ABSTRACT

This paper presents a numerical method to solve a free-surface flow interacted by the vortex-shedding phenomena in a two dimensional shallow channel. The numerical model based on the stream function and vorticity formulation analyzes the viscous free-surface flow past a submerged obstruction on the channel bottom. The obtained results show those associated effects of the water depth, Froude number and Reynolds number on the studied problem.

INTRODUCTION

The vortex shedding behind a blunt body is an important and interesting phenomenon in fluid dynamics. It is also well known that the surface wave disturbed by the bottom irregularity can be greatly nonlinear in a shallow water channel. In this paper, we attempt to solve numerically both mixed flow patterns due to an approaching stream past a two-dimensional submerged obstruction fixed on the bottom of a long channel. The present study applies the stream function and vorticity formulation with the viscous free-surface conditions to simulate the flow field. Because the position of the free surface is not known a priori, the boundary-fitted grid, evolving with the motion of the free surface, should construct a better coordinate system in the analysis (Tang, 1991). Meanwhile, the control of the grid density can enable us to resolve the certain interested area as desired, and to improve the accuracy of solutions, such as those in the boundary-layer flow region near the solid surface. In addition, the adaptive grid control applied on the separation and reattachment points on the channel bottom stablizes the calculation procedure and represents a suitable physical nature of the transient flow pattern. The treatment of the unsteady viscous free-surface conditions is quite complete in the present study. The resulting algebraic expressions are then solved by the LSOR iterative scheme.

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