Theoretical Investigation of the Hydrodynamics Force Experienced by Two Approaching Spheres Immersed in a Slightly Viscous Fluid

• Main Authors: Cho-Ning Hunag, 黃卓寧
• Other Authors: 楊馥菱
• Format: Others
• Language: en_US
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/55849214630401253914

碩士 === 國立臺灣大學 === 機械工程學研究所 === 102 === This thesis investigates the hydrodynamic force for two immersed sphere approaching each other via theoretical analysis. The particle Reynolds number is assume to be high enough so that the boundary layer equation was solved in junction with the corresponding potential flow theory for the outer invisid flow. The potential flow when two immersed spheres of arbitrary size move along the line of centers at arbitrary velocity is solved first and a general formula for the pressure drag is developed. We then focus on the special case when the two spheres are identical and at the same approaching velocity. The inviscid pressure field is developed first and integrated into the boundary layer equation to solve the wall shear stress. Both the pressure and the shear stress were integrated along the sphere surface to obtain a pressure and a friction drag which were summed to give the total drag. Both force components increase monotonically with diminishing inter-sphere separation and hence the same trend is found for the total drag. Further, it is also found that pressure drag dominates the total drag in far field but becomes a minor role in contributing to the total drag when friction drag rise dramatically at small separations.