Particles In Homogeneous Isotropic Turbulence Research Articles

Temperature statistics of settling particles in homogeneous isotropic turbulence

Heat transfer of settling particles in homogeneous isotropic turbulence is investigated in one-way coupled Eulerian–Lagrangian direct numerical simulations. In the absence of gravity, our observations highlight that there was a correlation between particles concentration and temperature fronts, which are characterized by high-temperature gradients. The particle clustering is mainly influenced by the preferential concentration and the non-local effect, the latter being the memory of their interaction with the flow along their trajectories. Nevertheless, gravity significantly affects the clustering of particles, which further influence the heat transfer of particles with the fluid. We find that the heat transfer of particles is intricately related to particle dynamic inertia and thermal inertia, which can be quantified by the particle Stokes number St and particle thermal Stokes number Stθ, respectively. In this study, we observe that the variance of particle temperature rate of change is independent of Stθ at small thermal inertia but inversely proportional to Stθ2 for large thermal inertia. In the presence of gravity, the variance converges to Stθ−1 for particles with negligible thermal inertia. Our findings reveal that the second-order structure function of the particle temperature, indicating the enhancement of Lagrangian scalar intermittency, adheres to a power-law behavior with limited thermal inertial particles in the dissipation region, denoted as r2. However, as Stθ increases, the power law of the structure function of the particle temperature is disrupted leading to ‘thermal caustics’. The present findings of the heat transfer behavior of settling particles advance the understanding of gravity effect, and are valuable for the modeling of heat transfer in particle-laden turbulent flows.

The influence of clustering in homogeneous isotropic turbulence on the ignition behavior of iron particles

We conduct carrier-phase direct numerical simulations (CP-DNS) to investigate the ignition of iron particles in homogeneous isotropic turbulence, and characterize the connection between particle clustering and particle ignition. A pseudo-spectral reacting multiphase flow solver using a low Mach number approximation is employed. It features an established point-particle sub-model for reacting iron particles and describes the mass, heat and momentum transfer across the particle boundary layers in a two-way coupled regime. Within this setup, we perform a series of simulations covering a broad range of Reynolds and Stokes numbers. The results confirm the well-known observation from incompressible dispersed multiphase flows that particle clustering is most pronounced for particle clouds with Stokes numbers of order one. Here, strong particle clustering additionally facilitates the earlier ignition of heterogeneously burning iron particles. This is because groups of neighboring particles locally deposit more heat per volume than a single isolated particle, thus more strongly increasing the local fluid temperature and shifting particle reactions from kinetically-limited to diffusion-limited particle conversion. A Voronoi tessellation analysis shows that the particles packed together in clusters tend to ignite first, even for small Stokes numbers, at which clustering is less prominent. An increase in Reynolds number reduces the ignition delay times, especially for high Stokes numbers, since particles with higher inertia are more sensitive to the larger scales of the turbulent motion. The present findings are of practical importance for the design and flame stabilization mechanisms in future iron combustion burners.

A further study of history force effect on particle clustering in turbulence

We examine the effects of the history force on the preferential concentration of small particles in homogeneous isotropic turbulence under a wide range of the particle-to-fluid mass density ratio γ (from 0 to 10000) by direct simulations of the Navier–Stokes equations. As to the history integral kernel, we introduce two expressions: i.e., the classical Basset kernel valid only in the limit of creeping flow conditions and for short times, and the Mei–Adrian kernel (Mei and Adrian, 1992) applicable for finite Reynolds numbers and large times. It is revealed that the presence of the history force weakens the level of preferential concentration to some extent, specifically under the conditions of the mass density ratio of around 1.5–10 for heavy particles (e.g., solid particles in liquid) and smaller than 0.7 for light particles (e.g., bubbles in liquid) and that the overprediction of particle accumulation by neglecting the history force is much more remarkable for light particles. A comparison between the Basset kernel and the Mei–Adrian kernel has shown that the Basset kernel overestimates the history effect but only slightly.

Parameterization of turbulence modulation by finite-size solid particles in forced homogeneous isotropic turbulence

Turbulence modulation by finite-size particles in homogeneous isotropic turbulence (HIT) has been investigated numerically and experimentally in many studies, but its controlling parameters are not fully clear. In this work, four non-dimensional parameters governing the turbulent modulation by non-settling particles, i.e. $Re_\lambda$ of the background HIT, the particle-to-fluid density ratio $\rho _p/\rho _f$ , the relative particle size $d_p/\eta$ and the particle volume fraction $\phi _v$ , are identified through dimensional analysis. Then, a parameterization study is conducted based on results from fully resolved direct numerical simulations to investigate the influence of the above non-dimensional parameters on the modulation of turbulent kinetic energy (TKE) and viscous dissipation rate. Empirical models that quantitatively predict the modulation of TKE and dissipation rate are then developed by fitting in the simulation results. These models are used to examine the turbulence modulation results reported in the literature. The model predictions and the data points of TKE modulation show reasonable agreement, but the model predicting the modulation of dissipation rate needs further deliberation as the credibility of the available data points is currently difficult to assess. The generality and the physics behind these empirical models also require further investigation.

Collision statistics and settling velocity of inertial particles in homogeneous turbulence from high-resolution DNS under two-way momentum coupling

Statistical quantities related to the motion of low inertia particles in homogeneous isotropic turbulence are investigated by means of direct numerical simulations applying the Eulerian–Lagrangian approach and the point-particle approximation. The modelled systems imitate, among others, the microphysical processes relevant for cloud droplets in typical atmospheric flows. To complement former studies, the turbulent flow is simulated using high-resolution grids, covering a wide range of Reynolds numbers, up to Rλ≈500. The effect of mutual interaction of the carrier and dispersed phases, known as two-way momentum coupling, is considered, and the new results are compared with those obtained under one-way coupling. The droplet kinematic statistics, including the radial relative velocity and radial distribution functions, and dynamic properties, such as the collision kernel and settling velocity, are reported over a wide range of mass loadings. The results show that the radial distribution function of “nearly touching” droplets decreases as the mass loading increases when gravity is not considered. In the presence of gravity there is an enhancement in clustering for dilute systems while a reduction occurs when the two-way coupling effect becomes considerable. An opposite trend is observed for relative velocities due to transfer of momentum from droplets to the fluid, decorrelating the motion of neighbouring droplets. By increasing Rλ, or equivalently enlarging the domain size at fixed energy dissipation rate, the clustering weakens if gravity is considered, while relative velocities augment, ultimately leading to a higher collision kernel. The average settling velocity increases with Rλ. It also increases with mass loading, especially for low-inertia droplets. When performing simulations of small particles at considerable mass loadings a parameterisation is unavoidable to reduce the numerical cost. We use the super-droplet approach and demonstrate its impact on physical fidelity of the modelled systems. The effect of the large-scale forcing scheme, deterministic or stochastic, on the droplet dynamic statistics is also investigated.

Modulation of fluid temperature fluctuations by particles in turbulence

Modulation of fluid temperature fluctuations by particles due to thermal interaction in homogeneous isotropic turbulence is studied. For simplicity, only thermal coupling between the fluid and particles is considered, and momentum coupling is neglected. Application of the statistical theory used in cloud turbulence research leads to the prediction that modulation of the intensity of fluid temperature fluctuations by particles is expressed as a function of the Damköhler number, which is defined as the ratio of the turbulence large-eddy turnover time to the fluid thermal relaxation time. Direct numerical simulations are conducted for two-way thermal coupling between the fluid temperature field and point particles in homogeneous isotropic turbulence. The simulation results are shown to agree well with the theoretical predictions.

Flocculation of suspended cohesive particles in homogeneous isotropic turbulence

Abstract

An Overview of the Lagrangian Dispersion Modeling of Heavy Particles in Homogeneous Isotropic Turbulence and Considerations on Related LES Simulations

Particle tracking is a competitive technique widely used in two-phase flows and best suited to simulate the dispersion of heavy particles in the atmosphere. Most Lagrangian models in the statistical approach to turbulence are based either on the eddy interaction model (EIM) and the Monte-Carlo method or on random walk models (RWMs) making use of Markov chains and a Langevin equation. In the present work, both discontinuous and continuous random walk techniques are used to model the dispersion of heavy spherical particles in homogeneous isotropic stationary turbulence (HIST). Their efficiency to predict particle long time dispersion, mean-square velocity and Lagrangian integral time scales are discussed. Computation results with zero and no-zero mean drift velocity are reported; they are intended to quantify the inertia, gravity, crossing-trajectory and continuity effects controlling the dispersion. The calculations concern dense monodisperse spheres in air, the particle Stokes number ranging from 0.007 to 4. Due to the weaknesses of such models, a more sophisticated matrix method will also be explored, able to simulate the true fluid turbulence experienced by the particle for long time dispersion studies. Computer evolution and performance since allowed to develop, instead of Reynold-Averaged Navier-Stokes (RANS)-based studies, large eddy simulation (LES) and direct numerical simulation (DNS) of turbulence coupled to Generalized Langevin Models. A short review on the progress of the Lagrangian simulations based on large eddy simulation (LES) will therefore be provided too, highlighting preferential concentration. The theoretical framework for the fluid time correlation functions along the heavy particle path is that suggested by Wang and Stock.

Effects of turbulence modulation and gravity on particle collision statistics

Dynamics of inertial particles in homogeneous isotropic turbulence is investigated by means of numerical simulations that incorporate the effect of two-way interphase momentum transfer. The continuous phase is solved in the Eulerian approach employing Direct Numerical Simulations (DNS). The dispersed phase is treated using the Lagrangian approach along with the point-particle assumption. The main focus is on computing collision statistics of inertial particles relevant to cloud droplets in typical atmospheric conditions. The vast majority of previous DNS were performed assuming one-way momentum coupling between continuous and dispersed phases. Such simplified approach is adequate only for dilute systems with relatively low mass loading. In this study we investigate the effect of two-way momentum coupling on the kinematic and dynamic collision statistics of the dispersed phase. A number of simulations have been performed at different droplet radii (inertia), mass loading, viscosity and energy dissipation rate. To assess the accuracy of numerical approach the coupling force (exerted by particles on the fluid) was computed using two different techniques, namely particle in cell and projection onto neighboring node. To address the effect of gravity, the simulations have been carried out simultaneously both with and without gravitational acceleration. It has been found that the effect of two-way coupling is significant both for droplet clustering and the radial relative velocity. It turns out that the collision kernel is more sensitive to the particle mass loading when the gravitational acceleration is considered. The collision kernel of settling droplets increases as the droplet mass loading increases. This is direct consequence of larger radial relative velocity. For non-settling droplets the effect of mass loading is opposite, namely, we observe a minor reduction of the collision kernel as the number of droplets increases.

A new time scale for turbulence modulation by particles

A new time scale for turbulence modulation by particles is introduced. This time scale is inversely proportional to the number density and the radius of particles, and can be regarded as a counterpart of the phase relaxation time, an important time scale in cloud physics, which characterizes the interaction between turbulence and cloud droplets by condensation–evaporation. Scaling analysis and direct numerical simulations of dilute inertial particles in homogeneous isotropic turbulence suggest that turbulence modulation by particles with a fixed mass-loading parameter can be expressed as a function of the Damköhler number, which is defined as the ratio of the turbulence large-eddy turnover time to the new time scale.

Quantification of preferential concentration of colliding particles in a homogeneous isotropic turbulent flow

This paper addresses the effect of inter-particle collisions on the segregation of non-settling inertial particles in homogeneous isotropic turbulence. For this purpose, direct numerical simulations of particles in statistically steady homogeneous isotropic turbulence have been performed by the lattice Boltzmann method considering inter-particle collisions. The preferential concentration of suspended particles is quantified using several clustering measures: segregation parameter, correlation dimension, radial distribution function, Voronoï diagrams and the topological tool of Minkowski functionals. Effects of particle inertia, inter-particle collisions and increasing volume fraction in the aforementioned measures are discussed. The obtained results show that collisions between particles have a remarkable influence on the formation of clusters. In particular, under locally dilute conditions, increasing particle volume fraction implies a moderate clustering intensification, but for locally dense conditions an increase of the mean inter-particle distance inside clusters can be envisaged as a consequence of the re-dispersing effect of inter-particle collisions.

LBM study of aggregation of monosized spherical particles in homogeneous isotropic turbulence

Direct numerical simulations of an aggregation system composed of monosized spherical particles in homogeneous isotropic turbulence have been performed using Lattice Boltzmann method (LBM). The effects of hydrodynamics on the aggregation process were considered by directly resolving the disturbance flows around finite-size solid particles using an interpolated bounce-back scheme. A nonuniform time-dependent large-scale stochastic forcing scheme was implemented within the mesoscopic multiple-relaxation-time LBM approach to maintain turbulence intensity at targeted levels. To simulate particle interactions, the non-contact surface force and the contact force were taken into account using the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory and the soft-sphere model, respectively. This interface-resolved direct numerical simulation (IR-DNS) combined with the well-known DLVO theory was employed to obtain an insight into the aggregation process of micron-size particles. Specifically, the model was used to study the effects of solid volume fraction on aggregate growth. Aggregates of larger sizes formed in local regions of higher concentration of particles due to higher encountering probability between particles. The effects of aggregating particles of different volume fractions on the statistically stationary homogeneous isotropic turbulent flow were investigated. It was found that the presence of particles attenuated the turbulent kinetic energy at large scales and augmented the kinetic energy at the small scales. This effect is more apparent with increasing volume concentration of particles.

Exponential scaling in early-stage agglomeration of adhesive particles in turbulence

We carry out direct numerical simulation together with an adhesive discrete element method calculation (DNS-DEM) to investigate agglomeration of particles in homogeneous isotropic turbulence (HIT). We report an exponential-form scaling for the size distribution of early-stage agglomerates, which is valid across a wide range of particle inertia and inter-particle adhesion values. Such scaling allows one to quantify the state of agglomeration using a single scale parameter. An agglomeration kernel is then constructed containing the information of agglomerate structures and the sticking probability. An explicit relationship between the sticking probability and microscale particle properties is also proposed based on the scaling analysis of the equation for head-on collisions. Our results extend Smoluchowski's theory to the condition of non-coalescing solid adhesive particles and can reproduce DNS-DEM results with a simple one-dimensional simulation.

Explanation of differences in experimental and computational results for the preferential concentration of inertial particles

Using one-way coupled direct numerical simulations of inertial particles in homogeneous isotropic turbulence we investigate the non-linear dependence of local particle concentrations in particle clusters on the number density of particles used in the simulation per volume. We show that the Reynolds-number dependence of local concentrations in clusters can be predicted for sufficiently high Reynolds numbers by a scaling relation that depends on the average particle number density and the Kolmogorov length. Depending on the average particle number density and gravity, a maximum of preferential concentration does not necessarily occur at Stokes numbers around unity. This explains the differences observed between recent experimental and computational results.

Enhanced settling of nonheavy inertial particles in homogeneous isotropic turbulence: The role of the pressure gradient and the Basset history force.

The Stokes drag force and the gravity force are usually sufficient to describe the behavior of sub-Kolmogorov-size (or pointlike) heavy particles in turbulence, in particular when the particle-to-fluid density ratio ρ_{p}/ρ_{f}≳10^{3} (with ρ_{p} and ρ_{f} the particle and fluid density, respectively). This is, in general, not the case for smaller particle-to-fluid density ratios, in particular not for ρ_{p}/ρ_{f}≲10^{2}. In that case the pressure gradient force, added mass effects, and the Basset history force also play important roles. In this study we focus on the understanding of the role of these additional forces, all of hydrodynamic origin, in the settling of particles in turbulence. In order to qualitatively elucidate the complex dynamics of such particles in homogeneous isotropic turbulence, we first focus on the case of settling of such particles in the flow field of a single vortex. After having explored this simplified case we extend our analysis to homogeneous isotropic turbulence. In general, we found that the pressure gradient force leads to a decrease in the settling velocity. This can be qualitatively understood by the fact that this force prevents the particles from sweeping out of vortices, a mechanism known as preferential sweeping which causes enhanced settling. Additionally, we found that the Basset history force can both increase and decrease the enhanced settling, depending on the particle Stokes number. Finally, the role of the nonlinear Stokes drag has been explored, confirming that it affects settling of inertial particles in turbulence, but only in a limited way for the parameter settings used in this investigation.

Symmetry Breaking Drift of Particles Settling in Homogeneous Shear Turbulence

We investigate the influence of shear on the gravitational settling of heavy inertial particles in homogeneous shear turbulence (HST). In addition to the well-known enhanced settling velocity, observed for heavy inertial particles in homogeneous isotropic turbulence (HIT), a horizontal drift velocity is also observed in the shearing direction due to the presence of a nonzero mean vorticity (introducing symmetry breaking due to the mean shear). This drift velocity is due to the combination of shear, gravity, and turbulence, and all three of these elements are needed for this effect to occur. We extend the mechanism responsible for the enhanced settling velocity in HIT to the case of HST. Two separate regimes are observed, characterized by positive or negative drift velocity, depending on the particle settling velocity.

Settling velocity of small inertial particles in homogeneous isotropic turbulence from high-resolution DNS

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 Rλ=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 Rλ. Finally, sensitivities of the DNS results to the large-scale forcing method and to the drag nonlinearity are also briefly discussed.

Sedimentation of finite-size spheres in quiescent and turbulent environments

Sedimentation of a dispersed solid phase is widely encountered in applications and environmental flows, yet little is known about the behaviour of finite-size particles in homogeneous isotropic turbulence. To fill this gap, we perform direct numerical simulations of sedimentation in quiescent and turbulent environments using an immersed boundary method to account for the dispersed rigid spherical particles. The solid volume fractions considered are ${\it\phi}=0.5{-}1\,\%$, while the solid to fluid density ratio ${\it\rho}_{p}/{\it\rho}_{f}=1.02$. The particle radius is chosen to be approximately six Kolmogorov length scales. The results show that the mean settling velocity is lower in an already turbulent flow than in a quiescent fluid. The reductions with respect to a single particle in quiescent fluid are approximately 12 % and 14 % for the two volume fractions investigated. The probability density function of the particle velocity is almost Gaussian in a turbulent flow, whereas it displays large positive tails in quiescent fluid. These tails are associated with the intermittent fast sedimentation of particle pairs in drafting–kissing–tumbling motions. The particle lateral dispersion is higher in a turbulent flow, whereas the vertical one is, surprisingly, of comparable magnitude as a consequence of the highly intermittent behaviour observed in the quiescent fluid. Using the concept of mean relative velocity we estimate the mean drag coefficient from empirical formulae and show that non-stationary effects, related to vortex shedding, explain the increased reduction in mean settling velocity in a turbulent environment.

Clustering of vertically constrained passive particles in homogeneous isotropic turbulence.

We analyze the dynamics of small particles vertically confined, by means of a linear restoring force, to move within a horizontal fluid slab in a three-dimensional (3D) homogeneous isotropic turbulent velocity field. The model that we introduce and study is possibly the simplest description for the dynamics of small aquatic organisms that, due to swimming, active regulation of their buoyancy, or any other mechanism, maintain themselves in a shallow horizontal layer below the free surface of oceans or lakes. By varying the strength of the restoring force, we are able to control the thickness of the fluid slab in which the particles can move. This allows us to analyze the statistical features of the system over a wide range of conditions going from a fully 3D incompressible flow (corresponding to the case of no confinement) to the extremely confined case corresponding to a two-dimensional slice. The background 3D turbulent velocity field is evolved by means of fully resolved direct numerical simulations. Whenever some level of vertical confinement is present, the particle trajectories deviate from that of fluid tracers and the particles experience an effectively compressible velocity field. Here, we have quantified the compressibility, the preferential concentration of the particles, and the correlation dimension by changing the strength of the restoring force. The main result is that there exists a particular value of the force constant, corresponding to a mean slab depth approximately equal to a few times the Kolmogorov length scale η, that maximizes the clustering of the particles.

Effects of gravity on the acceleration and pair statistics of inertial particles in homogeneous isotropic turbulence

Within the context of heavy particles suspended in a turbulent airflow, we study the effects of gravity on acceleration statistics and radial relative velocity (RRV) of inertial particles. The turbulent flow is simulated by direct numerical simulation (DNS) on a 2563 grid and the dynamics of O(106) inertial particles by the point-particle approach. For particles/droplets with radius from 10 to 60 μm, we found that the gravity plays an important role in particle acceleration statistics: (a) a peak value of particle acceleration variance appears in both the horizontal and vertical directions at a particle Stokes number of about 1.2, at which the particle horizontal acceleration clearly exceeds the fluid-element acceleration; (b) gravity constantly disrupts quasi-equilibrium of a droplet’s response to local turbulent motion and amplifies extreme acceleration events both in the vertical and horizontal directions and thus effectively reduces the inertial filtering mechanism. By decomposing the RRV of the particles into three parts: (1) differential sedimentation, (2) local flow shear, and (3) particle differential acceleration, we evaluate and compare their separate contributions. For monodisperse particles, we show that the presence of gravity does not have a significant effect on the shear term. On the other hand, gravity suppresses the probability distribution function (pdf) tails of the differential acceleration term due to a lower particle-eddy interaction time in presence of gravity. For bidisperse cases, we find that gravity can decrease the shear term slightly by dispersing particles into vortices where fluid shear is relatively low. The differential acceleration term is found to be positively correlated with the gravity term, and this correlation is stronger when the difference in colliding particle radii becomes smaller. Finally, a theory is developed to explain the effects of gravity and turbulence on the horizontal and vertical acceleration variances of inertial particles at small Stokes numbers, showing analytically that gravity affects particle acceleration variance both in horizontal and vertical directions, resulting in an increase in particle acceleration variance in both directions. Furthermore, the effect of gravity on the horizontal acceleration variance is predicted to be stronger than that in the vertical direction, in agreement with our DNS results.