光彈顆粒斜坡流中顆粒角速度之量測開發與非侵入式應力量測之探討

Abstract

顆粒流的運動是複雜的，我們使用光彈圓盤作為顆粒材料，利用它的雙折射性質來測量流場應力分佈，試圖更好地描述穩態斜坡顆粒流的本構關係，解析顆粒流從自由表面處以碰撞為主形成之快速運動的類氣體型態是如何連續地轉變至底部以摩擦為主的慢速運動類固體型態，找出中間過渡區的作用機制也是至關重要的。 依循既有理論，應力可區分成摩擦與碰撞兩種形式，來自單顆粒碰撞引起的應力分量，可透過顆粒動力學理論估計；而因顆粒摩擦所生成之應力，則可藉由光彈材料特有的梯度平方法來度量。本研究在陳[12]的研究上深化，旨在找出顆粒之間的摩擦在流動應力模型中是如何發揮作用的，並撰寫影像處理演算法，從有複雜光條紋的光彈顆粒影像中擷取所需資訊，包含前人開發的PTV[8]與光條紋特徵角演算法[12]外，我們進一步發展影像處理技術同步量測角速度。 我們參考陳[12]進行應力分析，除了依文獻測量條紋強度來估計摩擦法向應力外,也透過自有影像處理演算法來測量條紋角度以估計摩擦切向應力。透過光彈顆粒的溜槽實驗，將碰撞和摩擦應力這兩種分量與解析靜水壓進行比較,以確認應力確實從表面的純碰撞過渡到無滑移底部的純摩擦，發現摩擦與碰撞應力確實有互補性，但顆粒相互作用在碰撞和摩擦之間交替的過度區,相較於總應力的大小,碰撞和摩擦應力分量的疊加會低估。 換句話說，顆粒間交互作用微觀機制二分法的假設不夠詳盡，我們引入側牆摩擦應力與顆粒轉動離釐清可能不足的原因，顆粒轉動在過度區為顆粒的其他機轉機制或是儲能方式。

The motion of granular materials is complex and its constitutive relation is on demand for flow prediction and control. In particular, we study the dynamics and try to understand stress distribution in a steady inclined surface flow of photoelastic disks. In fact, granular flow stress can be decomposed into two types: frictional and collisional stress. The collision-induced stress component results from individual grain collisions and can be described by the granular kinetic theory [1] provided that flow dynamics (density, velocity, and granular temperature) can be measured. The other friction-induced stress comes from inter-grain friction and is associated with how a grain interacts with its neighbors through long-lasting contact. To see how granular flow continuously transits from a fast-moving gas-like form dominated by collision near the free surface to a slow-moving solid-like form dominated by friction at the bed, it is also crucial to find out the transition zone between the two, therein, properties of granular flow are quite unstable. Hence, an experimental method that can achieve concurrent measurement of flow dynamics and its stress components is highly desired and this study presents a non-intrusive stress measurement technique by exploiting the birefringence properties of photoelastic disks. We apply the gradient square method (G2) [2] to measure the mean normal stress from frictional contacts. We further develop a new method to estimate the tangential frictional stress using another feature of the fringe image. We calibrate the fringe-based method on a static pile and apply it to a steady surface flow of photoelastic disks. Furthermore, we program the image processing algorithm to extract disk dynamics from the experimental image of photoelastic disks with complex and fast-changing light fringes. In addition to the developed Particle Tracking Velocimetry (PTV) [8] and fringe angle algorithms [12], we further advance image processing techniques to synchronize angular velocity measurements. Drawing from Chen [12], we conduct stress analysis. We compare the superposition of the collisional and the frictional stress with the analytic hydrostatic profiles and find that the stress is pure collisional near the surface but pure frictional in a deeper bed and is well reproduced by the fringe-based method. However, the superposition of collisional and frictional stress underestimates the transition zone where particle interactions alternate between collisions and friction. Frictional and collisional stress are indeed complementary, but the duality is inadequate when explaining the microscopic mechanism of the inter-discs. To address potential deficiencies, we introduce wall sliding frictional stress and particle rotation to clarify the underlying reasons.