Modeling particle deposition from fully developed turbulent flow

An unsteady state transfer of immersed particles within the interval between the arrival of eddies is solved by use of the Laplace transform schemes. The mean particle flux and the mean particle transport mechanisms are automatically considered on the average sublayer growth period by formulating the mean distributions as a stochastic process with the aid of exponentially distributed density function. The proposed relationship for the particle deposition velocity of average time domain obtained by this analysis is expressed as the form of analytical equation, with the inclusion of the effects of Brownian diffusion, turbulent eddy diffusivity, turbophoresis, and thermophoresis. The solution of this equation is in reasonable agreement with the measured deposition velocities for three distinct categories. This mathematical framework offers a simple computation tool of practical use to aerosol engineers and can further extend by including appropriate forces in the analytical formulation through the equilibrium among acceleration terms.     

On Two-Phase Flow in a Rotating Boundary Layer

The two-phase flow induced by a rotating disk in a stationary unbounded mixture is considered. The generalized similarity assumption of von Karman reduces the averaged equations of motion with a linear drag between the phases to a system of ordinary differential equations. These are investigated by asymptotic and numerical techniques. The equations display a nontrivial behavior in a sublayer near the boundary, whose thickness is of the order of the particle size. The volume fraction of the dispersed phase is singular unless a small suction is applied on the disk or a small diffusion term is added to the continuity equations. Outside this sublayer, the velocity field is quite similar to a rescaled classical von Karman flow. Good agreement between asymptotic and numerical solution is obtained, although there is considerable stiffness in the equations. The motion of a solid particle in a von Karman flow is also discussed, but the present investigation is restricted to small radii because the shear-lift force is neglected.     

Monte carlo calculation of transport for three-dimensional magnetohydrodynamic equilibria

A Monte Carlo algorithm has been implemented which couples the results of a three-dimensional magnetohydrodynamic equilibrium code with particle transport calculations similar to those of Boozer and Kuo-Petravic. The equilibrium results are in a form which lends itself to easy and accurate computation of the coefficients required to follow particle orbits in flux variables at finite pressure. In particular, the parallel current and the Clebsch potential for the current are obtained from Fourier series solutions of first-order partial differential equations with constant coefficients. Confinement times are estimated from the exponential decay of expected values of appropriately chosen functionals of the particle distribution. The observation that these functionals satisfy boundary conditions helps us to compute confinement times over a wide range of collision frequencies, including cases where losses due to particle trapping are very high. Initial conditions are chosen to optimize the Monte Carlo calculation by using known information about the expected particle distribution. Results for actual and proposed stellarator experiment are given. Electron and ion confinement times are compared, since this is relevant to the issue of the effect of ambipolar electric fields on stellarator confinement. A spectral method is given to determine the electric field from charge neutrality, and numerical evidence is presented to suggest that anomalous electron transport may be due to small resonant terms in the electric potential. Also, comparisons are made with a simplified theory of particle transport already incorporated in the equilibrium code.     

Steady state numerical simulation of the particle collection efficiency of a new urban sustainable gravity settler using design of experiments by FVM

The aim of this work is to analyze the efficiency of a new sustainable urban gravity settler to avoid the solid particle transport, to improve the water waste quality and to prevent pollution problems due to rain water harvesting in areas with no drainage pavement. In order to get this objective, it is necessary to solve particle transport equations along with the turbulent fluid flow equations since there are two phases: solid phase (sand particles) and fluid phase (water). In the first place, the turbulent flow is modelled by solving the Reynolds-averaged Navier-Stokes (RANS) equations for incompressible viscous flows through the finite volume method (FVM) and then, once the flow velocity field has been determined, representative particles are tracked using the Lagrangian approach. Within the particle transport models, a particle transport model termed as Lagrangian particle tracking model is used, where particulates are tracked through the flow in a Lagrangian way. The full particulate phase is modelled by just a sample of about 2,000 individual particles. The tracking is carried out by forming a set of ordinary differential equations in time for each particle, consisting of equations for position and velocity. These equations are then integrated using a simple integration method to calculate the behaviour of the particles as they traverse the flow domain. The entire FVM model is built and the design of experiments (DOE) method was used to limit the number of simulations required, saving on the computational time significantly needed to arrive at the optimum configuration of the settler. Finally, conclusions of this work are exposed.     

Numerical simulation of the performance of a snow fence with airfoil snow plates by FVM

The aim of this work is to analyze the efficiency of a snow fence with airfoil snow plates to avoid the snowdrift formation, to improve visibility and to prevent blowing snow disasters on highways and railways. In order to attain this objective, it is necessary to solve particle transport equations along with the turbulent fluid flow equations since there are two phases: solid phase (snow particles) and fluid phase (air). In the first place, the turbulent flow is modelled by solving the Reynolds-averaged Navier-Stokes (RANS) equations for incompressible viscous flows through the finite volume method (FVM) and then, once the flow velocity field has been determined, representative particles are tracked using the Lagrangian approach. Within the particle transport models, we have used a particle transport model termed as Lagrangian particle tracking model, where particulates are tracked through the flow in a Lagrangian way. The full particulate phase is modelled by just a sample of about 15,000 individual particles. The tracking is carried out by forming a set of ordinary differential equations in time for each particle, consisting of equations for position and velocity. These equations are then integrated using a simple integration method to calculate the behaviour of the particles as they traverse the flow domain. Finally, the conclusions of this work are exposed.     

Simulation of free turbulent particle-laden jet using Reynolds-stress gas turbulence model

Free two-phase flows occur in many practical applications, such as sprays or particle drying and combustion. This paper deals with mathematical modelling of a free turbulent two-phase jet. A steady, axisymmetric, dilute, monodisperse, particle-laden, turbulent jet injected into a still environment, has been considered. The model treats the gas-phase from an Eulerian standpoint and the motion of particles from a Lagrangian one. Closure of the system of time averaged transport equations has been accomplished by using a Reynolds-stress turbulence model. The particles–fluid interaction has been considered by the PSI-Cell concept. Both the effect of interphase slip and the effect of particle dispersion have been taken into account.     

等离子体反常输运性质的量纲分析

反常输运现象是实验室等离子体和空间等离子体中的重要过程．该文运用量纲分析方法研究了无碰撞磁化等离子体的反常输运性质,得出反常电导率、反常扩散系数、反常热导系数和背景物理量之间的明显关系式．结果表明,反常扩散系数具有玻姆扩散系数形式,反常热导系数具有Ｎ_αＴ_α／ｅＢ形式,电导率表达式也符合实验结果．     

A rate-dependent algebraic stress model for turbulence

Based on the stress transport model, a rate-dependent algebraic expression for the Reynolds stress tensor is developed. It is shown that the new model includes the normal stress effects and exhibits viscoelastic behavior. Furthermore, it is compatible with recently developed improved models of turbulence. The model is also consistent with the limiting behavior of turbulence in the inertial sublayer and is capable of predicting secondary flows in noncircular ducts. The TEACH code is modified according to the requirements of the rate-dependent model and is used to predict turbulent flow fields in a channel and behind a backward-facing step. The predicted results are compared with the available experimental data and those obtained from the standard k-ε and algebraic stress models. It is shown that the predictions of the new model are in better agreements with the experimental data.     

SOIL EROSION AND DEGRADATION BASED ON SAND PARTICLES TRANSPORT CAUSED BY WIND BLOWING

Abstract In this paper, the effect of sand particles transport caused by wind blowing and its role in the land degradation and desertification process is considered. For the modeling of the 3D landscape, a grayscale height map has been used, the vegetation has been modeled using a Lindenmayer system, and the sand particles have been modeled as a 3D mesh‐free particles system. It was assumed that both the sand motion and the wind motion are incompressible continuum systems and their behavior follows the Navier–Stokes equations. To simulate the sand transport, the Navier–Stokes equations are discretized using the moving particle Semi‐implicit (MPS) method. Different types of revegetation patterns (windbreakers) have been used to show some effective measures preventing soils from erosion.     

On particle transport processes: A potential theoretic approach

This article provides a potential theoretic approach to the study of particle transport stochastic processes (x ( t,w) ,Y (t ?L?:) ) where x i t ) is the temporal evolution of a non-Plarkovian particle motion and y (t) is a Markovian physical process in the medium that governs the scattering or jump of the particle.As opposed to the perturbation technique, our approach immensely enhances the applicatory value of transport processes. We begin with a sample path construction of a transport process and continue with the existence ofcertain invariant measures. Expressing the particle motion x(t) as an additive functional of the transport process (x(t),y(t)), we establish a law of large number and a functional centxal limit theorem,(a Brownian motion approximation),for the non-Markovian particle motion.     

On the mathematical transport theory in microporous media: The billiard approach

This paper is an expository of the main dynamical properties of billiards, which depend on the shape of the walls of the container, and the recent developments like the introduction of an external field, which mimic the coupling with a thermostat.The class of dynamical system dealt with in this paper exhibits characteristics of hybrid systems as it links discrete and continuous, deterministic and stochastic dynamics.The contents are focused on applications. Specifically, transport dynamics in highly-confined regions has been of interest in the last few decades because of industrial and medical applications. Aspects of confined transport remain elusive, considering that in microporous membranes, whose size pores is about that of the molecules, the transport is sometimes ballistic, and sometimes diffusive. The classical kinetic and macroscopic approach can not be directly applied because collisions of particle fluid with walls prevail. The microscopic mathematical billiard theory can be applied as a mathematical tool since the interstices between obstacles can be considered as the pores of the membranes.     

Fluctuational transport of a Brownian particle in ratchet-like gravitational potential field

We treat analytically the problem of fluctuational transport of a Brownian particle in ratchet-like gravitational field in the presence of white noise. Given analytics allow to calculate the mean particle velocity depending on the particle mass and the noise intensity. We show that noise-induced current undergoes the reversal both with the increase of the particle mass and with the increase of the noise intensity.     

Modeling of the Wear Particle Flow in Tribological Contacts

The dynamics of tribological systems with pronounced memory effects are characterized by the complex coupling of mechanical, thermal, and chemical processes. At the Institute of Dynamics and Vibrations in Braunschweig, Cellular Automata have been developed that facilitate the evaluation of dynamics in technically relevant systems within a reasonable time. The flow of wear material is decisive for the formation, localization, and reconstitution of load-bearing structures or films. In this paper, two opposed frictional contacts are chosen exemplarily for the investigation of the wear particle flow: a vehicle brake system and the sanding of wood. For this purpose, a modeling technique is proposed that is based on established force laws for micro particles and differentiates mechanisms of transport for different phases of the particle movement. The resulting transport of a single particle interacting with the topology of the frictional gap is analyzed for varying particle properties and process parameters. In a second step the insights are transferred to a set of rules for a Cellular Automaton which allows for quick evaluation and the incorporation of coupled effects. The validity and quality of the model transfer are discussed. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical modeling and process simulation of perlite grain expansion in a vertical electrical furnace

Expanded perlite is a lightweight material with remarkable thermal and acoustic insulation properties, rendering it widely useful in the construction and manufacturing industries. Currently applied perlite expansion technology suffers numerous technical disadvantages, which adversely affect product quality and limit the range of its applications. To overcome these established drawbacks, a new perlite expansion process has been designed on the basis of a vertical electrically heated expansion furnace. The novel furnace enables precise control of experimental conditions, in order to allow for efficient adjustment of particle residence time and internal temperature. The quality of expanded perlite strongly depends on raw material thermophysical properties as well as furnace operating conditions, and the experimental investigation of the isolated effect of each parameter on expanded product quality is technically cumbersome and extremely time-consuming and expensive.A mathematical model for perlite grain expansion has been developed in order to perform a detailed numerical investigation of process efficiency, toward the optimization of the expansion process in the novel pilot-scale furnace. The dynamic model consists of ordinary differential equations for both air and particle heat and momentum balances, as well as nonlinear algebraic equations for both air and perlite melt thermophysical and transport properties, probing the air temperature distribution within the vertical electrical furnace as well as the particle velocity, temperature and size along its trajectory inside the heating chamber. The effect of raw material physical properties (raw feed origin, initial particle size, effective water content) as well as operating parameters (air inlet temperature and flowrate, furnace wall temperature) on evolution of the particle state variables is presented and discussed. Model results indicate perlite expansion is strongly affected by raw ore feed origin, size and water content. Moreover, operating conditions affect expansion considerably, and furnace wall temperature has the strongest effect on the final particle expansion ratio attained. The new dynamic model is instrumental towards achieving a detailed comprehension of perlite expansion in the vertical electrical furnace towards multi-parametric sensitivity analysis, process optimization and efficient control.     

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.     

Local expansion concepts for detecting transport barriers in dynamical systems

In the last two decades, the mathematical analysis of material transport has received considerable interest in many scientific fields such as ocean dynamics and astrodynamics. In this contribution we focus on the numerical detection and approximation of transport barriers in dynamical systems. Starting from a set-oriented approximation of the dynamics we combine discrete concepts from graph theory with established geometric ideas from dynamical systems theory. We derive the global transport barriers by computing the local expansion properties of the system. For the demonstration of our results we consider two different systems. First we explore a simple flow map inspired by the dynamics of the global ocean. The second example is the planar circular restricted three body problem with Sun and Jupiter as primaries, which allows us to analyze particle transport in the solar system.     

Effect of the potential shape and of a Brownian particle mass on noise-induced transport

The noise-induced transport of a Brownian particle with regard to its mass is considered. The results of approximate analytical calculations for the averaged probability flux in periodic ratchet-like potentials are presented. The influence of the potential shape on the mean particle velocity is traced. In the case of sufficiently small particle mass, it is shown that with increase in mass the reversal of flux is possible.     

基于游客年龄特征的旅游巴士定价研究

为旅游巴士设计合理的定价,对旅游公共交通的发展有着积极影响。通过对游客出行偏好的分析,考虑不同年龄阶段的游客在选择行为上有较大的差异,建立了上层以旅游巴士企业利润最大为目标,下层为多方式多人群弹性需求随机用户平衡的旅游巴士定价模型,并设计了改进粒子群算法求解问题。数值实验结果表明:1)年龄特征会影响最优定价策略,考虑游客年龄在选择行为上的差异得出的票价更优;2)舒适度敏感系数对定价有影响,且旅游巴士较常规公交,舒适度更好,一定程度上提高了旅游巴士企业的竞争力;3)改进粒子群算法较标准粒子群算法,有更好的求解性能和质量。     

Modeling Sediment Deposition Patterns Arising From Suddenly Released Fixed-Volume Turbulent Suspensions

Models presented in several recent papers [1–3] dealing with particle transport by, and deposition from, bottom gravity currents produced by the sudden release of dilute, well‐mixed fixed‐volume suspensions have been relatively successful in duplicating the experimentally observed long‐time, distal, areal density of the deposit on a rigid horizontal bottom. These models, however, fail in their ability to capture the experimentally observed proximal pattern of the areal density with its pronounced dip in the region initially occupied by the well‐mixed suspension and its equally pronounced local maximum at roughly the one‐third point of the total reach of the deposit. The central feature of the models employed in [1–3] is that the particles are always assumed to be vertically well‐mixed by fluid turbulence and to settle out through the bottom viscous sublayer with the Stokes settling velocity for a fluid at rest with no re‐entrainment of particles from the floor of the tank. Because this process is assumed from the outset in the models of [1–3], the numerical simulations for a fixed‐volume release will not take into account the actual experimental conditions that prevail at the time of release of a well‐mixed fixed‐volume suspension. That is, owing to the vigorous stirring that produces the well‐mixed suspension, the release volume will initially possess greater turbulent energy than does an unstirred release volume, which may only acquire turbulent energy as a result of its motion after release through various instability mechanisms. The eddy motion in the imposed fluid turbulence reduces the particle settling rates from the values that would be observed in an unstirred release volume possessing zero initial turbulent energy. We here develop a model for particle bearing gravity flows initiated by the sudden release of a fixed‐volume suspension that takes into account the initial turbulent energy of mixing in the release volume by means of a modified settling velocity that, over a time scale characteristic of turbulent energy decay, approaches the full Stokes settling velocity. Thereafter, in the flow regime, we assume that the turbulence persists and, in accord with current understanding concerning the mechanics of dense underflows, that this turbulence is most intense in the wall region at the bottom of the flow and relatively coarse and on the verge of collapse (see [22]) at the top of the flow where the density contrast is compositionally maintained. We capture this behavior by specifying a “shape function” that is based upon experimental observations and provides for vertical structure in the volume fraction of particles present in the flow. The assumption of vertically well‐mixed particle suspensions employed in [1–5] corresponds to a constant shape function equal to unity. Combining these two refinements concerning the settling velocity and vertical structure of the volume fraction of particles into the conservation law for particles and coupling this with the fluid equations for a two‐layer system, we find that our results for areal density of deposits from sudden releases of fixed‐volume suspensions are in excellent qualitative agreement with the experimentally determined areal densities of deposit as reported in [1, 3, 6]. In particular, our model does what none of the other models do in that it captures and explains the proximal depression in the areal density of deposit.     

Nonclassical boundary value problem for the transport equation

We consider a nonclassical boundary value problem for the transport equation. The particle transport process is described by a stationary linear integro-differential equation, and the outgoing particle flux density on some part of the boundary is specified as the boundary condition. We find the particle flux density for a given outgoing flux and known coefficients of the equation. We show that, under some restrictions on the medium, there exists a unique solution of the problem, which can be represented by an infinite convergent series.