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In this paper, the motion of inertial particles in three-dimensional (3D) unsteady cylindrical wake flow is investigated by a two-way coupled Eulerian–Lagrangian approach. At different flow Reynolds numbers (Re), the corresponding striking dynamic property and dispersion mechanism of four particle classes have been studied, with inertia parameterized by means of Stokes number (Sk). It is found that inertial particles with lower Stokes number are expelled from vortex cores, and coherent voids encompass the local Kármán vortex cells. As Stokes number increases, a low velocity particle channel could be formed, which almost coincides with the results in the literature. Moreover, with the increase of Reynolds number, numerous irregular coherent voids are observed in the cylinder wake, and the high-speed particles follow the fluid flow closely when they are contained in the vortices. Although the centrifugal force of Kármán vortex cells significantly affects the dynamics of inertial particles, the fluid flow modulation is believed to be responsible for the distinctive particle dispersion patterns in the vortex streets. For particles with medium inertia, the two-way coupled modulation weakens the centrifugal effect of vortex structures on the particles. This trend declines with the increase of Reynolds number, and vanishes with light particles, while both two-way coupled modulation and the centrifugal effect of vortex structures are almost equally effective with heavy particles. The investigations contribute to a better understanding of the particle-laden flows in practical applications, which will benefit the optimized design of certain machinery and equipment for the industry. [ABSTRACT FROM AUTHOR]

It has long been known that under the right circumstances, inertial particles (such as sand, dust, pollen, or water droplets) settling through the atmospheric boundary layer can experience a net enhancement in their average settling velocity due to their inertia. Since this enhancement arises due to their interactions with the surrounding turbulence it must be modelled at coarse scales. Models for the enhanced settling velocity (or deposition) of the dispersed phase that find practical use in mesoscale weather models are often ad hoc or are built on phenomenological closure assumptions, meaning that the general deposition rate of particles is a key uncertainty in these models. Instead of taking a phenomenological approach, exact phase-space methods can be used to model the physical mechanisms responsible for the enhanced settling, and these individual mechanisms can be estimated or modelled to build a more general parameterization of the enhanced settling of inertial particles. In this work, we use direct numerical simulations (DNS) and phase-space methods as tools to evaluate the efficacy of phenomenological modeling approaches for the enhanced settling velocity of inertial particles for particles with varying friction Stokes numbers and settling velocity parameters. We use the DNS data to estimate profiles of a drift–diffusion based parameterization of the fluid velocity sampled by the particles, which is key for determining the settling velocity behaviour of particles with low to moderate Stokes number. We find that by increasing the settling velocity parameter at moderate friction Stokes number, the magnitude of preferential sweeping is modified, and this behaviour is explained by the drift component of the aforementioned parameterization. These profiles indicate that that when eddy-diffusivity-like closures are used to represent turbulent transport, empirical corrections used in phenomenological models may be potentially compensating for their incompleteness. Finally, we discuss opportunities for reinterpreting phenomenological approaches for use in coarse-scale weather models in terms of the exact phase-space approach. [ABSTRACT FROM AUTHOR]

The predictions of the conditional quadrature methods of moments, conventional Lagrangian, and fully Lagrangian (FLA) approaches to the calculation of particle number densities in hyperbolic and Lamb vortex flows are compared. All these methods predict similar distributions of particle number densities at low Stokes numbers. For single-fold particle trajectory crossings (PTC) at high Stokes numbers in the hyperbolic flow, the two-point quadrature approximation is shown to be in good agreement with both Lagrangian approaches, while the three-point approximation of the VDF leads to worse prediction than the two-point approximation. Thus, the number of nodes in the approximation has to be chosen based on the characteristics of the flow. The predictions of the FLA are shown to agree with those of the conventional Lagrangian approach when sufficiently large numbers of particles are used in calculations. The FLA is shown to be the most CPU efficient method among those considered in our analysis. [ABSTRACT FROM AUTHOR]

A modified version of the adaptive moment inversion algorithm is suggested for the quadrature method of moments and conditional quadrature method of moments (QMOM, CQMOM), based on a new criterion for selection of the number of nodes in the quadrature approximation of the particle velocity distribution function (VDF) for the solution of the moment advection equations. In contrast to the conventional QMOM and CQMOM, the new approach guarantees that unphysical values of particle velocities are not predicted. It is shown that the number of nodes in the approximation of the VDF should be sufficiently high to predict physically meaningful results when modelling intersections of particle clouds. [ABSTRACT FROM AUTHOR]

In the present study, a theoretical model is proposed to calculate the settling velocity of solid particles in turbulence generated by both oscillatory and nearly horizontal flow motions. In contrast to other previous models that typically compartmentalize two flow conditions in their studies, this study takes a more comprehensive approach by considering the combined effects of both conditions. Taking into account the influence of drag nonlinearity, virtual mass and Basset history forces, the new theoretical model is formulated. The proposed model is obtained by solving the particle motion in fluid flow under some reasonable assumptions. Accordingly, we obtain a new dimensionless term to better take into account the effect of turbulence anisotropy on the settling velocity and the role of the sediment damping coefficient. Application of this term for other conditions is discussed in the paper. The present model shows satisfactory agreement with a wide range of experimental and numerical data and with different flow conditions found in the existing literature. These data include homogeneous isotropic turbulence with high resolution direct numerical simulations (DNS), turbulent open channel and vertical oscillation. [Display omitted] • Model calculates particle settling velocity in turbulent and oscillatory flows. • Includes drag nonlinearity, virtual mass, and Basset history forces in new equation. • Validated with experimental and numerical data for various turbulence scenarios. [ABSTRACT FROM AUTHOR]

Turbulent interfaces are ubiquitous in the nature and in many important canonical flows (wakes, jets, mixing layers, boundary layers). In nature, the sharp edges of atmospheric clouds are defined by a turbulent/non-turbulent interface, where the droplet-laden turbulent cloud interior mixes with the unladen outer air. This study presents statistics of sub-Kolmogorov-scale inertial particles, in a parameter range representative of cloud droplets, in a sheared turbulent–turbulent interface. The study focuses on the effect of the inhomogeneous turbulent field on the particles' clustering properties and settling velocity modification. Wind tunnel experiments were carried out in a well-characterised facility where a grid containing 81 independent gas/liquid injectors generates both high intensity turbulence and a field of small inertial droplets. These atomisers, located at the entrance of the test section, contribute significantly to the carrier phase turbulence and are used to create the sheared turbulent/turbulent interface. Selecting which atomisers are on or off enables us to control the mean velocity profile and the gradient of turbulent intensity through the tunnel cross-section. The resulting carrier flow is characterised by a gradient of mean velocity, turbulent velocity rms, and a sharp interface separating two regions with different turbulent scales. Particles' velocities and diameters were measured with a Phase Doppler Particle Analyser, at closely-spaced positions across the turbulent interface. In agreement with previous experimental studies on the topic, particles are shown to be transported from the turbulent side, with higher turbulence intensity, to the low-intensity side by large-scale-energetic eddies. Newly observed in our results is an enhancement of particle preferential concentration and settling velocity in the sheared interface region, caused by the interaction between particle trajectories and turbulent structures of different sizes. [Display omitted] • A particle-laden turbulent–turbulent interface is tested in a wind tunnel. • Clustering and settling of inertial particles in the interface are characterised. • Particles are transported into the low-turbulence region by energetic bursts. • Bursts are related to large particle concentration and enhanced settling. [ABSTRACT FROM AUTHOR]

The quadrature method of moments was used for solving the problem of modeling the dynamics of inertial polydisperse particles. Dispersed phase models that assumed particle distribution over size, mean velocity for all particles, and mean velocity conditioned by particle size were implemented. The comparison of the models was performed in the problem of moving evaporating particles in the vortex flow with using the Lagrangian approach as a reference method. The qualitative agreement of particle number density fields obtained by the methods of moments and the Lagranigan approach was demonstrated. It was shown that using models with two and three conditioned mean velocities results in the qualitative agreement of the mean size and variance fields obtained by the methods of moments and the Lagranigan approach.

Impacting particles such as rain, dust, and other debris can have devastating structural effects on wind turbines, but little is known about the interaction of such debris within turbine wakes. This study aims to characterize behavior of inertial particles within the turbulent wake of a wind turbine and relative effects on wake recovery. Here a model wind turbine is subjected to varied two-phase inflow conditions, with wind as the carrier fluid (R e λ = 49 −88) and polydisperse water droplets (18-40 μ m in diameter) at varied concentrations (Φ v = 0.24 × 10 − 5 - 1.3 × 10 − 5 ), comparing with sub-inertial particles [ i.e., tracers] that follow the inflow streamlines. Phase doppler interferometry (PDI) and particle image velocimetry (PIV) were employed at multiple downstream locations, centered with respect to turbine hub height. Analysis considers energy and particle size distribution within the wake focusing on turbulence statistics and preferential concentration. PDI data show droplet size varied with wake location and volume fraction, and the inflow velocity of R e λ = 66.58 demonstrated Φ v dependent increases in streamwise velocity deficits of 59.5%–62.6% and 15.8%–19.8% for near and far wake, respectively. PIV data indicated correlation of particle concentration to wake expansion and amplified downward trajectory over the entire interrogation field. Contributions to kinetic energy and momentum are diminished overall for inertial particle cases compared to single-phase, except turbulent momentum flux u ' v ' ¯ , where shearing effects are visible at the rotor top edge in near wake and concentrated magnitudes increase in far wake correlating with increased Φ v. Application of Voronoi analysis identifies clustering behavior in far wake and is validated as motivation for future studies. [ABSTRACT FROM AUTHOR]

Buoyant, finite-size, or inertial particle motion is fundamentally unlike neutrally buoyant, infinitesimally small, or Lagrangian particle motion. The de-jure fluid mechanics framework for the description of inertial particle dynamics is provided by the Maxey–Riley equation. Derived from first principles—a result of over a century of research since the pioneering work by Sir George Stokes—the Maxey–Riley equation is a Newton-type law with several forces including (mainly) flow, added mass, shear-induced lift, and drag forces. In this paper, we present an overview of recent efforts to transfer the Maxey–Riley framework to oceanography. These involved: (1) including the Coriolis force, which was found to explain behavior of submerged floats near mesoscale eddies; (2) accounting for the combined effects of ocean current and wind drag on inertial particles floating at the air–sea interface, which helped understand the formation of great garbage patches and the role of anticyclonic eddies as plastic debris traps; and (3) incorporating elastic forces, which are needed to simulate the drift of pelagic Sargassum. Insight into the nonlinear dynamics of inertial particles in every case was possible to be achieved by investigating long-time asymptotic behavior in the various Maxey–Riley equation forms, which represent singular perturbation problems involving slow and fast variables. [ABSTRACT FROM AUTHOR]

The quadrature method of moments (QMOM) and method of moments with a lognormal particle size distribution (PSD) are applied to simulate a cloud of evaporating droplets in a vortex ring flow. Results predicted by both methods are compared for the cases with a sinusoidal and lognormal initial particle size distribution, using Lagrangian particle tracking as a reference solution. Spatial distributions of droplet number density obtained by different methods are shown to be in a qualitative agreement. The method of moments with a lognormal PSD overestimates disappearance of particles leading to the underestimation of droplet mean size and higher values of the variance of PSD. QMOM showed better agreement with the Lagrangian approach than the method of moments with a lognormal PSD. [ABSTRACT FROM AUTHOR]

Clustering dynamics of inertial particles in turbulent channel flow are studied via tessellation-based analysis of high-fidelity simulation data at R e τ ≈ 230 with various values of mass loading (10 % − 100 %) and the Stokes number (S t + = [ 1 − 60 ]). We then characterise the solenoidal, rotational, and swirling motions of clusters by computing the probability density functions (PDFs) of the divergence, curl, and helicity of the particle velocity, as well as their dependence on wall-normal distance, using the methods of Oujia et al. (2020); Maurel–Oujia et al. (2023). Particle inertia gives heavier tails to the PDFs of divergence and curl, suggesting enhanced intermittency in the convergence/divergence of clusters, and in their rotational motions. The fluctuations of the divergence and curl are most intense in the buffer layer, due to the stronger fluctuations of fluid velocity there. Similarities are identified between the cluster dynamics in the logarithmic region and those in homogeneous isotropic turbulence, including the dependence of divergence, curl, and helicity on Stokes number. The effect of increasing mass loading on cluster dynamics is relatively small except in the viscous sublayer, where attenuation of clustering, rotation, and swirling motions are observed. The effect of increasing Stokes number on the viscous sublayer is different, resulting in more intense convergence/divergence and rotation of particle clusters, as the particles become more independent of the carrier fluid. [Display omitted] • Tessellation-based analysis of inertial particle motions in turbulent channel flow. • Increasing the Stokes number results in more intense convergence/divergence. • Amplitude of particle velocity divergence and curl is highest in the buffer layer. • Particle divergence/curl/helicity in the logarithmic layer is similar to HIT. [ABSTRACT FROM AUTHOR]

The motion of particles through density-stratified interfaces is a common phenomenon in environmental and engineering applications. However, the mechanics of particle-stratification interactions in various combinations of particle and fluid properties are not well understood. This study presents a novel machine-learning (ML) approach to experimental data of inertial particles crossing a density-stratified interface. A simplified particle settling experiment was conducted to obtain a large number of particles and expand the parameter range. Using ML, the study explores new correlations that collapse the data gathered in this and in previous work by Verso et al. (2019). The "delay time", which is the time between the particle exiting the interfacial layer and reaching a steady-state velocity, is found to strongly depend on six dimensionless parameters formulated by ML feature selection. The data shows a correlation between the Reynolds and Froude numbers within the range of the experiments, and the best symbolic regression is based on the Froude number only. This experiment provides valuable insights into the behavior of inertial particles in stratified layers and highlights opportunities for future improvement in predicting their motion. [Display omitted] • We suggest non-dimensional parameters shaping the particle-stratification dynamics. • We show a correlation between delay time in particle trajectory and the Froude number. • Novel ML approach to analyze particle-stratification interactions. [ABSTRACT FROM AUTHOR]

• Hydrodynamic effects play a role in accumulating (inertial) particles in porous media flow. • Clogging occurs when particles accumulate at the entrance of a narrow pore throat. • Clogs are formed in porous media with a heterogeneous pore size distribution, but not in microscopically homogeneous media. We study the transport of inertial particles in water flow in porous media. Our interest lies in understanding the accumulation of particles including the possibility of clogging. We propose that accumulation can be a result of hydrodynamic effects: the tortuous paths of the porous medium generate regions of dominating strain, which favour the accumulation of particles. Numerical simulations show that essentially two accumulation regimes are identified: for low and for high flow velocities. When particles accumulate at the entrance of a pore throat (high-velocity region), a clog is formed. This significantly modifies the flow, as the partial blockage of the pore causes a local redistribution of pressure, which diverts the upstream water flow into neighbouring pores. Moreover, we show that accumulation in high velocity regions occurs in heterogeneous media, but not in homogeneous media, where we refer to homogeneity with respect to the distribution of the pore throat diameters. [ABSTRACT FROM AUTHOR]

Stochastic flows mimicking 2D turbulence in compressible media are considered. Particles driven by such flows can collide and we study the collision (caustic) frequency. Caustics occur when the Jacobian of a flow vanishes. First, a system of nonlinear stochastic differential equations involving the Jacobian is derived and reduced to a smaller number of unknowns. Then, for special cases of the stochastic forcing, upper and lower bounds are found for the mean number of caustics as a function of Stokes number. The bounds yield an exact asymptotic for small Stokes numbers. The efficiency of the bounds is verified numerically. As auxiliary results we give rigorous proofs of the well known expressions for the caustic frequency and Lyapunov exponent in the one-dimensional model. Our findings may also be used for estimating the mean time when a 2D Riemann type partial differential equation with a stochastic forcing loses uniqueness of solutions.

Microplastic (MP) debris is recognized to be one of the most serious threats to marine environments. They are found in all seas and oceanic basins worldwide, even in the most remote areas. This is further proof that the transport of MPs is very efficient. In the present study, we focus our attention on MPs’ transport owing to the Stokes drift generated by sea waves. Recent studies have shown that the interaction between heavy particles and Stokes drift leads to unexpected phenomena mostly related to inertial effects. We perform a series of laboratory experiments with the aim to directly measure MPs’ trajectories under different wave conditions. The main objective is to quantify the inertial effect and, ultimately, suggest a new analytical formulation for the net settling velocity. The latter formula might be implemented in a larger scale transport model in order to account for inertial effects in a simplified approach.

We simulated the flow in a double diffusive turbulent layer using a periodic two-dimensional square computational domain. The conditions of the simulation correspond to those typically found in oceans ( Pr  = 7 and Sc  = 1000) and results are in good agreement with the literature. When the flow was in statistically steady state we tracked the paths of particles with different inertia assuming that the concentration of particles is small and their mutual interaction and their effect on the carrying fluid can be neglected (one-way coupling). Numerical experiments were carried out to reveal the effect of the different terms of the particle force balance and the particle inertia in the preferential concentration of the particles. The different numerically obtained particle concentration distributions were analyzed using the cluster index or lacunarity, the tortuosity and the Voronoï analysis. The departure of the instantaneous particle distributions from random distributions using different box sizes for the calculation of the lacunarity of the distributions show maxima at box sizes corresponding to the Kolmogorov length scale. The novel application of the concept of tortuosity to the analysis of the instantaneous particle distributions reveals the non-isotropic character of the particle distributions. The Voronoï analysis indicates larger areas of the voids and clusters for the simulations considering only the drag force in comparison with simulations considering all the terms of the particle force balance. These observations are consequence of the role of the stress gradient term which generates high particle concentrations along the boundaries of the ascending and descending concentration plumes and relatively low particle concentrations in the tail and head of the plumes. [ABSTRACT FROM AUTHOR]

In many atmospheric flows, a dispersed phase is actively suspended by turbulence, whose competition with gravitational settling ultimately dictates its vertical distribution. Examples of dispersed phases include snow, sea-spray droplets, dust, or sand, where individual elements of much larger density than the surrounding air are carried by turbulent motions after emission from the surface. In cases where the particle is assumed to deviate from local fluid motions only by its gravitational settling (i.e., they are inertialess), traditional flux balances predict a power-law dependence of particle concentration with height. It is unclear, however, how particle inertia influences this relationship, and this question is the focus of this work. Direct numerical simulations are conducted of turbulent open-channel flow, laden with Lagrangian particles of specified inertia; in this way the study focuses on the turbulent transport which occurs in the lowest few meters of the planetary boundary layer, in regions critical for connecting emission fluxes to the fluxes felt by the full-scale boundary layer. Simulations over a wide range of particle Stokes number, while holding the dimensionless settling velocity constant, are performed to understand the role of particle inertia on vertical dispersion. It is found that particles deviate from their inertialess behaviour in ways that are not easily captured by traditional theory; concentrations are reduced with increasing Stokes number. Furthermore, a similarity-based eddy diffusivity for particle concentration fails as particles experience inertial acceleration, precluding a closed-form solution for particle concentration as in the case of inertialess particles. The primary consequence of this result is that typical flux parametrizations connecting surface emission models (e.g., saltation models or sea-spray generation functions) to elevated boundary conditions may overestimate particle concentrations due to the reduced vertical transport caused by inertia in between; likewise particle emission may be underestimated if inferred from concentration measurements aloft. [ABSTRACT FROM AUTHOR]

We investigate the sedimentation properties of quasi-neutrally buoyant inertial particles carried by incompressible zero-mean fluid flows. We obtain generic formulae for the terminal velocity in generic space-and-time periodic (or steady) flows, along with further information for flows endowed with some degree of spatial symmetry such as odd parity in the vertical direction. These expressions consist in space-time integrals of auxiliary quantities that satisfy partial differential equations of the advection–diffusion–reaction type, which can be solved at least numerically, since our scheme implies a huge reduction of the problem dimensionality from the full phase space to the classical physical space. [ABSTRACT FROM AUTHOR]

Mixing of inertial point particles in a turbulent channel flow at Re τ = 950 is investigated by means of direct numerical simulations. We consider inertial particles, at varying Stokes number, released from pairs of sources located at different positions inside the channel and analyze the rate at which particles come into close proximity to each other. To do so, we employ a Lagrangian framework, which is suitable for the analysis of trajectories and in general for the study of mixing and dispersion problems. By varying the release position of particles along the wall-normal direction we obtain a thorough description of mixing in an anisotropic turbulent flow. Moreover, we analyze the effects of particle inertia and show that these are not univocal but also depend on the position and alignment of the sources, owing in particular to the dependence of the flow timescales on the distance from the wall. • Mixing of inertial particles in turbulent channel flow at R e τ = 950 is performed. • A Lagrangian framework, accounting for particle mutual distance, is employed. • The effects of the position and alignment of sources are considered. • Particles with different inertia experience peak clustering at different wall distances. [ABSTRACT FROM AUTHOR]

Two-phase turbulent flows with the dispersed phase in the form of small, spherical particles are increasingly often computed with the large-eddy simulation (LES) of the carrier fluid phase, coupled to the Lagrangian tracking of particles. To enable further model development for LES with inertial particles subject to gravity, we consider direct numerical simulations of homogeneous isotropic turbulence with a large-scale forcing. Simulation results, both without filtering and in thea prioriLES setting, are reported and discussed. A full (i.e.a posteriori) LES is also performed with the spectral eddy viscosity. Effects of gravity on the dispersed phase include changes in the average settling velocity due to preferential sweeping, impact on the radial distribution function and radial relative velocity, as well as direction-dependent modification of the particle velocity variance. The filtering of the fluid velocity, performed in spectral space, is shown to have a non-trivial impact on these quantities. [ABSTRACT FROM AUTHOR]

Heavy particles in a turbulent flow tend to leave regions of high vorticity and cluster into regions of high strain. The consequences of such clustering have been studied in a variety of situations over the past few decades, and this problem has seen several review papers already. Our objectives in this paper are three-fold. (i) We introduce the reader to the basic ideas, and explain why the problem is interesting. (ii) Using an N-vortex system we present an interesting case where particles are attracted to the vicinity of vortices. A new scaling for the critical Stokes number of attraction is obtained. (iii) We review a number of papers, which are related to cloud physics in this context. [ABSTRACT FROM AUTHOR]

Inertial particles are finite-sized objects that are carried by fluid flows and in contrast to massless tracer particles they are subject to inertia effects. In unsteady flows, the dynamics of tracer particles have been extensively studied by the extraction of Lagrangian coherent structures (LCS), such as hyperbolic LCS as ridges of the Finite-Time Lyapunov Exponent (FTLE). The extension of the rich LCS framework to inertial particles is currently a hot topic in the CFD literature and is actively under research. Recently, backward FTLE on tracer particles has been shown to correlate with the preferential particle settling of small inertial particles. For larger particles, inertial trajectories may deviate strongly from (massless) tracer trajectories, and thus for a better agreement, backward FTLE should be computed on inertial trajectories directly. Inertial backward integration, however, has not been possible until the recent introduction of the influence curve concept, which — given an observation and an initial velocity — allows to recover all sources of inertial particles as tangent curves of a derived vector field. In this paper, we show that FTLE on the influence curve vector field is in agreement with preferential particle settling and more importantly it is not only valid for small (near-tracer) particles. We further generalize the influence curve concept to general equations of motion in unsteady spatio-velocity phase spaces, which enables backward integration with more general equations of motion. Applying the influence curve concept to tracer particles in the spatio-velocity domain emits streaklines in massless flows as tangent curves of the influence curve vector field. We demonstrate the correlation between inertial backward FTLE and the preferential particle settling in a number of unsteady vector fields. [ABSTRACT FROM PUBLISHER]

The gravitational settling velocity of small heavy particles in a three-dimensional turbulent flow remains a controversial topic. In a homogeneous turbulence of zero mean velocity, both enhanced settling velocity and reduced settling velocity have been reported relative to the still-fluid terminal velocity. Dominant mechanisms for enhanced settling include the preferential sweeping and particle-particle hydrodynamic interactions. The reduced settling could result from loitering (falling particles spend more time in the regions with upward flow), vortex trapping, and drag nonlinearity. Here high-resolution direct numerical simulations (DNS) are used to investigate the settling velocity of non-interacting small heavy particles, for an extended range of flow Taylor microscale Reynolds numbers (up to R λ = 500 ) with varying particle terminal velocity (relative to the Kolmogorov velocity) and particle inertia, by changing the particle-to-fluid density ratio and energy dissipation rate. For the parameter regimes considered here, the preferential sweeping has a dominant effect leading to an increase of the average settling velocity relative to the terminal velocity; and this increase is mainly governed by particle Froude number (the ratio between the particle inertial response time and the residence time of the particle in a Kolmogorov eddy) and its magnitude depends linearly on the square root of the energy dissipation rate. The reduction of settling due to loitering rarely occurs in a homogeneous turbulence without organized large-scale vortical structures, but is found to emerge only if the particle horizontal motions are blocked (thus removing the preferential sweeping effect), as shown in Good et al. (2014). The DNS results were used to develop a parameterization that relates the settling velocity to the particle inertia ( St ), Froude number, and R λ . Finally, sensitivities of the DNS results to the large-scale forcing method and to the drag nonlinearity are also briefly discussed. [ABSTRACT FROM AUTHOR]

The motion of non-Brownian aerosols in an open laminar cavity flow is investigated by means of numerical and asymptotic methods. The cavity is a rectangular domain where air enters through an inlet located on the top, and exits in the horizontal direction through symmetric apertures near the bottom wall. While such flows are generally used to provide a clean (particle-free) environment, the introduction of any object inside the cavity can affect the flow topology and, in return, can lead to large aerosol residence times. In addition, it is known that the unsteadiness of the flow, though weak, significantly delays the exit of aerosols from the cavity. The goal of this paper is to analyze the conditions under which these phenomena occur, for heavy inertial particles with a small response time and a finite free-fall velocity, in a laminar cavity flow. A two-dimensional situation is considered and investigated by means of numerical simulations and perturbation methods, at moderate cavity Reynolds numbers. It is observed that any obstacle placed inside the cavity (along the symmetry axis) creates large quasi-steady triangular recirculation cells stretched by the outward flow, provided the Reynolds number is not too large. In particular, streamlines near the floor are reversed, so that deposited particles are swept inward and remain in the cavity. The probability of trapping has been calculated asymptotically, for inertia-free sedimenting particles, and compared to numerical results. Trapping in the wake of obstacles is observed to persist when the flow is slightly unsteady. In addition, it is shown that the small but finite unsteadiness of the flow can lead to the temporary trapping of a significant portion of particles by large recirculation cells near the upper corners of the cavity. This phenomenon takes place in spite of gravity and centrifuge effects due to the curvature of the cell, and leads to a long-term suspension which significantly increases the residence time of aerosols. By making use of separatrix map methods, the critical aerosol diameter below which this phenomenon occurs has been obtained and compared to numerical simulation results. [ABSTRACT FROM AUTHOR]

The motion of inertial particles suspended in the viscous boundary sublayer of a wall-bounded turbulent flow is considered. We show that there is the diffusional region near the wall occupied by the particle moving in the local-equilibrium with the turbulent fluctuations which are modelled by Ornstein–Uhlenbeck process. The stationary spatial distribution of inertial particles is found for arbitrary Stokes number (dimensionless measure of the inertia). The weakly inertial particles placed in the diffusional region go away from the wall and escape the viscous sublayer. However, the direction of particle migration reverses when the Stokes number is getting larger than the critical value that we determine. The standard turbophoresis becomes more and more pronounced with the increase of Stokes number so that sufficiently inertial particles turn out to be trapped in the viscous boundary sublayer. [ABSTRACT FROM AUTHOR]

The dynamics of heavy particles suspended in turbulent flows is of fundamental importance for a wide range of questions in astrophysics, atmospheric physics, oceanography, and technology. Laboratory experiments and numerical simulations have demonstrated that heavy particles respond in intricate ways to turbulent fluctuations of the carrying fluid: non-interacting particles may cluster together and form spatial patterns even though the fluid is incompressible, and the relative speeds of nearby particles can fluctuate strongly. Both phenomena depend sensitively on the parameters of the system. This parameter dependence is difficult to model from first principles since turbulence plays an essential role. Laboratory experiments are also very difficult, precisely since they must refer to a turbulent environment. But in recent years it has become clear that important aspects of the dynamics of heavy particles in turbulence can be understood in terms of statistical models where the turbulent fluctuations are approximated by Gaussian random functions with appropriate correlation functions. In this review, we summarise how such statistical-model calculations have led to a detailed understanding of the factors that determine heavy-particle dynamics in turbulence. We concentrate on spatial clustering of heavy particles in turbulence. This is an important question because spatial clustering affects the collision rate between the particles and thus the long-term fate of the system. [ABSTRACT FROM AUTHOR]

Recent experimental and numerical observations have shown the significance of the Basset-Boussinesq memory term on the dynamics of small spherical rigid particles (or inertial particles) suspended in an ambient fluid flow. These observations suggest an algebraic decay to an asymptotic state, as opposed to the exponential convergence in the absence of the memory term. Here, we prove that the observed algebraic decay is a universal property of the Maxey-Riley equation. Specifically, the particle velocity decays algebraically in time to a limit that is $$\mathcal {O}(\epsilon )$$ -close to the fluid velocity, where $$0<\epsilon \ll 1$$ is proportional to the square of the ratio of the particle radius to the fluid characteristic length scale. These results follow from a sharp analytic upper bound that we derive for the particle velocity. For completeness, we also present a first proof of the global existence and uniqueness of mild solutions to the Maxey-Riley equation, a nonlinear system of fractional differential equations. [ABSTRACT FROM AUTHOR]

The main goal of our research is to understand the forces responsible for particle suspension in turbulent flow, taking into account the complicated nature of turbulence and the interaction of turbulent flow with particles. Recent observations indicate that the acceleration (or the total force) probability density functions (PDFs) of relatively small spherical particles is invariant to the particle diameter. We prove the postulated role of particle/fluid interaction forces in maintaining suspension using unique dataset of Lagrangian information of flow tracers and inertial particles. The data was obtained using the three-dimensional particle tracking velocimetry (3D-PTV) method, applied simultaneously to obtain velocity and acceleration data along trajectories of flow tracers and inertial particles. Through the use of the particle’s equation of motion, the magnitude and direction of forces are derived and the components representing the turbulent flow compared to the components due to the flow-particle interactions. We demonstrate that the invariance of PDFs of the total force extends to the orthogonal components of forces and add an analytical model that explains the phenomenon. Furthermore, we show that the lift forces in turbulent flow are important contributions for both tracers and inertial particles. [ABSTRACT FROM AUTHOR]