影像量測顆粒角速度於穩態傾斜顆粒流之研究

Study of an image-based angular velocity measurement technique for its use in steady inclined granular flows

陸宏昱(Hong-Yu, Luh)

指導教授 ： 楊馥菱

國立臺灣大學/工學院/機械工程學研究所/碩士(2019年)

https://doi.org/10.6342/NTU201904049

摘要

本論文為了研究聚甲醛顆粒個別的轉動在粗糙傾斜滑道實驗中有效牆摩擦係數和顆粒運動的關係利用高速攝影機捕捉影像資訊並透過林跟楊提出的影像方法量測顆粒轉動[5]。透過荷重元量測牆摩擦係數，並且與楊跟黃[3]根據離散元素法模擬到的結果比較牆摩擦係數的趨勢。本實驗滑道傾斜角為20度，藉由調整開口高度來控制流量，開口高度為9公分，11公分，13公分和15公分。
為了改進影像處理量測顆粒轉動的技術，我們引進條件數跟弧長來改進計算的結果。再計算之前我們先過濾掉條件數大於1012的情況來優化演算法。得到顆粒轉動的結果後，我們計算了無因次化參數Ω=(R|ω|)/(〖|v〗_x |)並且用不同的平均方法來比較結果，再比較Ω跟有效牆摩擦係數的關係。我們發現顆粒的轉動運動會影響有效牆摩擦係數，我們可以透過Ω跟有效牆摩擦係數的量值來了解當下顆粒流流動時對邊牆造成的影響。

關鍵字

傾斜顆粒流 ； 顆粒轉動 ； 有效牆摩擦係數 ； 條件數

並列摘要

This thesis studies the rotational motion of individual spheres from the high-speed digital images captured at the boundary of a steady inclined granular flows based on the image processing technique proposed by Lin and Yang [5]. We also measured the effective wall friction coefficient by an array of load cells to study how its trend is associated with the grain motion following Yang and Huang [3]. The flow was generated by releasing spheres of diameter D = 6 mm down an incline at 20.0° and we changed the reservoir opening height ( 9, 11, 13, and 15 cm, respectively to achieve different volume flow rate.
To Improve the image processing technique for estimating rotational algorithm, we applied the condition number and the arc length in this algorithm. If the condition number is larger than 1012, we discarded those cases. The condition number criterion can affect the performance about 2~5 %. After collecting rotating information, we calculated dimensionless variable Ω=(R|ω|)/(〖|v〗_x |) through two different average schemes, and compared the relation with the effective wall coefficient of friction.

並列關鍵字

inclined granular flow ； grain rotation ； effective wall friction coefficient ； condition number

參考文獻

[1] Datta, B. N. Numerical Linear Algebra and Applications 2nd Edition.

[2] Hsu, Z.-W. Experimental investigation of effective wall friction coefficient for steady dry dense granular flows down a rough incline.

[3] Huang. Y.-T., Yang. F.-L., Lin. S.-R. 2017 Indirect measurement of μ(I) relation from finite granular avalanche down an inclined narrow reservoir of smooth bed. Granular Matter 19, 51.

[4] Jop, P., Forterre, Y. & Pouliquen, O. 2006 A constitutive law for dense granular flows. NATURE. 441, 727-730.

[5] Lin. C.-C., Yang. F.-L., 2018 A new image processing algorithm for three-dimensional angular velocity measurement and its application in a granular avalanche. Advanced Powder Technology 29, 506-517.