激光测速粒子对复杂流动的响应研究——Ⅱ典型流场中粒子跟随性的数值分析

以修正后适用于高颗粒雷诺数的粒子非恒定运动方程为基础,将该方程无量纲化,定义了一般流场中粒子跟随性的概念,给出了粒子跟随性的数学表述。据此对典型流场中粒子的运动进行了数值计算,并定量分析了粒径、密度等参数对不同流动中示踪粒子跟随特性的影响。     

对MPS法在溃坝模拟中数值压力振荡问题的改进

为探索模拟大变形自由面流体运动的高精度数值计算方法,以溃坝水流运动为例,基于MPS法(Moving Particle Semi-implicit method,移动粒子半隐式法)建立了一个垂向二维改良MPS法数值计算模型。首先,为了改善传统MPS法中存在的自由表面粒子误判以及数值能量耗散问题,提出新的自由表面粒子识别方法和高精度的压力梯度模型。在此基础上,以Lobovsky'等的溃坝物理模型实验为例,探讨不同形式压力泊松方程源项对溃坝冲击压计算精度的影响,提出一个新的源项形式。数值结果分析表明,新自由表面粒子识别方法和高精度压力梯度模型可以有效地减少自由面粒子的误判概率,抑制水流运动计算中的数值能量耗散。而压力计算结果与实验结果的对比表明,所提出的压力泊松方程源项可以有效地减少数值压力震荡的幅度。     

颗粒沉降问题的高解析度CFD-DEM-IBM流固耦合数值模拟方法

为实现颗粒沉降问题的精确数值模拟,探索稠密颗粒两相流中流体与颗粒间的影响机制,基于浸入边界法（IBM）,建立了高解析度CFD-DEM-IBM流固耦合数值模拟方法。分别通过流体动力学方法（CFD）及离散单元法（DEM）描述连续流体及非连续颗粒,引入浸入边界法处理颗粒移动边界,并在Navier-Stokes动量方程中附加体力项以体现流固相互作用,采用交错迭代算法在同一时间步内多次迭代求解直至收敛以实现流固间的强耦合。通过单、双、群颗粒的沉降行为模拟,结果表明:与传统CFD-DEM方法相比,该方法能够准确考虑颗粒间及流固两相间的相互作用,获得高解析度的流场信息。模拟结果与前人数值计算结果吻合,验证了该方法的准确性与有效性及其对稠密颗粒两相流问题的适用性与优越性。     

水科学进展第14卷(2003年)总目录

第 1期方腔回流区水流运动特性三维数值分析张修忠　王光谦 ( 1)………………………………………………………………………二维明渠非恒定流的格子Boltzmann模拟程永光　索丽生 ( 9)………………………………………………………………………漫滩恒定明渠水流的三维数值模拟槐文信　陈文学　童汉毅　卓建民 ( 15 )………………………………………………………激光测速粒子对复杂流动的响应研究———Ⅰ颗粒非恒定运动数学模型及其数值方法黄社华　魏庆鼎 ( 2 0 )……………………激光测速粒子对复杂流动的响应研究———Ⅱ典型流场中粒子跟…     

第二类非线性Fredholm型积分方程数值解

配置法研究了地球物理中常见的第二类非线性 Fredholm 型积分方程的数值解法,将第二类非线性 Fredholm 型积分方程转化为非线性代数方程组进行求解,采用高斯数值积分公式,给出了数值计算的具体实例.利用Matlab软件的符号运算功能编程计算,克服了非线性方程难于变成求解的困难,数值例子表明该方法编程简便有效.对非线性积分方程和非线性代数方程组的求解都有重要价值.     

非定常不稳定液固两相流动中旋涡对颗粒运动影响的数值研究

构建起双向耦合的液固两相流动旋涡动力学模型与数值方法;应用离散涡方法,计算非定常不稳定水流场;采用Lagrange方法模拟颗粒运动,颗粒对流体的反作用通过修正涡泡运动速度来实现。利用所建模型,计算了两种St数的泥沙粒子在圆柱绕流场中的运动。结果证明了液固两相流动中颗粒运动与旋涡存在着明确的相关结构:(1)当水沙混合物中的泥沙颗粒碰上旋涡时,泥沙颗粒被卷入旋涡中,被卷入旋涡中的泥沙颗粒在运动过程中始终分布于旋涡区;(2)均匀水沙混合物绕圆柱流动,由于流体流过圆柱时产生剧烈分离流动,使得在尾迹流内中等St数 (St～o (1))的泥沙颗粒从均匀水沙混合物中分离出来而往旋涡区聚集。     

不同粒度颗粒在非恒定管流中跟随性试验

管道中固液两相流水击对管道和输送系统可能产生严重的破坏,而固液两相在这种非恒定流中的运动特性是计算最大水击压力变化的重要依据。采用粒子图像测速技术（Particle Image Velocimetry,PIV）,通过试验研究水击发生时,水平圆管中不同平均流速、颗粒粒径条件下,流体介质和粗颗粒在管道断面的速度分布以及粗颗粒跟随性的变化规律。研究结果表明:①在水击发生的不同时刻,圆管流中粗颗粒的流速在管道断面分布呈不规则的抛物线型分布,主要表现为靠近管道壁面底部的颗粒流速略小于靠近管道顶部流速,当颗粒粒径大于1.5 mm,平均流速小于2.5 m/s时,粗颗粒表现出明显的沉降特性;②粗颗粒的跟随性与颗粒受力有密切关系,其中颗粒速度与流体速度的变化量是影响颗粒受力的重要参数;③基于试验数据拟合得到了水击条件下粗颗粒跟随性系数k的经验公式,并分析了颗粒粒径、管道直径、两相流平均流速以及水击发生时间等不同参数对粗颗粒跟随性系数的影响,公式计算值与实测值之间的误差在5%以内。     

基于显式时间积分的球颗粒DDA计算方法

非连续变形分析方法（DDA）是一种平行于有限元法的新型数值计算方法,该方法基于最小势能原理,把每个离散块体的变形、运动和块体之间的接触统一到平衡方程中进行隐式求解。然而,传统DDA方法在计算过程中需组装整体刚度矩阵并联立求解方程组,在用于大型岩土工程问题的三维数值模拟时占用内存较大、耗时较长、计算效率极低。因此,提出一种基于显式时间积分的三维球颗粒DDA方法。该方法在求解过程中不需要组装整体刚度矩阵,在求解加速度时,由于质量矩阵为对角矩阵,可存储为一维向量占用内存较少,且可分块逐自由度求解,效率较高,在接触判断上采用最大位移准则简化了接触算法,采用较小的时步,保证了计算的精确性;通过几个典型算例验证了该方法的准确性及计算效率。     

低电阻率差情况下三维激电法快速数值模拟

将一种快速数值模拟方法用于激电法正演模拟中,利用在低电阻率差情况下,积分方程法模拟时阻抗矩阵的非对角线项可忽略,而只需计算矩阵主对角值这一关键点。这里详细阐明了三维地电断面激电法快速模拟方法,推导了求解过程,并以此为基础编制了计算程序。实例试算结果说明,该模拟方法在计算速度、计算精度上都收到了较满意的结果。     

光滑粒子流体动力学二阶算法精度研究

光滑粒子流体动力学(SPH)由于无需网格生成和拉格朗日特性,对求解带有自由表面和大变形的力学问题有优势。但是该方法存在计算精度不高,计算效率较低等缺点。为此重点对SPH方法的精度提高进行研究。介绍了传统算法的基本公式,根据误差分析指出该算法精度不高的原因,提出了SPH二阶精度算法。通过精度验证分析,证明了该方法的精度的确能够达到二阶。通过二维计算实例,给出传统方法和二阶方法在粒子均匀分布和非均匀分布时函数值以及函数的一、二阶导数的误差分布,证明二阶算法能够克服传统算法的一些缺点,且计算精度有较大提高。     

Sensitivity of incipient particle motion to fluid flow penetration depth within a packed bed

A discrete element method is applied to a three‐dimensional analysis related to sediment entrainment on a micro‐scale. Sediment entrainment is the process by which a fluid medium accelerates particles from rest and advects them upward until they are either transported as bedload or suspended by the flow. Modelling of the entrainment process is a critically important aspect for studies of erosion, pollutant resuspension and transport, and formation of bedforms in environmental flows. Previous discrete element method studies of sediment entrainment have assumed the flow within the particle bed to be negligible and have only allowed for the motion of the topmost particles. At the same time, micro‐scale experimental studies indicate that there is a small slip of the fluid flow at the top of the bed, indicating the presence of non‐vanishing fluid velocity within the topmost bed layers. The current study demonstrates that the onset of particle incipient motion, which immediately precedes particle entrainment, is highly sensitive to this small fluid flow within the topmost bed layers. Using an exponential decay profile for the inner‐bed fluid flow, the discrete element method calculations are repeated with different fluid penetration depths within the bed for several small particle Reynolds numbers. For cases with slip velocity corresponding to that observed in previous experiments with natural sediment, the predicted particle velocity is found to be a few percent of the fluid velocity at the top of the viscous wall layer, which is a reasonable range of velocities for observation of incipient particle motion. This method for prescribing the fluid flow within the particle bed allows for the current discrete element method to be extended in future studies to the analysis of sediment entrainment under the influence of events such as turbulent bursting. Additionally, predictions for the slip velocities and fluid flow profile within the bed suggest the need for further experimental studies to provide the data necessary for additional improvement of the discrete element method models.     

The settling of consecutive spheres in viscoplastic fluids

One of the factors contributing to the uncertainties involved in the estimation of particle settling velocity in viscoplastic fluids is the time-dependent effect where the viscous parameters of the fluid change as a particle flows through and shears the medium. These changes, particularly at low shear Reynolds numbers, are reflected in the settling velocity of a following sphere that is released some time after an initial one, with the following sphere having a significantly greater velocity. This study found that changes in both fall velocity and equivalent viscosity can be correlated satisfactorily by a power law equation to the dimensionless form of the time interval between releases, and the rheogram shape factor for the fluid. A collision of particles occurs in cases where the time interval between releases is small, after which the particles combine and travel at a terminal velocity. A new variable, β, which takes into account the different surficial stress of the combined spheres, was introduced to the correlation of Wilson et al. [Wilson, K.C., Horsley, R.R., Kealy, T., Reizes, J.A., Horsley, M.R., 2003. Direct prediction of fall velocities in non-Newtonian materials. Int. J. Miner. Process. 71, 17–30] β was found to depend on the rheogram shape factor for the fluid and the shear Reynolds number for the particle. The validity of this approach was supported by experimental data.     

粘性泥石流的平均运动速度研究

粘性泥石流是泥石流类型中最常见也是危害最大的类型,泥石流的运动速度是泥石流的动力学参数中最重要的参数,因此准确而简洁地计算粘性泥石流的运动速度就显得非常重要。不同的泥石流地区的泥石流阻力有很大的不同:有的地区阻力较大,属于高阻力地区,泥石流运动速度较低;有的地区阻力较小,属于低阻力地区,泥石流运动速度较高。目前的粘性泥石流平均速度公式还不能兼顾计算所有地区的不同阻力类型的泥石流速度。泥石流的不均匀系数在不同的泥石流地区有很大的不同：不均匀系数小的地区阻力大,而不均匀系数大的地区阻力小,因此可以用不均匀系数划分泥石流沟的阻力特征,从而得到能兼顾所有不同地区的泥石流阻力规律。由一系列野外观测资料得到的由泥石流不均匀系数、泥石流运动底部纵比降和水力半径计算的粘性泥石流运动平均速度经验公式,能适应各种类型的泥石流沟,与其它系列的观测资料对比有很好的一致性,与粘性泥流的观测资料对比也很接近。由流体流动的福劳德数可以确定流动的缓急程度。一般的粘性泥石流都是急流,少数是缓流,极少数是运动速度非常缓慢的容重过大的粘性泥石流。粘性泥石流运动平均速度经验公式用于一般急流的粘性泥石流的速度计算结果很好,但不适用于容重过大的缓慢流动,对于缓流粘性泥石流速度计算偏大。在对泥石流的评估和治理中,平均速度公式可以用于泥石流堆积扇上游渠道中的粘性泥石流速度计算,对泥石流堆积扇上的粘性泥石流速度计算偏大,不适用于缓慢流动粘性泥石流,但在对泥石流的危害评估和治理中可以忽略缓慢流动的发生。     

Effects of concentration-dependent settling velocity on non-equilibrium transport of suspended sediment

In this study, non-equilibrium transport of suspended sediment from one equilibrium state to another is investigated. Based on a convective-diffusion equation, a numerical model for flow with suspended sediment is developed by considering the effect of concentration-dependent settling velocity. The numerical model is validated by comparing analytical solutions and experimental results. The concentration profiles, mean concentrations and distance necessary to reach a new equilibrium state are examined by comparing them with the results of constant settling velocity. For a high concentration flow, the results indicate that evident differences between the above three indicators can be determined with and without concentration-dependent settling velocity. Additionally, the effects of concentration-dependent settling velocity are sensitive to the sediment mobility parameter (or Rouse number), although they are nearly independent of the diffusion Reynolds number.     

颗粒沉降的格子Boltzmann模拟与PIV实验验证

在格子Boltzmann方法中引入大涡模拟,对球形颗粒在静水中沉降引起的紊动流场进行了数值模拟。数值模拟沉速与理论值以及粒子图像测速系统(PIV)实验结果吻合,验证了模型的合理性。同时分析比较了颗粒沉降过程中尾部紊动流场分布以及尾流流速值,发现数值模拟结果与实测结果趋势、数值基本一致,进一步说明了利用格子Boltzmann方法与大涡模拟技术相结合可以合理模拟泥沙颗粒在紊流区的沉降。     

Computational validation of the Generalized Sutherland Equation for bubble–particle encounter efficiency in flotation

Bubble–particle encounter during flotation is governed by liquid flow relative to the rising bubble, which is a function of the adsorbed frothers, collectors, and other surfactants and surface contaminants. Due to surface contamination, the bubble surface in flotation has been considered as immobile (rigid). However, surface contamination can be swept to the backside of the rising bubble due to the relative liquid flow, leaving the front surface of the rising bubble mobile with a non-zero tangential component of the liquid velocity. The bubble with a mobile surface was considered by Sutherland who applied the potential flow condition and analyzed the bubble–particle encounter using a simplified particle motion equation without inertia. The Sutherland model was found to over-predict the encounter efficiency and has been improved by incorporating inertial forces which are amplified at the mobile surface with a non-zero tangential velocity component of the liquid phase. An analytical solution was obtained for the encounter efficiency using approximate equations and is called the Generalized Sutherland Equation (GSE). In this paper, the bubble–particle encounter interaction with the potential flow condition has been analyzed by solving the full motion equation for the particle employing a numerical computational approach. The GSE model was compared with the exact numerical results for the encounter efficiency. The comparison only shows good agreement between the GSE prediction and the numerical data for ultrafine particles (< 10 μm in diameter), the inertial forces of which are vanishingly small. For non-ultrafine particles, a significant deviation of the GSE model from the numerical data has been observed. Details of the numerical methodology and solutions for the (collision) angle of tangency and encounter efficiency are described.     

明渠均匀流Q结构分布及运动特性

为了解明渠均匀流湍流Q结构(Quadrant events)第一象限事件(Q1)、第二象限事件(Q2)、第三象限事件(Q3)和第四象限事件(Q4)的时均与瞬态运动特性,使用高频粒子成像测速系统对3种明渠湍流二维瞬时流速矢量场进行测量,统计分析明渠湍流脉动流速场中Q结构的雷诺应力、发生频率、占据测量区域面积率以及Q结构与涡结构运动关系。结果表明:Q1与Q3结构时均特性相似,具有发生频率低、面积占据量少、负瞬时脉动动量通量小等特点;而Q2与Q4结构时均特性与之相反,且Q4结构发生频率沿水深增加而逐渐增多至0.8H附近达到最大,Q2结构发生频率在壁面区域为最大,沿水深增加而减小。明渠瞬态运动特性主要表现为水面区造成Q4结构向下运动,挤压、推进、爬升床面区的Q2结构伴随其自身形变的瞬态发展过程。     

A numerical study of particle motion and two‐phase interaction in aeolian sand transport using a coupled large eddy simulation – discrete element method

Wind‐blown sand movement, considered as a particle‐laden two‐phase flow, was simulated by a new numerical code developed in the present study. The discrete element method was employed to model the contact force between sand particles. Large eddy simulation was used to solve the turbulent atmospheric boundary layer. Motions of sand particles were traced in the Lagrangian frame. Within the near‐surface region of the atmospheric boundary layer, interparticle collisions will significantly alter the velocity of sand. The sand phase is quite dense in this region, and its feedback force on fluid motion cannot be ignored. By considering the interparticle collision and two‐phase interaction, four‐way coupling was achieved in the numerical code. Profiles of sand velocity from the simulations were in good agreement with experimental measurements. The mass flux shows an exponential decay and is comparable to reported experimental and field measurements. The turbulence intensities and shear stress of sand particles were estimated from particle root‐mean‐square velocities. Distributions of slip velocity and feedback force were analysed to reveal the interactions between sand particles and the continuous fluid phase.