低雷诺数下不可压缩流动问题的三维EFG法分析

发布时间：2018-06-20 08:57

本文选题：EFG法 + N-S方程　；参考：《湘潭大学》2017年硕士论文

【摘要】：目前,流体力学中非线性偏微分方程的求解有各式各样的数值解法。基于单元的数值方法在求解流体力学问题时均需要利用单元进行计算区域的离散,这不便于求解和应用。无单元Galerkin(Element-Free Galerkin,EFG)法作为一种有巨大研究及应用价值的数值方法,其采用的是基于离散点的近似,不需要单元信息,不仅便于处理复杂边界,而且计算准确,因此不少学者将其应用于流体力学问题的求解。近年来EFG法在流体力学领域的应用仍然处于发展阶段,而且主要用于求解二维流场问题,但是很多实际流动问题往往不能简化为二维流动问题进行分析,故本文以低雷诺数下三维不可压缩粘性流体流动为研究对象,以EFG法和计算流体力学为理论基础,编写计算程序对其流动进行数值研究,全文的主要研究工作和所得结论如下:(1)推导出三维Stokes流动的EFG法离散控制方程,以推导的离散方程和EFG法理论为依据编写算法程序对具有精确解的三维Stokes方程进行了求解,验证了所编程序和算法是有效可靠的。将其应用于立体空腔Stokes流动问题的求解时,重点分析了不同速度比和高宽比对流动的影响,数值结果表明随着速度比S值的增加,其内部流态由四个临界值分成五个不同的阶段;随着高宽比A的变化,其内部漩涡也经历了由一个到两个,随后又只有一个,接着发展为多个漩涡的过程。(2)考虑惯性项的作用,建立了三维定常Navier-Stokes(简称N-S)方程的EFG法离散表达式,编写程序数值研究了180°圆形截面弯管的流动特性,重点探究雷诺数和曲率直径比对其流场和漩涡生成的作用。结果表明,在曲率直径比相同时,入口雷诺数的取值影响着弯管内迪恩漩涡的结构和强度;在雷诺数相同时,理尼漩涡在小的曲率直径比弯管中出现的地方靠近弯曲段前沿,而在大的曲率直径比弯管中则往后一些。另外,弯管内速度和压力的分布受曲率直径比变化的影响更为明显。(3)考虑到与时间有关的流动情况,采用θ加权法进行时间项的离散,完成三维非定常N-S方程的EFG法离散格式的推导,编写求解程序对并列圆柱在低雷诺数下的绕流展开分析。结果显示,并列圆柱的三维流动特性明显,不同雷诺数下并列圆柱中的尾流形态存在差异。本文运用EFG法对三维定常Stokes流动、考虑惯性项的弯管定常流动以及考虑时间项的并列圆柱非定常流动展开了数值模拟,计算结果准确反映了其三维流场情况,给工程应用提供了一些有效的指导。
[Abstract]:At present, there are various numerical methods for solving nonlinear partial differential equations in fluid mechanics. The numerical method based on element is not easy to solve and be applied to solve the hydrodynamic problems because it needs to use the element to discretize the computational region. As a numerical method with great research and application value, the element-free Galerkini Element-Free Galerkini (EFG) method is based on discrete point approximation and does not require element information. It is not only convenient to deal with complex boundaries, but also accurate in calculation. Therefore, many scholars apply it to solving hydrodynamic problems. In recent years, the application of EFG method in the field of fluid mechanics is still in the developing stage, and it is mainly used to solve two-dimensional flow field problems. However, many practical flow problems can not be simplified to two-dimensional flow problems for analysis. Therefore, in this paper, the three-dimensional incompressible viscous fluid flow at low Reynolds number is taken as the research object, and the EFG method and computational fluid dynamics are used as the theoretical basis. The main research work and conclusions are as follows: (1) the EFG discrete governing equations of three-dimensional Stokes flow are derived. Based on the derived discrete equations and EFG theory, the three-dimensional Stokes equations with exact solutions are solved. The program and algorithm are proved to be effective and reliable. When it is applied to solve the Stokes flow problem in a solid cavity, the effect of different velocity ratio and aspect ratio on the flow is analyzed. The numerical results show that the flow rate increases with the increase of the velocity ratio. Its internal flow pattern is divided into five different stages from four critical values. With the change of aspect ratio A, the internal vortex also goes from one to two, then only one, and then develops into a number of whirlpools. The EFG discrete expression of the three-dimensional steady Navier-Stokes equation is established. The flow characteristics of 180 掳circular section bends are studied numerically. The effects of Reynolds number and curvature diameter ratio on the flow field and vortex generation are investigated. The results show that when the ratio of curvature to diameter is the same, the value of inlet Reynolds number affects the structure and strength of the Dean vortex in the bend, and when the Reynolds number is the same, the Lennis vortex is near the front of the bend section in the small curvature diameter ratio. In larger curvature diameters than in bends, a little later. In addition, the distribution of velocity and pressure in the bend is more obviously influenced by the change of curvature diameter ratio. Considering the time-related flow, theta weighted method is used to discretize the time term. The EFG discretization scheme of three-dimensional unsteady N-S equations is derived, and a program is written to analyze the flow around a parallel cylinder at low Reynolds number. The results show that the three-dimensional flow characteristics of parallel cylinders are obvious, and the wake patterns of parallel cylinders are different under different Reynolds numbers. In this paper, the EFG method is used to simulate the steady flow of three-dimensional steady Stokes flow, the steady flow of curved pipe with inertia term and the unsteady flow of parallel cylinder with time term. The calculated results accurately reflect the three-dimensional flow field. It provides some effective guidance for engineering application.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O35;O241.82

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