Some issues concerning Large-Eddy Simulation of inertial particle dispersion in turbulent bounded flows

The problem of an 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) for turbulent channel flow at shear Reynolds numbers equal to 150 and 300 and corresponding a-priori and a-posteriori LES on differently coarse grids. We then tracked swarms of different inertia particles and we examined the influence of filtering and of Sub-Grid Scale (SGS) modeling for the fluid phase on particle velocity and concentration statistics. We also focused on how particle preferential segregation is predicted by LES. Results show that even ``well-resolved'' LES is unable to reproduce the physics as demonstrated by DNS, both for particle accumulation at the wall and for particle preferential segregation. Inaccurate prediction is observed for the entire range of particles considered in this study, even when the particle response time is much larger than the flow timescales not resolved in LES. Both a-priori and a-posteriori tests indicate that recovering the level of fluid and particle velocity fluctuations is not enough to have accurate prediction of near-wall accumulation and local segregation. This may suggest that reintroducing the correct amount of higher-order moments of the velocity fluctuations is also a key point for SGS closure models for the particle equation. Another important issue is the presence of possible flow Reynolds number effects on particle dispersion. Our results show that, in small Reynolds number turbulence and in the case of heavy particles, the shear fluid velocity is a suitable scaling parameter to quantify these effects

Statistical properties of an ideal subgrid-scale correction for Lagrangian particle tracking in turbulent channel flow

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 Serie

Turbulence Modulation by Slender Fibers

In this paper, we numerically investigate the turbulence modulation produced by long flexible fibres in channel flow. The simulations are based on an Euler–Lagrangian approach, where fibres are modelled as chains of constrained, sub-Kolmogorov rods. A novel algorithm is deployed to make the resolution of dispersed systems of constraint equations, which represent the fibres, compatible with a state-of-the-art, Graphics Processing Units-accelerated flow-solver for direct numerical simulations in the two-way coupling regime on High Performance Computing architectures. Two-way coupling is accounted for using the Exact Regularized Point Particle method, which allows to calculate the disturbance generated by the fibers on the flow considering progressively refined grids, down to a quasi-viscous length-scale. The bending stiffness of the fibers is also modelled, while collisions are neglected. Results of fluid velocity statistics for friction Reynolds number of the flow (Formula presented.) and fibers with Stokes number (Formula presented.) = 0.01 (nearly tracers) and 10 (inertial) are presented, with special regard to turbulence modulation and its dependence on fiber inertia and volume fraction (equal to (Formula presented.) · (Formula presented.) and (Formula presented.) · (Formula presented.)). The non-Newtonian stresses determined by the carried phase are also displayed, determined by long and slender fibers with fixed aspect ratio (Formula presented.), which extend up to the inertial range of the turbulent flow

Settling tracer spheroids in vertical turbulent channel flows

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

Role of large-scale advection and small-scale turbulence on vertical migration of gyrotactic swimmers

In this work, we use direct-numerical-simulation-based Eulerian-Lagrangian simulations to 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 timescale, while others possess a reorientation time longer than the Kolmogorov timescale. 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 timescale of the flow, is larger than unity: This condition is associated to enhanced migration toward 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 toward 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 microorganisms 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

Large-eddy simulation of a particle-laden turbulent channel flow

Large-eddy simulations of a vertical turbulent channel flow with 420,000 solid particles are performed in order to get insight into fundamental aspects of a riser flow The question is addressed whether collisions between particles are important for the ow statistics. The turbulent channel ow corresponds to a particle volume fraction of 0.013 and a mass load ratio of 18, values that are relatively high compared to recent literature on large-eddy simulation of two-phase ows. In order to simulate this ow, we present a formulation of the equations for compressible ow in a porous medium including particle forces. These equations are solved with LES using a Taylor approximation of the dynamic subgrid-model. The results show that due to particle-uid interactions the boundary layer becomes thinner, leading to a higher skin-friction coefcient. Important effects of the particle collisions are also observed, on the mean uid prole, but even more o on particle properties. The collisions cause a less uniform particle concentration\ud and considerably atten the mean solids velocity prole

Lagrangian filtered density function for LES-based stochastic modelling of turbulent dispersed flows

The Eulerian-Lagrangian approach based on Large-Eddy Simulation (LES) is one of the most promising and viable numerical tools to study turbulent dispersed 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 (SGS) 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 for 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 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

Intrinsic filtering errors of Lagrangian particle tracking in LES flow fields

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.Comment: 39 pages, 1 table, 12 figures, submitted to Physics of Fluid

Simulation of deterministic energy-balance particle agglomeration in turbulent liquid-solid flows

An efficient technique to simulate turbulent particle-laden flow at high mass loadings within the four-way coupled simulation regime is presented. The technique implements large-eddy simulation, discrete particle simulation, a deterministic treatment of inter-particle collisions, and an energy-balanced particle agglomeration model. The algorithm to detect inter-particle collisions is such that the computational costs scale linearly with the number of particles present in the computational domain. On detection of a collision, particle agglomeration is tested based on the pre-collision kinetic energy, restitution coefficient, and van der Waals’ interactions. The performance of the technique developed is tested by performing parametric studies on the influence of the restitution coefficient (en = 0.2, 0.4, 0.6, and 0.8), particle size (dp = 60, 120, 200, and 316 μm), Reynolds number (Reτ = 150, 300, and 590), and particle concentration (αp = 5.0 × 10−4, 1.0 × 10−3, and 5.0 × 10−3) on particle-particle interaction events (collision and agglomeration). The results demonstrate that the collision frequency shows a linear dependency on the restitution coefficient, while the agglomeration rate shows an inverse dependence. Collisions among smaller particles are more frequent and efficient in forming agglomerates than those of coarser particles. The particle-particle interaction events show a strong dependency on the shear Reynolds number Reτ, while increasing the particle concentration effectively enhances particle collision and agglomeration whilst having only a minor influence on the agglomeration rate. Overall, the sensitivity of the particle-particle interaction events to the selected simulation parameters is found to influence the population and distribution of the primary particles and agglomerates formed