硬球加强模型在CFD-DEM耦合计算中的验证与分析

针对CFD-DEM耦合计算中,颗粒计算时间步的选取影响颗粒碰撞计算精度和效率的问题。本文引入插值算法,将动量定理求解颗粒碰撞前后速度进行加权平均;根据弹性理论计算得到颗粒碰撞力,进行动力学方程求解;通过速度收敛准则修正初值速度并自动调整迭代求解次数,提出一种计算精度不受计算时间步长影响,无需对碰撞过程进行精细描述的高效率和高精度的加强硬球模型。对两个颗粒匀和变速碰撞算例进行数值模拟,碰撞后速度、碰撞力和碰撞时间与理论计算误差小于4%,与采用软球碰撞模型的DEM方法相比,颗粒碰撞计算精度不受计算时间步长影响,计算效率提高36.3%和36.8%。对单个颗粒在静水中沉降进行数值模拟,计算步长取10 s～5 s,颗粒与壁面即可得到精确解,计算效率提高33.5%。通过压力损失实验验证了该模型能够准确计算颗粒体积分数小于12%条件下两相流的压力损失。     

基于IS–FEM的颗粒曳力系数计算与试验验证

基于浸没光滑有限元模型（immersed smooth finite element model,IS–FEM）,计算球形与非球形颗粒曳力系数。设计颗粒曳力图像测量试验,验证IS–FEM模拟精度。颗粒相的运动行为基于连续介质理论的光滑有限元法求解;流体控制方程通过特征分解的半隐式有限元法求解;颗粒与流体相通过非贴体网格交换数据。结果表明,球形颗粒流场特征对称分布,非球形颗粒稳定沉降时长轴与重力方向垂直。不同雷诺数下球形颗粒的曳力系数计算值与Stokes曳力系数一致,非球形颗粒曳力系数高于等效球形颗粒,IS–FEM计算值与沉降试验吻合良好。     

非连续边界元积分的精确表达式及相关问题

以二维位势问题边界元分析为例,给出了利用线性非连续边界元离散边界积分方程时系数矩阵积分计算的精确表达式,通过和利用Gauss积分方法计算系数矩阵所得数值结果的比较表明：配位点选择不同对数值计算结果精度影响的主要原因是积分计算的精度,尤其当配位因子选择较大时,存在的准奇异积分（Nearly Singular Integrals)很难利用常规Gauss积分方法准确求得。     

基于新型解耦算法的激波诱导燃烧过程数值模拟

对一种模拟化学非平衡流动的时间和空间二阶精度新型解耦算法进行两方面改进,流动算子采用基于Runge-Kutta方法的时间格式以后, 可以推广到更多的空间差分格式,化学反应源项求解算子可以采用梯形公式、拟稳态逼近法和变系数常微分方程求解器. 对H化学非平衡流动; 解耦算法; 计算方法对一种模拟化学非平衡流动的时间和空间二阶精度新型解耦算法进行两方面改进,流动算子采用基于Runge-Kutta方法的时间格式以后,可以推广到更多的空间差分格式,化学反应源项求解算子可以采用梯形公式、拟稳态逼近法和变系数常微分方程求解器.对H_2/Air预混气体中激波诱导振荡燃烧的Lehr试验进行模拟,考察了化学动力学模型、网格尺寸和差分格式耗散大小对计算结果的影响,同时对不同的化学反应源项算子求解算法的计算效率进行了比较.     

随机结构有限元分析的递推求解方法的改进

将随机结构有限元分析的递推求解方法和伽辽金投影方法相结合,提出了求解随机静力响应的改进的递推求解方法。利用随机收敛的非正交多项式展开表示由于材料、外部荷载或构件几何尺寸的随机性导致的结构随机响应。采用递推求解方法得到响应多项式展开的初始系数,并运用定义的数学算子显式地表达出来。然后,通过定义修正系数,应用伽辽金方法对随机力平衡方程在非正交多项式基上进行投影,得到了和响应展开阶次个数相同的确定的有限元方程,并进行求解得到了修正系数。数值算例表明,通过对递推求解方法中响应表达式系数的修正,以很小的计算代价较大地提高了随机响应的计算精度;与基于正交多项式展开的随机有限元方法相比,在精度相当的前提下新方法耗费的计算时间大大降低。     

热传导问题的非协调数值流形方法

数值流形方法通过引入数学与物理双重网格,将插值域与积分域分别定义在两个不同的覆盖上,其优点是网格划分随意,不受复杂边界形状和材料界面的限制,是较之于有限元方法更一般化的数值模拟方法。在计算精度方面,数值流形方法远远高于有限元法。但它的精度还是不够理想。为此本文在单元总体位移场上附加非协调位移基本项,使单元位移函数趋于完全,构造了非协调流形单元来改善流形单元的计算精度和计算效率,并将其应用于热传导问题,推导了势问题的非协调数值流形方法。     

非均质材料等效瞬态热传导时域分析

基于时域自适应算法,结合均匀化技术和有限元方法,从而提出一种瞬态温度场求解模型,用来预测非均质材料等效性能并评估宏观温度场的等效行为.在整个计算中,通过自适应算法保证计算精度和稳定性,避免时间段尺寸变化可能引起的计算误差.在数值算例中,等效分析的结果与利用ANSYS求解的非均质有限元解比较,从计算效率和计算精度综合效果而言,结果是令人满意的.     

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%.      

用非协调边界元处理角点问题

采用非协调单元,有效地解决了边界元的角点问题,给出了含有两个配位因子时非协调线性单元的系数矩阵的表达式,对弹性力学平面问题进行了数值计算.通过采用常数单元、线性非协调单元的计算结果与解析解的比较和分析,证明在均布载荷作用下,两者的计算结果都接近解析解;在非均布载荷作用下,线性单元的结果明显优于常数单元.结果表明,非协调边界元法是一种有效的处理角点问题的方法;线性非协调单元能够更好地处理非均布载荷,提高边界元法的计算精度.     

RCCD温度应力分析的非均匀单元方法

本文根据碾压混凝土坝的施工特点提出的非均匀模型和等效均匀模型能显著提高碾压混凝土坝温度应力分析的计算效率，并有与常规方法相同的计算精度．     

FPM改进算法及在应力波传播问题中的应用A specified improved algorithm for Finite Particle Method and its application to wave propagation

有限粒子法(FPM)是传统SPH方法的重要发展,大大提高了边界区域粒子的计算精度。然而在迭代计算过程中,高耗时和潜在的数值不稳定性是制约FPM应用的关键因素。通过对FPM基本方程进行矩阵分解,建立了一种特殊格式的FPM改进算法。该方法保持FPM方法在边界区域较高计算精度的同时,成功地规避了传统FPM方法对系数矩阵可逆性的限制,大大提高了计算效率。最后,将改进算法在一维应力波传播问题中予以实现,获得了较好的数值结果。     

Study on calculation methods for acoustic radiation of axisymmetric structures in finite water depth

In this paper, a kind of FEM–WSM (Finite Element Method–Wave​ Superposition Method) is used to calculate the acoustic radiation of axisymmetric structures in finite water depth. FEM is used to solve the dry modes of axisymmetric structures, and WSM is applied along with the dry mode method to consider fluid–structure interaction effects and calculate the acoustic radiated field. This method combines the advantages of FEM and WSM. On one hand, it is suitable for complex or large axisymmetric structures on the one hand. On the other hand, it has higher computational efficiency than the FEM, and the computational domain size for the water is not limited. As long as the Green’s function is tailored for the boundary condition, the acoustic radiated field of axisymmetric structures in more complex ocean acoustic environments can be calculated by using this method. Besides, a least-square method is used to reduce the distortion resulting from computational errors of the modal estimates. The influence of the number of source and field points and the finite element mesh density on the calculation accuracy are discussed, eliciting some disciplinary conclusions. Using a spherical shell and a capsule shell as models, the results from the present approach, a semi-analytical method, and the crude FEM are compared to verify the correctness and efficiency. Based on numerical examples, the influence of the sea surface and the seafloor on the acoustic radiated field of structures in finite water depth is also analyzed.     

二维稳态辐射声场的光滑有限元-完美匹配层解法

针对外场声学有限元计算精度偏低的问题, 将光滑有限元技术引入到二维稳态辐射声场预测中, 提出了光滑有限元-完美匹配层解法. 该解法采用完美匹配层截断声场计算域, 并将其离散为等参四边形单元, 采用指数吸收函数实现完美匹配层内参数坐标和笛卡尔坐标的映射关系, 采用光滑声压梯度技术计算辐射声场刚度矩阵, 将形函数梯度的域内积分转换为形函数域边界积分. 某汽车二维声腔辐射声场的数值分析结果表明, 与标准有限元-完美匹配层相比, 光滑有限元-完美匹配层解法在完美匹配层内的声波吸收效果更好, 在计算域内的数值计算精度更高, 具有良好的工程应用前景.      

一种考虑界面不连续的改进的有限粒子法

有限粒子法(finite particle method,FPM)作为SPH(smoothed particle hydrodynamics)方法的重要改进,有效提高了边界区域粒子的近似精度,但是当FPM处理多物理场时,在不连续界面附近的计算精度会大大降低,并且FPM必须满足的矩阵非奇异性也提高了对界面处理的要求。本文中基于DSPH(discontinuous SPH)方法,提出了一种考虑界面不连续的改进FPM—DSFPM(discontinuous special FPM)法,旨在改善FPM在界面不连续处的计算精度,从而进一步提高其计算效率和稳定性。首先,分析了DSFPM的核近似精度。其次,根据不同的工程问题,给出DSFPM处理小变形和大变形问题的算法流程。利用DSFPM、DSPH和FPM等3种方法对弹性铝块小变形碰撞冲击算例进行了模拟,通过对比分析铝块的速度和应力以及计算时间验证了DSFPM算法在非连续界面处计算精度和计算效率的优势。最后,通过结合DSFPM和DFPM(discontinuous FPM)实现了对于大变形问题的模拟。     

FPM改进算法及在应力波传播问题中的应用

有限粒子法(FPM)是传统SPH方法的重要发展,大大提高了边界区域粒子的计算精度。然而在迭代计算过程中,高耗时和潜在的数值不稳定性是制约FPM应用的关键因素。通过对FPM基本方程进行矩阵分解,建立了一种特殊格式的FPM改进算法。该方法保持FPM方法在边界区域较高计算精度的同时,成功地规避了传统FPM方法对系数矩阵可逆性的限制,大大提高了计算效率。最后,将改进算法在一维应力波传播问题中予以实现,获得了较好的数值结果。     

Second-order boundary element method calculations of hydrodynamic interactions between particles in close proximity

A second-order boundary element technique was developed to simulate the 3D hydrodynamic interactions between multiple particles of arbitrary shape. This paper reports the results of an extensive validation procedure aimed at demonstrating the convergence characteristics of the technique, especially in cases where the particles are in close proximity. The quadratic elements are superior to the lower-order elements in terms of accuracy, computer storage and CPU time required, thus resulting in a significant improvement in the overall computational efficiency. Superparametric discretization improves the accuracy over isoparametric discretization but lowers the convergence rate of the method. When the interparticle gap becomes very small (less than 1% of the particle radius), the numerical solution diverges owing to inaccurate determination of the element contributions in the gap region. An adaptive subdomain integration scheme was developed that dramatically improved the integration accuracy and provided convergent solutions for problems of very small gaps down to 0–01% of the particle diameter.     

Application of particle splitting method for both hydrostatic and hydrodynamic cases in SPH

Smoothed particle hydrodynamics(SPH) method with numerical diffusive terms shows satisfactory stability and accuracy in some violent fluid–solid interaction problems. However, in most simulations, uniform particle distributions are used and the multi-resolution, which can obviously improve the local accuracy and the overall computational efficiency, has seldom been applied. In this paper, a dynamic particle splitting method is applied and it allows for the simulation of both hydrostatic and hydrodynamic problems. The splitting algorithm is that, when a coarse(mother) particle enters the splitting region, it will be split into four daughter particles, which inherit the physical parameters of the mother particle. In the particle splitting process,conservations of mass, momentum and energy are ensured. Based on the error analysis, the splitting technique is designed to allow the optimal accuracy at the interface between the coarse and refined particles and this is particularly important in the simulation of hydrostatic cases. Finally, the scheme is validated by five basic cases, which demonstrate that the present SPH model with a particle splitting technique is of high accuracy and efficiency and is capable for the simulation of a wide range of hydrodynamic problems.Smoothed particle hydrodynamics(SPH)method with numerical diffusive terms shows satisfactory stability and accuracy in some violent fluid–solid interaction problems.However,in most simulations,uniform particle distributions are used and the multi-resolution,which can obviously improve the local accuracy and the overall computational efficiency,has seldom been applied.In this paper,a dynamic particle splitting method is applied and it allows for the simulation of both hydrostatic and hydrodynamic problems.The splitting algorithm is that,when a coarse(mother)particle enters the splitting region,it will be split into four daughter particles,which inherit the physical parameters of the mother particle.In the particle splitting process,conservations of mass,momentum and energy are ensured.Based on the error analysis,the splitting technique is designed to allow the optimal accuracy at the interface between the coarse and refined particles and this is particularly important in the simulation of hydrostatic cases.Finally,the scheme is validated by five basic cases,which demonstrate that the present SPH model with a particle splitting technique is of high accuracy and efficiency and is capable for the simulation of a wide range of hydrodynamic problems.     

Radiative-convective heat transfer in a flow past an evaporating semitransparent melt film

A conjugate problem of nonstationary radiative-convective heat transfer in a turbulent flow of a mixture of gases with solid particles around a horizontal evaporating semitransparent melt film is numerically solved. The moving film is subjected to intense radiative heating by an external source whose radiation interacts with the gas-particle medium and the film in a bounded spectral range. The temperature fields and velocities in the boundary layer and the film are calculated. The computational results given allow determination of the impact of radiation on heat transfer and film dynamics in the boundary layer-film system.     

柔性微粒介电泳分离过程的多尺度模拟

介电泳分离是一种高效的微细颗粒分离技术,利用非均匀电场极化并操纵分离微流道中的颗粒. 柔性微粒在介电泳分离过程中同时受多种物理场、多相流和微粒变形等复杂因素的影响,仅用单一的计算方法对其进行模拟存在一定的难度,本文采用有限单元——格子玻尔兹曼耦合计算的方法处理这一难题.介观尺度的格子玻尔兹曼方法将流体看成由大量微小粒子组成,在离散格子上求解玻尔兹曼输运方程,易于处理多相流及大变形问题,特别适合模拟柔性颗粒在介电泳分离过程中的变形情况.另一方面,介电泳分离过程的模拟需求解流体、电场和微粒运动方程,计算量相当庞大,通过有限单元法求解介电泳力,提高计算效率.利用这种多尺度耦合计算方法,对一款现有的介电泳芯片分离过程进行了模拟.分析了微粒在电场作用下产生的介电泳力,揭示了介电泳力与电场变化率等因素之间的关系.对微粒运动轨迹及其变形的情况进行了研究,发现微粒的变形主要与流体剪切作用有关.这种多尺度耦合计算方法,为复杂微流体的计算提供了一种有效的解决方案.