| Summary: | 碩士 === 國立臺灣大學 === 機械工程學研究所 === 89 === In this thesis, the drag force on the sphere moving constantly in a low-Reynolds-number pipe flow is investigated via numerical calculation. The incompressible Navier-Stokes equations are formulated in a pseudo-compressibility form. The numerical scheme makes use of a finite volume strategy and the numerical flux term are evaluated using the Total-Variation Diminishing (TVD) technology commonly applied to the compressible flow. Steady solution is obtained by marching (iterating) in time until the artificial time derivative of pressure term in the continuity equation drops to zero.
In the final calculation, six different Reynolds numbers (Re) ranging from 0.1 to 1 and 7 different pipe diameter and sphere diameter ratios (D/d) are selected. In each case, the drag force on the sphere is calculated and the results are compared with the existing approximate theoretical values derived from correcting the Stokes’ formula. Both results agree well in trends, the slight deviation is due to the fact that theoretical value were obtained based on the linearized Navier-Stokes equations (Stokes creeping-flow equations), while the fully nonlinear form of the Navier-Stokes equations are adopted in the present calculations. Finally, a least-squared regression technique is applied to collapse the calculated result into a single expression exhibiting the functional relationship between the drag force and the Reynolds numbers (Re), and the pipe- sphere diameter ratio parameter (D/d).
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