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Research Papers

# Flow of Damp Powder in a Rotating Impervious Cone

[+] Author and Article Information
Arnaud F. M. Bizard

Department of Engineering, Cambridge University, Cambridge CB2 1PZ, UKafmb2@cam.ac.uk

Digby D. Symons

Department of Engineering, Cambridge University, Cambridge CB2 1PZ, UKdds11@cam.ac.uk

Norman A. Fleck

Department of Engineering, Cambridge University, Cambridge CB2 1PZ, UKnaf1@cam.ac.uk

David Durban

Faculty of Aerospace Engineering, Technion, Israel Institute of Technology, Technion City, Haifa 32000, Israelaer6903@techunix.technion.ac.il

J. Appl. Mech 78(2), 021017 (Dec 20, 2010) (10 pages) doi:10.1115/1.4002581 History: Received June 25, 2010; Revised September 10, 2010; Posted September 17, 2010; Published December 20, 2010; Online December 20, 2010

## Abstract

A one dimensional analytical model is developed for the steady state, axisymmetric flow of damp powder within a rotating impervious cone. The powder spins with the cone but migrates up the wall of the cone (along a generator) under centrifugal force. The powder is treated as incompressible and Newtonian viscous, while the shear traction at the interface is taken to be both velocity and pressure dependent. A nonlinear second order ordinary differential equation is established for the mean through-thickness velocity as a function of radius in a spherical coordinate system, and the dominant nondimensional groups are identified. For a wide range of geometries, material parameters, and operating conditions, a midzone exists wherein the flow is insensitive to the choice of inlet and outlet boundary conditions. Within this central zone, the governing differential equation reduces to an algebraic equation with an explicit analytical solution. Furthermore, the bulk viscosity of the damp powder does not enter this solution. Consequently, it is suggested that the rotating impervious cone is a useful geometry to measure the interfacial friction law for the flow of a damp powder past an impervious wall.

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## Figures

Figure 1

Cross-section of a typical conical centrifugal filter

Figure 2

Microstructure and volume fraction of the solid/liquid/air phases at stations A, B, and C

Figure 3

(a) Cone geometry and (b) element of material of thickness h and of infinitesimal radial thickness δr

Figure 4

Friction law A: solution compared with U¯ for α=30 deg and QA=0.1

Figure 5

Friction law A: solutions for various values of Rout compared with U¯ with α=30 deg and QA=0.1

Figure 6

Friction law A: contours of Routlim in the (α,QA) plane, the star marks the working point of a typical low-grade sugar continuous centrifuge

Figure 7

Friction law A: dimensionless stresses for α=30 deg, QA=0.1, and Rout=2. (a) Hydrostatic stress σh and wall traction (τ,p) and (b) direct components of the deviatoric stress tensor.

Figure 8

Model B: ODE solution for α=30 deg, b̂=0.9, μ̂=10−1, QB=10−2, and Rout=1.5

Figure 9

Model B: ODE solutions for various values of Rout with α=30 deg, b̂=0.9, μ̂=10−1, and QB=10−2

Figure 10

Model B: Limit radius Routlim linearized contours versus (a) QB and α and (b) μ̂ and b̂ with the appropriate parameters held constant at α=30 deg, b̂=0.87, μ̂=1.1×10−2, PB=4.4×10−2, and QB=3.6×10−2. The star on each map marks the working point of a typical low-grade sugar continuous centrifuge.

Figure 11

Model B nondimensionalized stresses: (a) hydrostatic stress σh and wall traction (τ,p) (b) direct components of the deviatoric stress tensor, α=30 deg, b̂=0.9, μ̂=10−1, QB=10−2, and Rout=1.5

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