顆粒形狀對顆粒體在旋轉鼓內流動行為之影響

楊意驊(Yi-hua Yang)

指導教授 ： 鍾雲吉

國立中央大學/工學院/機械工程學系/碩士(2015年)

摘要

本研究利用離散元素法(DEM, discrete element method)模擬球形及非球形顆粒在類二維的旋轉鼓中的運動行為。本研究旨在探討因顆粒形狀所產生的差異，利用多球法分別組成球形、雙球形、兩種橢球形及膠囊形顆粒，藉由計算不同的填充率及轉速下旋轉鼓中顆粒的擾動速度分佈、粒子溫度、擴散位移、和平均動能等傳輸性質，探討五種形狀顆粒的流動行為。本研究結果顯示，深度方向及旋轉方向的流動層擾動速度分佈呈現馬克士威速度分佈，且以膠囊形速度最均勻，旋轉方向的擾動速度分佈圖中，其旋轉速度的均勻程度以膠囊形最大、球形最小，且不隨旋轉鼓受載條件改變而影響。粒子溫度的結果則顯示五種形狀顆粒的總體粒子溫度趨勢與平移的粒子溫度相近，且因受到互鎖效應之影響，使得各形狀顆粒的分佈及大小皆有不同。五種顆粒的擴散位移與時間的關係圖趨勢相當接近直線，旋轉的擴散係數以球形最大、橢球形Ⅱ最小，且其大小排序也不隨旋轉鼓受載條件改變而影響。平均動能的結果則顯示，顆粒的堆積崩塌與顆粒形狀有密切相關，使各形狀顆粒的圖形並不交疊。沿著深度方向的速度分佈可以發現，主動層呈現混合型的流況，且愈接近主動層表面，則各形狀顆粒的差異愈明顯。剪應變率的結果顯示，以橢球形Ⅱ成長最快且有最大的剪應變率，而膠囊形的剪應變率則為最小，最大剪應變率則發生在距主動層約4顆顆粒短軸直徑處。在翻滾形態時，流動層的形狀會隨轉速變化，且各形狀顆粒的流動層形狀及變化皆不相同。動態安息角的部分則發現，除了雙球形顆粒之外，動態安息角會隨轉速的變大而增加，而填充率增加也會使其小幅提升，雙球形顆粒則因受到較強的互鎖效應之影響，使其只有在較高轉速下才有此現象，動態安息角幾乎以球形為最小，橢球形Ⅱ則略大於橢球形Ⅰ，膠囊形顆粒則大致介於橢球形Ⅰ及球形之間。

關鍵字

顆粒物質 ； 旋轉鼓 ； 非球形顆粒 ； 形狀效應 ； 離散元素法

並列摘要

This thesis studies dynamic behavior of spherical and non-spherical particles in a qusi-2D rotating drum by using discrete element method (DEM) simulation. The purpose of this study is to investigate the effect of particle shape on the flow behavior of granular materials. Five kinds of particles with different shapes, namely spherical, cylindrical, ellipsoidalⅠ(aspect ratio of 1.5), ellipsoidalⅡ (aspect ratio of 2.0) and paired particles, are selected and made up of spherical elements by using multi-sphere method. The transport properties, including the local average velocities, local fluctuation velocities, granular temperatures, fluctuation velocity distributions and self-diffusion coefficients, were calculated for investigating the shape effect. The numerical results show that the distributions of fluctuation velocity in the transverse and rotational directions are very close to the Maxwellian distributions, and that the cylindrical particles exhibit the most uniform velocity distribution. The total and translation granular temperatures are almost equal, indicating that the flow behavior is not dominated by particle rotation but particle translation. The particle shape effect leads to the differences in the magnitude and distribution of the granular temperatures. The mean square diffusive displacements and rotations increase linearly with time. In the diffusive rotations, spherical and ellipsoidalⅡ particles respectively produce the largest and smallest self-diffusion coefficients. The stream-wise velocity along with depth shows a mixed velocity profile for the five kinds of particles, and the maximum shear rate occurs beneath the flowing surface (about four times particle diameter in depth). The ellipsoidalⅡ particles exhibit the highest shear rate, whereas the cylindrical particles exhibit the lowest shear rate. The paired particles have the strongest inter-locking effect, hence inducing the largest dynamic angle of repose.

並列關鍵字

granular assembly ； rotating drum ； non-spherical particle ； shape effect ； DEM

參考文獻

[1] A. Rosato, K. J. Strandburg and F. Prinz, and R. H. Swendsen, “Why the Brazil nuts are on top: size segregation of particulate matter by shaking” Physical Review Letters, 58 (1987) 1038-1040.

[2] D. V. Khakhar, J. J. McCarthy, and J. M. Ottino, “Radial segregation of granular mixtures in rotating cylinder” Physics of Fluids, 9 (1997) 3600-3614.

[3] Y. Xu, C. Xu, Z. Zhou, J. Du and D. Hu, “2D DEM simulation of particle mixing in ro-tating drum: A parametric study” Particuology, 8 (2010) 141-149.

[4] H. Henein, J. K. Brimacomble, and A.P. Watkinson, “Experimental study of transverse bed motion in rotary kilns” Metallurgical Transactions B, 14 (1983) 191-205.

[5] J Rajchenbach., “Flow in powders: from discrete avalanches to continuous regime,” Physical Review Letters, 65 (1990) 2221-2224.