穩態乾顆粒流於粗糙傾斜槽中流變特性之直接與間接量測

Abstract

本論文利用系統性直接與間接之量測方法探討乾顆粒流於粗糙傾斜滑道中之流變行為。透過陣列荷重元直接量測顆粒流與底床及側邊界之正向與側向交互作用力，並進一步求得相對應之底床與側牆摩擦係數 μ 及 μ_w。此外，我們利用側向高速影像求得顆粒流運動資訊與荷重元擷取表面作用力，搭配擬二維控制體積法來分析動量守恆，在靜水壓力的假設下反求流場內部摩擦力，及相關內摩擦係數。我們更進一步利用不同資訊估算流場慣性數(inertial number I)，以探討相對應之 μ-I 流變關係。不論是以系統平均或局部資訊所得到的 μ-I 數據，均可觀察到 μ 隨I單調且非線性遞增的趨勢，與廣為接受的 μ-I 流變定律吻合，惟利用局部性質所得的數據與利用整體平均所的關係式比起來有較大的變異性，顯示非穩態流場流變行為之局部性。

The dynamics and rheological properties of dry granular inclined steady flows of nearly identical polydisperse spheres down a rough inclined chute are investigated through systematic experiments in this thesis. Direct force measurements via normal and shear normal cells are conducted at both the chute base and one lateral wall so that bulk basal and wall friction coefficients, μ and μw, are captured. To extract internal friction, indirect measurement based on quasi-two-dimensional control volume analysis of bulk stream-wise momentum is performed. In this analysis, the body force and assumed hydrostatic normal pressure are input from the basal normal load cell signal and so does the friction from the lateral frictional walls so that the only unknown is the tangential stress at a specific flow heights. Such indirectly measured internal friction and that from load cell measurements are examined with respect to bulk inertial number I. In calculating I, different estimations of an effective bulk shear strain rate were attempted for the current non-uniform flow. For the direct or indirect μ and all the estimated I, a rather robust trend that increases nonlinearly and monotonically with I is observed. However, the data using local μ and I possess greater dispersion from that use bulk averaged properties which poses questions to the feasibility of capturing local rheological property with mean flow properties.