A Numerical Study on Turbulent Oscillatory Plane Couette Flow

This dissertation, "A Numerical Study on Turbulent Oscillatory Plane Couette Flow" by Wai-man, Ho, 何慧敏, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of the thesis entitled A Numerical Study On Turbulent Oscillatory Plane Couette Flow Submitted by Wai-man Ho for the degree of Master of Philosophy at The University of Hong Kong in June 2004 Steady turbulent plane Couette flow can be readily solved by assuming that the classical log-laws hold locally near the walls. In a sharp contrast, no simple analyses are available if the flow becomes unsteady, as in the case when one of the walls oscillates periodically with time in its own plane. Difficulties arise owning to the time-dependent accelerating terms in the Navier-Stokes equations. The oscillatory boundary may lead to a periodic flow reversal and therefore a detachment of the boundary layer from the wall. Therefore the classical theory of wall turbulence no longer applies to the turbulent oscillatory plane Couette flow. The problem is now handled with the computational technique known as direct numerical simulation (DNS). In this study, turbulent structures and passive scalar transport in an oscillatory plane Couette flow at Reynolds number of 5000 are studied numerically by solving the unsteady incompressible Navier-Stokes equations directly. The oscillatory plane Couette flow consists of a working fluid isandwiched between a lower stationary wall and an upper wall that moves with a prescribed velocity of UA =1+ sin(2πft), where the velocity ratio A = 0, 1/4 and 1/2. The calculation is made using a three-dimensional trilinear Galerkin finite element code. Implicit coupling between velocity and pressure is handled by a fractional-step method. The convection and diffusion terms are respectively computed by the third-order accurate Runge Kutta method and the second-order accurate Crank-Nicolson method. In the oscillatory flow, the velocity and its components are significantly influenced under the wall-oscillation. The scalar transport, however, almost exhibits a consistency in the flows. Comparisons are also made of temperature fluctuations, correlation coefficients, shear stress and heat flux. Although there is no symmetry in the oscillatory-flow channel, most of the DNS data still agrees well with the lower part of the steady-flow channel. Finally, the flow visualization further illustrates the mechanism of high-speed fluid and hot streaky structure. ii DOI: 10.5353/th_b2977083 Subjects: Turbulence - Mathematical models Fluid dynamics