Flow and heat transfer close to a rotating disk with wavy-shaped surface

Abstract

A numerical and theoretical study is performed for an incompressible, laminar rotating flow in a cylindrical container or over a disk. The endwall disk of the cylinder and the disk have a sinusoidal wavy surface shape or a concentrically grooved surface. The system Reynolds number is large, such that a boundary-layer flow pattern prevails. Comprehensive numerical solutions are established for various surface topography amplitudes and wave numbers. The major emphasis is placed on the surface roughness effect on the rotating flows. Solutions of boundary layer type governing equations are obtained and researches for full Navier-Stokes validation is conducted. In chapter 2, finite volume numerical solutions are obtained for the rotating flow in a cylindrical container that has a steadily rotating groove endwall disk. Details of flow fields are displayed for a large rotational Reynolds number, Re, of $O(10^4)$ and a cylinder aspect ratio Ar=1. The groove endwall disk shapes have a sinusoidal wavy or square wave form. The flow patterns in a cylinder and near the rotating bottom are scrutinized for the various groove amplitudes and wave numbers. The most distinct features are the intensification of azimuthal velocities for moderate bottom roughness. In order to systematically measure the intensification rate, the volume flow rates are calculated numerically. The flow activation is explained by an angular momentum transfer that initially starts from the rotating grooved disk and then moves along the meridional flows. For a qualitative analysis, the disk torque coefficients are calculated for various Reynolds numbers, groove amplitudes, and wave numbers. In chapter 3, an infinite wavy disk having a surface that is characterized by axisymmetric, sinusoidally-shaped roughness is also considered. The representative Reynolds number is large. Numerical solutions to the governing boundary-layer-type equations are acquired. Detailed flow data which describe the flow and h...