颗粒群碰撞搜索及CFD-DEM耦合分域求解的推进算法研究

在采用计算流体力学-离散元耦合方法(computational fluiddynamics-discrete element method, CFD-DEM)进行固液两相耦合分析时, 颗粒计算时间步的选取直接影响到耦合计算精度和计算效率. 为此, 本文选取每个目标颗粒为研究对象, 引入插值函数计算时间步的运动位移, 构建可变空间搜索网格; 通过筛选可能碰撞颗粒建立搜索列表, 采用逆向搜索方式判断碰撞颗粒, 从而提出一种改进的DEM方法(modified discreteelement method, MDEM). 该算法在颗粒群与流体耦合计算中, 颗粒计算初始时间步选取不受颗粒碰撞时间限制, 通过自动调整和修正实现大步长, 由颗粒和流体耦合条件实时更新流体计算时间步, 使颗粒计算时间步选取过小导致计算效率低、选取过大导致颗粒碰撞漏判的问题得以解决, 为颗粒与流体耦合的数值模拟提供了行之有效的计算方法. 通过两个颗粒和多个颗粒的数值模拟, 得到的颗粒间碰撞力、碰撞位置及次数, 与理论计算结果的相对误差均低于2%, 与传统的DEM碰撞搜索算法相比, 在选取的3种计算时间步均不会影响计算精度, 且有较高的计算效率. 通过多个颗粒与流体的耦合数值模拟, 采用传统的CFD-DEM方法, 只有颗粒计算时间步选取10$^{-6}$ s或更小才能得到精确解, 而采用本文方法取10$^{-4}$ s也能够得到精确解, 避免了颗粒碰撞随时间步增大而出现的漏判问题, 且计算耗时降低了16.7%.      

考虑颗粒碰撞的多重Monte Carlo算法

从减少计算代价和改进碰撞算法出发, 提出了考虑颗粒碰撞的多重Monte Carlo算法, 它采用直接模拟Monte Carlo算法来考虑颗粒碰撞, 并与求解颗粒拉氏Langevin方程的Monte Carlo算法耦合起来, 跟踪比实际颗粒数目小得多的虚拟颗粒. 提出了时间步长选定标准、虚拟碰撞伙伴所在控制容积的判断准则、颗粒碰撞发生的判 断准则、虚拟碰撞伙伴的选择、基于随机碰撞角度的碰撞动力学, 构成了考虑颗粒碰撞的完整多重Monte Carlo算法. 对理想工况的细微颗粒流和粗重颗粒流进行了数值模拟, 颗粒碰撞率的模拟结果与理论分析解和DNS结果均符合很好, 颗粒场演变的细节信息, 如时间平均和特定时刻的颗粒数密度, 速度和颗粒湍动能等, 均与DNS结果符合很好. 数值模拟结果证明该算法不仅具有较低的计算代价, 而且能够达到足够的计算精度.     

固体火箭冲压发动机补燃室沉积数值模拟

考虑液态颗粒碰撞和聚合过程、液态颗粒和壁面碰撞过程,建立了固体火箭冲压发动机补燃室沉积数值计算模型,对模型发动机补燃室内颗粒之间碰撞、沉积的相互作用过程进行了数值模拟,得到了颗粒沿轴向和沿出口平面径向方向的分布情况,并计算得到了补燃室壁面不同段的沉积层厚度值。将计算结果与试验结果进行对比,最大误差为0.8mm,表明该计算模型具有较高的计算精度。     

基于无量纲分析的法向恢复系数模型研究

作为描述接触碰撞过程能量损失的重要参量,恢复系数的深入研究对于提升现有接触碰撞力模型预测性能、准确描述接触碰撞现象,并进一步探明其对机械系统整体动态特性影响规律方面具有重要作用.鉴于现有恢复系数模型计算精度的局限性,本文基于无量纲分析方法,提出了一种考虑材料特性与初始碰撞速度的新型恢复系数模型.具体实施过程如下:首先,利用有限元软件ABAQUS建立弹性球-理想弹塑性基底法向接触碰撞数值仿真模型,分别从最小网格尺寸设置与接触碰撞能量转换角度验证了所建模型的有效性;基于此模型开展多工况下的数值模拟研究,分析不同材料弹塑性参数与初始碰撞速度对接触碰撞响应的影响;在此基础上,引入无量纲化参数E*/(ρv_nc²)与σ_y/E*,寻找恢复系数与弹塑性参数及初始碰撞速度间的函数关系;进一步结合Johnson塑性碰撞理论,反向推算获取屈服速度与材料属性的映射关系,最终建立无量纲化恢复系数新模型;通过与低速试验数据、高速有限元模拟结果的对比,验证了新模型的预测精度和泛化性能.     

高黏性流动有限元模拟的迭代稳定分步算法

分步算法已被广泛应用于数值求解不可压缩N-S方程. Guermond等认为时间步长必须大于 某个临界值方能使算法稳定. 然而在高黏性流动模拟中,已有的显式和半隐式分步算法由于 其显式本质,必须采用小时间步长计算,不但降低了计算效率,同时也常与为使分步算法稳 分步算法已被广泛应用于数值求解不可压缩N-S方程. Guermond等认为时间步长必须大于 某个临界值方能使算法稳定. 然而在高黏性流动模拟中,已有的显式和半隐式分步算法由于 其显式本质,必须采用小时间步长计算,不但降低了计算效率,同时也常与为使分步算法稳 定必须满足的最小时间步长要求冲突. 本文目的是构造一种含迭代格式的分步算法,它能在 保证精度的前提下大幅度地增大时间步长. 方腔流和平面Poisseuille流数值计算结果证实 了此特点,该方法被有效应用于充填流动过程的数值模拟.     

气固两相流中颗粒碰撞的Monte-Carlo数值模拟

利用颗粒碰撞动力学模型和颗粒几何碰撞率模型,采用Monte—Carlo算法来模拟颗粒之间碰撞,把该算法与求解雷诺应力-概率密度函数模型的有限差分-Monte Carlo算法耦合起来,对轴对称突扩通道内的两相旋流场进行了数值模拟,模拟结果表明,由于颗粒碰撞使颗粒的动能和湍动能在三个坐标方向上进行了再分配,从而导致颗粒的动能和湍动能在三个坐标方向上趋于各向同性;另外,由于颗粒碰撞破坏了颗粒-颗粒、颗粒-流体微团之间的速度关联,从而造成颗粒湍动能及两相速度脉动关联的降低。     

粗糙颗粒动理学及稠密气固两相流动的数值模拟

考虑颗粒碰撞过程中摩擦作用,给出了粗糙颗粒碰撞动力学.引入颗粒相拟总温来表征颗粒平动和转动脉动能量的特征.基于气体分子运动论,建立颗粒碰撞中平动和旋转共同作用的粗糙颗粒动理学,给出了颗粒相压力和黏度等输运参数计算模型.运用基于颗粒动理学的欧拉-欧拉气固两相流模型,数值模拟了流化床内气体颗粒两相流动特性,分析了颗粒旋转流动对颗粒碰撞能量交换和耗散的影响.模拟得到的流化床内径向颗粒浓度和提升管内颗粒轴向速度与他人实验结果相吻合.模拟结果表明随着颗粒浓度的增加,颗粒相压力和能量耗散逐渐增加,而颗粒拟总温先增加后下降.随着颗粒粗糙度系数的增加,床内平均颗粒相拟总温和能量耗散增加,表明颗粒旋转产生的摩擦将导致颗粒旋转脉动能量的改变,影响床内气体-颗粒两相宏观流动特性.      

带自由表面水流与离散颗粒耦合模型研究

基于考察泥沙运动的细观行为特征,采用离散单元法(DEM)模拟泥沙颗粒运动,结合带自由表面的水动力学计算模型,建立了CFD-DEM耦合数值模型。计算程序开发基于Fortran语言来实现。耦合模型中实现了硬球模型和软球模型两种颗粒碰撞模型,应用范围较广。作为自由表面水流与泥沙颗粒流数值模型的初步研究,在模型建立的基础上,对模型做了基本的验证。分别通过单颗粒静水沉降和混合颗粒群分选两个计算工况,验证了模型的正确性及模拟精度。该耦合模型可进一步丰富带自由表面水流条件下泥沙运动的研究手段。     

Biot-Cosserat连续体-离散颗粒集合体模型的非饱和土连接尺度方法

耦合了非饱和多孔多相介质有限元模型和颗粒介质离散元(DEM)模型,提出了以宏、细观尺度分别耦合Biot-Cosserat连续体模型和离散颗粒集合体模型的连接尺度方法来分析非饱和含液颗粒材料的力学渗流耦合问题。根据被动空气压力假定和对空间离散孔隙水质量守恒方程的约化,从非饱和土有限元控制方程的基本未知量中消去了孔隙水压力,而将其取作有限元积分点上定义取值的内状态变量,进而建立了节点未知量仅包含固相线位移和转角的非饱和Cosserat多孔连续体约化有限元数值模型。基于连接尺度方法(BSM)宏、细观尺度数值过程的解耦计算的特点,对宏、细观两尺度数值模型的时域积分分别采用隐式Newmark方法和显式中心差分法,且取不同时间步长以提高计算效率。与全域采用DEM的精细分析方法相比,本文BSM在保证计算精度的前提下可大幅节省计算时间。在不考虑湿化效应的边坡稳定算例中,在得到类似计算精度条件下它比全域采用DEM节省计算时间高达86.65%。二维边坡稳定算例结果验证了本文连接尺度方法的有效性,以及在揭示含液颗粒结构细观破坏机理上的优点。数值算例结果显示,边坡承载能力因降雨大幅下降约50%,这表明本文发展的计及伴随湿化过程的颗粒材料结构中饱和度及吸力分布演变及其对结构破坏失效影响的非饱和颗粒材料多尺度计算模型是很有必要的。     

颗粒流体系统的格子Boltzmann数值方法研究进展

介绍Euler-Lagrange框架下基于格子Boltzmann方法 LBM(Lattice Boltzmann Method)发展的两种不同层次（即不同时-空尺度和精度）的颗粒流体系统离散模拟方法,即格子Boltzmann颗粒解析直接数值模拟（LB-based PR-DNS）方法和格子Boltzmann离散颗粒模拟（LB-based DPS）方法,总结了Euler-Euler框架下基于格子Boltzmann双流体模型（LB-based TFM）方面的探索研究。LB-based PR-DNS方法中颗粒尺寸远大于格子步长,能够直接解析出流体在颗粒表面的流动以及颗粒所受完整的动力学信息;LB-based DPS方法中格子步长远大于颗粒直径,其在计算精度、时间耗费和计算效率之间能达到很好的平衡,可获得流体的宏观平均流动及颗粒的运动轨迹信息。LB-based DNS和DPS是探索颗粒流体系统的有力手段,但LB-based TFM应用于模拟颗粒流体系统仍需进一步探索。     

304L/Q235B大面积金属板爆炸焊接物质点法模拟分析

大面积金属板材304L/Q235B的爆炸焊接过程涉及炸药爆轰、金属板材的高速碰撞和塑性变形等。采用有限元法计算模拟这个问题时,网格单元会发生扭曲畸变现象,导致计算精度下降,甚至出现单元负体积而使计算终止,并且炸药爆轰形成气体产物飞散过程也很难模拟。为了能模拟大面积金属板材的爆炸焊接整个过程并获得合理的技术工艺参数,采用物质点法进行三维数值模拟分析。物质点法作为一种无网格法,在模拟冲击动力学问题中主要采用显式积分算法。通过将拉格朗日质点单元与固定的欧拉背景网格相结合,可以实现爆炸焊接的复板与基板的高速碰撞、炸药滑移爆轰、金属板面的塑性变形过程的数值模拟,并给出爆炸复合板材的形变、有效塑性应变和复板与基板的碰撞速度的计算结果。采用物质点法模拟的复合板材变形与爆炸焊接实验结果基本一致。计算复板与基板的碰撞速度这个重要的物理参数时,物质点法与Richter理论公式的相对误差不超过13%。数值计算和实验结果表明,物质点法在数值精度和计算效率方面具有优势,物质点法是研究金属焊接爆炸问题的一种有效数值方法。     

一维轴对称杆件爆源模型及其在台阶爆破模拟中的应用

为了解决在实体炮孔建模时需要加密网格、计算量大等问题,提出了一种一维轴对称爆源模型:利用一维线状杆件表述炮孔及炸药,实体单元表述周围岩体,通过杆件节点与实体单元的拓扑关系,将杆件节点上的爆生气体压力施加至周围实体单元上,并根据实体单元的体应变计算出杆件节点处的横截面变化情况,从而实现模拟炸药与周围岩体的相互作用。通过与实体炮孔模型的数值对比分析,发现压力衰减指数为1.25时,一维轴对称爆源模型获得的径向质点峰值振动速度（peak particle velocity, PPV）衰减规律及振动速度时程曲线与实体炮孔模型基本一致,证明了该模型在模拟爆破问题中的精确性。针对混凝土块动态爆破破坏特性的研究,通过与文献对比分析,进一步验证了该模型的正确性。为验证该一维轴对称爆源模型在台阶爆破模拟中的应用,以鞍钢露天铁矿台阶爆破开采为研究对象,建立了5排50炮孔三维台阶爆破概化模型,模拟了爆区内露天边坡的损伤破坏状态。数值计算结果表明,爆区内拉伸破坏为主,并且除了离爆源较近的第一个测点外,其余测点处的振动速度峰值大小及其随距离的变化规律与现场实测数据基本一致,证明了所提爆源模型在三维台阶爆破远场模拟的可行性。     

Effect of collision and velocity model of lattice Boltzmann model on three-dimensional turbulent flow simulation

Various collision and velocity models of the lattice Boltzmann model (LBM) were compared to determine their effects on the efficiency of a three-dimensional homogeneous isotropic decaying turbulent flow simulation. We determined that a decrease in the number of velocities, in particular, 13-velocities, which can be used in the quasi-equilibrium lattice Boltzmann and in the multiple-relaxation time models (MRT), could considerably decrease the computational effort. However, decreasing the number of velocities deteriorates the stability and the accuracy of the results. By comparing the collision models, we also determined that the stability of the entropic lattice Boltzmann model (ELBM), and 19- and 27- velocity MRT is much higher than in other models. However, the numerical viscosity introduced by the ELBM underestimates the enstrophy, and the computational effort increases because of the calculation overhead required to solve the additional equations if special care is not given to the calculation.     

Efficient modelling of particle collisions using a non-linear viscoelastic contact force

In this paper the normal collision of spherical particles is investigated. The particle interaction is modelled in a macroscopic way using the Hertzian contact force with additional linear damping. The goal of the work is to develop an efficient approximate solution of sufficient accuracy for this problem which can be used in soft-sphere collision models for Discrete Element Methods and for particle transport in viscous fluids. First, by the choice of appropriate units, the number of governing parameters of the collision process is reduced to one, which is a simple combination of known material parameters as well as initial conditions. It provides a dimensionless parameter that characterizes all such collisions up to dynamic similitude. Next, a rigorous calculation of the collision time and restitution coefficient from the governing equations, in the form of a series expansion in this parameter is provided. Such a calculation based on first principles is particularly interesting from a theoretical perspective. Since the governing equations present some technical difficulties, the methods employed are also of interest from the point of view of the analytical technique. Using further approximations, compact expressions for the restitution coefficient and the collision time are then provided. These are used to implement an approximate algebraic rule for computing the desired stiffness and damping in the framework of the adaptive collision model (Kempe and Fröhlich, J. Fluid Mech. 709: 445–489, 2012). Numerical tests with binary as well as multiple particle collisions are reported to illustrate the accuracy of the proposed method and its superiority in terms of numerical efficiency.     

基于2D网格的轴对称浸没边界法

浸没边界法是处理颗粒两相流中运动边界问题的一种常用数值模拟方法. 当研究的物理问题的无量纲参数满足一定要求时, 该流场结构呈现轴对称状态. 为此本文提出了一种基于2D笛卡尔网格和柱坐标系的轴对称浸没边界法. 该算法采用有限体积法(FVM)对动量方程进行空间离散, 并通过阶梯状锐利界面替代真实的固体浸没边界来封闭控制方程. 为了提高计算效率, 本文采用自适应网格加密技术提高浸没边界附近网格分辨率. 由于柱坐标系的使用, 使得动量方程中的黏性项产生多余的源项, 我们对其作隐式处理. 此外, 在对小球匀速近壁运动进行直接数值模拟时, 由于球壁间隙很小, 间隙内的压力变化比较剧烈. 因此想要精确地解析流场需要很高的网格分辨率. 此时, 需要在一个时间步内多次实施投影步来保证计算的稳定性. 而在小球自由碰壁运动中, 我们通过引入一个润滑力模型使得低网格分辨率下也能模拟小球近壁处的运动. 最后通过小球和圆盘绕流、Stokes流小球近壁运动以及小球自由下落碰壁弹跳算例验证本算法对于轴对称流的静边界和动边界问题均是适用和准确的.      

A stochastic approach for the simulation of collisions between colloidal particles at large time steps

This paper presents a new approach for the detection and treatment of colloidal particle collisions. It has been developed in the framework of Lagrangian approaches where a large number of particles is explicitly tracked. The key idea is to account for the continuous trajectories of both colliding partners during a time step that is not restricted. Unlike classical approaches which consider only the distances between a pair of particles at the beginning and at the end of each time step (or assume straight-line motion in between), we model the whole relative, and possibly diffusive, trajectory. The collision event is dealt with using the probability that the relative distance reaches a minimum threshold (equal to the sum of the two particle radii). In that sense, the present paper builds on the idea of a previous work. However, in this first work, the collision event was simulated with a simplified scheme where one of the collision partners was removed and re-inserted randomly within the simulation domain. Though usually applied, this treatment is limited to homogeneous situations. Here, an extension of the stochastic model is proposed to treat more rigorously the collision event via a suitable evaluation of the time and spatial location of the collision and an adequate calculation of subsequent particle motion. The resulting collision kernels are successfully compared to theoretical predictions in the case of particle diffusive motion. With these promising results, the feasibility of simulating the collisional regime over a whole range of particle sizes (even nanoscopic) and time steps (from a ballistic to a purely diffusive regime) with a numerical method of reasonable computational cost has been confirmed. The present approach thus appears as a good candidate for the simulation of the agglomeration phenomenon between particles also in complex non-homogeneous flows.     

Development and validation of a reduced order history force model

The history force model accounts for temporal development in fluid gradients in the viscous region surrounding a particle in point particle methods. The calculation of the history force typically requires storing and using relative velocity information during the life time of the particle. For a large number of particles integrated over large times, history force calculation can become prohibitively expensive. The current work presents a new modeling approach to calculate the history force in which a decay function is applied to a stored cumulative value of the history force. The proposed formulation is equivalent to applying the same function obtained from a constant acceleration assumption to a running average of the acceleration within the memory time of the particle. The new force model is validated with experimental measurements of settling spheres at Reynolds numbers ranging from around one to a few hundreds and at density ratios from 1.2 to about 9.32. More validation work was carried-out with experimental measurements of oscillating spheres at different frequencies and amplitudes, as well as bouncing spheres at different Reynolds numbers and density ratios. The model shows very good agreement with the experiments of settling spheres and reasonable/good agreement with oscillating and bouncing sphere experiments. The proposed model significantly reduces the computational resources required to calculate the history force especially when large number of particles need to be integrated over long times.     

Improvement,validation and application of CFD/DEM model to dense gas–solid flow in a fluidized bed

Dense gas–solid flow with solid volume fraction greater than 10% and at moderate Reynolds number is important in many industrial facilities such as fluidized beds. In this work, the Euler–Lagrange approach in combination with a deterministic collision model is applied to a laboratory-scale fluidized bed. The fluid–particle interaction is studied using a new procedure called the offset method, which results in several numbers of spatial displacements of the fluid grid. The proposed method is highly precise in determining porosity and momentum transfer, thus improving simulation accuracy. A validation study was carried out to assess the results using this in-house CFD/DEM code against 5-s operation of a Plexiglas spouted-fluidized bed, showing good qualitative correlation of solid distribution in the bed and acceptable quantitative agreement of pressure drops at different positions in the bed. In view of high computing cost, special emphasis is placed on effective program design, such as application of advanced detection algorithm for particle–particle/wall collisions, the multi-grid method and parallel calculation. In this context, the influence of increasing the processor number, up to 36, on calculation efficiency was investigated.