表面滑移球形粒子緩慢轉動之慣性效應

Effects of inertia on the slow rotation of a slip spherical particle

李明全(Ming-Chuan Lee)

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(2021年)

https://doi.org/10.6342/NTU202101944

摘要

本論文探討一個具有滑移表面的球形粒子在無邊界的靜止流體中，於微小但為有限值雷諾數情況下之緩慢轉動的慣性效應。吾人利用正規微擾法解析求解，將粒子周圍之軸對稱流動場對於微小的轉動雷諾數Re展開，此流動場展開式必須滿足Navier-Stokes方程式，並於需要時使用流線函數求解。吾人最終獲得流體作用於粒子之阻力矩展開到Re^3之表示式，此力矩展開式為粒子之無因次滑移係數的函數。從微擾法分析的結果中發現無慣性效應下之流場受到雷諾數的擾動自Re的一次項開始，這與粒子進行緩慢移動所得的拖曳力結果一致，然而對於無慣性效應下阻力矩的首次修正項則出現在Re^2，相較於作用在移動粒子上的無慣性效應下拖曳力，其首次修正項出現在雷諾數Re的一次項，粒子轉動雷諾數對阻力矩的影響顯得比較微弱。分析結果顯示正規化之阻力矩會隨著Re的增加而增加，隨著無因次滑移係數的增加而減少，這與慣性效應作用於一個緩慢移動之滑移粒子的拖曳力情形相似。作用在阻力矩上的慣性效應很明顯受到滑移係數的影響，且慣性效應的影響在具完全滑移表面的粒子時會消失。一般而言，慣性效應對阻力矩的影響在Re小於3時可以忽略，而在Re大於10的情況下變得顯著。

關鍵字

粒子轉動 ； 滑移表面 ； 慣性效應 ； 力矩

並列摘要

The steady rotational motion of a spherical particle with frictionally slip surface about a diameter in a quiescent unbounded fluid is studied analytically for a small but finite Reynolds number Re. The Navier-Stokes equation governing the axisymmetric fluid flow around the particle is solved by using a regular perturbation method. The expansion expression for the retarding torque exerted by the fluid on the particle good to Re^3 is obtained as a function of the scaled slip coefficient of the particle in closed form. This perturbation analysis shows that the perturbed fluid velocity field is of Re, the same as that for the translation of the particle, but the first correction to the hydrodynamic torque occurs at Re^2, much weaker than that to the hydrodynamic drag force acting on a translating particle which is still of Re. The hydrodynamic torque is found to be a monotonic increasing function of the Reynolds number and a monotonic decreasing function of the scaled slip coefficient, similar to the effect of fluid inertia on the hydrodynamic force on a slip particle undergoing translation. The inertial effect on the hydrodynamic torque, which can be a sensitive function of the slip coefficient and vanishes as the particle surface is fully slip, is generally negligible for the case of Re<3 but significant as Re is greater than about 10.

並列關鍵字

Particle rotation ； Slip surface ； Inertial effect ； Hydrodynamic torque

參考文獻

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