0
TECHNICAL PAPERS

Bifurcation Characteristics of Flows in Rectangular Sudden Expansion Channels

[+] Author and Article Information
Francine Battaglia1

Department of Mechanical Engineering, Iowa State University, Ames, IA 50011francine@iastate.edu

George Papadopoulos

 ATK GASL, Ronkonkoma, NY 11779George.Papadopoulos@atk.com

1

Corresponding author.

J. Fluids Eng 128(4), 671-679 (Nov 30, 2005) (9 pages) doi:10.1115/1.2201639 History: Received May 19, 2005; Revised November 30, 2005

The effect of three dimensionality on low Reynolds number flows past a symmetric sudden expansion in a channel was investigated. The geometric expansion ratio in the current study was 2:1 and the aspect ratio was 6:1. Both experimental velocity measurements and two- and three-dimensional simulations for the flow along the centerplane of the rectangular duct are presented for Reynolds numbers in the range of 150 to 600. Comparison of the two-dimensional simulations with the experiments revealed that the simulations failed to capture completely the total expansion effect on the flow, which is influenced by both geometric and hydrodynamic effects. To properly do so requires the definition of an effective expansion ratio, which is the ratio of the downstream and upstream hydraulic diameters and is therefore a function of both the expansion and aspect ratios. When two-dimensional simulations were performed using the effective expansion ratio, the new results agreed well with the three-dimensional simulations and the experiments. Furthermore, in the range of Reynolds numbers investigated, the laminar flow through the expansion underwent a symmetry-breaking bifurcation. The critical Reynolds number evaluated from the experiments and the simulations were compared to other values reported in the literature. Overall, side-wall proximity was found to enhance flow stability, thus sustaining laminar flow symmetry to higher Reynolds numbers. Last, and most important, when the logarithm of the critical Reynolds number was plotted against the reciprocal of the effective expansion ratio, a linear trend emerged that uniquely captured the bifurcation dynamics of all symmetric double-sided planar expansions.

FIGURES IN THIS ARTICLE
<>
Copyright © 2006 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Schematic of the geometric configuration and coordinate system

Grahic Jump Location
Figure 2

Velocity profiles along the x-y plane at z=0 measured with PIV at x∕D2=−0.163 for Re=171: Streamwise mean velocity u shown as ◻; solid line is parabolic fit; transverse mean velocity v shown as ▿.

Grahic Jump Location
Figure 3

Normalized streamwise velocity u∕u0 profiles shown relative to channel positions x∕D2 along the centerplane for Re=171: Symbols are PIV measurements (every other measurement shown for clarity); dashed line represents numerical simulations for ER=2

Grahic Jump Location
Figure 5

Normalized streamwise velocity u∕u0 contours along the channel centerplane for Re=171: (a) measured using PIV for ER=2; and numerically predicted by two-dimensional simulations for (b) ER=2, (c) ER=1.61, and three-dimensional simulations for (d) ER=2

Grahic Jump Location
Figure 8

Aspect ratio influence on the effective expansion ratio for the double-sided planar expansion: Symbols denote experimental and 3D numerical investigations involving finite ER and AR parameters

Grahic Jump Location
Figure 9

Critical Reynolds number variation comparison for experimental data reporting influence of aspect ratio: Versus expansion ratio (top) and versus hydraulic diameter ratio (bottom)

Grahic Jump Location
Figure 10

Critical Reynolds number as a function of the hydraulic diameter ratio for the double-sided planar expansion

Grahic Jump Location
Figure 7

Symmetry-breaking pitchfork bifurcation measured at the channel centerline at x∕D2=0.877 for ER=2 and AR=6: Symbols are PIV measurements; solid line represents numerical simulations

Grahic Jump Location
Figure 6

Normalized streamwise velocity u∕u0 contours along the channel centerplane for Re=585: (a) Measured using PIV for ER=2, and numerically predicted by two-dimensional simulations for (b) ER=2, (c) ER=1.61, and three-dimensional simulations for (d) ER=2

Grahic Jump Location
Figure 4

Normalized streamwise velocity profiles u∕u0 at x∕D2=1.75 and 2.75 along the centerplane of the channel for Re=171: Symbols are PIV measurements (every other measurement shown for clarity); various lines represent numerical simulations

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In