中空多孔球形粒子在球形孔洞中之緩流運動

Creeping motions of a porous spherical shell in a concentric spherical cavity

呂揚生(Yang-Sheng Lu)

指導教授 ： 葛煥彰

國立臺灣大學/工學院/化學工程學研究所/碩士(2004年)

https://doi.org/10.6342/NTU.2004.00372

摘要

本文是以解析方法探討一球形對稱多孔殼粒子於一充滿不可壓縮牛頓流體的球形孔洞中央位置的擬穩態移動現象與穩態轉動現象。在流體可穿透的多孔球殼中，假設各處的流體流動摩擦阻力是均勻分布的。於Reynolds數很小的情況下，分別以Brinkman與Stokes方程式求解多孔殼內外之流體速度分布，進而計算出流體作用於多孔球殼的拖曳力及力矩，此力及力矩分別與多孔球殼之移動速度及轉動角速度成正比。對於一給定系統，球殼的正規化移動及轉動的可動度隨著其可滲透度的減少呈現單調遞減的狀況。在一般的情況下，孔壁邊界效應對於多孔球殼之緩流運動，具有相當顯著的影響。在某些特殊狀況下，一多孔球殼之阻力及力矩的解或移動及轉動可動度的解可被視為與一固體實心球粒及一均勻多孔球粒的解相同。

關鍵字

邊界效應 ； 多孔球殼 ； 多相流,緩流

並列摘要

An analytical study is presented for the quasisteady translation and steady rotation of a spherically symmetric porous shell located at the center of a spherical cavity filled with an incompressible Newtonian fluid. In the fluid-permeable porous shell, idealized hydrodynamic frictional segments are assumed to distribute uniformly. In the limit of small Reynolds number, the Stokes and Brinkman equations are solved for the flow field of the system, and the hydrodynamic drag force and torque exerted by the fluid on the porous shell which are proportional to the translational and angular velocities, respectively, are obtained in closed forms. For a given geometry, the normalized wall-corrected translational and rotational mobilities of the porous shell decrease monotonically with a decrease in its permeability. The boundary effects of the cavity wall on the creeping motions of a porous shell can be quite significant in appropriate situations. In the limiting cases, the analytical solutions describing the drag force and torque or mobilities for a porous spherical shell in the cavity reduce to those for a solid sphere and for a porous sphere.

並列關鍵字

Creeping ； Porous spherical shell ； Multiphase flow

參考文獻

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