1. 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

2. 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.

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

4. 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

5. Silo scales

6. 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 , Warzawa, 1977

7. Particle history

8. 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

9. 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)

10. The centrifuge model - filling

11. Centrifuge, continuum approach

12. Stacking the particles

13. Landslide

14. Cone squeeze

15. Distributed filing

16. Fluidized powder

17. Anisotropy from inclined filling

18. Preferred orientation - anisotropy

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

20. From contact forces to pressure

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

22. Pressure cell reading -fluctuations

23. Pressure distribution with time and height24 4

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

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

26. Large pressure gradients

27. Geometrical wall imperfections

28. Load consequences of geometrical wall imperfections

29. Dilating boundary layer

30. Dilating boundary layer, details

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

32. Formation of rupture planes in dense materials

33. Dynamics

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

35. 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

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

37. 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

38. 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