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A numerical study of incompressible Navier-Stokes equations in three-dimensional cylindrical coordinates.

机译：三维圆柱坐标系中不可压缩的Navier-Stokes方程的数值研究。

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摘要

This dissertation is on a numerical study in primitive variables of three-dimensional Navier-Stokes equations and energy equation in an annular geometry. A fast direct method is developed to solve the Poisson equation for pressure with Neumann boundary conditions in radial and axial directions, and periodic boundary conditions in azimuthal direction. The velocities and temperature are solved using Douglas-Gunn ADI method, which makes use of an implicit Crank-Nicholson scheme to discretize the governing equations. The numerical method developed in this study, after being validated by comparing the numerical solutions to analytical known solutions and results published in the literature, is then used to study thermocapillary convection, Rayleigh-Benard convection, and Taylor-Couette flow.; In the thermocapillary convection in an annulus with heated inner cylinder, the free surface was assumed to be flat. The resulting flow is two-dimensional and axisymmetric. The flow becomes three-dimensional when a theta-dependent temperature boundary condition is applied on the inner cylinder.; Numerical solution of Rayleigh-Benard convection in a shallow annular disk results in two-dimensional axisymmetric flow when the Rayleigh number is above a critical value. A layer of concentric rolls are formed encircling the inner cylinder. The axisymmetricity and concentricity are destroyed by an initial temperature disturbance at a single grid point, or a non-uniform boundary condition on the bottom.; Numerical solution of Taylor-Couette flow results in a series of axisymmetric toroidal rolls which encircle the inner cylinder between the cylinders and are stacked in the axial direction when Taylor number exceeds a critical value. As Taylor number further increases, the flow becomes non-axisymmetric and azimuthal waves are formed and superimposed on the Taylor vortices (wavy vortex flow).
机译：本文是对环形几何中三维Navier-Stokes方程和能量方程的原始变量的数值研究。提出了一种快速直接方法来求解泊松方程的压力，其中径向和轴向具有Neumann边界条件，方位角方向具有周期性边界条件。使用Douglas-Gunn ADI方法求解速度和温度，该方法利用隐式Crank-Nicholson方案离散控制方程。通过将数值解与已知的解析解和文献中发表的结果进行比较，验证了本研究中开发的数值方法，然后将其用于研究热毛细管对流，瑞利-贝纳德对流和泰勒-库埃特流。在带加热内筒的环带中的热毛细管对流中，自由表面被认为是平坦的。产生的流动是二维的并且是轴对称的。当在内胎上施加与θ相关的温度边界条件时，流动变成三维。当瑞利数大于临界值时，浅环形盘中瑞利-贝纳德对流的数值解会导致二维轴对称流动。围绕内筒形成一层同心辊。轴对称性和同心度被单个网格点处的初始温度扰动或底部的不均匀边界条件所破坏。泰勒-库埃特流的数值解导致一系列轴对称的环形辊，当泰勒数超过临界值时，这些辊围绕着圆柱体之间的内圆柱体并沿轴向堆叠。随着泰勒数的进一步增加，流变为非轴对称，并且形成了方位波并将其叠加在泰勒涡旋上（波浪涡流）。

著录项

  • 作者

    Zhu, Douglas Xuedong.;

  • 作者单位

    The Ohio State University.;

  • 授予单位 The Ohio State University.;
  • 学科 Engineering Mechanical.
  • 学位 Ph.D.
  • 年度 2005
  • 页码 153 p.
  • 总页数 153
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 机械、仪表工业;
  • 关键词

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