Presentation on theme: "Granular flow in silos - observations and comments"— Presentation transcript:
1 Granular flow in silos - observations and comments SAMSI Workshop on Fluctuations and continuum Equations for Granular flow, April 16-17, 2004Granular flow in silos - observations and commentsJørgen NielsenDanish 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 testsComments related toPhysical and mathematical modelling – Continuum / discrete particlesPhenomena observed in silosStochastic approach
4 Physical modelling versus mathematical modelling Mathematical modelling is needed to generalise our understanding of physical phenomena and to predict behaviour under specified circumstancesPhysical 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
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 equationsLeads to the model law: Model Requirements and a Scaling LawRef: J. Nielsen ”Model laws for granular media and powders with special view to silo models”, Archives of Mechanics, 29, 4, pp , Warzawa, 1977
8 Discrete particlesEquations 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 foreseenSome may be arranged for – as the field of gravity – becomming a model requirementOthers comes out as Scaling laws
9 Model law – discrete, particles Model requirementsKx (scaled particles)Kg = 1/ Kx (centrifuge)……..Scaling lawK = 1K = 1Kt = Kx (Forces of inertia)Kt = 1 (Time dep. Konst. rel.)Kt = 1 (Pore flow)
34 On the search of a suitable model for the stress-strain relationship in granular materials
35 The modelling challenges SiloModelNatural field of gravityCentrifuge field of gravityGrainImperfectionsBoundary layerScaled particlesFillingPowder(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 powderAerated fillingLow wall frictionMass flow
37 A ”bad” silo problem - may be characterised by: Coarse-grained sticky particlesEccentric fillingHigh wall frictionPipe 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 geometryThe value of material parameters for the (future) stored materialThe wall friction coefficientThe formation of unsymmetrical flow patterns in symmetrical silos – and their load implicationsWall pressure fluctuations - load redistributionsThe formation of rupture planes in dense materials
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