傾斜平滑儲存槽內定量乾顆粒崩塌流之有效摩擦係數之實驗量測

Experimental Investigation of Effective Friction Coefficient for Finite Dry Granular Mass in Avalanche down an Inclined Smooth Reservoir

魏立(Li Wei)

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(2018年)

https://doi.org/10.6342/NTU201802919

摘要

本論文透過實驗來探究有限質量乾顆粒於平底傾斜儲存槽內崩塌之動態及流變行為，其目的為利用近二維控制體積同時分析顆粒所受之內摩擦力及牆摩擦力進而計算其摩擦係數與無因次慣性數(inertial number, I)之μ-I流變關係是否也與在針對穩態均勻顆粒流之μ-I流變關係相似以及在牆摩擦係數為未知數之情況下是否可以利用此分析方法量測出其隨深度衰退之關係。
實驗上以高速攝影機記錄位於儲存槽牆邊之顆粒運動，所錄製之影像透過影像處理標定及追蹤求得顆粒速度，再利用面積加權平均取得此顆粒流之平均顆粒密度ϕ(t,x,y)、流向速度U(t,x,y)以及徑向速度V(t,x,y)，並將此類資訊代入近二維控制體積分析搭配由黃永達(2015)之離散元素法模擬所提供之資訊進一步求得摩擦力及其係數。
另外，為了解決未知數多於方程式的問題，除了透過黃永達(2015)之離散元素法模擬所提供之資訊外，在假設為固體旋轉體下力矩方程式被考慮用來連結內摩擦力與角速度之間的關係，離散元素法模擬所提供之資訊包含正向應力的分布以及非等向性正向應力之關係。我們得到摩擦係數隨深衰退之關係以及μ隨慣性數I遞增之關係。
最後，將牆面玻璃利用水刀加工切割出十個矩形區域並安裝荷重元傳感器直接量測崩塌狀態下顆粒與牆面的剪切與正向力，得到並驗證了牆摩擦係數隨深度遞減之關係。

關鍵字

乾顆粒材料 ； 崩塌行為 ； 控制體積分析 ； 有效摩擦係數 ； μ-I流變關係式 ； 荷重元傳感器

並列摘要

This work investigates the dynamics and rheology of a finite number of dry granular spheres in avalanche down a narrow inclined reservoir of smooth frictional bed and glass-made walls at different inclination angles. Systematic experiments were conducted and high-speed imaging technique was used to measure the bulks properties at the sidewall based on individual sphere dynamics. Flow streamwise, transverse velocity components and solid volume fraction U(t,x,y), V(t,x,y) and ϕ(t,x,y) were employed in a quasi-two-dimensional control volume analysis.
The objective is first to extract normal stress, isotropic internal stress, and wall frictional stress all together and hence an additional equation of motion is required and we used the balance equation of angular momentum. Depth profiles of these stress and flow variables were reported at different streamwise locations and collected onto the same plot to examine how the internal and wall friction coefficient varies with local inertial number.
On the other hand, in order to solve the three-unknown parameters problem, we add a torque equation which connects the internal frictions and angular velocity. And apply the discrete element method data from the previous work by Yung-TA Huang to define the pressure force and the application of non-isotropic normal stress to solve the frictions. Then we calculate the friction coefficients of wall and internal and found that the depth weakening phenomenon of both coefficients. Moreover, both friction coefficients grow with I increases.
Finally, the glass wall is cut off ten rectangle areas and then the load cell sensors are set on to directly measure the wall shear and normal forces during avalanche. The depth weakening phenomenon of wall friction coefficient is observed and verified.

並列關鍵字

dry granular material ； avalanche ； control volume analysis ； effective friction coefficient ； μ-I rheological law ； load cell sensors

參考文獻

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