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

Zhu, Douglas Xuedong
http://rave.ohiolink.edu/etdc/view?acc_num=osu1118433979

Abstract Details

2005, Doctor of Philosophy, Ohio State University, Mechanical Engineering.
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, Reyleigh-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 angular 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 on the resulting wavy vortex flow.
Seppo Korpela (Advisor)
Engineering, Mechanical
velocity; convection; free surface; Poisson equation; boundary conditions

Recommended Citations

Citations

  • Zhu, D. X. (2005). A numerical study of incompressible Navier-Stokes equations in three-dimensional cylindrical coordinates [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1118433979

    APA Style (7th edition)

  • Zhu, Douglas. A numerical study of incompressible Navier-Stokes equations in three-dimensional cylindrical coordinates. 2005. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1118433979.

    MLA Style (8th edition)

  • Zhu, Douglas. "A numerical study of incompressible Navier-Stokes equations in three-dimensional cylindrical coordinates." Doctoral dissertation, Ohio State University, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=osu1118433979

    Chicago Manual of Style (17th edition)

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© 2005, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.