granular powder grains

Proceedings of Conference “Powder and Grains”, Stuttgart, 18-12. July 2005, editor: Garcia-Rojo R., Herrmann H.J., McNamara S., London, 2005, pp. 469-473

1 INTRODUCTION

Finite Element programmes are becoming a wide-spread tool to analyse the structural behaviour of si-los (Joffriet et al.,1977; Eibl and Häußler,1984). The analysis of silos with arbitrary shape, eccentric dis-charge openings (Rombach, 1991; Couto, 2000) incl. the numerical simulation of the interaction between the wall and the bulk solid is possible thanks to this method. However, as a recent international study has shown (Rotter et al., 1998; Holst et al.,1999), even for a given, clearly defined silo geometry and pa-rameters of the bulk solid, a wide range of results is predicted by different research groups. In this study, the filling and discharging processes have been stud-ied for various silo geometries by using the com-mercial finite element software ANSYS (ANSYS 8.1, 2004) and the research program SILO (Gladen, 1985; Rombach, 1991). The main purpose of this study was to analyse the results obtained in order to see the differences, similarities and capabilities of these programmes.

Filling and discharge processes in the bin are simulated for several 2-d and 3-d silo geometries. Wheat was used as bulk solid. Moreover, two differ-ent filling methods were used: a filling over the whole height and a filling layer by layer.

One of the main differences between ANSYS and SILO was the material model for the granular media. The Drucker-Prager elastoplastic criterion (Drucker and Prager, 1952) was used in ANSYS and the Kolymbas hypoplastic (Kolymbas, 1988) model was

selected in SILO. Therefore, the comparison of re-sults predicted by both models will allow to study the influence of the material model.

2 FINITE ELEMENT MODELLING

The Finite Element method is a suitable technique to analyse the structural behaviour of silos with arbi-trary shape. The interaction between the silo wall and the bulk solid is considered as well as the non-linear behaviour of the bulk material itself. As will be shown later, the material law and the interaction criteria has to be chosen with great care, as both have a great influence on the results of the simula-tions.

2.1 Finite element model Various geometries of square and flat bottom silos in 2-dimensions and 3-dimensions were analysed. Only 3-d results are presented in the following. For more details see Rombach (2005). The main characteris-tics and dimensions are summarised in table 1. The flat bottom geometry was selected to simplify the comparison between ANSYS and SILO.

Three different simulations were made for the filling process: a 2-d axisymmetric model (2DAM), a 2-d plane stress model (2DPSM) and a 3-d model (3DM). Moreover, for the 2DPSM and 3DM dis-charge models (Fig. 1), an outlet width of 0.64 m and outlet eccentricities of 0% and 100% were con-sidered.

Modelling of granular flow in silos based on finite element method ANSYS vs. SILO

G.A. Rombach Prof. Dr.-Ing. Department of Concrete Structures. Hamburg University of Technology

F. Ayuga Prof. Department of Construction and Rural Roads. Polytechnic University of Madrid.

F. Neumann Dipl.-Ing. Department of Concrete Structures. Hamburg University of Technology

E. Gallego Vázquez Dipl.-Ing. Department of Construction and Rural Roads. Polytechnic University of Madrid

ABSTRACT: Great effort has been made to improve the knowledge about the flow of granular material in si-los. Nevertheless, many important aspects such as wall pressures, to which silo structures are subjected, still appear uncertain. Numerical simulations based on the finite element method have become a valuable tool to simulate the behaviour of granular material in silos during at rest conditions and during flow and to estimate the actions the structure has to be designed for. Nevertheless great differences between various FE-software packages had been observed. In this paper the results of two different FE-programmes, the general purpose software ANSYS and a special non-linear dynamic programme called SILO are compared. Stresses of granu-lar material during filling and discharge for 2- and 3-dimensional geometries incl. different eccentricities of the outlet are calculated.


Table 1. Geometries analyzed _____________________________________________

Outlet (discharge) width eccentricity

Case studied

Length (m)

Height (m)

(m) 0% 100% 2DAM1 0.955 5.0 - - - 2DPSM2 1.91 5.0 0.64 - Yes 3DM3 1.91 5.0 0.64 Yes Yes

1: 2-d axisymmetric model 2:2-d plane stress model 3:3-d model

Figure 1. Discharge models.

Two procedures to simulate the filling process

were selected: the first one was the filling over the whole height where the full weight of the stored ma-terial is reached after several numerical steps. Great differences had been observed for silos with inclined walls. The second method was the filling of the silo in different layers. It is closer to the reality, but some numerical problems may occur. In this study, the geometries analysed were filled in ten layers.

2.2 Contact simulation In the present study, the silo wall is considered to be made of smooth steel. Wheat is used as bulk mate-rial stored in the bin. As it can be clearly understood, the behaviour and properties of both materials is completely different. Hence, it is very important to select an adequate contact model in order to get ac-curate results. In the FE-analyses the walls have been considered as rigid in order to simplify the comparison between both Finite Element programs.

ANSYS uses a surface-to-surface contact model, where both the target surface and the contact surface have to be specified. The former one is supposed to be the rigid surface meanwhile the latter one is the deformable surface. Hence, the target surface is de-fined as the silo wall and the contact surface is rep-resented by the boundary surface of the bulk solid in this analysis.

In ANSYS, one of the most important factors to create a contact model is the contact stiffness factor (FKN), whose value controls the stiffness of the con-tact element and the amount of artificial penetration in the wall. As in this study the walls are considered to be rigid, this value should be as high as possible (Guaita, 1995) to avoid any kind of penetration. Gallego et al. (2004) showed in some geometries

that when FKN is lower that a specific value, the wall normal pressures are overestimated in the hop-per meanwhile they are underestimated in the bin. Hence, the contact model in a silo analysis is a criti-cal point.

In the SILO program, the contact-layer is de-scribed by a “thin layer” – interface element. The in-terpolation functions, normal to the wall direction, are linear (related to the friction model). In a 3d simulation a 3d and 16-node interface element is used.

The well known Coulomb’s friction model (Equation 1) is used to describe the interaction be-tween the walls and the granular media.

p cτ µ= ⋅ + (1) where τ = equivalent shear stress; µ= wall friction coefficient; p = wall normal pressure; and c = cohe-sion sliding resistance.

The wall friction coefficient is the only parame-ter needed for this model. It can be obtained by sim-ple shear tests, as shown in Moya (2001).

2.3 Material models Granular materials are usually path - and rate de-pendant. Thus the history of the load process has to be known to determine the stress state of the mate-rial, because there is no unique correlation between strains and stresses. The material exhibits a different response that depends on the load rate when stresses become greater than the elastic limit.

Table 2. Material parameters for wheat

Material Parameter Value Angle of dilatancy of bulk material, ψi 8.0° Cohesion, c (kPa) 10 Effective angle of internal friction of bulk material, φi

25.2º

Modulus of elasticity, E (kPa) 4838. Poisson’s ratio 0.31 Wall friction coefficient, µ 0.24

Because of this complexity, many mathematical models have been developed to simulate the behav-iour of granular media. First, many elastoplastic formulations were published. Nowadays, hypoplas-ticity is becoming a widespread approach. A very extensive description of this type of material model can be found in Kolymbas (2000). In this study the Kolymbas hypoplastic model has been used in SILO and the Drucker-Prager elastoplastic criteria has been used in ANSYS. The elastic part has the com-mon linear approach. Hence, the modulus of elastic-ity and the Poisson´s ratio are the required parame-ters (table 2). On the other hand, the Drucker-Prager perfect plastic criterion has been considered. In this case, the cohesion and the angle of internal friction are needed. In addition, ANSYS gives the possibility of taking into account non-associative flow rules


and, therefore, the angle of dilatancy of bulk mate-rial is the third parameter required by this pro-gramme. The material parameters for the Kolymbas model are given in Rombach (1991).

A summary of the main differences between the 2 codes are given in Table 3. Table 3. Main differences between SILO and ANSYS

SILO ANSYS source code for granular flow general purpose description of motion

Eulerian descrip-tion

Lagrangian descrip-tion

contact thin layer interface element

surface to surface contact

material models hypoplastic model

(Kolymbas) with viscous part

elastoplastic model(Drucker-Prager)

without viscous part

3 RESULTS 3.1 Filling analysis Results obtained with both programmes after filling are in a good agreement, either the pattern of pres-sures or the quantitative values. Only two small dif-ferences exist. First, the different boundary condi-tions applied in the silo bottom make the pattern of pressures to be different from 0 to 0.2 m wall height. Next, results given by SILO are usually slightly greater than those predicted by ANSYS due to the small initial stresses required by the Kolymbas model.

When a progressive filling is considered, both programs show some leaps in the contact surface be-tween two consecutive layers. With respect to this phenomenon, ANSYS exhibits much greater pres-sure fluctuations than SILO (Fig. 2), especially in 2-d axisymmetric simulations. Moreover, it can be seen in Fig. 2 that lines for the full filling are the en-velope of those corresponding to the filling process in several layers. Hence, there is not really any in-fluence of the filling method in the pattern and the level of pressures. It should be also mentioned that the SILO programme has some problems to calcu-late 2-d axisymmetric models, because leaps are greater than in 2-d plane stress models. Moreover, a wall normal pressure of appr. 5 kPa is calculated in the top of the silo for the 2-d axisymmetric progres-sive filling in SILO. Nevertheless, this value should be almost zero.

It is expected that the pressure fluctuation are caused by numerical effects, but a further study about it should be conducted. The existence of rough meshes, different stiffness of the filled layer and the layer above it or the stiffness of the interface ele-ments could be an explanations of this problem. On the other hand, these leaps are really more important in ANSYS, so it is not recommended to simulate a silo progressive filling with it unless the causes of the problem are fully understood.

Figure 2. Normal wall pressure by using a filling method layer by layer for 2-d axisymmetric conditions (2DA).

3.2 Full eccentric discharge in a three dimensional model

The greatest wall normal pressure is nearly the same in both programmes. However, it has to be noted that ANSYS stops the simulation process after 0.7 s of discharge due to numerical problems. On the other hand, SILO detects a fast expansion of the flow regime in the lower region. After a discharge time of 0.64 s, normal wall pressures are almost zero for the first 2.5 m height (Fig. 3). Wall normal pres-sures are quite similar in both cases during the fol-lowing time intervals: 0 to 0.5 s in ANSYS and 0 to 0.27 s in SILO. After this time, results diverge. First, ANSYS is able to calculate only another 0.2 s and all results remain the same for the time interval 0.5 s to 0.7 s, which is unexpected. If the discharge simu-lation is carried out with SILO, it could be seen that the wall normal pressures during the corresponding time interval 0.22 s to 0.64 s decrease significantly in both walls, especially in that one closer to the out-let, as a result of the existing flow regime of the bulk material. A similar behaviour can be detected for the wall frictional stresses. With the SILO package it is possible to simulate the whole discharge process for unlimited time.

3.3 Full eccentric discharge in a two dimensional plane stress model

The results from SILO showed a switch pressure in the wall next to the outlet. The wall pressures oppo-site to the outlet increased from 12.7 kPa (t = 0.10 s) up to 17.2 kPa (t = 0.35 s). After this time step, the material begins to flow and the stresses are getting smaller than before.

The pressures on the bottom increase from the outlet-side to the opposite-side. A numerical prob-lem produces a peak in the transition, next to the opening. It can be minimize by a more refined ele-ment mesh and by better modelled boundary condi-tions.


On the other hand, normal pressures on the right wall are nearly zero in ANSYS in the upper part of the bin from 2 to 5 m for the discharge time 0.2 s, and even small tension stresses appear in some points. However, average stresses in the lower part are closer to the SILO calculation because wall nor-mal pressures are greater in ANSYS near the outlet (max.: 22.9 kPa in ANSYS vs. 15.2 kPa in SILO).

Figure 3. Normal pressures on the left wall for a fully eccentric discharged silo with ANSYS and SILO. 3-d model with an out-let width of 0.64 m (3DE0.64m). Discharge times of 0.64 s in SILO and 0.70 s in ANSYS.

4 CONCLUSIONS

Most results of ANSYS and SILO are in good agreement, especially in static analysis or in dy-namic cases when there is a reduced flow. ANSYS has great problems with silo calculations when sig-nificant flow of material appears due to the material model used. In this case, it is not possible to deter-mine parts of viscosities or velocities, because no velocity term is considered in the Drucker-Prager formulation used.

Results obtained with progressive filling gives similar results to those obtained considering a full filling for silos with vertical walls. Though, some numerical problems appear in both programmes, es-pecially in ANSYS, where many pressure leaps can be observed in the contact between consecutive lay-ers. It should be also noted that axisymmetric calcu-lations show more problems in both programmes if a progressive filling is simulated.

There are some differences in both programmes near the bottom of the silo due to the different boundary conditions applied, both in the filling and discharge processes. Moreover, SILO has problems with axisymmetric calculations during discharge simulation because wall normal pressures in the top of the silo are greater than expected.

Discharge simulations are usually faster than dis-charging processes in reality to save computation time. The evolution of the material velocities de-

pends on various parameters of the constitutive models for the bulk material. Whether the time fac-tor has some influence or not, should be part of the further investigations.

REFERENCES

ANSYS 8.1. 2004. ANSYS User's Manual. Ver. 8.0. Houston: Swanson Analysis Systems, Inc.

Couto, A. 2000. Métodos avanzados de cálculo de presiones estáticas en silos cilíndricos y prismáticos con tolva ex-céntrica mediante el método de los elementos finitos. PhD thesis. ETSI. Agronomos, Madrid: Polytechnic University of Madrid, Department of Construction and Rural Roads.

Drucker, D.C. and Prager, W. 1952. Soil Mechanics and Plastic Analysis or Limit Design. Quart. Appl. Math. 10 (2): 157-165.

Eibl, J.; Häußler U. 1984. Numerical Investigations in Dischar-ging Silos. Journal of Engineering Mechanics 110 (6): 957 – 971.

Gallego, E., Goodey, R. J., Ayuga, F. and Brown, C.J. 2004. Some practical features in modelling silos with finite ele-ments. ASAE Paper No. 044150. St. Joseph, Mich.: ASAE. Proc. of the 2004 ASAE/CSAE Annual International Mee-ting. Ottawa, August 2004.

Gladen, W. 1985. Numerische Untersuchung der Lasten in Si-lozellen beim exzentrischen Entleeren. Dissertation, Univer-sität Karlsruhe

Guaita, M. 1995. Creación de modelos para la simulación de silos por el método de elementos finitos y análisis de los empujes estáticos del material almacenado. PhD thesis. ET-SI. Agronomos, Madrid: Polytechnic University of Madrid, Department of Construction and Rural Roads.

Holst, J.M.F.G., Ooi, J.Y., Rotter, J.M. and Rong, G.H. 1999. Numerical Modeling of silo filing. I: Continuum Analyses. Journal of Engineering Mechanics. January: 94 – 103.

Kolymbas, D. 1988. Eine konstitutive Theorie für Böden und andere körnige Stoffe. Veröffentlichungen des Institutes für Boden- und Felsmechanik der Universität Karlsruhe, Heft 109, Karlsruhe

Kolymbas, D. 2000. Constitutive Modelling of Granular Mate-rials. Berlin: Springer

Moya, M. 2001. Determinación de parámetros físicos de mate-riales agrícolas granulares utilizados en el cálculo de silos por métodos numéricos. PhD thesis. ETSI. Agronomos, Madrid: Polytechnic University of Madrid, Department of Construction and Rural Roads.

Rombach, G.A. 1991. Schüttguteinwirkungen auf Silozellen – Exzentrische Entleerung. PhD. thesis, Universität Karlsruhe

Rombach, G.A., Ayuga, F., Gallego, E., Neumann, F. 2005.

Filling and discharging simulations with different Finite Element programmes - ANSYS VS. SILO.

Rotter, J.M., Holst, J.M.F.G., Ooi, J.Y. and Sanad, A.M. 1998. Silo pressure predictions using discrete – element and finite – element analyses. Phil. Trans. R. Soc. Lond. A. 356: 2685 – 2712.

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