Granular flow in silos - observations and comments

Jørgen Nielsen

Danish Building and Urban Research

Jn@dbur.dk

SAMSI Workshop onFluctuations and continuum Equations for Granular flow, April 16-17, 2004

Silo versus hydrostatic pressure

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

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

0

244

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 challengesSilo Model

Natural field of gravity

Model

Centrifuge field of gravity

Grain Imperfections Imperfections

Boundary layer

Imperfections

Boundary layer

Scaled particles

FillingPowder (Cohesion)

Pore pressure

(Filling)

Pore pressure

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