Direct particle motion and interaction modeling method applied to simulate propellant burn

A direct particle motion and particle interaction modeling method was developed to provide an alternative means of capturing the fundamental phenomena occurring during the burning of propellant grains. Individual propellant grains and other moving components are directly incorporated into the computational domain, removing the need for correlations for particle drag and interaction effects. The motion of the individual particles is calculated from the locally acting fluid induced and collision effect forces and moments. Particle/object interactions are handled through a soft particle collision algorithm. Localized mass and energy sources, accompanied by a shrinking particle size, simulate the effects of the combustion process.     

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.     

Dispersion of solid particles in turbulant flow through pipe expansions

Studies of the effects upon gas-liquid two-phase flows of pipefittings such as expansions, contractions, bends, and valveshave usually concentrated upon pressuredrop correlations andhave not attempted to determine changes in the distributionsof the gas and liquid phases caused by the fitting. However,it is known that such information is important if, for example,flow separators, which divide the gas and liquid phases in avariety of industrial processes, are to function efficiently.It is therefore important to gain an understanding of the influenceupon phase distributions of the common pipe fittings mentionedabove, which will be found in almost any industrial pipeworksystem. As a first step, the dispersion of solid particles carriedby turbulent gas flows through a pipe expansion has been modellednumerically. The commercial fluid-flow code CFDS-FLOW{smalltilde}hDas been used to model the gas flow, together with aneddy interaction model for determination of the motion of thesolid particles. Mean particle velocities and root-mean-squarevalues of the particle velocity fluctuations, as well as particleconcentrations, are evaluated and compared with recent experimentalresults. The influence of different eddy-length and eddy-lifetimespecifications upon the dispersion of particles of various sizesis investigated. It is found that the different eddy characteristicshave little effect on predicted mean particle velocities, whereasfluctuations in particle velocities and particle concentrationare sensitive to the changes made. By comparing the resultswith experimental data, it is possible to draw conclusions aboutthe relative merits of the different eddy specifications.     

Numerical simulation of scour around a submarine pipeline using computational fluid dynamics and discrete element method

Scour under a submarine pipeline can lead to structural failure; hence, a good understanding of the scour mechanism is paramount. Various numerical methods have been proposed to simulate scour, such as potential flow theory and single-phase and two-phase turbulent models. However, these numerical methods have limitations such as their reliance on calibrated empirical parameters and inability to provide detailed information. This paper investigates the use of a coupled computational fluid dynamics-discrete element method (CFD-DEM) model to simulate scour around a pipeline. The novelty of this work is to use CFD-DEM to extract detailed information, leading to new findings that enhance the current understanding of the underlying mechanisms of the scour process. The simulated scour evolution and bed profile are found to be in good agreement with published experimental results. Detailed results include the contours of the fluid velocity and fluid pressure, particle motion and velocity, fluid forces on the particles, and inter-particle forces. The sediment transport rate is calculated using the velocity of each single particle. The quantitative analysis of the bed load layer is also presented. The numerical results reveal three scour stages: onset of scour, tunnel erosion, and lee-wake erosion. Particle velocity and force distributions show that during the tunnel erosion stage, the particle motion and particle–particle interactive forces are particularly intense, suggesting that single-phase models, which are unable to account for inter-particle interactions, may be inadequate. The fluid pressure contours show a distinct pressure gradient. The pressure gradient force is calculated and found to be comparable with the drag force for the onset of scour and the tunnel erosion. However, for the lee-wake erosion, the drag force is shown to be the dominant mechanism for particle movements.     

Incorporating dust lift-off into a CFD model of a blast furnace gravity dust-catcher

A gravity dust-catcher separates a mixture of dusts from the spent top gas flow of a blast furnace. These dusts are predominantly made up of limestone, iron ore and coke/coal. As a result of the turbulent gas flow patterns within a dust-catcher, modelling of the flow pattern can be very complex, attributed to the turbulent vortices that can be formed within the main body of the structure. Using data from an experimental prototype test rig, a simple model to capture the lift-off characteristics of particle lift-off from dust pile surfaces is created and incorporated into a computational fluid dynamics (CFD) model of the dust-catcher.The variation of particle separation performance over a typical blast furnace (BF) operational cycle is analysed. An attempt is made to explain the observed phenomena in terms of particle–fluid interaction. It is found that particle separation efficiency is largely unaffected by dust lift-off at low dust-catcher hopper fullness levels, but is significant at higher levels. It is found that the topography of the dust surface is important when predicting particle lift-off trends. It is concluded that this is due to the exposure experienced by a given particle when subjected to a surface velocity.     

CFD of turbulent transport of particles behind a backward-facing step using a new model—k-ε-Sp

The k-ε-S_p model, describing two-dimensional gas–solid two-phase turbulent flow, has been developed. In this model, the diffusion flux and slip velocity of solid particles are introduced to represent the particle motion in two-phase flow. Based on this model, the gas–solid two-phase turbulent flow behind a vertical backward-facing step is simulated numerically and the turbulent transport velocities of solid particles with high density behind the step are predicted. The numerical simulation is validated by comparing the results of the numerical calculation with two other two-phase turbulent flow models (k-ε-A_p, k-ε-k_p) by Laslandes and the experimental measurements. This model, not only has the same virtues of predicting the longitudinal transport of the solid particles as the present practical two-phase flow models, but also can predict the lateral transport of the solid particles correctly.     

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.     

Numerical investigation of blood flow. Part I: In microvessel bifurcations

In some diseases there is a focal pattern of velocity in regions of bifurcation, and thus the dynamics of bifurcation has been investigated in this work. A computational model of blood flow through branching geometries has been used to investigate the influence of bifurcation on blood flow distribution. The flow analysis applies the time-dependent, three-dimensional, incompressible Navier–Stokes equations for Newtonian fluids. The governing equations of mass and momentum conservation were solved to calculate the pressure and velocity fields. Movement of blood flow from an arteriole to a venule via a capillary has been simulated using the volume of fluid (VOF) method. The proposed simulation method would be a useful tool in understanding the hydrodynamics of blood flow where the interaction between the RBC deformation and blood flow movement is important. Discrete particle simulation has been used to simulate the blood flow in a bifurcation with solid and fluid particles. The fluid particle method allows for modeling the plasma as a particle ensemble, where each particle represents a collective unit of fluid, which is defined by its mass, moment of inertia, and translational and angular momenta. These kinds of simulations open a new way for modeling the dynamics of complex, viscoelastic fluids at the micro-scale, where both liquid and solid phases are treated with discrete particles.     

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.     

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)     

Dynamics of chain particle aggregates in viscous flow

The dynamics of aggregates consisting of chains of particles and their union in the form of a two-dimensional network in viscous flow is numerically simulated. It is assumed that the particles in a chain can move relative to each other so that the distance between two neighboring ones remains unchanged. The hydrodynamic interaction forces between all particles in an aggregate are taken into account. The deposition of particle chains and their dynamics in a linear flow are considered in the case an unbounded fluid volume and near a flat wall. The interaction forces between the particles necessary for retaining them in a chain are calculated, and places of the most probable breakage in the chain are determined.     

A numerical study on statistical temporal scales in inertia particle dispersion

The statistical temporal scales involved in inertia particle dispersion are analyzed numerically. The numerical method of large eddy simulation, solving a filtered Navier-Stokes equation, is utilized to calculate fully developed turbulent channel flows with Reynolds numbers of 180 and 640, and the particle Lagrangian trajectory method is employed to track inertia particles released into the flow fields. The Lagrangian and Eulerian temporal scales are obtained statistically for fluid tracer particles and three different inertia particles with Stokes numbers of 1, 10 and 100. The Eulerian temporal scales, decreasing with the velocity of advection from the wall to the channel central plane, are smaller than the Lagrangian ones. The Lagrangian temporal scales of inertia particles increase with the particle Stokes number. The Lagrangian temporal scales of the fluid phase ‘seen’ by inertia particles are separate from those of the fluid phase, where inertia particles travel in turbulent vortices, due to the particle inertia and particle trajectory crossing effects. The effects of the Reynolds number on the integral temporal scales are also discussed. The results are worthy of use in examining and developing engineering prediction models of particle dispersion.     

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.     

A Lagrangian simulation of particle deposition in a turbulent boundary layer in the presence of thermophoresis

Knowledge of particle deposition in turbulent flows is often required in engineering situations. Examples include fouling of turbine blades, plate-out in nuclear reactors and soot deposition. Thus it is important for numerical simulations to be able to predict particle deposition. Particle deposition is often principally determined by the forces acting on the particles in the boundary layer. The particle tracking facility in the CFD code uses the eddy lifetime model to simulate turbulent particle dispersion, no specific boundary layer being modelled. The particle tracking code has been modified to include a boundary layer. The non-dimensional yplus, y⁺, distance of the particle from the wall is determined and then values for the fluid velocity, fluctuating fluid velocity and eddy lifetime appropriate for a turbulent boundary layer used. Predictions including the boundary layer have been compared against experimental data for particle deposition in turbulent pipe flow. The results giving much better agreement. Many engineering problems also involve heat transfer and hence temperature gradients. Thermophoresis is a phenomena by which small particles experience a force in the opposite direction to the temperature gradient. Thus particles will tend to deposit on cold walls and be repulsed by hot walls. The effect of thermophoresis on the deposition of particles can be significant. The modifications of the particle tracking facility have been extended to include the effect of thermophoresis. A preliminary test case involving the deposition of particles in a heated pipe has been simulated. Comparison with experimental data from an extensive experimental programme undertaken at ISPRA, known as STORM (Simplified Tests on Resuspension Mechanisms), has been made.     

Correlation of design parameters with performance for electrostatic Precipitator. Part I. 3D model development and validation

As the first part of a two-paper series, this paper develops a three-dimensional model that describes corona discharge, turbulent flow, particle charging and tracking in electrostatic precipitators (ESP). To capture the shielding effects between discharge wires in a multi-wire ESP, the corona-discharge-induced space charge density at an arbitrary point between the discharge wire and grounded plates is specified as the sum of two components: (i) a uniform value on the wire surface which is resolved individually for each wire; and (ii) a space-dependent variation relative to the uniform part. The present model is solved with the finite element method and validated with experimental and numerical results from literature. Good agreement is obtained and illustrated in terms of distributions of electric potential, current density, electrohydrodynamic flow pattern, and particle trajectories, as well as corona current and particle collection efficiency. This validated model will be applied in Part II and integrated with the design-of-experiment approach to analyze both individual and interactive effects of design parameters on ESP performance.     

Improving cyclone performance by proper selection of the exit pipe

Cyclone performance is determined by pressure drop and collection efficiency. This study aims to optimize the dimensions of the exit pipe to improve cyclone performance. A numerical technique was used which is based on an Eulerian–Lagrangian approach. The behavior of the cyclone was studied by solving the three-dimensional, incompressible turbulent flow governing equations. The turbulent flow was modeled by using Reynolds Stress Model. Particle trajectories were obtained by solving the particle equation of motion. The collection efficiency was obtained by releasing a specified number of particles at the inlet of the cyclone and by counting the collected particles. The model was verified by comparing the numerical results to published experimental measurements. It was found through this study that increasing exit pipe diameter decreases the pressure drop through the cyclone and affects also the collection efficiency while exit pipe length does not affect cyclone performance significantly. It was concluded that the performance of the standard cyclone can be improved by prober selection for the diameter of the exit pipe. The data obtained through this study was represented in performance maps. These maps allowed the selection of the exit pipe diameter to obtain the maximum collection efficiency while avoiding excessive pressure drop.     

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.     

气固两相弯管湍流场中圆柱状颗粒取向和沉积特性的研究北大核心CSCD

针对在Reynolds数Re=3000~50000、Stokes数S_(tk)=0.1~10、Dean数De=1400~2800的情况下,长径比β=2~12的圆柱状颗粒流经弯管湍流场时的取向与沉积特性进行了研究.圆柱状颗粒的运动采用细长体理论结合Newton第二定律进行描述,取向分布函数由Fokker-Planck方程给出,平均湍流场通过求解Reynolds平均运动方程结合Reynolds应力方程得到,作用在颗粒上的湍流脉动速度由动力学模拟扫掠模型描述.通过求解湍流场以及颗粒的运动方程和取向分布函数方程,得到并分析了沿流向不同截面和出口处颗粒的取向分布,讨论了各因素对颗粒沉积特性的影响.研究结果表明,随着S_(tk)和颗粒长径比β的增加、De和Re的减少,颗粒的主轴更趋向于流动方向.颗粒的沉积率随着De,Re,S_(tk)和颗粒长径比的增大而增加,所得结论对于工程实际应用具有参考价值.     

Modified sublayer approach model for analysis of turbulent particle transports

Attempt is to extend the sublayer approach model to capture the combined effects of thermophoresis and turbophoresis on the particle transport in the turbulent boundary flow with thermal gradients. Analytical solution relying on a more detailed picture of the periodic sublayer development in the wall region has been obtained. During the average growth period of viscous sublayer, the physical trend of the modeling parameters has been quantitatively revealed in some extent, and the calculated results of the particle deposition rate for the different ranges of the particle relaxation time are in general agreement with available particle transport data.     

Large eddy simulation and PIV experiments of air–water mixing tanks

The simulations and experiments of a turbulent bubbly flow are carried out in a cylindrical mixing vessel. Dynamics of the turbulent bubbly flow is visualized using a novel two-phase particle image velocimetry (PIV) with a combination of back lighting, digital masking and fluorescent tracer particles. Using an advanced technique, Mie’s scattering at surfaces of bubbles is totally filtered out and, henceforth, images of tracer particles and of bubbles are obtained with high quality. In parallel to the comprehensive experimental studies, numerical results are obtained from large eddy simulations (LES) of the two-phase air–water mixer. The impeller-induced flow at the blade tip radius is modeled by using sliding mesh method. The results demonstrate the existence of large structures such as tip-vortex tips, and also some finer details. In addition, the stability of the jet is found to be connected with the fluctuations of the tip vortices whose dynamics are affected by the presence of bubbles. Numerical results are used to interpret the measurement data and to guide the refinement of consistent theoretical analyses. Such information is invaluable in the development of advanced theories capable of describing bubbly flows in the presence of complex liquid flow. This detailed information is of real significance in facilitating the design and scale-up of practical stirred tanks.