Journal of Fluid Mechanics



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Surface velocity in three-dimensional granular tumblers


NICHOLAS A. POHLMAN a1, STEVEN W. MEIER a2, RICHARD M. LUEPTOW a1 and JULIO M. OTTINO a1a2
a1 Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA
a2 Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL 60208, USA

Article author query
pohlman na   [Google Scholar] 
meier sw   [Google Scholar] 
lueptow rm   [Google Scholar] 
ottino jm   [Google Scholar] 
 

Abstract

A fundamental characteristic of granular flows is that they are typically restricted to thin layers of rapid surface flow. Thus, a complete understanding of surface flows is key for an accurate representation of the dynamics of the entire flow. Experiments were conducted in three-dimensional tumblers: cylindrical tumblers of various diameters, a double-cone tumbler, and a spherical tumbler, the Froude number for the last two being a function of the local geometry and ranging from $2.6\times10^{-5}$ to $7.5\times10^{-4}$. Surface velocity measurements for 1 mm and 2 mm glass particles were obtained using particle tracking velocimetry. Results indicate that the streamwise surface velocity at the midpoint of the flowing layer is a linear function of local flowing layer length, regardless of tumbler shape, particle size, rotation rate, and fill fraction. In addition, the axial velocity of particles at the free surface is negligible. These results are key for the development of three-dimensional models of granular flows.

(Published Online July 20 2006)
(Received June 8 2005)
(Revised January 5 2006)



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