臺灣博碩士論文加值系統

本論文利用系統性的實驗探討聚甲醛乾顆粒穩態流於粗糙傾斜滑道中邊牆有效摩擦係數μw。藉由滑道底床及側牆上安裝的正向力與剪力荷重元來直接量測底床及側牆之正向及剪切受力，因而可利用正向及剪切受力值同時獲得底床及側牆的摩擦係數。此外利用高速影像處理技術實現顆粒追蹤測速以及球面角速度量測，並將量測數據經過平均處理，我們獲得速度νx、角速度ω及顆粒溫度Tx的深度分布圖，並從獲取的數據進行無因次參數分析來描述側牆摩擦係數μw。我們利用滑台實驗量測球體與傾斜滑道側牆之純滑動摩擦係數μpw來標準化側牆摩擦係數µw/µpw，從而檢查其與慣性數I、無因次化之顆粒溫度√Tx/νx以及旋轉指標Ω = Rω/νx之關連。最後將實驗量測數值之間的關連性和模擬離散元素的文獻的結果進行比較，並且解釋了兩者之間的相似性及差異性原因。

This work investigates the effective wall friction coefficient μw for steady dry granular flows of mono-sized Polyoxymethylene spheres down an inclined rough chute through systematic experiments. Direct force measurements via normal and shear load cells were conducted on chute base and at chute lateral wall so that bulk basal and lateral friction coefficients were obtained simultaneously. In addition, particle tracking velocimetry and sphere angular velocity measurement were achieved with high-speed imaging technique. Through averaging, we obtained depth profiles for bulk velocity νx, angular speed ω, and granular temperature Tx from which different dimensionless parameters were evaluated to describe μw. We also conducted sliding table experiment to measure pure sliding friction coefficient between the sphere and the chute side wall, μpw, so that a normalized µw/µpw was examined with respect to inertial number, I, scaled granular temperature, √Tx/νx, and rotation index, Ω = Rω/νx. The measured correlations were compared to those reported from discrete element simulation literature and we explains the similarities and discrepancies.

Abstract I
摘要 II
Contents III
List of Figures VI
List of Tables XV
List of parameters XVI
Chapter 1 Introduction 1
Chapter 2 Experiment Facility 13
2.1 Granular materials, reservoir and chute 13
2.2 High-speed imaging facility 16
2.3 Load-cell system and calibration 17
Chapter 3 Image processing and bulk properties 23
3.1 Particle location with circular Hough transformation 23
3.2 Location error 24
3.3 Volume fraction 25
3.4 Flow height 28
3.5 Particle tracking by variable size matrix and the nearest neighbor method 31
3.6 Particle Tracking Velocimetry (PTV) 33
3.6.1 Error analysis and bulk velocity 34
3.6.2 Volume flow rate and weight of the chute base based on image 38
3.7 Image processing for angular velocity 41
3.7.1 Rotation angle detection method 41
3.7.2 Test the credibility of this method 45
3.7.3 Error analysis and the angular velocity results of experiment 49
Chapter 4 Load-cell signal analysis 55
4.1 Reproducibility of experiment and volume flow rate 55
4.2 Basal force of different case and volume fraction 63
4.3 Lateral force of different case 69
Chapter 5 Flow analysis 76
5.1 Basal µ - I along stream 76
5.2 Lateral µw – Iw relation along depth 81
5.3 µw/µpw – νx/√Tx relation 90
5.4 Rω - √Tx relation 96
5.5 Ω - Txρ/P relation 98
5.6 µw/µpw - Ω relation 102
Chapter 6 Summary 108
References 115

[1] Heinrich M. Jaeger and Sidney R. Nagel, “Granular solids, liquids, and gases”, Reviews of Modern Physics, 1996
[2] Y. Forterre and O. Pouliquen, “Flows of Dense Granular Media”, Annu. Rev. Fluid Mech., 2008
[3] GDR MiDi, “On dense granular flows”, The European Physical Journal E 14, 2004
[4] Christophe Ancey, “Dry granular flows down an inclined channel: Experimental investigations on the frictional-collisional regime”, Physical Review E, 2001
[5] P. Jop, Y. Forterre and O. Pouliquen, “A constitutive law for dense granular flows”, Nature, 2006
[6] P. Jop, Y. Forterre and O. Pouliquen “Crucial role of side walls for granular surface flows: consequences for the rheology”, Journal of Fluid Mechanics, 2005
[7] Andrew Schofield and Peter Wroth, “Critical state soil mechanics”, Lectures in Engineering at Cambridge University, 1968
[8] F. Da Cruz, S. Emam, M. Prochnow, J.-N. Rous and F. Chevoir, “Rheophysics of dense granular materials: Discrete simulation of plane shear flows”, Physical Review, 2005
[9] Yoe ̈l Forterre and Olivier Pouliquen, “Granular flow”, Se ́minaire Poincare ́, 2009
[10] O. Pouliquen, C. Cassar, P. Jop, Y. Forterre and M. Nicolas, “Flow of dense granular material: towards simple constitutive laws”, Journal of Statistical Mechanics: Theory and Experiment, 2006
[11] D. Ertas and T. C. Halsey, “Granular gravitational collapse and chute flow”, Europhysics Letters, 2002
[12] Riccardo Artoni and Patrick Richard, “Effective Wall Friction in Wall-Bounded 3D Dense Granular Flows”, Physical Review Letters, 2015
[13] R. Artoni, A. Santomaso and P. Canu, “Effective boundary conditions for dense granular flows”, Physical Review, 2009
[14] Joe Estep and Josef Dufek, “Discrete element simulations of bed force anomalies due to force chains in dense granular flows”, Journal of Volcanology and Geothermal Research, 2013
[15] L. E. Silbert, G. S. Grest and S. J. P;impton, “Boundary effects self-organization in dense granular flows”, Physics of Fluids, 2002
[16] B. Sumer and M. Sitti, “Rolling and Spinning Friction Characterization of Fine Particles using Lateral Force Micro Microscopy based Contact Pushing”, Journal of Adhesion and Technology, 2008
[17] Fu-Ling Yang and Yung-Ta Huang, “New aspects for friction coefficients of finite granular avalanche down a flat narrow reservoir”, Granular Matter, 2016
[18] P. V. C. Hough, “Method and means for recognizing complex patterns”, U. S. Patent, 1962
[19] Richard O. Duda and Peter E. Hart, “Use of the Hough Transformation To Detect Lines and Curves in Pictures”, Communications of the ACM, 1972
[20] Murat Guler, Tuncer B. Edil and Peter J. Bosscher, “Measurement of particle movement in granular soils using image analysis”, J. Comput. Civ. Eng., 1999
[21] P. Richard, A. Valance, J.-F. Me ́tayer, P. Sanchez, J. Crassous, M. Louge and R. Delannay, “Rheology of Confined Granular Flows: Scale Invariance, Glass Transition, and Friction Weakening”, Physical Review Letters, 2008
[22] Brodu, N., Richard, P., Delannay, R., “Shallow granular flows down flat frictional channels: Steady flows and longitudinal vortices”, Phys. Rev, 2013