising of bottom-heavy self-propelling cells depends strongly on the strength of stratification, especially near the thermocline where high temperature and velocity gradients occur: Here hydrodynamic shear may disrupt directional cell motility and hamper near-surface accumulation. For al...

The problem of assessing accurate Eulerian-Lagrangian modeling of heavy particle dispersion in Large Eddy Simulation (LES) is addressed. This issue is investigated in a systematic way by performing a priori and a posteriori LES coupled with Lagrangian particle tracking of fully developed channel flow, in which different grid resolutions and different values of the particle response time are considered. The accuracy in the prediction of the particle velocity statistics, near wall accumulation (turbophoresis) and preferential concentration is assessed trough comparison against DNS data. Both a priori and a posteriori tests indicate that turbophoresis and particle segregation can not be accurately predicted without introducing a model in the particle motion equations, also for particles having a response time much larger than the scales non resolved in LES. Furthermore, the present results indicate that the reintroduction of the correct level of fluid and particle velocity fluctuations is not the only issue for a closure model for particle equations.