Nonhydraulic Effects in Particle-Driven Gravity Currents in Deep Surroundings

In this article, we present an approach to modeling the flow of particle-driven gravity currents produced by the sudden release of well-mixed, fixed-volume suspensions into deep surroundings. Our model accounts for the initial turbulent energy of mixing in the release volume, characteristic of the classical lock–release experiments, as well as the spatiotemporal variability in the driving buoyancy forces attributable to particle settling. We show that, in contrast to compositionally driven flows, particle-driven flows cannot be described consistently in terms of shallow water theory. Specifically, we show that the presence of particles in the flow dynamics produces significant horizontal velocity shear, thereby changing the flow configuration in important ways from flows assumed to be governed by the shallow water equations. These new flow properties are calculated and contrasted with flow properties derived on the basis of the shallow water equations to show that the shallow water analysis misses dynamical features of the flow. We also show that our model provides significant improvement over the previous shallow water-based models in predicting the experimentally determined deposition patterns associated with the lock–release experiments.     

Particle transport in a bottom-feed separation vessel

A two-dimensional, axisymmetric numerical model of particle separation in a bottom-feed separation vessel is presented. The model includes six separate particle classes and assumes that the settling velocity of each particle class is sufficiently small when compared to the high inflow turbulence levels that the effect of the particles on turbulence can be neglected. Low particle settling velocities coupled with low particle volume fractions allows application of a drift-flux multi-phase model. The comparison between numerical results and measured plant data is in good agreement for overflow of all particle classes. Results of simulations show that bottom feeding results in a negatively buoyant, particle-laden jet being formed in the core of the vessel. The fraction of large particles that is carried out through the overflow is found to be critically dependent on the inlet velocity. The most effective way to reduce carry-over of large particles at the same time as maintaining through-put is to increase the diameter of the inlet feed pipe.     

Computational fluid dynamics simulation of fluid particle fragmentation in turbulent flows

A simulation methodology is presented that allows detailed studies of the breakup mechanism of fluid particles in turbulent flows. The simulations, based on large eddy and volume of fluid simulations, agree very well with high-speed measurements of the breakup dynamics with respect to deformation time and length scales, and also the resulting size of the daughter fragments. The simulations reveal the size of the turbulent vortices that contribute to the breakup and how fast the interaction and energy transfer occurs. It is concluded that the axis of the deformed particle and the vortex core axis are aligned perpendicular to each other, and that breakup sometimes occurs due to interaction with two vortices at the same time. Analysis of the energy transfer from the continuous phase turbulence to the fluid particles reveals that the deformed particle attains it maximum in interfacial energy before the breakup is finalized. Similar to transition state theory in chemistry this implies that an activation barrier exists. Consequently, by considering the dynamics of the phenomenon, more energy than required at the final stage needs to be transferred from the turbulent vortices for breakup to occur. This knowledge helps developing new, more physical sound models for the breakup phenomenon required to solve scale separation problems in computational fluid dynamics simulations.     

Sediment Transport and Deposition from a Two-layer Fluid Model of Gravity Currents on Sloping Bottoms

This article reports on a theoretical and numerical study of noneroding turbulent gravity currents moving down mildly inclined surfaces while depositing sediment. These flows are modeled by means of two-layer fluid systems appropriately modified to account for the presence of a sloping bottom and suspended sediment in the lower layer. A detailed scaling argument shows that when the density of the interstitial fluid is slightly greater than that of the ambient and the suspension is such that its volume fraction is of the order of the aspect ratio squared, for low aspect ratio flows a two-layer shallow-water theory is applicable. In this theory there is a decoupling of particle and flow dynamics. In contrast, however, when the densities of interstitial and ambient fluids are equal, so that it is the presence of the particles alone that drives the flow, we find that a consistent shallow-water theory is impossible no matter how small the aspect ratio or the initial volume fraction occupied by the particles. Our two-layer shallow-water formulation is employed to investigate the downstream evolution of flow and depositional characteristics for sloping bottoms. This investigation uncovers a new phenomenon in the formation of a rear compressive zone giving rise to shock formation in the post-end-wall-separation phase of the particle-bearing gravity flow. This separation of flow from the end wall in these fixed volume releases differs from what has been observed on horizontal surfaces where the flow always remains in contact with the end wall.     

宾汉流体稠密两相湍流流动中的二阶矩模型

建立的Bingham流体稠密两相流动的二阶矩-颗粒动力论湍流模型（USM-theta模型）既体现了两相的作用,又体现了屈服应力所引起的附加项,并提出了USM-theta模型下考虑浓度修正值影响的两相湍流流动的算法．利用该模型对圆管内Bingham流体的单相湍流流动、稠密液固两相的湍流流动进行了计算,并和五方程湍流模型进行了比较,结果表明该模型的预测效果更好．利用USM-theta模型对含颗粒的Bingham流体的两相湍流流动进行了模拟,随着屈服应力的增加,Bingham流体相与颗粒相在管道中心附近的主流速度减小．液固两相湍流和Bingham流体两相湍流的计算结果表明屈服应力引起的附加项对流动有很重要的影响．     

Re.ned Modeling of the pressure redistribution/scrambling under consistent consideration of scalar turbulence effects in turbulent combustion

In practical turbulent flow problems of engineering importance the coupling between velocity and scalar turbulence along with the variable density plays a non negligible role. For computations using second moment closure approach, the pressure redistribution/scrambling is the most critical term to be modeled as well known. Almost all existing models consist in rescating models derived on a constant density basis in a density weighted form. With regard to turbulent premixed combustion in fact, the application of such models to a range of transient one‐dimensional and two‐dimensional premixed flames in the flamelet regime has been found to yield unsatisfactory results, see [1]. As pointed out by Sadiki [2], the use of the Favre method must be consistently considered as far as open thermodynamic systems are concerned. Furthermore, the need for maintaining certain invariance properties, physical and mathematical realizability conditions in formulating turbulence models is well accepted. Because turbulent processes are irreversible, these efforts demand a carefull consideration of thermodynamic concepts. Based on the results in [1] and following [2], this work aims to derive a physically consistent formulation of the pressure redistribution/scrambling term under consideration of the variable density. Considering the case of premixed flames, the thermochemistry is included by means of a single reactive scalar ‐ the reaction progress variable. The accuracy of the model extensions proposed is demonstrated by comparing the numerical results with experimental data in opposed jet premixed flame configuration.     

Turbulent particle dispersion in an electrostatic precipitator

The behaviour of charged particles in turbulent gas flow in electrostatic precipitators (ESPs) is crucial information to optimise precipitator efficiency. This paper describes a strongly coupled calculation procedure for the rigorous computation of particle dynamics during ESP taking into account the statistical particle size distribution. The turbulent gas flow and the particle motion under electrostatic forces are calculated by using the commercial computational fluid dynamics (CFD) package FLUENT linked to a finite volume solver for the electric field and ion charge. Particle charge is determined from both local electrical conditions and the cell residence time which the particle has experienced through its path. Particle charge density and the particle velocity are averaged in a control volume to use Lagrangian information of the particle motion in calculating the gas and electric fields. The turbulent particulate transport and the effects of particulate space charge on the electrical current flow are investigated. The calculated results for poly-dispersed particles are compared with those for mono-dispersed particles, and significant differences are demonstrated.     

Forces acting on particles in separated wall‐bounded shear flow

Trajectories of solid particles in laminar and turbulent flow over a backward‐facing step (BFS) were numerically computed by integrating the equation of motion for particles. The various forces acting on the particles [5],[6] were calculated for a variety of flow Reynolds numbers and for different particle characteristics such as the Stokes number and the particle‐to‐fluid density ratio. The investigation was conducted for the distinct flow regimes of the BFS flow separately. Generally, the drag and gravitation were found to be the most significant forces. The lift and history force were the next most important, mostly two orders of magnitude smaller, but in some cases closing up to the other two in importance. The pressure and virtual mass effects were very small for the majority of cases. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling the impact of two different flocculants on the performance of a thickener feedwell

The performance of a thickener feedwell depends not only on its ability to generate large-sized aggregates from feed particles but also on aggregate density. The performance of the flocculant BASF Rheomax® DR 1050 has been previously compared to a conventional anionic flocculant in turbulent pipe flocculation of mineral suspension, suggesting that the flocculant can generate denser aggregates (i.e. larger effective fractal dimension). Such aggregates are generally stronger and reduce the need for solids dilution, with both factors favouring faster settling velocity at the feedwell exit. To investigate the impact of the internal aggregate structure on the flocculation performance of a feedwell, Computational Fluid Dynamics (CFD) simulations of a basic open feedwell with shelf design were carried out for both flocculants. A calcite with a fine particle size (Omyacarb 5) was modelled to emphasise the impact of the flocculation process on flow fields at the feedwell exit. Simulations were conducted using CFX-4.4 two-phase flow formulation incorporating equations for a population balance model of the flocculation process. The impact of the fractal dimension on the effectiveness of the aggregation process is presented for low and high solids concentrations. Comparison of the performance of the flocculants is presented in terms of both predicted mean aggregate size and settling flux.     

Numerical simulation of indoor suspension particles based on v-f model

This paper presents a new algorithm for the prediction of indoor suspension particle dispersion based on a v²-f model. In order to handle the near-wall turbulence anisotropy properly, which is significant in the dispersion of fine particles, the particle eddy diffusivity is calculated using different formulae among regions of the turbulent core and in the vicinity of walls. The new algorithm is validated by several cases performed in two ventilated rooms with various air distribution patterns. The simulation results reveal that v²-f nonlinear turbulence model combined with a particle convective equation gives satisfactory agreement with the experimental data. It is generally found that the dynamic equation combined with the v²-f model can properly handle low Reynolds number (LRN) flows which are usually encountered in indoor air flows and fine particle dispersion.     

On the Settling Speed of Free and Fixed Suspensions

Dilute suspensions of small spheres in a viscous fluid are examined for the three cases of: I, a regular periodic array; II, a random array of freely moving particles; and III a random array in which the particles are held rigidly. It is known that the difference between average force and average velocity for a particle is a different function of concentration for the three cases. A unified analytical treatment is given for the point particle approximation, which explains the different qualitative dependence on concentration. It is shown that the differences between I and II are kinematical in nature, depending entirely on the difference between the geometries of regular and random arrays. The different result for case III is due to the shielding effect of a dilute suspension when the velocities, but not the forces, of the particles are fixed.     

两相流中柱状固粒对流体湍动特性影响的研究

对含柱状固粒的两相流场,建立了包含柱状固粒对流场影响的流体脉动速度方程,在求解脉动速度方程的基础上,经平均得到流体的湍流强度和雷诺应力.将该方法用于槽流湍流场的求解,并与单相流实验结果进行了比较.计算中变化柱状固粒的参数,给出了固粒的体积分数、长径比、松驰时间对流场湍动特性的影响,说明粒子对流场的湍动特性起着抑制作用,其抑制的程度与粒子的体积分数、长径比成正比,与粒子的松弛时间成反比.     

Isothermic Surfaces Generated via Bäcklund and Moutard Transformations: Boomeron and Zoomeron Connections

The asymptotic expansions for (1) the slow changes in particle number/energy density; namely, the kinetic equation, (2) frequency renormalization; and (3) the Nth‐order structure functions for wave turbulence systems are almost always nonuniform at either small or large length scales. The manifestation of this nonuniformity is fully nonlinear behavior either in the form of localized structures (coherent structures, shocks) or condensates (nonzero mean over large distances). The result is intermittent behavior dominated by large fluctuation events, anomolous scaling, and far from joint Gaussian statistics. Despite this unexpected surprise, and it is a surprise considering that wave turbulence has been the subject of continuous and intense investigation for several decades, wave turbulence still offers an advantage over systems that are nonlinear over all scales. The advantage is that the nature of the fully nonlinear behavior often can be identified, which gives us reasonable hope that wave turbulent systems may be treated as a two species gas of random wavetrains and randomly occurring coherent structures.     

Direct numerical simulation of bi-disperse particle-laden gravity currents in the channel configuration

We present a numerical investigation of bi-disperse particle-laden gravity currents in the lock-exchange configuration. Previous results, based on numerical simulation and laboratory experiments, are used to establish comparisons. Our discussion focuses on explaining how the presence of more than one particle diameter influences the main features of the flow, such as deposit profile, the evolution of the front location and suspended mass. We develop the complete energy budget equation for bi-disperse flows. A set of two and three-dimensional direct numerical simulations (DNS), with different initial compositions of coarse and fine particles, are carried out for Reynolds number equal to 4000. Such simulations show that the energy terms are strongly affected by varying the initial particle fractions. The addition of a small amount of fine particles into a current predominantly composed of coarse particles increases its run-out distance. In particular, it is shown that higher amounts of coarse particles have a dumping effect on the current development. Comparisons show that the two-dimensional simulation does not reproduce the intense turbulence generated in 3D cases accurately, which results in a significant difference in the suspended mass, front position as well as the dissipation term due to the advective motion.     

基于内变量理论的电流变液本构关系

研究了电流变液的微结构本构关系.其理论框架是基于内变量理论和机理的分析.电流变液是由高介电常数的颗粒悬浮在某种液体中组成的.在电场作用下,极化的颗粒将沿着电场方向聚集在一起形成链状结构.颗粒聚集体的大小和方向将随外加电场和应变率的变化进行调整,因而可以通过建立起能量守恒方程和力平衡方程来确定颗粒聚集体的大小和方向的变化.那么,一个三维的、清晰的本构关系可以由相互作用能和系统的耗散能导出.具体考虑和讨论了在简单剪切载荷作用下的系统响应,发现电流变液的切变剪薄粘滞系数同系统Mason数之间近似于幂指数∝(Mn)-082的关系.     

On models of polydisperse sedimentation with particle-size-specific hindered-settling factors

Polydisperse suspensions consist of particles differing in size or density that are dispersed in a viscous fluid. During sedimentation, the different particle species segregate and create areas of different composition. Spatially one-dimensional mathematical models of this process can be expressed as strongly coupled, nonlinear systems of first-order conservation laws. The solution of this system is the vector of volume fractions of each species as a function of depth and time, which will in general be discontinuous. It is well known that this system is strictly hyperbolic provided that the Masliyah–Lockett–Bassoon (MLB) flux vector is chosen, the particles have the same density, and the hindered-settling factor (a multiplicative algebraic expression appearing in the flux vector) does not depend on the particle size but is the same for all species. It is the purpose of this paper to prove that this hyperbolicity result remains valid in a fairly general class of cases where the hindered-settling factor does depend on particle size. This includes the common power-law type hindered-settling factor in which the exponent, sometimes called Richardson–Zaki exponent, is determined individually for each species, and is a decreasing function of particle size. The importance of this paper is two-fold: it proves stability for a class of polydisperse suspensions that was not covered in previous work, and it offers a new analysis of real data.     

On dispersion of settling particles from an elevated source in an open-channel flow

Longitudinal dispersion of suspended particles with settling velocity in a turbulent shear flow over a rough-bed surface is investigated numerically when the settling particles are released from an elevated continuous line-source. A combined scheme of central and four-point upwind differences is used to solve the steady turbulent convection–diffusion equation and the alternating direction implicit (ADI) method is adopted for the unsteady equation. It is shown how the mixing of settling particles is influenced by the ‘log-wake law’ velocity and the corresponding eddy diffusivity when the initial distribution of concentration is regarded as a line-source. The concentration profiles for the steady-state conditions agree well with the existing experimental data and some other numerical results when the settling velocity is zero. The behaviours of iso-concentration lines in the vertical plane for different releasing heights are studied in terms of the relative importance of convection, eddy diffusion and settling velocity.     

Separation of magnetic particles in channel flows by BEM

In-line separation of suspensions can become difficult in case of particles with comparable values of densities. For flows in micro devices in such cases gravitational settling is inefficient, and other separation techniques must be applied. In case of magneto active particles, the action of Kelvin magnetic force in a non-uniform magnetic field could be used in order to achieve a higher degree of particles separation. The contribution therefore deals with Euler-Lagrangian formulation of dilute two-phase flows. The Boundary element based computational algorithm solves the incompressible Navier-Stokes equations written in velocity-vorticity formulation. The non-uniform magnetic field is defined analytically for the case of a set of long thin wires. The particle trajectories are computed by applying the 4th order Runge-Kutta method. The computed test case consists of a narrow channel with laminar flow of suspension under Re = 1 − 10. Particle trajectories under the influence of a non-uniform magnetic field are computed for the case of magnetite and aluminium particles suspended in water. The efficiency of separation on basis of particle trajectories for different values of Re number and magnetic field strength is performed, clearly indicating superior separation of magneto active particles. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Physical Modelling of Point Source Dispersion Inside Atmospheric Boundary Layer

One of the most important problems in the turbulence theory is the process of turbulent mixing. Although many theoretical and experimental studies on the structure functions of a passive scalar as well as the probability density functions of its increment and gradient in a turbulent fluid have been published so far, the instantaneous feature of an advected scalar has not been explored very well. There are only a few experimental studies on a scalar concentration fluctuation analysis in turbulent flows. In this study the time‐series of both longitudinal velocity component and concentration analysis are to be presented. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Development of boundary transfer method in simulation of gas–solid turbulent flow of a riser

Computational fluid dynamics (CFD) is used to simulate the behavior of two phase gas solid in a fluid catalytic cracking (FCC) riser. Gas and particle phases are considered as separate fully interpenetrating continuous media within each control volume. Each phase described in terms of its own separate mass and momentum conservation equations. Simple k–epsilon (k_g–?_g) turbulence model is used for the gas phase and the solid phase is handled with the kinetic theory of granular flows. Source terms are used to account for the influence of hydrodynamic drag on the production, dissipation and exchange of turbulent kinetic energy between the phases. For the particles partial slip condition is considered at the wall.