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The turbulent energy dissipation rate is an important parameter that determines the transfer rates of mass, heat and momentum in chemical engineering industry. Especially in a multiphase reactor, the local instantaneous turbulent dissipation rate affects the breakage and coalescence of bubbles or droplets. To directly determine the local turbulent dissipation rate, fluctuating velocity gradients have to be measured down to the Kolmogorov length scale. This paper compares the advantages and disadvantages of three different methods, namely, correlation method, optical flow method and hybrid method, in the evaluation of velocity fields, which are subsequently used to calculate the turbulent dissipation rate. An instantaneous flow field of homogeneous isotropic turbulence from DNS results is used as a benchmark. The velocity field and turbulent dissipation rate field obtained by these three methods are compared to the DNS results. It is shown that the hybrid method performs better in both velocity field evaluation and local turbulent dissipation rate estimation compared to the other two methods. This is because the hybrid method combines the advantages of the correlation method in achieving a stable averaged velocity field and the optical flow method in achieving pixel-level resolution measurement of the flow field.

In this study, the behaviours of subgrid-scale (SGS) turbulence are investigated with direct numerical simulations when an isotropic turbulence is brought to interact with imposed rapid waves. A partition of the velocity field is used to decompose the SGS stress into three parts, namely, the turbulent part$\unicode[STIX]{x1D749}^{T}$, the wave-induced part$\unicode[STIX]{x1D749}^{W}$and the cross-interaction part$\unicode[STIX]{x1D749}^{C}$. Under strong wave straining,$\unicode[STIX]{x1D749}^{T}$is found to follow the Kolmogorov scaling$\unicode[STIX]{x1D6E5}_{c}^{2/3}$, where$\unicode[STIX]{x1D6E5}_{c}$is the filter width. Based on the linear Airy wave theory,$\unicode[STIX]{x1D749}^{W}$and the filtered strain-rate tensor due to the wave motion,$\tilde{\unicode[STIX]{x1D64E}}^{W}$, are found to have different phases, posing a difficulty in applying the usual eddy-viscosity model. On the other hand,$\unicode[STIX]{x1D749}^{T}$and the filtered strain-rate tensor due to the turbulent motion,$\tilde{\unicode[STIX]{x1D64E}}^{T}$, are only weakly wave-phase-dependent and could be well related by an eddy-viscosity model. The linear wave theory is also used to describe the vertical distributions of SGS statistics driven by the wave-induced motion. The predictions are in good agreement with the direct numerical simulation results. The budget equation for the turbulent SGS kinetic energy shows that the transport terms related to turbulence are important near the free surface and they compensate the imbalance between the energy flux and the SGS energy dissipation.

Understanding the two-way interactions between finite-size solid particles and a wall-bounded turbulent flow is crucial in a variety of natural and engineering applications. Previous experimental measurements and particle-resolved direct numerical simulations revealed some interesting phenomena related to particle distribution and turbulence modulation, but their in-depth analyses are largely missing. In this study, turbulent channel flows laden with neutrally buoyant finite-size spherical particles are simulated using the lattice Boltzmann method. Two particle sizes are considered, with diameters equal to 14.45 and 28.9 wall units. To understand the roles played by the particle rotation, two additional simulations with the same particle sizes but no particle rotation are also presented for comparison. Particles of both sizes are found to form clusters. Under the Stokes lubrication corrections, small particles are found to have a stronger preference to form clusters, and their clusters orientate more in the streamwise direction. As a result, small particles reduce the mean flow velocity less than large particles. Particles are also found to result in a more homogeneous distribution of turbulent kinetic energy (TKE) in the wall-normal direction, as well as a more isotropic distribution of TKE among different spatial directions. To understand these turbulence modulation phenomena, we analyse in detail the total and component-wise volume-averaged budget equations of TKE with the simulation data. This budget analysis reveals several mechanisms through which the particles modulate local and global TKE in the particle-laden turbulent channel flow.

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.

Cascades of temperature and entropy fluctuations are studied by numerical simulations of stationary three-dimensional compressible turbulence with a heat source. The fluctuation spectra of velocity, compressible velocity component, density and pressure exhibit the $-5/3$ scaling in an inertial range. The strong acoustic equilibrium relation between spectra of the compressible velocity component and pressure is observed. The $-5/3$ scaling behaviour is also identified for the fluctuation spectra of temperature and entropy, with the Obukhov–Corrsin constants close to that of a passive scalar spectrum. It is shown by Kovasznay decomposition that the dynamics of the temperature field is dominated by the entropic mode. The average subgrid-scale (SGS) fluxes of temperature and entropy normalized by the total dissipation rates are close to 1 in the inertial range. The cascade of temperature is dominated by the compressible mode of the velocity field, indicating that the theory of a passive scalar in incompressible turbulence is not suitable to describe the inter-scale transfer of temperature in compressible turbulence. In contrast, the cascade of entropy is dominated by the solenoidal mode of the velocity field. The different behaviours of cascades of temperature and entropy are partly explained by the geometrical properties of SGS fluxes. Moreover, the different effects of local compressibility on the SGS fluxes of temperature and entropy are investigated by conditional averaging with respect to the filtered dilatation, demonstrating that the effect of compressibility on the cascade of temperature is much stronger than on the cascade of entropy.

The lattice Boltzmann method is employed to conduct direct numerical simulations of turbulent open channel flows with the presence of finite-size spherical sediment particles. The uniform particles have a diameter of approximately 18 wall units and a density of ρp=2.65ρf, where ρp and ρf are the particle and fluid densities, respectively. Three low particle volume fractions ϕ=0.11%, 0.22%, and 0.44% are used to investigate the particle-turbulence interactions. Simulation results indicate that particles are found to result in a more isotropic distribution of fluid turbulent kinetic energy (TKE) among different velocity components, and a more homogeneous distribution of the fluid TKE in the wall-normal direction. Particles tend to accumulate in the near-wall region due to the settling effect and they preferentially reside in low-speed streaks. The vertical particle volume fraction profiles are self-similar when normalized by the total particle volume fractions. Moreover, several typical transport modes of the sediment particles, such as resuspension, saltation, and rolling, are captured by tracking the trajectories of particles. Finally, the vertical profiles of particle concentration are shown to be consistent with a kinetic model.

Discrete unified gas-kinetic scheme (DUGKS) has been developed recently as a general method for simulating flows at all Knudsen numbers. In this study, we extend DUGKS to simulate fully compressible thermal flows. We introduce a source term to the Boltzmann equation with the Bhatnagar-Gross-Krook (BGK) collision model [1] to adjust heat flux and thus the Prandtl number. The fully compressible Navier-Stokes equations can be recovered by the current model. As a mesoscopic CFD approach, it requires an accurate mesoscopic implementation of the boundary conditions. Using the Chapman-Enskog approximation, we derive the “bounce-back” expressions for both temperature and velocity distribution functions, which reveal the need to consider coupling terms between the velocity and thermal fields. To validate our scheme, we first reproduce the Boussinesq flow results by simulating natural convection in a square cavity with a small temperature difference ( ϵ = 0.01 ) and a low Mach number. Then we perform simulations of steady natural convection ( R a = 1.0 × 10 6 ) in a square cavity with differentially heated side walls and a large temperature difference ( ϵ = 0.6 ) , where the Boussinesq approximation becomes invalid. Temperature, velocity profiles, and Nusselt number distribution are obtained and compared with the benchmark results from the literature. Finally, the unsteady compressible natural convection with R a = 5.0 × 10 9 , ϵ = 0.6 is studied and the turbulent fluctuation statistics are computed and analyzed.

The enhancement of heat transfer between parallel surfaces, including parallel plates, parallel disks, and two concentric pipes, is vital because of their wide applications ranging from lubrication systems to water purification processes. Various techniques can be utilized to enhance heat transfer in such systems. Adding nanoparticles to the conventional working fluids is an effective solution that could remarkably enhance the heat transfer rate. No published review article focuses on the recent advances in nanofluid flow between parallel surfaces; therefore, the present paper aims to review the latest experimental and numerical studies on the flow and heat transfer of nanofluids (mixtures of nanoparticles and conventional working fluids) in such configurations. For the performance analysis of thermal systems composed of parallel surfaces and operating with nanofluids, it is necessary to know the physical phenomena and parameters that influence the flow and heat transfer characteristics in these systems. Significant results obtained from this review indicate that, in most cases, the heat transfer rate between parallel surfaces is enhanced with an increase in the Rayleigh number, the Reynolds number, the magnetic number, and Brownian motion. On the other hand, an increase in thermophoresis parameter, as well as flow parameters, including the Eckert number, buoyancy ratio, Hartmann number, and Lewis number, leads to heat transfer rate reduction.

Background Effect of hydrodynamic heterogeneity on particle dispersion in a Taylor-Couette flow (TC) reactor with variable configurations of inner cylinder has been investigated using CFD modelling. Methods Particle dispersion was tracked based on the Eulerian-Lagrangian approach, where the reactant solution phase was solved in the Eulerian reference frame, while the particle dispersion was calculated by tracking a large number of particles with consideration of the hydrodynamic forces acting on particles and adopting actual particle properties measured from the particle synthesis experiments. Significant Findings The simulation reveals that particle dispersion is significantly enhanced by increasing the inner cylinder rotational speed, characterized by particle distribution for both circular inner cylinder Taylor-Couette flow reactor (CTC) and lobed cross-section inner cylinder Taylor-Couette flow reactor (LTC). Particle trajectories or dispersion are influenced by the turbulent Taylor vortices. Particle radial dispersion affects the particle classification by presenting different particle axial velocities in radial direction, while particle axial dispersion can be seen as an indicator for global mixing occurring in the TC reactor, which is enhanced at high rotational speed, especially in the LTC. The calculated dispersion coefficient is found to be similar to the shape of particle size distribution found in the experiments.

In this work, an immersed boundary-discrete unified gas kinetic scheme (IB-DUGKS) is proposed and presented for the simulation of natural convection with a curved body surface. In this method, two distribution functions are employed for velocity and temperature field, respectively, and they are coupled under the Boussinesq approximation. The IB-DUGKS provides an effective way for the DUGKS to treat a curved boundary. The Strang-splitting method is used to handle the IB force, and its accuracy is first validated by comparing with another implementation method for the base case of natural convection in a square cavity. The widely used direct-forcing immersed boundary method is adopted due to its simplicity, with an iteration procedure to ensure the accuracy of no-slip condition on the immersed boundary. Natural convection between an outer square and an inner circular cylinder is then simulated under different geometric configurations, including different aspect ratios and locations of the cylinder relative to the cavity. The numerical results are in excellent agreement with the results from the literature, confirming the accuracy and robustness of the proposed method.

In this paper, turbulent pipe flows laden with finite-size particles are investigated, using the direct numerical simulations based on the lattice Boltzmann method. Our focus is on the modulation of turbulence statistics in the pipe due to the presence of finite-size neutrally buoyant particles, and the question if the characteristics of modulation differ from those in a turbulent channel flow under comparable system parameters in order to reveal the effect of curved walls in the pipe. The mechanisms responsible for modulations of the turbulent intensity in the pipe flow are clarified through a quantitative budget analysis of the turbulent kinetic energy.

The transport and deposition of aerosol particles through a fibrous filter is encountered in many natural and industrial processes. As the filtration performance for a stationary filter has been extensively studied in the literature, the present work focuses on the effect of fiber oscillation in a filter where the fibers are allowed to vibrate periodically. The transport and deposition of dilute aerosol particles in such a system is simulated using an efficient numerical model, where an iterative immersed-boundary lattice Boltzmann method is applied to solve the background flow with finite-size moving fibers, and the motion of aerosol particles is then tracked by a one-way coupling Lagrangian approach. In the present scheme, the no-slip boundary condition at the fiber surface can be exactly enforced with an iterative approach and the numerical stability is improved by adopting the MRT collision model. After the model validation in the two special cases of flow over an oscillating fiber in a quiescent fluid and particle capture by a stationary fiber, the filtration performance of an oscillating multi-fiber filter is investigated to study the effects of fiber number, arrangement and vibration mode. It is found that the oscillating motion of fiber has significant influence on the filtration performance. For a single fiber, with larger oscillation amplitude, the distribution ranges of the release position and impact angle of captured particles both increase. On the other hand, a larger fiber oscillation frequency tends to reduce the width of release position but increase the width of impact angle of deposited particles. Furthermore, the collection efficiency is found to be linearly related to the oscillation amplitude or frequency. For multiple fibers, the collection efficiency always increases with larger fiber number, but it is a non-monotonic function of the arrangement parameters, i.e., the longitudinal and transverse spacings, and the vibration parameters such as the amplitude, frequency and vibration mode. It is interesting to find that the in-phase mode can usually lead to excellent collection efficiency.

In this paper, we present a first direct numerical simulation (DNS) of a turbulent pipe flow using the mesoscopic lattice Boltzmann method (LBM) on both a D3Q19 lattice grid and a D3Q27 lattice grid. DNS of turbulent pipe flows using LBM has never been reported previously, perhaps due to inaccuracy and numerical stability associated with the previous implementations of LBM in the presence of a curved solid surface. In fact, it was even speculated that the D3Q19 lattice might be inappropriate as a DNS tool for turbulent pipe flows. In this paper, we show, through careful implementation, accurate turbulent statistics can be obtained using both D3Q19 and D3Q27 lattice grids. In the simulation with D3Q19 lattice, a few problems related to the numerical stability of the simulation are exposed. Discussions and solutions for those problems are provided. The simulation with D3Q27 lattice, on the other hand, is found to be more stable than its D3Q19 counterpart. The resulting turbulent flow statistics at a friction Reynolds number of Re τ = 180 are compared systematically with both published experimental and other DNS results based on solving the Navier–Stokes equations. The comparisons cover the mean-flow profile, the r.m.s. velocity and vorticity profiles, the mean and r.m.s. pressure profiles, the velocity skewness and flatness, and spatial correlations and energy spectra of velocity and vorticity. Overall, we conclude that both D3Q19 and D3Q27 simulations yield accurate turbulent flow statistics. The use of the D3Q27 lattice is shown to suppress the weak secondary flow pattern in the mean flow due to numerical artifacts.

A lattice Boltzmann model (LBM) for two-phase flows with liquid-vapor phase transition based on a dynamic van der Waals theory [Phys. Rev. Lett. 94, 054501 (2005)] is proposed. The proposed model consists of two lattice Boltzmann equations (LBE): one for the Navier-Stokes-Korteweg (NSK) equations and the other for the temperature equation. In the thermal LBE, the equilibrium distribution function is redesigned by introducing a reference temperature, which is used to reduce the numerical errors of velocity divergence in the thermal LBE. A free-energy-based LBE is developed for the hydrodynamic equations and a novel force term is used to correctly recover the NSK equations. Several numerical simulations, including the liquid-vapor coexistence curve, phase separation, stationary droplet, droplet on partially wetting surface, droplet evaporation and bubble nucleate and departure, are conducted to validate the capability and performance of the present model. The numerical results of the proposed model are found to be in excellent agreement with the results of theoretical and/or the hybrid method. It is also shown that numerical stability and accuracy of the present models can be greatly improved by adjusting the reference temperature. The present models provide an effective predictive tool for two-phase flows involving phase change.

The principle of an optical flow method is formulated for neutron radiography (NR) flow diagnostics to determine high-resolution velocity fields of two-phase flows. This method is based on solving an optical flow equation derived from the continuous equation for NR image analysis as an inverse problem using a variational method. The mathematical definition and physical meaning of the optical flow in NR images of a two-phase flow are clarified. As an example, the optical flow method is used to extract complex velocity fields from a time sequence of dynamic NR images acquired in an air–water two-phase flow in a flat bubbler.

The dynamics of a single or a group of slippery spheres settling under gravity in a Newtonian fluid is studied numerically. We focus particularly on the effect of particle surface slip on the sedimentation behavior. The flows containing moving slippery spheres are solved by a three-dimensional lattice Boltzmann model where a kinetic boundary condition is used to handle the slip phenomenon at the curved particle surface. The method is first validated by simulating the slip flow in a cylindrical tube, and the no-slip flows around one and two spheres settling in a container. The hydrodynamic behaviors of one, two and multiple slippery spheres settling under gravity are then investigated. The results for a single sphere show that the surface slip makes the sphere fall faster than a no-slip particle and the wall correction factor decreases as the level of particle-surface slip is increased, indicating a drag reduction caused by the slip condition. For two settling spheres, when the no-slip particle is placed below the slip one, the two spheres will enter into the kissing phase earlier; on the contrary, deploying the no-slip particle above the slip one, the DKT process does not occur beyond a critical slip level and initial gap distance. If the two spheres are both slippery, the settling dynamics are similar to the no-slip case, but the time duration of the kissing phase decreases. As for the sedimentation of multiple spheres, it is found that the initial geometric arrangement has a significant impact on the sedimentation behavior. In general, slippery spheres in a cluster will experience larger fluctuations in the vertical velocity and position in the accelerated-falling stage, and smaller fluctuations in the decelerated-falling stage.

A parallel direct-forcing fictitious domain method is applied in fully-resolved numerical simulations of particle-laden turbulent flows in a square duct. The effects of finite-size heavy particles on the mean secondary flow, the mean streamwise velocity, the root-mean-square velocity fluctuation, and the particle concentration distribution are investigated at the friction Reynolds number of 150, the particle volume fraction of 2.36%, the particle diameter of 0.1 duct width, and the Shields number ranging from 1.0 to 0.2. Our results show that the particle sedimentation breaks the up-down symmetry of the mean secondary vortices, and results in a stronger secondary-flow circulation which transports the fluids downward in the bulk center region and upward along the side walls at a low Shields number. This circulation has a significant impact on the distribution of the mean streamwise velocity, whose maximum value occurs in the lower half duct, unlike in the plane channel case. The flow resistance is increased and the turbulence intensity is reduced, as the Shields number is decreased. The particles accumulate preferentially at the face center of the bottom wall, due to the effect of the mean secondary flow. It is observed that the collision model has an important effect on the results, but does not change the results qualitatively.

The spurious currents observed in multiphase flow simulations with pseudo-potential lattice Boltzmann (LB) models are usually understood to be the result of the lack of isotropy of the model-generated interaction force between phases. Remedies have been proposed to utilize larger stencils to compute the interaction force with higher orders of isotropy. In this document, we point out the incompleteness in the current understanding and propose a new consistent implementation to more effectively suppress the spurious currents. We also demonstrate theoretically that certain low-level spurious currents cannot be eliminated by increasing isotropy if the local hydrostatic balance inside the diffuse interface is not established in the LB models.

We investigate three-dimensional natural convection flow in an air-filled, differentially heated cubical cavity. The vertical wall on the left is heated and the vertical wall on the right is cooled, with the remaining four walls being adiabatic. We performed direct numerical simulations of the natural convection flow using discrete unified gas-kinetic scheme (DUGKS), with an improved implementation of boundary conditions. Thin boundary layers are developed along the two isothermal walls. The laminar to turbulent flow transition inside the boundary layers is studied in this paper. The simulations are conducted at three Rayleigh numbers of 1.5 × 10 9 , 1.0 × 10 10 , 1.0 × 10 11 using nonuniform grids with resolution up to 320 3 . The Prandtl number is fixed at 0.71. We provide a detailed analysis of the transition from laminar to turbulent flow inside the vertical boundary layers and its influence on the rate of heat transfer. Time traces of temperature and velocity, time-averaged flow field, statistics of fluctuation fields are presented to illustrate distinct behaviors in the laminar and turbulent thermal boundary layer, as well as to determine the transition location at different R a numbers. The average Nusselt numbers for different R a numbers are compiled and compared to previous results. A guideline of the resolution requirement is suggested based on the R a scaling of laminar thermal boundary layer.

Accurate simulations of moving particles in a viscous flow require an adequate grid resolution near the surface of a moving particle. Within the framework of the lattice Boltzmann approach, inadequate grid resolution could also lead to numerical instability and large fluctuations of the computed hydrodynamic force and torque. Here we explore the use of local grid refinement around a moving particle to improve the simulation results using the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). We first re-examine the necessary relationships, within MRT LBM, between the relaxation parameters and the distribution functions on the coarse and fine grids, in order to meet the physical requirements of the fluid hydrodynamics.We also propose additional relationships based on the Chapman–Enskog multi-scaling analysis. Several aspects of the implementation details are discussed, including the treatment of interface buffer nodes, the method to transfer information between the coarse domain and fine domain, and the computation of macroscopic variables including stress components. Our approach is then applied in two numerical tests to demonstrate that the local grid refinement can significantly improve the physical results with a high computational efficiency. We compare simulation results from three grid configurations: a uniformly coarse grid, a uniformly coarse grid with local refinement, and a uniformly fine grid. For the lid-driven cavity flow, the local refinement essentially yields a local flow field that is comparable to the use of uniformly fine grid, but with much less computational cost. In the Couette flow with a moving cylinder, the local refinement suppresses the level of force fluctuations. In these tests, the stress profiles are carefully examined to help illustrate the benefits of local grid refinement. We also confirm that the coarse-fine grid relationships between the non-equilibrium moments of energy square and energy fluxes do not affect the simulation results.

In this work, we revisit implementation issues in the lattice Boltzmann method (LBM) concerning moving rigid solid particles suspended a viscous fluid. Three aspects relevant to the interaction between flow of a viscous fluid and moving solid boundaries are considered. First, the popular interpolated bounce back scheme is examined both theoretically and numerically. It is important to recognize that even though significant efforts had previously been devoted to the performance, especially the accuracy, of different interpolated bounce back schemes for a fixed boundary, there were relatively few studies focusing on moving solid surfaces. In this study, different interpolated bounce back schemes are compared theoretically for a moving boundary. Then, several benchmark cases are presented to show their actual performance in numerical simulations. Second, we examine different implementations of the momentum exchange method to calculate hydrodynamic force and torque acting on a moving surface. The momentum exchange method is well established for fixed solid boundaries, however, for moving solid boundaries there are still open issues such as unphysical force fluctuations and Galilean invariance errors. Recent progress in this direction is discussed, along with our own interpretations and modifications. Several benchmark cases, including a particle-laden turbulent channel flow, are used to demonstrate the effects of different modifications on the accuracy and physical results under different physical configurations. The third aspect is the refilling scheme for constructing the unknown distribution functions for the new fluid nodes that emerge from the previous solid region as a particle moves relative to a fixed lattice grid. We examine and compare the performance of the refilling schemes introduced by Fang etźal. (2002), Lallemand and Luo (2003), and Caiazzo (2008). We demonstrate that improvements can be made to suppress force fluctuations resulting from refilling.

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

A comprehensive literature review on the estimation of the dissipation rate of turbulent kinetic energy is presented to assess the current state of knowledge available in this area. Experimental techniques (hot wires, LDV, PIV and PTV) reported on the measurements of turbulent dissipation rate have been critically analyzed with respect to the velocity processing methods. Traditional hot wires and LDV are both a point-based measurement technique with high temporal resolution and Taylor’s frozen hypothesis is generally required to transfer temporal velocity fluctuations into spatial velocity fluctuations in turbulent flows. Multi probes of hot wires and multi points LDV could be used to measure velocity spatial gradients for a direct calculation of turbulent dissipation rate from its definition. Nevertheless, only PIV and PTV could provide simultaneous measurements of the distribution of turbulent dissipation rate in a turbulent field. These methods all suffer from the deficiency of spatial resolution as velocity measurements are required to resolve down to Kolmogorov scales for a strictly direct calculation of turbulent dissipation rate from fluctuating velocity gradients. To eliminate the necessity of resolving down to Kolmogorov scales, a large eddy simulation analogy and Smagorinsky model could be used for estimating the unresolved small scales, but Smagorinsky constant acts as an adjustment parameter at this stage. Different velocity processing methods are compared in the estimation of turbulent dissipation rate. The estimation of turbulent dissipation rate using structure function, energy spectrum and dimensional analysis methods could reduce the effects of low resolution, but it only provides temporal or spatial mean turbulent dissipation rate. Nevertheless, the field of turbulent dissipation rate, which is not distributed homogeneously, has intermittent spatio-temporal nature. The aim of this paper is to review the developments and limitations of the existing experimental techniques and different calculating methods and identify the future directions in successfully estimating turbulent dissipation rate in turbulent multiphase flows.

In the current paper, a Scraped Surface Heat Exchanger (SSHE), composed of an encased rotor on which two blades are mounted, is studied. The focus is on the effects of the rotor speed, mass flow rate, and outgoing heat flux applied on the shell on the Convection Heat Transfer Coefficient (CHTC) and the Outlet Temperature (OT). To this end, the Response Surface Methodology (RSM) is utilized to achieve the regression modeling and sensitivity analysis. Then, the Nondominated Sorting Genetic Algorithm II (NSGA-II) algorithm is applied to best balance the two conflicting objectives of maximizing CHTC and minimizing OT. The results show that an increase in either the rotation speed of the rotor or mass flow rate leads to a rise in CHTC. Furthermore, decreasing the outgoing heat flux reduces CHTC and amplifies the temperature at the outlet. The sensitivity analysis indicates that OT is most sensitive to a slight change in the mass flow rate and least sensitive to change in the rotor speed. Moreover, an optimal Pareto front with 35 non-dominated optimal points is obtained.

Rarefied pressure-driven gaseous flow with heat transfer in a microchannel with a backward facing micro-step is investigated in this paper using the lattice Boltzmann method (LBM) in slip and transition flow regimes. In a novel approach, a two-relaxation-time LB equation is used to solve the flow velocity and the single-relaxation-time to handle the heat transfer. The asymmetric relaxation time is determined by equating the analytical second-order slip velocity boundary condition and the slip velocity obtained from applying the implemented bounce back specular boundary condition in the LBM. A second-order implicit temperature jump boundary condition is also implemented to capture the rarefaction effect on the fluid temperature at walls. Velocity slip, temperature jump, centerline temperature, and Nusselt number variations are evaluated for channels with and without the micro-step for a wide range of the Knudsen number. Effects of the micro-step on the rarefied gaseous flow and convective heat transfer are evaluated and discussed. The numerical model is verified by comparing with direct simulation Mont Carlo results.

International audience; During the last decade, many approaches for resolved-particle simulation (RPS) have been developed for numerical studies of finite size particle-laden turbulent flows. In this paper, three RPS approaches are compared for a particle-laden decaying turbulence case. These methods are, the Volume-of-Fluid Lagrangian method, based on the viscosity penalty method (VoF-Lag); a direct forcing Immersed Boundary Method, based on a regularized delta-function approach for the fluid/solid coupling (IBM); and the Bounce Back scheme developed for Lattice Boltzmann method (LBM-BB). The physics and the numerical performances of the methods are analyzed. Modulation of turbulence is observed for all the methods, with a faster decay of turbulent kinetic energy compared to the single-phase case. Lagrangian particle statistics, such as the velocity probability density function and the velocity autocorrelation function, show minor differences among the three methods. However, major differences between the codes are observed in the evolution of the particle kinetic energy. These differences are related to the treatment of the initial condition when the particles are inserted in an initially single-phase turbulence. The averaged particle/fluid slip velocity is also analyzed, showing similar behavior as compared to the results referred in the literature. The computational performances of the different methods differ significantly. The VoF-Lag method appears to be computationally most expensive. Indeed, this method is not adapted to turbulent cases. The IBM and LBM-BB implementations show very good scaling.

A parallel direct-forcing (DF) fictitious domain (FD) method for the simulation of particulate flows is reported in this paper. The parallel computing strategies for the solution of flow fields and particularly the distributed Lagrange multiplier are presented, and the high efficiency of the parallel code is demonstrated. The new code is then applied to study the effects of particle density (or particle inertia) on the turbulent channel flow. The results show that the large-scale vortices are weakened more severely, and the flow friction drag increases first and then reduces, as particle inertia is increased.

Modulation of the carrier phase turbulence by finite-size solid particles is relevant to many industrial and environmental applications. Here we report particle-resolved simulations of a turbulent channel flow laden with finite-size solid particles. We discuss how the mesoscopic lattice Boltzmann method (LBM) can be applied to treat both the turbulent carrier flow and moving fluid-particle interfaces. To validate the LBM approach, we first simulate the single-phase turbulent channel flow at a frictional Reynolds number of 180. A non-uniform force field is designed to excite turbulent fluctuations. The resulting mean flow profiles and turbulence statistics were found to be in excellent agreement with the published data based on the Chebychev-spectral method. We also found that the statistics of the fully-developed turbulent channel flow are independent of the setting of some of the relaxation parameters in the LBM approach. We then consider a particle-laden turbulent channel flow under the same body force. The particles have the same density as the fluid. The particle diameter is 5% of the channel width and the average volume fraction is 7.09%. We found that the presence of the particles reduces the mean flow speed by 4.6%, implying that the fluid-particle system is more dissipative than the single-phase flow. The maximum local reduction of the mean flow speed is about 7.5%. The effects of the solid particles on the fluid rms velocity fluctuations are mixed: both reduction and augmentation are observed depending on the direction and spatial location relative to the channel walls. Overall, particles enhance the relative turbulence intensity in the near wall region and suppress the turbulence intensity in the center region. The particle concentration distribution across the channel is also complicated. We find that there is a dynamic equilibrium location resembling the Segŕe–Silberberg effect known for a laminar wall-bounded flows. Our LBM results were found to be in good agreement with results based on a finite-difference method with direct forcing to handle the moving solid particles. Additionally, phase-partitioned statistics are obtained and compared.

A discrete unified gas kinetic scheme (DUGKS) coupled with the immersed boundary (IB) method is developed to perform interface-resolved simulation of particle-laden flows. The present method (IB-DUGKS) preserves the respective advantages of the IB and DUGKS, i.e., the flexibility and efficiency for treating complex flows, and the robustness and low numerical-dissipation. In IB-DUGKS, the IB method is used to treat the fluid-solid interfaces and the DUGKS is applied to simulate the fluid flow, making use of the Lagrangian and Eulerian meshes, respectively. Those two meshes are fully independent, which contributes to the avoidance of grid regeneration when a solid particle moves. Specifically, in the present implementation of IB-DUGKS, the no-slip boundary condition at the particle surface is accurately enforced by introducing an efficient iterative forcing algorithm, and the IB force induced by the particle boundary is conveniently incorporated into the DUGKS with the Strange-Splitting scheme. The accuracy of the IB-DUGKS is first verified in the flows past a stationary cylinder and an oscillating cylinder in a quiescent fluid. After that, several well-established two- and three-dimensional particulate flow problems are simulated, including the sedimentation of a particle and the DKT dynamics of two particles in a channel, and a group of particles settling in an enclosure. In all test cases, the results are in good agreement with the data available in the literature, demonstrating that the proposed IB-DUGKS is a promising tool for simulating particulate flows., Comment: 25 pages, 19 figures

A parallel direct-forcing fictitious domain method is employed to perform fully resolved numerical simulations of turbulent channel flow laden with finite-size particles. The effects of the particle-fluid density ratio on the turbulence modulation in the channel flow are investigated at the friction Reynolds number of 180, the particle volume fraction of 0.84%, and the particle-fluid density ratio ranging from 1 to 104.2. The results show that the variation of the flow drag with the particle-fluid density ratio is not monotonic, with a larger flow drag for the density ratio of 10.42, compared to those of unity and 104.2. A significant drag reduction by the particles is observed for large particle-fluid density ratios during the transient stage, but not at the statistically stationary stage. The intensity of particle velocity fluctuations generally decreases with increasing particle inertia, except that the particle streamwise root-mean-square velocity and streamwise-transverse velocity correlation in the near-wall region are largest at the density ratio of the order of 10. The averaged momentum equations are derived with the spatial averaging theorem and are used to analyze the mechanisms for the effects of the particles on the flow drag. The results indicate that the drag-reduction effect due to the decrease in the fluid Reynolds shear stress is counteracted by the drag-enhancement effect due to the increase in the total particle stress or the interphase drag force for the large particle-inertia case. The sum of the total Reynolds stress and particle inner stress contributions to the flow drag is largest at the density ratio of the order of 10, which is the reason for the largest flow drag at this density ratio. The interphase drag force obtained from the averaged momentum equation (the balance theory) is significantly smaller than (but agrees qualitatively with) that from the empirical drag formula based on the phase-averaged slip velocity for large density ratios. For the neutrally buoyant case, the balance theory predicts a positive interphase force on the particles arising from the negative gradient of the particle inner stress, which cannot be predicted by the drag formula based on the phase-averaged slip velocity. In addition, our results show that both particle collision and particle-turbulence interaction play roles in the formation of the inhomogeneous distribution of the particles at the density ratio of the order of 10.

Simulations of a particle-bubble collision system composed of monosized spherical solid particles and air bubbles in a quiescent liquid and homogeneous isotropic turbulence have been performed using the pseudo-spectral method for the fluid flow and Lagrangian tracking for particles and bubbles. Particle-bubble collisions in a quiescent liquid were first simulated and compared to the existing theoretical models of particle-bubble collisions. Both numerical results and theoretical models indicate that decreasing bubble size and increasing particle size can increase the particle-bubble collision efficiency. A DNS model for studying the effect of turbulence on the collisions between particles and unloaded bubbles was then developed. A nonuniform time-dependent stochastic forcing scheme was implemented to maintain turbulence intensity at targeted levels. A statistical analysis of a group of particles and bubbles in the forced turbulent flow was performed to probe the mechanism of particle-bubble collision in a turbulent flow. A simplifying assumption (motivated purely by computational limitations) has been made that bubbles and particles can be randomly relocated during the simulation, unlike what happens in reality, but the size of the effect that this simplifying assumption will have on our results is unknown. Reductions in particle-bubble collisions due to preferential concentrations of particles and bubbles in different flow regions were not found. Comparing respectively the contributions of radial relative velocity and radial distribution function to the collision kernel, the contribution of radial distribution function could be neglected because the radial relative velocity increases by about 1900% (from 1.55 cm/s to 28.87 cm/s) while the radial distribution function decreases by only 33% (from 1.33 to 1.00). Collisions between particles and bubbles increased with turbulent dissipation rate primarily due to the fact that radial relative velocities between particles and bubbles increased with the flow dissipation rate.

The paper describes application of the mesoscopic lattice Boltzmann (LB) method to the simulations of both single-phase turbulence and particle-laden turbulence which are maintained by a large-scale forcing. The disturbance flows around finite-size solid particles are resolved, providing the opportunity to study the detailed interactions between fluid turbulence and solid particles at the particle-fluid interfaces. Specifically, a nonuniform time-dependent stochastic forcing scheme is implemented within the mesoscopic multiple-relaxation-time LB approach. The statistics of single-phase forced turbulence obtained from the LB approach are found to be in excellent agreement with those from the pseudo-spectral simulations, provided that the grid resolution in the LB simulation is doubled. It is shown that the flow statistics is not sensitive to the velocity scale used for the LB simulation. Preliminary results on forced turbulence laden with non-sedimenting solid particles at a particle-to-fluid density ratio of 5, solid volume fraction of 0.102, and particle diameter to Kolmogorov length ratio of 8.05 are interpreted, using a systematic analysis conducted at three levels: whole-field, phase-partitioned, and profiles as a function of distance from the surface of solid particles. It is found that the particle-laden turbulence is much more dissipative in terms of the non-dimensional dissipation rate, due to both reduction of the effective flow Reynolds number and the viscous boundary layer on the surfaces of solid particles. The thickness of the boundary layer is found to be about 0.4r"p. While this boundary layer region accounts for 19.5% of the space within the fluid, it contributes to 57.5% of total viscous dissipation. The vorticity magnitude exhibits a maximum inside the boundary layer and a minimum outside the boundary layer, showing detachment of the vorticity structure from the solid surface. The sharp gradients near the particle surface contribute dominantly to the value of velocity derivative flatness, making the flatness in particle-laden flow much larger than that of single-phase turbulence. In the spectral space, presence of solid particles attenuates energy at large scales including the forcing shells and augments energy at the small scales. The pivot wavenumber is found to be very similar to the value previously found in decaying particle-laden turbulence under the similar parameter setting.

In the first part of this study [1], we compared the performances of two categories of no-slip boundary treatments, i.e., the interpolated bounce-back schemes and the immersed boundary methods in a series of laminar flow simulations within the lattice Boltzmann method. In this second part, these boundary treatments are further compared in the simulations of turbulent flows with complex geometry to provide a next-level assessment of these schemes. Two non-trivial turbulent flow problems, a fully developed turbulent pipe flow at a low Reynolds number, and a decaying homogeneous isotropic turbulent flow laden with a large number of resolved spherical particles are considered. The major problem of the immersed boundary method revealed by the present study is its incapability in computing the local velocity gradients inside the diffused interface, which can result in significantly underestimated dissipation rate and viscous diffusion locally near the particle surfaces. Otherwise, both categories of the no-slip boundary treatments are able to provide accurate results for most of turbulent statistics in both the carrier and dispersed phases, provided that sufficient grid resolutions are used. The criteria of sufficient grid resolutions for each examined flow are also addressed in this document.

In this paper, an exact solution is developed to predict the single-fiber interception efficiency of spherical particles carried by a potential flow over a circular-arc fibrous filter. The flow field around the arc fiber has recently been calculated based on the Zhukovsky conversion. It is shown that the interception efficiency is a function of three parameters: the arc shape parameter, the flow-approaching angle, and the particle size. The results show that slim and long arc fibers have higher interception efficiency. The interception efficiency increases as the particle diameter increases. The orientation angle also affects the interception efficiency. Overall, the results demonstrate the importance of flow asymmetry and singular points on the interception efficiency. Together with our previous results on elliptic fibers published in Wang et al. [Wang WX, Xie ML, Wang LP. An exact solution of interception efficiency over an elliptical fiber collector. Aerosol Sci Technol 2012;46:843–51.], a range of fiber cross-sectional shapes on the interception efficiency can now be analytically modeled.

The paper describes a particle-resolved simulation method for turbulent flow laden with finite size particles. The method is based on the multiple-relaxation-time lattice Boltzmann equation. The no-slip boundary condition on the moving particle boundaries is handled by a second-order interpolated bounce-back scheme. The populations at a newly converted fluid lattice node are constructed by the equilibrium distribution with non-equilibrium corrections. MPI implementation details are described and the resulting code is found to be computationally efficient with a good scalability. The method is first validated using unsteady sedimentation of a single particle and sedimentation of a random suspension. It is then applied to a decaying isotropic turbulence laden with particles of Kolmogorov to Taylor microscale sizes. At a given particle volume fraction, the dynamics of the particle-laden flow is found to depend mainly on the effective particle surface area and particle Stokes number. The presence of finite-size inertial particles enhances dissipation at small scales while reducing kinetic energy at large scales. This is in accordance with related studies. The normalized pivot wavenumber is found to not only depend on the particle size, but also on the ratio of particle size to flow scales and particle-to-fluid density ratio.

In the present study, a compact and fast MATLAB program coupled with the Taylorseries expansion method of moments (TEMOM) was developed to simulate the effect of coherent structures on the particle Brownian coagulation in the temporal mixing layer. The distributions of number concentration, mass concentration and particle average volume driven by coagulation, advection and diffusion are obtained. The developed TEMOM method has no prior requirement for the particle size distribution (PSD), and it is a promising method to approximate the aerosol general dynamics equation (GDE). The fluid and particle fields are coupled together and are presented with three nondimensional parameters (i.e., Reynolds number, Re; Schmidt number based on particle moment, ScM, and Damkohler number, Da) in the governing equations. The temporal evolutions of the first three moments are discussed for different Damkohler numbers (Da ¼0.5, 1.0, 2.0). As the fluid flow evolves in time, the number concentration of nanoparticles decreases gradually, while the particle average volume increase. The distribution of number concentration, mass concentration, and average volume of nanoparticles are spatially inhomogeneous due to the mixing of coherent vortex structures. Far away from the eddy structure, the effect of the fluid advection on particle coagulation is small; however, the particle coagulation within the eddy core has an obvious wave-like distribution because of the large-scale eddy. The results reveal that the coherent structures play a significant role in the particle Brownian coagulation in the mixing layer. The particle coagulation affects quantitatively the distribution of particle number concentration, volume concentration and average diameter, but the qualitative characteristics of these distributions remain unchanged.

Using a simulated highly compressible isotropic turbulence field with turbulent Mach number around 1.0, we studied the effects of local compressibility on the statistical properties and structures of velocity gradients in order to assess salient small-scale features pertaining to highly compressible turbulence against existing theories for incompressible turbulence. A variety of statistics and local flow structures conditioned on the local dilatation – a measure of local flow compressibility – are studied. The overall enstrophy production is found to be enhanced by compression motions and suppressed by expansion motions. It is further revealed that most of the enstrophy production is generated along the directions tangential to the local density isosurface in both compression and expansion regions. The dilatational contribution to enstrophy production is isotropic and dominant in highly compressible regions. The emphasis is then directed to the complicated properties of the enstrophy production by the deviatoric strain rate at various dilatation levels. In the overall flow field, the most probable eigenvalue ratio for the strain rate tensor is found to be −3:1:2.5, quantitatively different from the preferred eigenvalue ratio of −4:1:3 reported in incompressible turbulence. Furthermore, the strain rate eigenvalue ratio tends to be −1:0:0 in high compression regions, implying the dominance of sheet-like structures. The joint probability distribution function of the invariants for the deviatoric velocity gradient tensor is used to characterize local flow structures conditioned on the local dilatation as well as the distribution of enstrophy production within these flow structures. We demonstrate that strong local compression motions enhance the enstrophy production by vortex stretching, while strong local expansion motions suppress enstrophy production by vortex stretching. Despite these complications, most statistical properties associated with the solenoidal component of the velocity field are found to be very similar to those in incompressible turbulence, and are insensitive to the change of local dilatation. Therefore, a good understanding of dynamics of the compressive component of the velocity field is key to an overall accurate description of highly compressible turbulence.

This study theoretically evaluated interactions between spherical colloids and rough surfaces in three-dimensional space using Derjaguin-Landau-Verwey- Overbeek (DLVO) energy/force map and curve. The rough surfaces were modeled as a flat surface covered by hemispherical protrusions. A modified Derjaguin approach was employed to calculate the interaction energies and forces. Results show that more irreversible attachments in primary minima occur at higher ionic strengths, which theoretically explains the observed hysteresis of colloid attachment and detachment during transients in solution chemistry. Secondary minimum depths can be increased significantly in concave regions (e.g., areas aside of asperities or between asperities) due to sidewall interactions. Through comparing the tangential attractive forces from asperities and the hydrodynamic drag forces in three-dimensional space, we showed that attachment in secondary minima can be located on open collector surfaces of a porous medium. This result challenges the usual belief that the attachment in secondary minima only occurs in stagnation point regions of the porous medium and is absent in shear flow systems such as parallel plate flow chamber and impinging jet apparatus. Despite the argument about the role of secondary minima in colloid attachment remained, our study theoretically justified the existence of attachment in secondary minima in the presence of surface roughness. Further, our study implied that the presence of surface roughness is more favorable for attachment in secondary minima than in primary minima under unfavorable chemical conditions.

In this survey we consider the impact of turbulence on cloud formation from the cloud scale to the droplet scale. We assess progress in understanding the effect of turbulence on the condensational and collisional growth of droplets and the effect of entrainment and mixing on the droplet spectrum. The increasing power of computers and better experimental and observational techniques allow for a much more detailed study of these processes than was hitherto possible. However, much of the research necessarily remains idealized and we argue that it is those studies which include such fundamental characteristics of clouds as droplet sedimentation and latent heating that are most relevant to clouds. Nevertheless, the large body of research over the last decade is beginning to allow tentative conclusions to be made. For example, it is unlikely that small-scale turbulent eddies (i.e. not the energy-containing eddies) alone are responsible for broadening the droplet size spectrum during the initial stage of droplet growth due to condensation. It is likely, though, that small-scale turbulence plays a significant role in the growth of droplets through collisions and coalescence. Moreover, it has been possible through detailed numerical simulations to assess the relative importance of different processes to the turbulent collision kernel and how this varies in the parameter space that is important to clouds. The focus of research on the role of turbulence in condensational and collisional growth has tended to ignore the effect of entrainment and mixing and it is arguable that they play at least as important a role in the evolution of the droplet spectrum. We consider the role of turbulence in the mixing of dry and cloudy air, methods of quantifying this mixing and the effect that it has on the droplet spectrum. Copyright © 2012 Royal Meteorological Society and British Crown Copyright, the Met Office

A b s t r a c t This paper describes implementation of the warm-rain bin microphysics in a LES model based on the EULAG fluid flow solver. The binmicrophysics EULAG is applied to the case of shallow nonprecipitating tropical convection to investigate the impact of the secondary activation of cloud droplets above the cloud base. In a previous study applying the EULAG model with the double-moment bulk warm-rain microphysics scheme, the in-cloud activation was shown to have significant implications for the mean microphysical and optical characteristics of the cloud field. By contrasting the simulations with and without in-cloud activation as in the previous study, we show that the in-cloud activation has qualitatively similar but quantitatively smaller eect. In particular, the concentration of cloud droplets in the bin simulation without in-cloud activation decreases with height not as strongly as in corresponding simulations applying the double-moment bulk scheme.

Motivated by a need to improve the representation of short-range interaction forces in hybrid direct numerical simulation of interacting cloud droplets, an efficient method for treating the aerodynamic interaction of two spherical particles settling under gravity is developed. An effort is made to ensure the accuracy of our method for any inter-particle separation by considering three separation ranges. The first is the long-range interaction where a multipole method is applied. After a decomposition into six simple configurations, explicit formulae for drag forces and torques are derived from an approximate Force-Torque-Stresslet (FTS) formulation. The FTS formulation is found to be accurate when the separation distance normalized by the average radius is larger than 5. The second range concerns the short-range interaction where the interaction force could be very large. Leading-order lubrication expansions are employed for this range and are found to be accurate when the normalized separation is less than about 0.01. Finally, for the intermediate range where no simple method is available, a third-order polynomial fitting is proposed to bridge the treatments for long-range and short-range interactions. After optimizing the precise form of polynomial fitting and matching locations, the force representation is found to be highly accurate when compared with the exact solution for Stokes flows. Using this method, collision efficiencies of cloud droplets sedimenting under gravity have been calculated. It is shown that the results of collision efficiency are in excellent agreement with results based on the exact Stokes flow solution. Collision efficiency results are also compared to previous results to further illustrate the accuracy of our calculations. The effects of particle rotation and the attractive van der Waals force on the collision efficiency are also studied. The efficient force representation developed here is more general than the usual lubrication expansion and thus can serve as a better approach to correct unresolved short-range interactions in particle-resolved simulations.

Large-eddy simulation (LES) has emerged as a promising tool for simulating turbulent flows in general and, in recent years,has also been applied to the particle-laden turbulence with some success (Kassinos et al., 2007). The motion of inertial particles is much more complicated than fluid elements, and therefore, LES of turbulent flow laden with inertial particles encounters new challenges. In the conventional LES, only large-scale eddies are explicitly resolved and the effects of unresolved, small or subgrid scale (SGS) eddies on the large-scale eddies are modeled. The SGS turbulent flow field is not available. The effects of SGS turbulent velocity field on particle motion have been studied by Wang and Squires (1996), Armenio et al. (1999), Yamamoto et al. (2001), Shotorban and Mashayek (2006a,b), Fede and Simonin (2006), Berrouk et al. (2007), Bini and Jones (2008), and Pozorski and Apte (2009), amongst others. One contemporary method to include the effects of SGS eddies on inertial particle motions is to introduce a stochastic differential equation (SDE), that is, a Langevin stochastic equation to model the SGS fluid velocity seen by inertial particles (Fede et al., 2006; Shotorban and Mashayek, 2006a; Shotorban and Mashayek, 2006b; Berrouk et al., 2007; Bini and Jones, 2008; Pozorski and Apte, 2009).However, the accuracy of such a Langevin equation model depends primarily on the prescription of the SGS fluid velocity autocorrelation time seen by an inertial particle or the inertial particle–SGS eddy interaction timescale (denoted by $\delt T_{Lp}$ and a second model constant in the diffusion term which controls the intensity of the random force received by an inertial particle (denoted by C_0, see Eq. (7)). From the theoretical point of view, dTLp differs significantly from the Lagrangian fluid velocity correlation time (Reeks, 1977; Wang and Stock, 1993), and this carries the essential nonlinearity in the statistical modeling of particle motion. dTLp and C0 may depend on the filter width and particle Stokes number even for a given turbulent flow. In previous studies, dTLp is modeled either by the fluid SGS Lagrangian timescale (Fede et al., 2006; Shotorban and Mashayek, 2006b; Pozorski and Apte, 2009; Bini and Jones, 2008) or by a simple extension of the timescale obtained from the full flow field (Berrouk et al., 2007). In this work, we shall study the subtle and on-monotonic dependence of $\delt T_{Lp}$ on the filter width and particle Stokes number using a flow field obtained from Direct Numerical Simulation (DNS). We then propose an empirical closure model for $\delta T_{Lp}$. Finally, the model is validated against LES of particle-laden turbulence in predicting single-particle statistics such as particle kinetic energy. As a first step, we consider the particle motion under the one-way coupling assumption in isotropic turbulent flow and neglect the gravitational settling effect. The one-way coupling assumption is only valid for low particle mass loading.