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Technical Briefs

Development Length Requirements for Fully Developed Laminar Pipe Flow of Yield Stress Fluids

[+] Author and Article Information
R. J. Poole

Department of Engineering, University of Liverpool, Brownlow Street, Liverpool L69 3GH, United Kingdomrobpoole@liv.ac.uk

R. P. Chhabra

Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208016, Indiachhabra@iitk.ac.in

This is the Reynolds number obtained when the friction-factor Reynolds number relationship is forced to be equal to the Newtonian one in a laminar flow (e.g., f(Re)=16 for a pipe). It is the Bingham model equivalent of the Metzner-Reed Reynolds number for power-law fluids.

J. Fluids Eng 132(3), 034501 (Mar 17, 2010) (4 pages) doi:10.1115/1.4001079 History: Received July 22, 2009; Revised December 14, 2009; Published March 17, 2010; Online March 17, 2010

In this technical brief, we report the results of a systematic numerical investigation of developing laminar pipe flow of yield stress fluids, obeying models of the Bingham-type. We are able to show that using a suitable choice of the Reynolds number allows, for high Reynolds number values at least, the development length to collapse to the Newtonian correlation. On the other hand, the development length remains a weak, nonmonotonic, function of the Bingham number at small values of the Reynolds number (Re40).

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 2

Comparison of the numerical simulation velocity profiles at the pipe exit with the fully developed analytical solution at Re=0.001 for a range of Bingham numbers (bi-viscosity model, μyield/μp=104, mesh M3 10D length)

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Figure 3

Development length variation for Bingham fluids

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Figure 4

Variation in the creeping-flow development length with the Bingham number

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Figure 1

Schematic of the computational domain and boundary conditions

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