The effect of particles on fluid turbulence in a turbulent boundary layer over a cylinder

The turbulent fluid and particle interaction in the turbulent boundary layer for cross flow over a cylinder has been experimentally studied. A phase-Doppler anemometer was used to measure the mean and fluctuating velocities of both phases. Two size ranges of particles (30μm–60μm and 80μm–150μm) at certain concentrations were used for considering the effects of particle sizes on the mean velocity profiles and on the turbulent intensity levels. The measurements clearly demonstrated that the larger particles damped fluid turbulence. For the smaller particles, this damping effect was less noticeable. The measurements further showed a delay in the separation point for two phase turbulent cross flow over a cylinder. The project supported by the National Natural Science Foundation of China     

Calculation of the momentum and heat transfer in turbulent gas-particle jet flows

The equations for the second moments of the dispersed-phase velocity and temperature fluctuations are used for calculating gas-suspension jet flows within the framework of the Euler approach. The advantages of introducing the equations for the second moments of the particle velocity fluctuations has previously been quite convincingly demonstrated with reference to the calculation of two-phase channel boundary flows [9–11]. The flows considered below have a low solid particle volume concentration, so that interparticle collisions can be neglected and, consequently, the stochastic motion of the particles is determined exclusively by their involvement in the fluctuating motion of the carrier flow. In addition to the equations for the turbulent energy of the gas and its dissipation, the calculation scheme includes the equations for the turbulent energy and turbulent heat transfer of the solid phase; however, the model constructed does not contain additional empirical constants associated with the presence of the particles in the flow.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 69–80, May–June, 1992.     

The simulation of turbulent particle‐laden channel flow by the Lattice Boltzmann method

We perform direct numerical simulation of three‐dimensional turbulent flows in a rectangular channel, with a lattice Boltzmann method, efficiently implemented on heavily parallel general purpose graphical processor units. After validating the method for a single fluid, for standard boundary layer problems, we study changes in mean and turbulent properties of particle‐laden flows, as a function of particle size and concentration. The problem of physical interest for this application is the effect of water droplets on the turbulent properties of a high‐speed air flow, near a solid surface. To do so, we use a Lagrangian tracking approach for a large number of rigid spherical point particles, whose motion is forced by drag forces caused by the fluid flow; particle effects on the latter are in turn represented by distributed volume forces in the lattice Boltzmann method. Results suggest that, while mean flow properties are only slightly affected, unless a very large concentration of particles is used, the turbulent vortices present near the boundary are significantly damped and broken down by the turbulent motion of the heavy particles, and both turbulent Reynolds stresses and the production of turbulent kinetic energy are decreased because of the particle effects. We also find that the streamwise component of turbulent velocity fluctuations is increased, while the spanwise and wall‐normal components are decreased, as compared with the single fluid channel case. Additionally, the streamwise velocity of the carrier (air) phase is slightly reduced in the logarithmic boundary layer near the solid walls. Copyright © 2015 John Wiley & Sons, Ltd.     

Modeling fluid-particle interaction in dilute-phase turbulent liquid-particle flow simulation

The present work examines the predictive capability of a two-fluid CFD model that is based on the kinetic theory of granular flow in simulating dilute-phase turbulent liquid-particle pipe flows in which the inter-stitial fluid effect on the particle fluctuating motion is significant.The impacts of employing different drag correlations and turbulence closure models to describe the fluid-particle interactions(i.e.drag force and long-range interaction)are examined at both the mean and fluctuating velocity levels.The model pre-dictions are validated using experimental data of turbulent liquid-particle flows in a vertical pipe at different particle Reynolds numbers(ReP > 400 and ReP < 400),which characterize the importance of the vortex shedding phenomenon in the fluid-phase turbulence modulation.The results indicate that(1)the fluctuating velocity level predictions at different ReP are highly sensitive to the drag correlation selec-tion and(2)different turbulence closure models must be employed to accurately describe the long-range fluid-particle interaction in each phase.In general,good agreement is found between the model predic-tions and the experimental data at both the mean and fluctuating velocity levels provided that appropriate combinations of the drag correlation and the turbulence closure model are selected depending on Rep.     

Eulerian prediction of the fluid/particle correlated motion in turbulent two-phase flows

An approximate equation governing the turbulent fluid velocity encountered along discrete particle path is used to derive the fluid/particle turbulent moments required for dispersed two-phase flows modelling. Then, closure model predictions are compared with results obtained from large-eddy simulation of particle fluctuating motion in forced isotropic fluid turbulence.     

Two- and Four-Way Coupled Euler–Lagrangian Large-Eddy Simulation of Turbulent Particle-Laden Channel Flow

Large-eddy simulations (LES) of a vertical turbulent channel flow laden with a very large number of solid particles are performed. The motivation for this research is to get insight into fundamental aspects of co-current turbulent gas-particle flows, as encountered in riser reactors. The particle volume fraction equals about 1.3%, which is relatively high in the context of modern LES of two-phase flows. The channel flow simulations are based on large-eddy approximations of the compressible Navier–Stokes equations in a porous medium. The Euler–Lagrangian method is adopted, which means that for each individual particle an equation of motion is solved. The method incorporates four-way coupling, i.e., both the particle-fluid and particle–particle interactions are taken into account. The results are compared to single-phase channel flow in order to investigate the effect of the particles on turbulent statistics. The present results show that due to particle–fluid interactions the mean fluid profile is flattened and the boundary layer is thinner. Compared to single-phase turbulent flow, the streamwise turbulence intensity of the gas phase is increased, while the normal and spanwise turbulence intensities are reduced. This finding is generally consistent with existing experimental data. The four-way coupled simulations are also compared with two-way coupled simulations, in which the inelastic collisions between particles are neglected. The latter comparison clearly demonstrates that the collisions have a large influence on the main statistics of both phases. In addition, the four-way coupled simulations contain stronger coherent particle structures. It is thus essential to include the particle–particle interactions in numerical simulations of two-phase flow with volume fractions around one percent.     

稀疏两相湍流的惯性颗粒倾向性弥散

气相采用大涡模拟、颗粒相采用拉格朗日轨道模型的方法对后台阶突扩流、充分发展槽道流和圆湍射流3种典型的稀疏气固两相流动进行了数值模拟,研究了颗粒倾向性弥散的特征和规律. 研究表明颗粒的跟随性和倾向性相联系,颗粒惯性和大涡结构同时决定颗粒的倾向性分布特征. Stokes数量级为1(气相时间参考尺度取为宏观特征时间尺度)左右的颗粒,倾向性分布特征最强烈. 颗粒倾向分布于低涡量(或是低脉动速度)的湍流区域.      

Modeling droplet dispersion and interphase turbulent kinetic energy transfer using a new dual-timescale Langevin model

Dispersion of spray droplets and the modulation of turbulence in the ambient gas by the dispersing droplets are two coupled phenomena that are closely linked to the evolution of global spray characteristics, such as the spreading rate of the spray and the spray cone angle. Direct numerical simulations (DNS) of turbulent gas flows laden with sub-Kolmogorov size particles, in the absence of gravity, report that dispersion statistics and turbulent kinetic energy (TKE) evolve on different timescales. Furthermore, each timescale behaves differently with Stokes number, a non-dimensional flow parameter (defined in this context as the ratio of the particle response time to the Kolmogorov timescale of turbulence) that characterizes how quickly a particle responds to turbulent fluctuations in the carrier or gas phase. A new dual-timescale Langevin model (DLM) composed of two coupled Langevin equations for the fluctuating velocities, one for each phase, is proposed. This model possesses a unique feature that the implied TKE and velocity autocorrelation in each phase evolve on different timescales. Consequently, this model has the capability of simultaneously predicting the disparate Stokes number trends in the evolution of dispersion statistics, such as velocity autocorrelations, and TKE in each phase. Predictions of dispersion statistics and TKE from the new model show good agreement with published DNS of non-evaporating and evaporating droplet-laden turbulent flow.     

research on rotational dispersion coefficient of fiber in turbulent shear flow of fiber suspension

The rotational dispersion coefficient of the fiber in the turbulent shear flow of fiber suspension was studied theoretically. The function of correlation moment between the different fluctuating velocity gradients of the flow was built firstly. Then the expres- sion, dependent on the characteristic length, time, velocity and a dimensionless parameter related to the effect of wall, of rotational dispersion coefficient is derived. The derived expression of rotational dispersion coefficient can be employed to the inhomogeneous and non-isotropic turbulent flows. Furthermore it can be expanded to three-dimensional turbulent flows and serves the theoretical basis for solving the turbulent flow of fiber suspension.     

Theoretical research on rotational dispersion coefficient of fiber in turbulent shear flow of fiber suspension

The rotational dispersion coefficient of the fiber in the turbulent shear flow of fiber suspension was studied theoretically. The function of correlation moment between the different fluctuating velocity gradients of the flow was built firstly. Then the expression, dependent on the characteristic length, time, velocity and a dimensionless parameter related to the effect of wall, of rotational dispersion coefficient is derived. The derived expression of rotational dispersion coefficient can be employed to the inhomogeneous and non-isotropic turbulent flows. Furthermore it can be expanded to three-dimensional turbulent flows and serves the theoretical basis for solving the turbulent flow of fiber suspension.     

Turbulent transport of particles in a straight square duct

Turbulent flow through a duct of square cross-section gives rise to off-axis secondary flows, which are known to transfer momentum between fluid layers thereby flattening the velocity profile. The aim of this study is to investigate the role of the secondary flows in the transport and dispersion of particles suspended in a turbulent square duct flow. We have numerically simulated a flow through a square duct having a Reynolds number of Re_τ = 300 through discretization of the Navier–Stokes equations, and followed the trajectories of a large number of passive tracers and finite-inertia particles under a one-way coupling assumption. Snapshots of particle locations and statistics of single-particle and particle pair dispersion were analyzed. It was found that lateral mixing is enhanced for passive tracers and low-inertia particles due to the lateral advective transport that is absent in straight pipe and channels flows. Higher inertia particles accumulate close to the wall, and thus tend to mix more efficiently in the streamwise direction since a large number of the particles spend more time in a region where the mean fluid velocity is small compared to the bulk. Passive tracers tend to remain within the secondary swirling flows, circulating between the core and boundary of the duct.     

Development of Gas-Particle Euler-Euler LES Approach: A Priori Analysis of Particle Sub-Grid Models in Homogeneous Isotropic Turbulence

A new large eddy simulation (LES) approach for particle-laden turbulent flows in the framework of the Eulerian formalism for inertial particle statistical modelling is developed. Local instantaneous Eulerian equations for the particle cloud are first written using the mesoscopic Eulerian formalism (MEF) proposed by Février et al. (J Fluid Mech 533:1–46, 2005), which accounts for the contribution of an uncorrelated velocity component for inertial particles with relaxation time larger than the Kolmogorov time scale. Second, particle LES equations are obtained by volume filtering the mesoscopic Eulerian ones. In such an approach, the particulate flow at larger scales than the filter width is recovered while sub-grid effects need to be modelled. Particle eddy-viscosity, scale similarity and mixed sub-grid stress (SGS) models derived from fluid compressible turbulence SGS models are presented. Evaluation of such models is performed using three sets of particle Lagrangian results computed from discrete particle simulation (DPS) coupled with fluid direct numerical simulation (DNS) of homogeneous isotropic decaying turbulence. The two phase flow regime corresponds to the dilute one where two-way coupling and inter-particle collisions are not considered. The different particle Stokes number (based on Kolmogorov time scale) are initially equal to 1, 2.2 and 5.1. The mesoscopic field properties are analysed in detail by considering the particle velocity probability function (PDF), correlated velocity power spectra and random uncorrelated velocity moments. The mesoscopic fields measured from DPS+DNS are then filtered to obtain large scale fields. A priori evaluation of particle sub-grid stress models gives comparable agreement than for fluid compressible turbulence models. It has been found that the standard Smagorinsky eddy-viscosity model exhibits the smaller correlation coefficients, the scale similarity model shows very good correlation coefficient but strongly underestimates the sub-grid dissipation and the mixed model is on the whole superior to pure eddy-viscosity model.     

Turbulent transport dissimilarity with modulated turbulence structure in channel flow of viscoelastic fluid

This experimental study investigated the turbulent transport dissimilarity with a modulated turbulence structure in a channel flow of a viscoelastic fluid using simultaneous particle image velocimetry and planar laser-induced fluorescence measurements. An instantaneous dye concentration field with fluctuating velocity vectors showed that mass was transferred by hierarchically large-scale wavy motions with inclination. A co-spectral analysis showed that the spatial phase modulation of the streamwise velocity and dye concentration fluctuations for the wall-normal velocity fluctuation corresponded to the relaxation time. The occurrence of intense dye concentration fluctuation and small streamwise velocity fluctuation in a thin boundary layer caused dissimilar turbulent transport because of the non-zero negative correlation of the streamwise velocity and dye concentration fluctuations for the wall-normal velocity fluctuation only on large scales. This explains the turbulent transport dissimilarity which leads to the zero averaged Reynolds shear stress and non-zero wall-normal turbulent mass flux.     

Statistical models for predicting the effect of bidisperse particle collisions on particle velocities and stresses in homogeneous anisotropic turbulent flows

The purpose of this paper is to present and compare two statistical models for predicting the effect of collisions on particle velocities and stresses in bidisperse turbulent flows. These models start from a kinetic equation for the probability density function (PDF) of the particle velocity distribution in a homogeneous anisotropic turbulent flow. The kinetic equation describes simultaneously particle–turbulence and particle–particle interactions. The paper is focused on deriving the collision terms in the governing equations of the PDF moments. One of the collision models is based on a Grad-like expansion for the PDF of the velocity distributions of two particles. The other model stems from a Grad-like expansion for the joint fluid–particle PDF. The validity of these models is explored by comparing with Lagrangian simulations of particle tracking in uniformly sheared and isotropic turbulent flows generated by LES. Notwithstanding the fact that the fluid turbulence may be isotropic, the particle velocity fluctuations are anisotropic due to the impact of gravitational settling. Comparisons of the model predictions and the numerical simulations show encouraging agreement.     

气固两相流动的湍流脉动扩散数学模型及其应用

本文提出了气固两相流动的湍流扩展数学模型，本模型用k-ε双方程模型求解气相湍流场，并根据气流脉动的频谱、能谱曲线提出了随机富工级数来模拟气相脉动速度，用拉氏方法描述颗粒的运动，故称为脉动频谱随机颗粒轨道模型。本文还给出了本模型在气固多相射流和流化床内应用的实例。     

A scaling analysis of added-mass and history forces and their coupling in dispersed multiphase flows

Accurate momentum coupling model is vital to simulation of dispersed multiphase flows. The overall force exerted on a particle is divided into four physically meaningful contributions, i.e., quasi-steady, stress-gradient, added-mass, and viscous-unsteady (history) forces. Time scale analysis on the turbulent multiphase flow and the viscous-unsteady kernel shows that the integral representation of the viscous-unsteady force is required except for a narrow range of particle size around the Kolmogorov length scale when particle-to-fluid density ratio is large. Conventionally, the particle-to-fluid density ratio is used to evaluate the relative importance of the unsteady forces (stress-gradient, added-mass, and history forces) in the momentum coupling. However, it is shown from our analysis that when particle-to-fluid density ratio is large, the importance of the unsteady forces depends on the particle-to-fluid length scale ratio and not on the density ratio. Provided the particle size is comparable to the smallest fluid length scale (i.e., Kolmogorov length scale for turbulence or shock thickness for shock-particle interaction) or larger, unsteady forces are important in evaluating the particle motion. Furthermore, the particle mass loading is often used to estimate the importance of the back effect of particles on the fluid. An improved estimate of backward coupling for each force contribution is established through a scaling argument. The back effects of stress-gradient and added-mass forces depend on particle volume fraction. For large particle-to-fluid density ratio, the importance of the quasi-steady force in backward coupling depends on the particle mass fraction; while that of the viscous-unsteady force is related to both particle mass and volume fractions.     

Instabilities during batch sedimentation in geometries containing obstacles: A numerical and experimental study

Batch sedimentation of non‐colloidal particle suspensions is studied with nuclear magnetic resonance flow visualization and continuum‐level numerical modelling of particle migration. The experimental method gives particle volume fraction as a function of time and position, which then provides validation data for the numerical model. A finite element method is used to discretize the equations of motion, including an evolution equation for the particle volume fraction and a generalized Newtonian viscosity dependent on local particle concentration. The diffusive‐flux equation is based on the Phillips model (Phys. Fluids A 1992; 4 :30–40) and includes sedimentation terms described by Zhang and Acrivos (Int. J. Multiphase Flow 1994; 20 :579–591). The model and experiments are utilized in three distinct geometries with particles that are heavier and lighter than the suspending fluid, depending on the experiment: (1) sedimentation in a cylinder with a contraction; (2) particle flotation in a horizontal cylinder with a horizontal rod; and (3) flotation around a rectangular inclusion. Secondary flows appear in both the experiments and the simulations when a region of higher density fluid is above a lower density fluid. The secondary flows result in particle inhomogeneities, Rayleigh–Taylor‐like instabilities, and remixing, though the effect in the simulations is more pronounced than in the experiments. Published in 2007 by John Wiley & Sons, Ltd.     

Transport and deposition of neutral particles in magnetohydrodynamic turbulent channel flows at low magnetic Reynolds numbers

The effect of Lorentz force on particle transport and deposition is studied by using direct numerical simulation of turbulent channel flow of electrically conducting fluids combined with discrete particle simulation of the trajectories of uncharged, spherical particles. The magnetohydrodynamic equations for fluid flows at low magnetic Reynolds numbers are adopted. The particle motion is determined by the drag, added mass, and pressure gradient forces. Results are obtained for flows with particle ensembles of various densities and diameters in the presence of streamwise, wall-normal or spanwise magnetic fields. It is found that the particle dispersion in the wall-normal and spanwise directions is decreased due to the changes of the underlying fluid turbulence by the Lorentz force, while it is increased in the streamwise direction. The particle accumulation in the near-wall region is diminished in the magnetohydrodynamic flows. In addition, the tendency of small inertia particles to concentrate preferentially in the low-speed streaks near the walls is strengthened with increasing Hartmann number. The particle transport by turbophoretic drift and turbulent diffusion is damped by the magnetic field and, consequently, particle deposition is reduced.