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TECHNICAL PAPERS

Development-Length Requirements for Fully Developed Laminar Pipe Flow of Inelastic Non-Newtonian Liquids

[+] Author and Article Information
R. J. Poole1

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

B. S. Ridley2

Department of Engineering, University of Liverpool, Brownlow Street, Liverpool L69 3GH, United Kingdomblake.ridley@mwhglobal.com

1

Corresponding author.

2

Present address: MWH-Process and Hydraulics Department, Dominion House, Birchwood Warrington, UK.

J. Fluids Eng 129(10), 1281-1287 (Apr 20, 2007) (7 pages) doi:10.1115/1.2776969 History: Received January 02, 2007; Revised April 20, 2007

In the current study, we report the results of a detailed and systematic numerical investigation of developing pipe flow of inelastic non-Newtonian fluids obeying the power-law model. We are able to demonstrate that a judicious choice of the Reynolds number allows the development length at high Reynolds number to collapse onto a single curve (i.e., independent of the power-law index n). Moreover, at low Reynolds numbers, we show that the development length is, in contrast to existing results in the literature, a function of power-law index. Using a simple modification to the recently proposed correlation for Newtonian fluid flows (Durst, F., 2005, “The Development Lengths of Laminar Pipe and Channel Flows  ,” J. Fluids Eng., 127, pp. 1154–1160) to account for this low Re behavior, we propose a unified correlation for XDD, which is valid in the range 0.4<n<1.5 and 0<Re<1000.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of computational domain and boundary conditions

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Figure 2

Variation of development length for Newtonian and power-law fluids versus (a) Reynolds number based on Collins and Schowalter (3), (b) Re based on wall viscosity in fully-developed flow, and (c) Re based on definition of Metzner and Reed (30)

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Figure 3

Variation of creeping-flow (ReCS=0.001) development length with power-law index

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Figure 4

Creeping-flow (ReCS=0.001) axial velocity development at various axial locations for (a) Newtonian fluid, (b) n=0.6, (c) n=0.4, and (d) n=1.5

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Figure 5

Variation of centerline velocity for creeping-flow cases (ReCS=0.001): (a) normalized by bulk velocity and (b) scaled to remove influence of flattened velocity profile

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Figure 6

Variation of development length for Newtonian and power-law fluids versus ReMR together with universal correlation based on a modification to correlation of Durst (10)

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