Numerical Analysis of Groundwater Flow in a Bore Hole with a Cylindrical Obstacle: Basic Relationship for Measurement of Seepage Flow Velocity

A numerical analysis and an experiment were done on groundwater flow past a bore hole with a cylindrical obstacle at its center. Flow around the obstacle in the bore hole was studied in detail. Two dimensional governing equations to simulate this flow were written for the hydraulic head and seepage velocity in a porous medium and for the vorticity, stream function, and velocity in the bore hole. These equations were non-dimensionalized and solved by using the alternating direction implicit and successive-over-relaxation finite difference methods. Flow visualization experiments and velocity measurements in the bore hole were done with a two dimensional model composed of a porous medium. The numerical analysis procedures were validated by a comparison of numerical and experimental results. Effects of the Reynolds number and obstacle size on flow in the bore hole are clearly shown in the velocity and streamline profiles. The quantitative relation between the seepage velocity in the porous medium and the velocity of flow around the obstacle in the bore hole also were estimated.