Force-coupling method for particulate two-phase flow: Stokes flow

In this paper we describe a force-coupling method for particle dynamics in fluid flows. The general principles of the model are described and it is tested on three different Stokes flow problems; a single isolated sphere, a pair of otherwise isolated spheres, and a single sphere in a channel. For sphere to sphere or sphere to wall distances larger than 1/4 of the sphere radius the force-coupling results compared well with analytical and accurate numerical values. For smaller distances the results agree qualitatively, but lubrication effects are not included and this leads to a quantitative discrepancy.     

Large eddy simulation of orientation and rotation of ellipsoidal particles in isotropic turbulent flows

The rotational motion and orientational distribution of ellipsoidal particles in turbulent flows are of significance in environmental and engineering applications. Whereas the translational motion of an ellipsoidal particle is controlled by the turbulent motions at large scales, its rotational motion is determined by the fluid velocity gradient tensor at small scales, which raises a challenge when predicting the rotational dispersion of ellipsoidal particles using large eddy simulation (LES) method due to the lack of subgrid scale (SGS) fluid motions. We report the effects of the SGS fluid motions on the orientational and rotational statistics, such as the alignment between the long axis of ellipsoidal particles and the vorticity, the mean rotational energy at various aspect ratios against those obtained with direct numerical simulation (DNS) and filtered DNS. The performances of a stochastic differential equation (SDE) model for the SGS velocity gradient seen by the particles and the approximate deconvolution method (ADM) for LES are investigated. It is found that the missing SGS fluid motions in LES flow fields have significant effects on the rotational statistics of ellipsoidal particles. Alignment between the particles and the vorticity is weakened; and the rotational energy of the particles is reduced in LES. The SGS-SDE model leads to a large error in predicting the alignment between the particles and the vorticity and over-predicts the rotational energy of rod-like particles. The ADM significantly improves the rotational energy prediction of particles in LES.     

微通道内椭球颗粒惯性聚焦行为数值研究

基于浸没边界-格子Boltzmann方法,对方形截面微通道内椭球颗粒的惯性迁移与旋转动力学行为进行数值研究,发现微通道内椭球颗粒的惯性迁移存在两种主要的运动状态：①翻转状态,即椭球颗粒前进过程中长轴始终在中心对称平面内;②滚动状态,即椭球颗粒前进过程中长轴始终垂直于中心对称平面.研究表明：在低Re数（Re=10）下颗粒以两种状态随流体迁移至平衡位置;在较大Re数（50≤Re≤200）下最终均以翻转状态随流体迁移,随Re数增加,平衡位置先逼近壁面后远离壁面.通过对不同运动状态下椭球颗粒周围的微观流场进行分析,提示该微观流动在颗粒惯性聚焦行为特征中有重要影响,并从流体和颗粒的惯性角度对颗粒不同运动状态的转换机理给出解释.     

高雷诺数气固湍流射流的直接数值模拟

本文对流动雷诺数 Re=5990的空间发展的气固两相湍流射流进行了直接数值模拟。其中对流场的求解采用具有四阶精度的紧致差分格式,对颗粒场的跟踪采用拉格朗日方法。结果表明,湍流拟序结构逐渐由对称模式发展到非对称模式;较小 Stokes 数的颗粒在流场中均匀分布,较大 Stokes 数的颗粒沿横向没有明显的扩散,而 Stokes 数为 1的量级的颗粒则大量聚集在大涡结构的外围。     

3-D numerical analysis of EHD turbulent flow and mono-disperse charged particle transport and collection in a wire-plate ESP

The present study attempts to develop a detailed numerical approach and a simulation procedure to predict the motion of gas, ions and particles inside a simple parallel plate channel containing a single corona wire. A hybrid Finite Element (FEM)-Flux Corrected Transport (FCT)-Finite Volume (FVM) method is used: the FEM–FCT numerical algorithm is applied for modeling the steady-state corona discharge, while the turbulent gas flow and the particle motion under electrostatic forces are modeled using the commercial CFD code FLUENT. Calculations for the gas flow are carried out by solving the Reynolds-averaged Navier–Stokes equations and turbulence is modeled using the k–? turbulence model. An additional source term is added to the gas flow equation to include the effect of the electric field, obtained by solving a coupled system of the electric field and charge transport equations using User-Defined Functions (UDFs). The particle phase is simulated based on the Lagrangian approach, where a large number of particles is traced with their motion affected by the gas flow and electrostatic forces using the Discrete Phase Model (DPM) in FLUENT. The developed model is useful to gain insight into the particle collection phenomena that take place inside an ESP.     

An examination of the flow induced by the motion of many buoyant bubbles

The results of direct numerical simulations of the motion of many three-dimensional buoyant bubbles in periodic domains are examined. The bubble motion is computed by solving the full Navier-Stokes equations by a parallelized finite difference/front tracking method that allows a fully deformable interface between the bubbles and the ambient fluid and the inclusion of surface tension. The governing parameters are selected such that the average rise Reynolds number is about 25. Two cases are examined. In one, the bubbles are nearly spherical; in the other, the bubbles rise with an ellipsoidal shape. The ellipsoidal bubbles show a much larger fluctuation velocity and by visualizing the flow field it is possible to show that the difference is due to larger vorticity generation and stronger interactions of the deformable bubbles. The focus here is on the early stage of the flow, when both the spherical and the deformable bubbles are nearly uniformly distributed.     

Modified periodic-shell boundary condition for dissipative particle dynamics simulations

We have developed the modified periodic-shell boundary condition (BC) for dissipative particle dynamics (DPD) simulations, which enables us to simulate an outer flow problem around an obstacle using a small simulation region. In order to clarify the validity of this BC, we have treated a uniform flow past a circular cylinder. The present BC has been compared with the ordinary BC such as the uniform flow condition. Also, the present results have been compared with those of the numerical results of the Navier–Stokes equation. The ordinary uniform BC is seen to give rise to significantly distorted flow fields and also to significant disappearance of dissipative particles from the simulation region. In contrast, for the present modified periodic-shell BC, the number density of dissipative particles is kept almost constant during a simulation run, and the flow field is in reasonable agreement with the result, which has been obtained by numerical simulations of the Navier–Stokes equation.     

椭球颗粒搅拌运动及混合特性的数值模拟研究

为探讨在强制搅拌下同属性颗粒由分层到分布均匀状态的运动特征及规律, 本研究利用三维离散单元法模拟不同转速下U形罐体内等粒径椭球颗粒的混合过程. 从单颗粒随机运动轨迹、宏观颗粒流运动矢量图的角度分析颗粒混合过程的宏观混合规律及局部混合特征, 定量描述混合度与搅拌叶片旋转圈数的数学关系. 结果表明, 强制搅拌下同属性分层颗粒的混合是在对流混合及四个局部混合共同作用下实现的; 分层颗粒的混合度与搅拌轴的转速无关, 而与搅拌轴旋转圈数直接相关; 混合度与圈数的关系符合指数增长模型. 研究结果可为散体物料增混行业的设备改进及操作控制提供依据和参考.     

Constrained Brownian Motion of a Single Ellipsoid in a Narrow Channel

We study the Brownian motion of a single ellipsoidal particle diffusing in a narrow channel by video-microscopy measurement. The experiments allow us to obtain the trajectories of ellipsoids and measure the diffusion coefficients. It is found that the channel constraints lead to suppression of the particle motion, especially the perpendicular motion to the channel, and the long axis of the particle tends to be parallel to the channel. A stable stratification phenomenon is observed, which is rarely discussed in studies of spherical particles. We also derive an approximate solution of theoretical prediction with the method of reflections, and obtain numerical simulation results using finite element software. They are proven to be effective by comparing them with the experimental results. All of these indicate that the aspect ratio and size of ellipsoid, the width of channel, and the transverse position distinctly affect the Brownian motion of ellipsoids.     

A level set projection model of lipid vesicles in general flows

A new numerical method to model the dynamic behavior of lipid vesicles under general flows is presented. A gradient-augmented level set method is used to model the membrane motion. To enforce the volume- and surface-incompressibility constraints a four-step projection method is developed to integrate the full Navier–Stokes equations. This scheme is implemented on an adaptive non-graded Cartesian grid. Convergence results are presented, along with sample two-dimensional results of vesicles under various flow conditions.     

Modeling slender bodies with the method of regularized Stokeslets

The motion and flow generated by immersed structures in a fluid in the Stokes regime can be modeled with a variety of different numerical methods. The mathematical structure of the Stokes equations allows one to describe the flow around a three-dimensional object using only information regarding its geometry. This leads to computational techniques such as boundary integral methods or the method of regularized Stokeslets that discretize the surface of the immersed object in the flow. However, when the body in question is slender, a more computationally efficient alternative is to represent the flow by a one-dimensional discretization along the centerline of the object rather than a discretization of the boundary. Using an exact and an asymptotic solution describing the nontrivial three-dimensional fluid flow generated by a slender precessing spheroid, we present a careful analysis of the approximation of the flow using the method of regularized Stokeslets, where the regularized Stokeslets are placed along the centerline of the spheroid. Guidance is presented on how best to choose the numerical parameters within the method of regularized Stokeslets to minimize the error for a given application.     

A velocity decomposition approach for moving interfaces in viscous fluids

We present a second-order accurate method for computing the coupled motion of a viscous fluid and an elastic material interface with zero thickness. The fluid flow is described by the Navier–Stokes equations, with a singular force due to the stretching of the moving interface. We decompose the velocity into a “Stokes” part and a “regular” part. The first part is determined by the Stokes equations and the singular interfacial force. The Stokes solution is obtained using the immersed interface method, which gives second-order accurate values by incorporating known jumps for the solution and its derivatives into a finite difference method. The regular part of the velocity is given by the Navier–Stokes equations with a body force resulting from the Stokes part. The regular velocity is obtained using a time-stepping method that combines the semi-Lagrangian method with the backward difference formula. Because the body force is continuous, jump conditions are not necessary. For problems with stiff boundary forces, the decomposition approach can be combined with fractional time-stepping, using a smaller time step to advance the interface quickly by Stokes flow, with the velocity computed using boundary integrals. The small time steps maintain numerical stability, while the overall solution is updated on a larger time step to reduce computational cost.     

Particle transport behavior in air channel flow with multi-group Lagrangian tracking

The particle motions of dispersion and transport in air channel flow are investigated using a large eddy simulation(LES) and Lagrangian trajectory method. The mean and fluctuating velocities of the fluids and particles are obtained,and the results are in good agreement with the data in the literature. Particle clustering is observed in the near-wall and low-speed regions. To reveal the evolution process and mechanism of particle dispersion and transport in the turbulent boundary layer, a multi-group Lagrangian tracking is applied when the two-phase flow has become fully developed: the fluid fields are classified into four sub-regions based on the flow characteristics, and particles in the turbulent region are divided accordingly into four groups when the gas–particle flow is fully developed. The spatiotemporal transport of the four groups of particles is then tracked and analyzed. The detailed relationship between particle dispersion and turbulent motion is investigated and discussed.     

High-order non-uniform grid schemes for numerical simulation of hypersonic boundary-layer stability and transition

The direct numerical simulation of receptivity, instability and transition of hypersonic boundary layers requires high-order accurate schemes because lower-order schemes do not have an adequate accuracy level to compute the large range of time and length scales in such flow fields. The main limiting factor in the application of high-order schemes to practical boundary-layer flow problems is the numerical instability of high-order boundary closure schemes on the wall. This paper presents a family of high-order non-uniform grid finite difference schemes with stable boundary closures for the direct numerical simulation of hypersonic boundary-layer transition. By using an appropriate grid stretching, and clustering grid points near the boundary, high-order schemes with stable boundary closures can be obtained. The order of the schemes ranges from first-order at the lowest, to the global spectral collocation method at the highest. The accuracy and stability of the new high-order numerical schemes is tested by numerical simulations of the linear wave equation and two-dimensional incompressible flat plate boundary layer flows. The high-order non-uniform-grid schemes (up to the 11th-order) are subsequently applied for the simulation of the receptivity of a hypersonic boundary layer to free stream disturbances over a blunt leading edge. The steady and unsteady results show that the new high-order schemes are stable and are able to produce high accuracy for computations of the nonlinear two-dimensional Navier–Stokes equations for the wall bounded supersonic flow.     

Accurate computation of Stokes flow driven by an open immersed interface

We present numerical methods for computing two-dimensional Stokes flow driven by forces singularly supported along an open, immersed interface. Two second-order accurate methods are developed: one for accurately evaluating boundary integral solutions at a point, and another for computing Stokes solution values on a rectangular mesh. We first describe a method for computing singular or nearly singular integrals, such as a double layer potential due to sources on a curve in the plane, evaluated at a point on or near the curve. To improve accuracy of the numerical quadrature, we add corrections for the errors arising from discretization, which are found by asymptotic analysis. When used to solve the Stokes equations with sources on an open, immersed interface, the method generates second-order approximations, for both the pressure and the velocity, and preserves the jumps in the solutions and their derivatives across the boundary. We then combine the method with a mesh-based solver to yield a hybrid method for computing Stokes solutions at N² grid points on a rectangular grid. Numerical results are presented which exhibit second-order accuracy. To demonstrate the applicability of the method, we use the method to simulate fluid dynamics induced by the beating motion of a cilium. The method preserves the sharp jumps in the Stokes solution and their derivatives across the immersed boundary. Model results illustrate the distinct hydrodynamic effects generated by the effective stroke and by the recovery stroke of the ciliary beat cycle.     

Optical equivalence of isotropic ensembles of ellipsoidal particles in the Rayleigh-Gans-Debye and anomalous diffraction approximations and its consequences

Light scattering by isotropic ensembles of ellipsoidal particles is considered in the Rayleigh-Gans-Debye approximation. It is proved that randomly oriented ellipsoidal particles are optically equivalent to polydisperse randomly oriented spheroidal particles and polydisperse spherical particles. Density functions of the shape and size distributions for equivalent ensembles of spheroidal and spherical particles are presented. In the anomalous diffraction approximation, equivalent ensembles of particles are shown to also have equal extinction, scattering, and absorption coefficients. Consequences of optical equivalence are considered. The results are illustrated by numerical calculations of the angular dependence of the scattering phase function using the T-matrix method and the Mie theory.     

Computation of three-dimensional Brinkman flows using regularized methods

The Brinkman equations of fluid motion are a model of flows in a porous medium. We develop the exact solution of the Brinkman equations for three-dimensional incompressible flow driven by regularized forces. Two different approaches to the regularization are discussed and compared on test problems. The regularized Brinkman model is also applied to the unsteady Stokes equation for oscillatory flows since the latter leads to the Brinkman equations with complex permeability parameter. We provide validation studies of the method based on the flow and drag of a solid sphere translating in a Brinkman medium and the flow inside a cylindrical channel of circular cross-section. We present a numerical example of a swimming organism in a Brinkman flow which shows that the maximum swimming speed is obtained with a small but non-zero value of the porosity. We also demonstrate that unsteady Stokes flows with oscillatory forcing fall within the same framework and are computed with the same method by applying it to the motion of the oscillating feeding appendage of a copepod.     

Variable-range projection model for turbulence-driven collisions

We discuss the relative speeds DeltaV of inertial particles suspended in a highly turbulent gas when the Stokes number, a dimensionless measure of their inertia, is large. We identify a mechanism giving rise to the distribution P(DeltaV) approximately exp(-C|DeltaV|(4/3)) (for some constant C). Our conclusions are supported by numerical simulations, and by the analytical solution of a model equation of motion. The results determine the rate of collisions between suspended particles. They are relevant to the hypothesized mechanism for formation of planets by aggregation of dust particles in circumstellar nebula.     

气固轴对称射流中固粒扩散的研究

由三维离散涡丝方法对气固轴对称射流场数值模拟的结果表明,当固粒 Ｓｔ数＜＜１时,固粒明显受到流场运动的影响; Ｓｔ＝ １时,固粒均匀分布在涡结构周围;当 Ｓｔ ＞＞１时,固粒受流场影响较弱。对涡环沿周向施以五个波长扰动时,固粒扩散范围较宽。     

驻波声场中圆柱形管道周围颗粒的运动特性

针对圆柱形管道外部的流体与颗粒介质运动问题,提出了结合圆柱周围声辐射力和声流Stokes力的研究方法。从柱体外部声流方程出发,得到影响涡流结构的无量纲参数Rem≥325.27时,外涡最大流速大于内涡最大流速。在此基础上,采用Nyborg的边界滑移速度理论,获得管道外部声流的极限滑移速度,推导得出圆柱附近的声辐射力公式。基于此公式,在理论上推导出颗粒速度为0、声辐射力和声流Stokes力平衡时,颗粒临界直径的表达式。通过对圆柱位于不同位置时,圆柱外部的颗粒运动进行仿真模拟,得到与理论公式相一致的结论:颗粒的临界直径的大小与声波频率有关,当颗粒直径小于临界直径时,声流Stokes力为主导,颗粒随声流运动,颗粒直径大于等于临界直径时,声辐射力为主导,颗粒在声辐射力作用下逐渐向声辐射力的节点聚集。理论与仿真结果表明该方法可用于分析管道外颗粒的分布状态,其研究结果有助于解决电站中换热器的管道结垢、热交换率降低等问题。