Computers and Chemical Engineering 40 (2012) 22–32 Contents lists available at SciVerse ScienceDirect Computers and Chemical Engineering jou rn al h om epa ge: w ww.elsevier.com/locate/compchemeng Modeling, numerical analysis and simulation Three dimensional discrete element models for simulating the filling and emptying of silos: Analysis of numerical results C. González-Montellano ∗ , E. Gallego, Á. Ramírez-Gómez, F. Ayuga BIPREE Research Group, Universidad Politécnica de Madrid, Madrid, Spain a r t i c l e i n f o Article history: Received 24 October 2011 Received in revised form 20 January 2012 Accepted 7 February 2012 Available online 16 February 2012 Keywords: Discrete element model Silo Hopper Pressures Flow Bulk density a b s t r a c t The discrete element method (DEM) is a promising technique that allows the mechanical behaviour of the material stored in silos and hoppers to be studied. The present work analyses the numerical results obtained by two three-dimensional DEM models that simulate the filling and discharge of a silo for two materials: glass beads or maize grains. The aim of the present work was to assess the capacity of these models to predict the behaviour of the studied materials. To guarantee the maximum representativeness of the results, many of the simplifications usually used in DEM models were avoided. The results analysed included the vertical distributions of the normal pressure, tangential pressure and mobilised friction, the horizontal distribution of normal pressure, velocity profiles and the spatial distribution of the bulk density. The results of this analysis highlight the potential of DEM models for studying the behaviour of granular materials in silos and hoppers, provided that simplifications are minimized. © 2012 Elsevier Ltd. All rights reserved. 1. Introduction Silos are structures designed for the storage of very different granular materials in the agricultural, food, mining, chemical, phar- maceutical and other industries (Langston, Tüzün, & Heyes, 1995). Given the size these structures can sometimes reach, their design must take into account structural safety as well as adequate func- tioning. Meeting the requirements of structural safety demands knowledge of the pressures a stored material will exert on the silo walls, while meeting the requirements of functionality demands an understanding of the factors that affect the flow of the stored material during discharge. Traditionally, analytical procedures have been used to deter- mine the values of pressures inside silos (Janssen, 1895; Reimbert & Reimbert, 1956) and for predicting the characteristics of the flow pattern (Jenike, 1964). However, these procedures are too simplis- tic and usually cannot be used to describe situations other than those for which they were formulated. These problems led to the use of numerical techniques for the study of the pressures and flow characteristics in silos. One of these is the finite element method (FEM) (Zienkiewicz & Taylor, 2005), which has been used with relative success to predict the pressures and flow patterns gen- erated in silos (Sadowski & Rotter, 2011a, 2011b). However, this ∗ Corresponding author at: ETSI Agrónomos, Avda. Complutense s/n, 28040 Madrid, Spain. Tel.: +34 91 336 5620; fax: +34 91 336 5625. E-mail address: carlos.gonzalez.montellano@upm.es (C. González-Montellano). method contemplates the granular mass as a continuum, prevent- ing it from being able to correctly simulate dynamic conditions such as those encountered during discharge. Other numerical methods were therefore sought, such as the discrete element method (DEM) (Tijskens, Ramon, & Baerdemaeker, 2003). This allows the individ- ualised simulation of all the particles making up a granular mass (Cundal & Strack, 1979). The DEM is therefore particularly indi- cated for the mechanical study of granular materials, both under static and dynamic conditions. The DEM allows one to obtain a great deal of detail on the vari- ables governing the behaviour of granular materials. In the research setting, this affords a great advantage over the experimental tech- niques commonly employed. Indeed, many researchers are now using DEM models to describe the distribution of pressures in silos (Goda & Ebert, 2005; Masson & Martinez, 2000), the flow patterns produced (González-Montellano, Ayuga, & Ooi, 2011; Ketterhagen & Hancock, 2010), segregation phenomena (Ketterhagen et al., 2007) and discharge rates (Balevicius, Sielamowicz, Mroz, & Kacianauskas, 2011; Mankoc et al., 2007). However, this method is still being developed. The capacity of many computers does not meet the demands of the technique, obliging the use of simplifica- tions (González-Montellano, Ramirez, Fuentes, & Ayuga, 2012) that do not always represent reality well. In addition, there are currently very few valid procedures for measuring the material properties involved in numerical models (Asaf, Rubinstein, & Shmulevich, 2007), meaning they often have to be estimated. Finally, many of these models have not been experimentally validated; the adequate correspondence of numerical results with reality cannot always, therefore, be guaranteed. 0098-1354/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.compchemeng.2012.02.007