Aerated granular flow over a horizontal rigid surface

Abstract

The effect of a vertical gas flow on the dynamics of a coulombic granular material moving over a horizontal rigid porous surface has been studied experimentally and theoretically. The presence of a fluidizing gas significantly alters the granular flow dynamics. When the gas velocity, ug, is below the minimum fluidization velocity, umf, the effect of the gas is to reduce the angle of repose θ from the value measured in the absence of a gas flow. When material is poured from a point source onto a horizontal surface it forms a pile, which adjusts through episodic avalanching to a self-similar conical shape. Under these conditions, the development of the pile is determined by the local force balance on individual particles and its extent may be expressed in terms of the volume of particles added and the angle of repose. A volume of material is poured continuously from a point source onto a surface according to Qtα. Below the minimum uidization velocity, a quasi-static description gives the encroachment distance of the granular pile as l = (2Q/(2π/3)n−1 tan θ)1/n+1tα/n+1 where n = 1 for a planar release and n = 2 for an axisymmetric release.A continuum description of fluidized granular flow has been developed by vertically averaging the mass and momentum conservation equations and including the momentum exchange between the gas and granular flow. The bulk movement is driven along the ground by horizontal gradients of particle pressure and is resisted by a viscous drag force due to the particles moving horizontally through a vertical gas flow. Above the minimum fluidization velocity the character of the granular flow is significantly altered and takes on fluid-like properties. The model predicts the shape of the fluidized granular pile and that the encroachment distance grows as l = λnα (Q(ug + umf) / ε)1/n+2tα+1/n+2, where ε is the void fraction in the bed and λnα is a constant. Below the conditions for fluidization (ug < umf), the pile of granular material grows quasi-statically when t > t∗, where t∗ ∼ (εn+1Qug + umf) / μ2+n (umf − ug)2+n) 1/1+n−α corresponds to the critical time when frictional forces are comparable to gradients of particle pressure and the drag force. Numerical solutions describing the granular flow are presented.Experimental observations of the shape and extent of planar and axisymmetric granular flows when α = 1 compare well with theoretical predictions for various values of particle volume flux Q, time t, and gas flow rate ug. The mathematical description of fluidized granular flows along rigid surfaces indicates a strong analogy with buoyancy-driven flows in a porous medium. This analogy permits extension of our description to include flows down slopes and the effect of internal stratification.