Fluid Force on Moving Particles with Non-uniform Velocity

變速運動顆粒體上的流體作用力研究

周雙(SHUANG ZHOU) ； 張根廣(GENGUANG ZHANG) ； 王愉樂(YULE WANG) ； MAN CHANDARA

《台灣水利》 68卷2期 (2020/06) Pp. 78-87

https://doi.org/10.6937/TWC.202006/PP_68(2).0007

摘要

In order to study the fluid force of non-uniform moving particles, the settlement process of glass sphere ＂particles＂ of different sizes was recorded by a high-speed camera. Based on the nonlinear relationship between the instantaneous settling velocity, and the process time of the glass sphere particles' settlement, formulas for particle settling velocity and critical Reynolds number are provided. Formulas for the total time and distance required for a particle to reach its settling velocity are also given. From the dynamic analysis of the settling motion of the observed particles, the fluid force coefficient of a particle body with a varying velocity is derived, and the relationship between the coefficient and the particle size is presented. In addition to the density of the solid particles and the density and viscosity of the liquid, the drag coefficient of non-uniform moving particles is mainly affected by the particle's size and the Reynolds number. Comparison with natural gravel measured data and other published formulas, shows that our proposed formula is not only applicable to moving particles with non-uniform velocity, but also to the fluid force law of moving particles with uniform velocity; and is in good agreement with the natural gravel measured data. This study can therefore be used as a reference for bed load motion characteristics studies and sediment incipience research.

關鍵字

Reynolds number ； Fluid force ； Spherical particles ； Settling velocity ； High-speed camera system

並列摘要

為了探索非勻速運動顆粒的流體阻力規律，作者採用高速攝影技術，對不同粒徑玻璃圓球顆粒的沉降過程進行觀測。本文基於圓球顆粒沉降過程中的瞬時沉降速度與時間變量間呈現的非線性關係，提出一種顆粒沉速的判定標註，給出了顆粒沉速與臨界雷諾數的表達式，同時建立了顆粒達到沉速時所經歷的時間、沉降距離的表達式。通過對顆粒的沉降運動過程進行動力分析，推導得到變速運動顆粒體的流體阻力係數計算式，並給出式中係數與粒徑間的定量關係。變速運動顆粒的阻力係數除受固體顆粒的密度、液體的密度及液體粘性的影響外，主要受粒徑和雷諾數影響。與天然礫石實測資料及其他研究者公式的對比結果表明，本文公式不僅適用於非定常運動顆粒體的流體阻力計算，同樣適用於定常運動顆粒體的流體阻力計算，且與天然礫石阻力係數的實測數據符合較好。本文對推移質運動特性研究、泥沙起動研究有一定的借鑒意義。

並列關鍵字

雷諾數 ； 流體阻力 ； 圓球顆粒 ； 沉速 ； 高速攝影