复杂管系中水击波传播特性的分析和计算

本文利用水击波在管系中传播特性导出了分叉管端的边界条件,采用拉普拉斯变换方法得到了管系中水击波传播的解析解,並且运用拉格朗日一欧拉方法进行数值计算。     

SPH方法的运动边界条件研究

提出一种设置运动边界条件的方法,研究边界附近流体粒子积分截断和非物理穿透边界的问题。边界外的虚粒子在每个时间步由边界附近流体粒子对称生成,赋予相应的物理量,并在虚粒子中引入排斥力,利用拉格朗日形式的N-S方程自编SPH程序,参考一维激波管的精确解验证边界方法的适用性,研究运动边界条件在计算模型中应用。激波管的模拟结果与精确解基本一致,且在运动边界模型中也计算获得合理的结果。文中提出的运动边界条件,避免了边界附近流体粒子积分截断问题,阻止流体粒子在边界处发生非物理穿透的现象。     

SPH方法的运动边界条件研究Research on the moving boundary condition in SPH method

提出一种设置运动边界条件的方法,研究边界附近流体粒子积分截断和非物理穿透边界的问题。边界外的虚粒子在每个时间步由边界附近流体粒子对称生成,赋予相应的物理量,并在虚粒子中引入排斥力,利用拉格朗日形式的N‐S方程自编SPH程序,参考一维激波管的精确解验证边界方法的适用性,研究运动边界条件在计算模型中应用。激波管的模拟结果与精确解基本一致,且在运动边界模型中也计算获得合理的结果。文中提出的运动边界条件,避免了边界附近流体粒子积分截断问题,阻止流体粒子在边界处发生非物理穿透的现象。     

单支开口薄壁梁屈曲分析的Riccati有限条传递矩阵法

针对单支开口薄壁梁屈曲问题,通过采用半解析有限条法推导薄壁梁的条元控制方程、传递矩阵基础形成单元传递方程、Riccati变换改善数值计算稳定性,提出了开口单支薄壁梁屈曲分析的Riccati有限条传递矩阵法。为了验证该方法的正确性与高效性,通过提出的Riccati有限条传递矩阵法和有限元法分析了一般支撑条件下两种不同截面形式的薄壁梁屈曲临界载荷与屈曲模态,计算发现两种方法的结果具有很好的一致性,且与传递矩阵法相比,Riccati有限条传递矩阵法数值稳定性好。因此,Riccati有限条传递矩阵法可计算广义边界条件的薄壁结构屈曲问题。     

闭口薄壁曲杆的弯扭分析

本文利用 A·A·乌曼斯基对闭口薄壁直杆问题中截面轴向位移所作的假定推广到闭口薄壁曲杆的弯扭问题,导出了基本微分方程和对应边界条件,并给出了它的初参数解.当 J_p→∞时问题退化为开口薄壁曲杆弯扭问题的解.另外,从实例计算结果中看出:对闭口薄壁曲杆的边界条件需特别注意。     

压力谐振管的数值计算

本文应用格杜诺夫(c.K.)差分格式计算了具有周期性边界条件的一维非定常流动,在计算中同时还考虑了粘性与传热的影响.计算结果表明格杜诺夫差分格式具有较好的稳定性,并与实验结果符合较好.计算过程表明,本文的方法原则上可以用于多种形式的周期性一维非定常流动的计算,如热分离器中变压管的计算.     

集中载荷作用下薄壁开口曲杆的稳定性

本文研究了薄壁开口曲杆的稳定性问题.该曲杆的边界条件比较复杂,一端固支,另一端既有对位移的限制,又有集中力和集中力矩作用.本文从薄壁开口曲杆的平衡方程出发,应用假想分布载荷法,导出一组关于曲杆稳定性的变系数常微分方程.为了解特征值问题,应用有限差分法,将特征方程用矩阵形式表达.对某一产品结构中的实际构件进行了数值计算与稳定性试验,构件为一Ⅰ字形截面的薄壁开口曲杆,对特征方程应用矩阵迭代法求得临界载荷的理论计算值.应用Southwell法结合最小二乘法整理了重复试验所获得的数据,得到临界载荷的实验值,理论计算值与实验值接近.     

任意厚度层合开口柱壳的温度应力

基于层合柱壳混合状态方程和边界条件的弱形式,建立了具有固支边的层合开口柱壳的温度应力混合方程,给出了任意厚度层合开口柱壳在温度荷载和机械荷载共同作用下的解析解。     

复合材料周期结构数学均匀化方法的一种新型单胞边界条件

数学均匀化方法是计算周期复合材料结构的有效方法之一,单胞边界条件施加的合理性直接决定了影响函数控制方程的计算效率和精度,进而影响均匀化弹性参数和摄动位移的计算精度.本文首先将单胞影响函数作为虚拟位移处理,给出了单胞在结构中真实的边界条件,结果表明,四边固支适合作为二维结构单胞边界条件;其次,针对二维结构提出了超单胞周期边界条件,有效提高了影响函数的计算精度,并使用与虚拟位移相对应的虚拟势能泛函验证超单胞周期边界条件的有效性;最后,利用数值分析验证多尺度渐进展开方法的计算精度,强调了二阶摄动的必要性.     

格子Boltzmann方法中基于内插值的曲线边界处理新方法

对格子Boltzmann方法提出了一种新的曲面边界条件处理方法。在笛卡尔坐标系中,这种处理方法是现有的格子Boltzmann方法有关边界条件处理与浸入式边界条件的混合,它采用内插值方法计算靠近物理边界的网格点速度,使其保证最低精度为二阶,然后利用格子Boltzmann方法中的边界条件技术得到相应的分布函数。由理论推导和数值计算表明,本文提出的方法比其他方法更稳定且具有二阶精度。     

THREE-DIMENSIONAL EXTRUDATE SWELL: FORMULATION WITH THE STREAM TUBE METHOD AND NUMERICAL RESULTS FOR A NEWTONIAN FLUID

Stream tube analysis, already applied to two-dimensional extrudate swell problems involving rate and integral constitutive equations for incompressible fluids, is now considered in the problem of free surface determination in a three-dimensional flow situation. The method allows computation of the unknown free surface by considering only a ‘peripheral stream tube’ limited by the wall and the jet surface and an inner stream surface. Those boundary surfaces are determined by considering the conservation equations together with boundary condition equations, solved by the Levenberg/Marquatdt optimization algorithm. The method leads to a considerable reduction in the number of degrees of freedom and the storage area. As in a previous study in the two-dimensional case, singularity problems in the vicinity of the junction points between the wall and the free surface are avoided. However, the numerical method still allows evaluati on of stress peaks due to the singularity at the exit, as may be observed for results obtained with a Newtonian fluid in a duct of square cross-section.     

Closed-form solutions for the nonlinear problem of an air-inflated,heavy membrane tube rolling down an incline

This study considers an air-inflated, heavy membrane tube section rolling down an incline without slipping. This problem is modeled as four simultaneous nonlinear ordinary equations with an undetermined boundary condition. The boundary condition at the upper separation point is carefully examined. Through an analytic approach, the general solutions for shape and tension are expressed in closed form. The unknown acceleration of the tube section is determined by imposing the boundary condition. The effect of the velocity is reflected in the so-called apparent tension. In addition, the acceleration results in an exponential decay of the apparent tension along the arc length. Some specific cases for shape and apparent tension are presented and discussed.     

Determination of heat transfer coefficients on the surfaces of plastic tubes

 The paper discusses the statistical steady heat and momentum transfer problem in the inlet section of the plastic tubes. The modified two equation k–ɛ turbulent model utilizing variability of turbulent Prandtl number, Pr_t, was used for the analysis. Considering the thermophysical anisotropy of the tube material, a balance of local temperatures and local heat fluxes on the boundary between the fluid and the tube wall was assumed (conjugate heat transfer problem). The thermal boundary condition on the external surface of the tube (temperature) measured in the experiment was taken into account. The boundary problem described was solved by the control volume method. The values of the parameters of Pr and Re obtained from the experiments were included in the numerical calculations. Based on the results obtained, profiles of mean fluid temperatures, local Nusselt numbers on the internal and external surface of the tube, and profiles of temperatures on the internal surface of the tube and inside of the tube wall were determined. The analysis shows that changes in Pr_tand turbulence intensity, Tu, influence the local values of Nusselt numbers, and it also shows that the results for the local Nusselt numbers inside the tube obtained from numerical calculations are of great accuracy in comparison with results published in the available literature. Received on 11 June 2001     

A comparative study of poiseuille flow of a polar fluid under various boundary conditions with applications to blood flow

In this paper, Poiseuille flow of a polar fluid (model of a red blood cell suspension) under various boundary conditions at the wall, viz., slip or no-slip in the axial velocity and couple stresses zero or non-zero at the boundary, is considered from the point of view of its applications to blood flow. Analytic expressions for axial and rotational velocities, flow rate, effective viscosity and stresses are obtained. The magnitudes of the length ratioL and the coupling number N are determined in accordance with concentration and tube radius (in the existing literature, values ofL andN are chosen arbitrarily). Velocity profiles (both axial and rotational) and the variation of the effective viscosity with concentration, tube radius and for various values of the boundary condition parameters are shown graphically. The analytic results obtained are compared with experimental results (for blood flow). It is found that they are in a reasonably good agreement. The effective viscosity exhibits the Inverse Fahraeus-Lindquist Effect in all the cases (including the slip or no-slip in the velocity fields). A method is given for determining the non-zero couple stress boundary condition for a given concentration. Applications of this theory to blood flow are briefly discussed.     

旋转导向系统底部钻具组合力学计算新方法

底部钻具组合(Bottom Hole Assembly, BHA)的力学计算是进行旋转导向系统钻具组合设计和井眼轨迹控制的基础．本文在纵横弯曲法、加权余量法和有限元法的基础上,提出了一种基于管柱单元组合的BHA力学求解方法．该方法以保持微分方程特解相同的条件作为管柱单元划分依据,对底部钻具组合进行单元划分;将管柱单元的挠曲线通解替代传统加权余量法的试函数,结合单元节点类型和组合关系,构建出包含边界条件和通解系数的线性方程组．对于边界条件未知问题,以支点反力符号条件为约束条件,以挠曲线越界程度、切点处弯矩平衡条件为目标函数,建立了以边界条件未知量为变量的多目标优化数学模型．应用多目标优化算法求解出边界变量,进而得出通解系数;最后,得出管柱单元内各点位移和载荷．以推靠式旋转导向系统BHA力学计算为案例,对比本文方法与加权余量法的计算结果,发现两者计算结果相差较小,表明本文方法可用于旋转导向系统底部钻具组合的力学计算．     

Simulation of three-dimensional polymer mould filling processes using a pseudo-concentration method

Mould filling processes, in which a material flow front advances through a mould, are typical examples of moving boundary problems. The moving boundary is accompanied by a moving contact line at the mould walls causing, from a macroscopic modelling viewpoint, a stress singularity. In order to be able to simulate such processes, the moving boundary and moving contact line problem must be overcome. A numerical model for both two- and three-dimensional mould filling simulations has been developed. It employs a pseudo-concentration method in order to avoid elaborate three-dimensional remeshing, and has been implemented in a finite element program. The moving contact line problem has been overcome by employing a Robin boundary condition at the mould walls, which can be turned into a Dirichlet (no-slip) or a Neumann (free-slip) boundary condition depending on the local pseudo-concentration. Simulation results for two-dimensional test cases demonstrate the model's ability to deal with flow phenomena such as fountain flow and flow in bifurcations. The method is by no means limited to two-dimensional flows, as is shown by a pilot simulation for a simple three-dimensional mould. The reverse problem of mould filling is the displacement of a viscous fluid in a tube by a less viscous fluid, which has had considerable attention since the 1960's. Simulation results for this problem are in good agreement with results from the literature. © 1998 John Wiley & Sons, Ltd.     

Practical techniques for a three‐dimensional FEM analysis of incompressible fluid flow contained with slip walls and a downstream tube bundle

Two practical techniques are proposed in this paper to simulate a flow contained in a plenum with a downstream tube bundle under a PC environment. First, a technique to impose slip wall conditions on smooth‐faced planes and sharp edges is proposed to compensate for the mesh coarseness relative to boundary layer thickness. In particular, a new type of Poisson equation is formulated to simultaneously satisfy both such velocity boundary conditions on walls and the incompressibility constraint. Second, a numerical model for a downstream tube bundle is proposed, where hydraulic resistance in a tube is imposed as a traction boundary condition on a fluid surface contacting the tube bundle end. The effectiveness of the techniques is numerically demonstrated in the application to a flow in a condenser water box. Copyright © 2001 John Wiley & Sons, Ltd.     

AN ARTIFICIAL BOUNDARY CONDITION FOR TWO-DIMENSIONAL INCOMPRESSIBLE VISCOUS FLOWS USING THE METHOD OF LINES

We design an artificial boundary condition for the steady incompressible Navier–Stokes equations in streamfunction–vorticity formulation in a flat channel with slip boundary conditions on the wall. The new boundary condition is derived from the Oseen equations and the method of lines. A numerical experiment for the non-linear Navier–Stokes equations is presented. The artificial boundary condition is compared with Dirichlet and Neumann boundary conditions for the flow past a rectangular cylinder in a flat channel. The numerical results show that our boundary condition is more accurate.     

Asymptotics for eigenvalues of the Laplacian with a Neumann boundary condition on a thin cut-out tubeComportement asymptotique des valeurs propres du laplacien avec conditions de Neumann sur un tube extrait

We consider the eigenvalue problem for the Laplace operator in a bounded three-dimensional domain where a thin tube is cut out. Imposing a Neumann boundary condition on the boundary of this tube, we construct asymptotics for eigenvalues on the small parameter that is a diameter of the tube. To cite this article: M.Yu. Planida, C. R. Mecanique 331 (2003).