A numerical study of wall pressure and granular flow in a flat-bottomed silo

Abstract This paper presents a numerical study of the granular flow in the discharge of a flat-bottomed model silo. The behaviour of the stored granular material is modelled using the finite element (FE) method based on an Arbitrary Lagrangian–Eulerian (ALE) frame of reference, which has shown advantageous performance over the classical FE methods in simulating the silo filling and discharge process in a series of studies leading up to this investigation. Experimental results have been used to validate the computational model using the ALE technique. The spatial distribution and time history of the pressures acting on the vertical silo walls predicted by the FE model are found to resemble well the test results. A semi-mass flow pattern has been predicted by the numerical model, which is very consistent with the corresponding experimental observation. With the validated numerical model, the flow behaviour specifically under a flat-bottomed geometry of silos is examined. Based on the velocity distribution in the granular material, a critical velocity ratio criterion is proposed and used to identify the flow channel boundary. A further numerical study has shown that the flow behaviour in the flat-bottomed silo is closely related to the shear strength of the material, which is represented by the internal friction angle for the cohesionless sand considered in the present study.

[1]  Irena Sielamowicz,et al.  Empirical description of granular flow inside a model silo with vertical walls , 2011 .

[2]  Francisco Ayuga,et al.  Analysis of dynamic discharge pressures in cylindrical slender silos with a flat bottom or with a hopper: comparison with Eurocode 1 , 2005 .

[3]  W. Wall,et al.  The extended finite element method for flow problems , 2014 .

[4]  Colin Thornton,et al.  Effects of Material Properties on Granular Flow in a Silo Using DEM Simulation , 2002 .

[5]  Jian Fei Chen,et al.  Flow pattern measurement in a full scale silo containing iron ore , 2005 .

[6]  J. M. Rotter,et al.  Guide for the Economic Design of Circular Metal Silos , 2001 .

[7]  J. M. Rotter,et al.  A finite element kinematic analysis of planar granular solids flow , 1996 .

[8]  J. M. Rotter,et al.  The sensitivity of silo flow and wall stresses to filling method , 2001 .

[9]  Paul W. Cleary,et al.  DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge , 2002 .

[10]  Jin Y. Ooi,et al.  The influence of a cone-in-cone insert on flow pattern and wall pressure in a full-scale silo , 2008 .

[11]  Francisco Ayuga,et al.  Some unresolved problems in the design of steel cylindrical silos , 2008 .

[12]  J. M. Rotter,et al.  Experiments on a square planform steel silo , 2000 .

[13]  Yin Wang,et al.  Numerical modelling of dynamic pressure and flow in hopper discharge using the Arbitrary Lagrangian–Eulerian formulation , 2013 .

[14]  Icíar Alfaro,et al.  Simulation of axisymmetric discharging in metallic silos. Analysis of the induced pressure distribution and comparison with different standards , 2002 .

[15]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[16]  Z. Mroz,et al.  Effect of rolling friction on wall pressure, discharge velocity and outflow of granular material from a flat-bottomed bin , 2012 .

[17]  V. Askegaard,et al.  Results from tests with normal and shear stress cells in a medium-scale model silo , 1985 .

[18]  Jacek Tejchman,et al.  Modeling of shear localization during confined granular flow in silos within non-local hypoplasticity , 2009 .

[19]  D. C. Drucker,et al.  Soil mechanics and plastic analysis or limit design , 1952 .

[20]  Jian Fei Chen,et al.  Finite element simulation of the pressure dip in sandpiles , 2013 .

[21]  Jørgen Nielsen,et al.  On the use of plate-type normal pressure cells in silos: Part 2: Validation for pressure measurements , 2010 .

[22]  R. M. Nedderman,et al.  A kinematic model for the flow of granular materials , 1979 .

[23]  Ankit Gupta,et al.  Predicting flow mode in cylindrical hopper , 2012 .

[24]  Songxiong Ding,et al.  Investigations of flow and pressure in silos during filling and discharging in presence of inserts , 2004 .

[25]  P. M. Blair-Fish,et al.  Flow Patterns and Wall Stresses in a Mass-Flow Bunker , 1973 .

[26]  Yin Wang,et al.  Finite element modelling of wall pressures in a cylindrical silo with conical hopper using an Arbitrary Lagrangian-Eulerian formulation , 2014 .

[27]  J. M. Rotter,et al.  Patterns of wall pressure on filling a square planform steel silo , 2002 .

[28]  Jin Y. Ooi,et al.  Numerical and experimental studies of the base pressures beneath stockpiles , 2011 .

[29]  S. Masson,et al.  Effect of particle mechanical properties on silo flow and stresses from distinct element simulations , 2000 .

[30]  Jin Y. Ooi,et al.  Experimental Investigation of the Flow Pattern and Wall Pressure Distribution in a Silo with a Double‐Cone Insert , 2007 .

[31]  Jennifer S. Curtis,et al.  Predicting the flow mode from hoppers using the discrete element method , 2009 .

[32]  Francisco Ayuga,et al.  On the use of plate-type normal pressure cells in silos , 2006 .

[33]  J. R. Johanson,et al.  Bin Loads—Part 3: Mass-Flow Bins , 1973 .

[34]  J. M. Rotter,et al.  Measured pressures in full scale silos: a new understanding , 1991 .

[35]  J. M. Rotter,et al.  Normal pressures and frictional tractions on shallow conical hopper walls after concentric filling: Predictions and experiments , 2013 .

[36]  Jørgen Munch-Andersen,et al.  Silo model tests with sand , 1992 .

[37]  Jin Y. Ooi,et al.  Wall pressures in squat steel silos from simple finite element analysis , 1990 .

[38]  J. Smid,et al.  Flow patterns and stresses on the wall in a two‐dimensional flat‐bottomed bin , 2003 .

[39]  Yunming Yang,et al.  Numerical analysis of silo behavior using non-coaxial models , 2011 .

[40]  Graham Redpath Watson.  Flow patterns in flat-bottomed silos , 1993 .