Theoretical Investigation of Hydrodynamic Force when Dual Spheres Move Constantly and Perpendicularly to the Line of Centers

• Main Authors: Kuan-Yu Chen, 陳冠宇
• Other Authors: 楊馥菱
• Format: Others
• Language: en_US
• Published: 2017
• Online Access: http://ndltd.ncl.edu.tw/handle/fdxm45

碩士 === 國立臺灣大學 === 機械工程學研究所 === 105 === This thesis integrates potential flow theory and boundary layer theory to derive an approximate flow solution when two rigid spheres move constantly and perpendicularly to the line connecting their centers in an incompressible fluid of infinite extent. Particular interest is to derive the hydrodynamic force when the two spheres are kept at various separation distances. Potential flow theory is first applied to derive the inviscid force experienced by the spheres and the spheres are shown to attract each other when moving side-by-side. Furthermore, the phenomenon of the stagnation points shifting away from the foremost and the rearmost points of the spheres due to the presence of a second sphere is observed. Viscous force acting on the spheres is approximated by the boundary layer theory using the pressure field solved from the inviscid problem. Due to flow asymmetry from the foremost sphere point, an approximation based on Blasius series method is proposed to estimate the drag coefficient. The approach successfully captures the trend of decreasing drag coefficient with increasing gap between the spheres, observed in experiments and simulations, at single sphere Reynolds number of 100. However, quantitative discrepancy is found and will be discussed together with the model limitations and implementation issues.