由邊界力探討儲存槽顆粒流之暫態發展與其連續體模型
Other Title
Modeling the transient development of a granular silo flow in view of its boundary force
Date Issued
2020
Author(s)
Advisor
楊馥菱
Abstract
本論文欲探討堆積顆粒自儲存槽中釋放時的暫態應力於深度上之分布，暫態區間於本實驗中定義為儲存槽門開啟後至質量流率達到穩定值前。數個力感測器設置在壓克力儲存槽的側牆上以同時量測顆粒施加於不同深度之正向應力與剪應力。吾人發現釋放過程中之應力分布具有一時間性規律震盪，並引用近年來發現的儲存槽中之疏密波解釋之。疏密波的來源為接近儲存槽開口的顆粒快速流動時，顆粒間的接觸力陸續消失所造成的擾動。吾人利用疏密波的行為特徵與同一深度上顆粒的質量守恆法則，並以μ(I)流變模型預測內部應力如何傳遞至側牆，建立一暫態模型以側牆所受之應力預測自儲存槽中釋放之顆粒總重。經與實際量測之釋放顆粒總重比較後，該模型成功透過量測應力預測暫態中之質量流率。基於該模型的立論點，吾人以一偏心出口之儲存槽對疏密波的行為進行進一步的分析，該偏心出口可使顆粒自儲存槽釋放時，快速流動區域恰好平行於設有正向應力感測器之側牆。吾人將側牆上的應力分布依時間前後區分為三個階段：靜止階段，穩定釋放階段，與衰減階段，其中衰減階段的行為被吾人經實驗證實其應力行為與分布皆與液態流體相同。吾人並定義一無因次之影響因子，描述側牆正向應力於穩定釋放階段隨時間變化的趨勢。最後，吾人將偏心出口儲存槽中之顆粒流場可視化，透過觀察顆粒流場在釋放過程中的行為來驗證吾人於推導疏密波模型和影響因子過程之假設正確與否。最後，吾人以莫爾圓上應力間的交互關係推導顆粒由靜止階段下破壞的過程，預測破壞過程中並定存在一不穩定態，且其擁有之摩擦係數恰等同於實驗所量測之上限值。
To survey the evolution of force distribution for granular flow in the transient duration, which was defined as the duration after the silo opening was released and before the discharge mass flow rate reached a steady value. We established a silo with several force modules at the lateral wall to measure the boundary shear force and the normal force at different immersion depths. During the transient duration, we discovered a force oscillation phenomenon that could be related to the compaction-rarefaction wave in a silo. Compaction-rarefaction wave resulted from the losing contact force between the discharged deeper bed spheres and would propagate upward to the shallower spheres. We derived a model which was based on the mass conservation under the disturbance of compaction-rarefaction waves and applied the μ(I) rheology to describe how the internal force transfer to the boundary. The model predicted the loss of mass during the transient duration by the lateral force and matched well with the measured loss mass. To get more understanding about the compaction-rarefaction wave, we then established an eccentric silo. An eccentric opening was located close to the lateral wall to measure the force oscillation during the formation and propagation process of the compaction-rarefaction wave directly. We separated the successive lateral force distribution by three stages: the static stage, the steady discharge stage, and the hydrostatic decayed stage. A dimensionless influence factor I_f was defined to describe the lateral force behavior in the steady discharge stage. At last, a visualized flow field was revealed for the eccentric silo. We confirmed the defective assumptions for the compaction-rarefaction wave model and derived a continuum model based on the Mohr circle theory to fill them up.
Subjects
儲存槽
顆粒流
暫態應力
疏密波
silo
granular flow
transient lateral stress
compaction-rarefaction wave
Type
thesis