University of Wollongong Research Online University of Wollongong Thesis Collection University of Wollongong Thesis Collections 1990 Static and dynamic analysis of the flow of bulk materials through silos Yong Hong Wu University of Wollongong Recommended Citation Wu, Yong Hong, Static and dynamic analysis of the flow of bulk materials through silos, Doctor of Philosophy thesis, Department of Civil and Mining Engineering, University of Wollongong, 1990. http://ro.uow.edu.au/theses/1271 Research Online is the open access institutional repository for the University of Wollongong. For further information contact Manager Repository Services: [email protected]. STATIC AND DYNAMIC ANALYSES OF THE FLOW OF BULK MATERIALS THROUGH SILOS A thesis submitted in fulfilment of the requirements for the award of the degree of Doctor of Philosophy from THE UNIVERSITY OF WOLLONGONG by 1 UNIVERSITY OF I WOLLONGONG | LIBRARY YONG HONG WU, B.E.(Hons), M.E.(Hons) DEPARTMENT OF CIVIL AND MINING ENGINEERING February, 1990 -ii- DECLARATION This is to certify that the work presented in this thesis was carried out by the author in the Department of Civil and Mining Engineering, The University of Wollongong, and has not been submitted to any other university or institute for a degree except where specifically indicated. Yong Hong Wu -iii- ACKNOWLEDGEMENTS This study was conducted in the Department of Civil and Mining Engineering, The University of Wollongong. The author is indebted to his supervisor Professor L.C. Schmidt, Head of the Department, for the close supervision, fruitful discussions, invaluable suggestions, generous help and the beneficial training throughout the course of this thesis. The author is very grateful to The University of Wollongong for providing him a University of Wollongong Scholarship for his PhD study. The help and assistance provided by Professor R.W. Upfold and the staff of the Wollongong University Computer Center in using computer facilities is gratefully Acknowledged. Acknowledgement is also made to all the staff of the department, in particular to Mrs. J. Thompson, Dr. N.I. Aziz, Dr. V.U. Nguyen, and Mr. A. Grant. Acknowledgement is also given to Dr. A.G. McLean for his help. The author also wishes to express his thanks to all his colleagues and friends, in particular to Ms J.P. Lu and Mr. J.K.L.Hii, for their encouragement and help. Finally, special acknowledgement is made to his wife Hui Wang for her encouragement and all sort of help during the period of this study. -iv- ABSTRACT Storing and handling of bulk materials are essential aspects of grain, chemical and mining operations. Problems that commonly occur in silo operation mainly include flow blockages and structural failure of silos, which reduce the silo capacity and cause high maintenance cost. In most cases the problems occur principally due to inadequate design analysis together with a lack of knowledge of dynamic behaviour of the bulk material - containment structure system during the discharge of materials from silos. This thesis focusses on the simulation of the filling and the discharge process of bulk materials in silos. Emphasis has been placed on the development of the numerical methods for the prediction of bulk material pressures on silo walls and the internal stresses in silo shells under both static and dynamic conditions. The motion of bulk materials flowing through silos is modelled as the motion of a no-tension, viscous, elastic-plastic material. As large deformation occurs during discharge of the material, geometry nonlinearity is considered in the analysis. A finite element method formulated in terms of velocity as the primary variable is developed for the simulation of the flow of bulk materials and the structural response of the silo shell. The behaviour of the flowing bulk material is coupled with the behaviour of the containment structure by the contact condition of the bulk material and the silo wall. A computer program has been developed for the analysis. -V - Experiments have been carried out to verify the numerical model. An automatic monitoring system has been developed for the measurement of the pressure on silo walls. The data processing method based on a power spectrum analysis is employed to separate the random noise from the original signals. The experimental results have shown that the developed numerical models can predict the bulk material pressures on silo walls in a satisfactory manner. The method of analysis has been applied to simulate the discharge of bulk material from silos. Distribution of wall pressures and internal stresses in silo shells have been computed and presented in the thesis. -vi- TABLE OF CONTENTS TITLE PAGE - i - DECLARATION - ii - ACKNOWLEDGEMENTS -iii - ABSTRACT -iv - TABLE OF CONTENTS -vi- LIST OF FIGURES -xii- NOTATION -xvi- LIST OF PUBLICATION DURING PhD STUDY -xxiii- Chapter One Introduction 1.1 Objective 1-1 1.2 Scope 1-2 1.3 Outline of the Thesis 1-3 Chapter Two Review of Past Work 2.1 General 2-1 2.2 Pressures on Silo Walls 2-1 2.2.1 Analytical studies 2-2 2.2.2 Experimental studies 2-8 2.2.3 Numerical studies 2-10 2.3 Discharge Rate 2-13 2.3.1 Empirical equations 2-13 2.3.2 Theoretical analysis 2-13 - vii- 2.3.3 Numerical method 2-16 2.4 Structural Stability 2-17 2.5 Summary and Concluding Remarks 2-18 Chapter Three Fundamental Equations For the Motion of Bulk Material-Silo System 3.1 General 3-1 3.2 Stress Equilibrium Equations of Motion 3-1 3.3 Kinematic Equations 3-2 3.4 Conservation of Mass 3-3 3.5 Contact Conditions , 3-3 3.6 System Boundary Conditions 3-5 3.7 Constitutive Models 3-6 3.7.1 A viscous, elastic-plastic constitutive law 3-6 3.7.1-1 General form of the law 3-6 3.7.1-2 General form of the elastic-plastic matrix H 3-8 3.7.1 -3 A few specified forms of the elastic-plastic matrix 3-14 3.7.2 Elastic-plastic constitutive laws 3-21 3.8 Summary and Concluding Remarks 3-22 Chapter Four Boundary Element Method for the Prediction of Filling Pressures 4.1 General 4-1 4.2 Mathematical Description of the Problem 4-3 4.3 Boundary Integral Equation 4-6 4.4 Boundary Element Discretization 4-7 4.5 Evaluation of Boundary Coefficients 4-10 4.6 Solution Procedure and Computer Program 4-11 -VU1 4.7 Examples 4- 4.8 Summary and Concluding Remarks 4-21 Chapter Five Simulation of the Flow of Bulk Materials through Rigid-Walled Silos 5.1 General 5-1 5.2 Virtual Work Equations 5-2 5.3 Finite Element Discretization in Space 5-3 5.4 Discretization in Time 5-4 5.5 Element Characteristics 5-6 5.5.1 Velocity 5-8 5.5.2 Strain rate 5-9 5.5.2-1 Plane strain condition 5-9 5.5.2-2 Axisymmetric condition 5-10 5.5.3 Stress rate 5-11 5.5.4 Transformation of coordinates 5-14 5.5.5 Numerical integration and evaluation of element matrices... 5-18 5.6 Procedure of Solution 5-22 5.7 Example 5-25 5.8 Summary and Concluding Remarks 5-31 Chapter Six Finite Element Simulation of the Flow of Bulk Materials through Flexible Silos 6.1 General 6-1 6.2 Finite Element Formulae for the Motion of Bulk Materials 6-2 6.3 Finite Element Formulae for the Motion of Silo Structures 6-3 6.4 Coupling of the Bulk Granular Material and the Structure 6-4 6.5 Procedure of Solution 6-7 -ix- 6.6 Example 6-8 6.7 Summary and Concluding Remarks 6-16 Chapter Seven Experimental Analysis of Flow Mechanisms and Pressure Distributions 7.1 General 7-1 7.2 Experimental Program 7-2 7.2.1 The model silos 7-2 7.2.2 The bulk material 7-2 7.2.3 Experiment procedures 7-4 7.3 Data Acquisition and Control System 7-4 7.4 Signal Processing Technique 7-6 7.4.1 Power spectrum analysis 7-7 7.4.2 Design of digital filter 7-9 7.4.3 Suitability evaluation of filter parameter 7-11 7.5 Distribution of Pressures 7-12 7.5.1 Pressures on the flat-bottomed silo (Model 1) 7-12 7.5.2 Pressures on the silo-hopper combination (Model 2) 7-15 7.5.3 Pressures on the silo-hopper combination (Model 3) 7-15 7.6 Flow Patterns and Flow Mechanisms 7-20 7.6.1 Flow behaviour in the flat-bottomed silo (Model 1) 7-20 7.6.2 Flow behaviour in the silo-hopper combination (Model 2).. 7-23 7.6.3 Flow behaviour in the silo-hopper combination (Model 3).. 7-25 7.7 Summary and Concluding Remarks 7-27 Chapter Eight Comparison of Numerical Prediction With Experimental Results and Other Predictions 8.1 General 8-1 -X- 8.2 Comparison of Pressures in a Silo-hopper Combination 8-2 8.2.1 Filling pressures 8-3 8.2.2 Discharge pressures 8-4 8.3 Comparison of Pressures in a Hopper 8-5 8.3.1 Filling pressures 8-6 8.3.2 Discharge pressures 8-7 8.4 Summary and Concluding Remarks 8-8 Chapter Nine Parametric Study for Silo Design 9.1 General 9-1 9.2 Effect of Varying Hopper Half Angle 9-2 9.3 Effect of Wall Friction Coefficient 9-7 9.4 Effect of Wall Flexibility on the Distribution of Wall Pressures 9-11 9.5 Effect of Using Different Constitutive Laws 9-13 9.5.1 pressures in a rigid-walled silo 9-14 9.5.2 Pressures in a silo with flexible wall 9-14 9.5.3 Concluding remarks 9-15 9.6 Prediction of Dynamic Pressures Exerted by Broken Ore in Underground Storage Structures 9-17 9.7 Summary and Concluding Remarks 9-23 Chapter Ten Conclusions 10.1 Methodology for the Prediction of Bulk Material Pressures and Internal Stresses in the Walls of Silos 10-1 10.2 Distributions of Pressures in Silo Walls 10-2 10.3 Structural Response of Silo Shells 10-4 10.4 Flow Mechanism of Bulk Materials from Hopper-Bin Combinations 10-5 -xi - 10.5 Parameters Affecting the Pressures and the Internal Stresses in Silo Walls 10-5 10.6 Recommendations for Future Work 10-6 References -xii- LIST OF FIGURES Figure No.