Post on 27-Mar-2015
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
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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