Granular flow in silos - observations and comments SAMSI Workshop on Fluctuations and continuum Equations for Granular flow, April 16-17, 2004 Granular flow in silos - observations and comments Jørgen Nielsen Danish Building and Urban Research Jn@dbur.dk

Silo versus hydrostatic pressure Unfortunately it is not that simple. Liquid pressure may call for a stocastic treatment cocerning the filling height, while it is much more complicated with silos – even to decide where the stocastic treatment should start.

Focus on understanding phenomena Observations from silo tests Comments related to Physical and mathematical modelling – Continuum / discrete particles Phenomena observed in silos Stochastic approach

Physical modelling versus mathematical modelling Mathematical modelling is needed to generalise our understanding of physical phenomena and to predict behaviour under specified circumstances Physical modelling is wanted for controlled experiments in order to systematically observe and explore phenomena as a basis for mathematical modelling - and to verify such models

Silo scales

A good scientific physical model is more than just a small scale structure The creation of a model law calls for some considerations: Which phenomena to cover? Discrete particles or continuum approach? Which mathematical model to be based on? – Must be precisely formulated, but you may not be able to solve the equations Leads to the model law: Model Requirements and a Scaling Law Ref: J. Nielsen ”Model laws for granular media and powders with special view to silo models”, Archives of Mechanics, 29, 4, pp 547-560, Warzawa, 1977

Particle history

Discrete particles Equations of continuity, movement + stress strain relations for solids (individual particles) and fluids (air in pores) from basic continuum mechanisc. The model requirements must be satisfied if scale errors shall not be foreseen Some may be arranged for – as the field of gravity – becomming a model requirement Others comes out as Scaling laws

Model law – discrete, particles Model requirements Kx (scaled particles) Kg = 1/ Kx (centrifuge) …….. Scaling law K = 1 K = 1 Kt = Kx (Forces of inertia) Kt = 1 (Time dep. Konst. rel.) Kt = 1 (Pore flow)

The centrifuge model - filling

Centrifuge, continuum approach

Stacking the particles

Landslide

Cone squeeze

Distributed filing

Fluidized powder

Anisotropy from inclined filling

Preferred orientation - anisotropy

Outcomes of filling from the stacking process Density Pore pressure Homogeneity Anisotropy - and thus strength, stiffness and rupture mode of the ensiled solids

From contact forces to pressure

From contact forces to pressure Relative standard deviation Test Diameter of particle Pressure cell diameter Surface area of pressure cell

Pressure cell reading -fluctuations

Pressure distribution with time and height 24 4

Circumferential distribution of maximum discharge pressures – Wheat, eccentric inlet and outlet

Circumferential distribution of maximum discharge pressures – Barley, eccentric inlet and outlet

Large pressure gradients

Geometrical wall imperfections

Load consequences of geometrical wall imperfections

Dilating boundary layer

Dilating boundary layer, details

Rotational symmetrical pressure distribution – almost (Jørgen Munch-Andersen)

Formation of rupture planes in dense materials

Dynamics

On the search of a suitable model for the stress-strain relationship in granular materials

The modelling challenges Silo Model Natural field of gravity Centrifuge field of gravity Grain Imperfections Boundary layer Scaled particles Filling Powder (Cohesion) Pore pressure (Filling) P.S. Time dependent material behaviour may cause scale errors

A ”friendly” silo problem - may be characterised by: A non-cohesive powder Aerated filling Low wall friction Mass flow

A ”bad” silo problem - may be characterised by: Coarse-grained sticky particles Eccentric filling High wall friction Pipe flow expanding upwards until the full cross section has become involved

Items for a stochastic/statistic treatment Redistribution of pressure due to imperfections of wall geometry The value of material parameters for the (future) stored material The wall friction coefficient The formation of unsymmetrical flow patterns in symmetrical silos – and their load implications Wall pressure fluctuations - load redistributions The formation of rupture planes in dense materials