顆粒流在垂直旋轉式流變儀的運動型態與參數檢定

The Motion of Granular Flow in Rotating Viscometer and Rheological Parameters Calibration

宋立閔(Li-Ming Sung)

指導教授 ： 劉格非

國立臺灣大學/工學院/土木工程學研究所/碩士(2009年)

https://doi.org/10.6342/NTU.2009.01662

摘要

本研究針對石流理論基礎，配合實驗數據以求取不同材料的流變參數特性。理論部分，採用SH-theory的觀點，假設流況為符合長波理論，而且材料也符合Mohr-Coulomb特性，並將Mohr-Coulomb特性作為本構關係式，再利用正規化方程式與邊界條件，藉由尺度分析簡化問題，最後使用動量積分法求各個控制方程式的第零階解。
實驗數據方面，引用劉、張（2008）的實驗數據，從中挑選較為符合尺度假設的圓珠細磨石，以該材料作為主要的檢定對象。以不同的材料用量作為分組依據，利用多變數迴歸模式與最小平方法，最後可以檢定出實驗材料在本文理論下的流變參數，而所得的流變關係式為厚度 以微擾法展開的微分方程式，最後捨去高次項得到一階解。利用檢定出的流變參數代回關係式檢驗實際量測厚度與推估厚度，最大誤差值都在25%以內，表示此檢定結果可以接受，理論模式可以適用於此實驗材料。

關鍵字

垂直旋轉式流變儀 ； 顆粒流 ； 流變參數

並列摘要

In this thesis we focus on the theory basic on the granular flow theory and compare with experimental data to obtain the characteristic of rheological parameters applying different material. In the theory analysis, first we adopted SH-theory and assumed Hydrological regime was fitted in with Long-wave theory. Second, the material characteristic is one kind of Mohr-Coulomb material and we used its characteristic to build constitutive relation. We normalized the equations and boundary conditions with scaling analysis. Finally, we used the momentum integral method to obtain the leading order solution. In this thesis, we adopted the experimental data provided from Liu and Chung (2008). We choose spherically artificial material which is better fitted in with scaling assumption and calibrated rheological parameters using this material. We set a series cases with changing the amount of material and using linear regression model and least square method to obtain the rheological parameters. We used perturbation and set the depth of granular flow as H to obtain the differential equation which is rheological relation. Finally we erased high order terms and left the solution of first order term. In this thesis, we calibrated the rheological parameters to put back to rheological relation and we could test the actual depth and estimated depth of granular flow. The maximum error is about in 25 percent and this consequence is acceptable. The theory is suitable to apply this experimental material.

並列關鍵字

Rotating Viscometer ； Granular flow ； Rheological parameter ； SH-theory ； Mohr-Coulomb

參考文獻

6. 詹錢登、陳晉祺，（1997），「應用直立旋轉式水槽研究土石流體之流動現象」，中華水土保持學報，第28卷第2期，第157-164頁。

1. Bagnold, R. A. (1954). "Experiments on a Gravity-Free Dispersion of Large Solid Spheres in a Newtonian Fluid under Shear." Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 225(1160): 49-63.

2. GRAY, J. M. N. T. (2001). "Granular flow in partially filled slowly rotating drums." Journal of Fluid Mechanics 441(-1): 1-29.

3. Greve, R., T. Koch, et al. (1994). "Unconfined Flow of Granular Avalanches along a Partly Curved Surface. I. Theory." Proceedings: Mathematical and Physical Sciences 445(1924): 399-413.

4. Savage, S. B. and K. Hutter (1989). "The motion of a finite mass of granular material down a rough incline." Journal of Fluid Mechanics Digital Archive 199(-1): 177-215.