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TECHNICAL BRIEF

# Variation of the Recirculation Length of Newtonian and Non-Newtonian Power-Law Fluids in Laminar Flow Through a Suddenly Expanded Axisymmetric Geometry

[+] Author and Article Information
Debabrata Nag

Department of Mechanical Engineering,  Jadavpur University, Kolkata 700 032, India

Amitava Datta

Department of Power Engineering,  Jadavpur University, Salt Lake Campus, Kolkata 700 098, Indiaamdatta̱ju@yahoo.com

J. Fluids Eng 129(2), 245-250 (Sep 05, 2006) (6 pages) doi:10.1115/1.2409361 History: Received March 17, 2006; Revised September 05, 2006

## Abstract

A numerical study has been carried out for the laminar flow of Newtonian and non-Newtonian power-law fluids through a suddenly expanded axisymmetric geometry. Mathematical correlations are proposed for the prediction of the length of the recirculating eddy in terms of Reynolds number, expansion ratio and rheological parameters. A wide range of expansion ratios $(1.25⩽ER⩽8.0$) has been covered for the Newtonian fluid and both the shear-thinning and shear-thickening flow characteristic fluids have been considered for the non-Newtonian fluids.

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## Figures

Figure 1

Physical geometry of flow path. Dotted line shows the computational domain of the geometry.

Figure 2

Variation of nondimensional corner recirculation length with Reynolds number for various ER of a Newtonian fluid (n=1.0)

Figure 3

Variation of coefficient α=Lr∕hRe with expansion ratio

Figure 4

(a) Variation of recirculation length of n=0.7 for different expansion ratios. (b) Variation of recirculation length of n=1.0 for different expansion ratios. (c) Variation of recirculation length of n=1.3 for different expansion ratios. (d) Variation of recirculation length as a function of flow index for ER=3.0.

Figure 5

(a) Variation of α=Lr∕hRegen as function of expansion ratio for different flow indices of non-Newtonian fluids. (b) Variation of α=Lr∕hRegen as a function of flow index for different expansion ratios of non-Newtonian fluids.

Figure 6

Comparison of experimental Lr∕h (Halmos (see Ref. 6)) against predicted Lr∕h from present numerical prediction, present correlation (Eq. 7) and correlation of Eq. 9 (Nguyen (see Ref. 8)) for 50⩽Re⩽200, ER=2.0, and n=0.8

Figure 7

Comparison of the prediction of Lr∕h values from correlation Eqs. 5,7 for Newtonian flow (n=1)

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