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Eddy structures in a transitional backward-facing step flow

Published online by Cambridge University Press:  24 September 2007

H. P. RANI,
TONY W. H. SHEU and
ERIC S. F. TSAI
H. P. RANI
Affiliation:
Department of Engineering Science and Ocean Engineering, National Taiwan University, Taipei, Taiwan
TONY W. H. SHEU
Affiliation:
Department of Engineering Science and Ocean Engineering, National Taiwan University, Taipei, Taiwan
ERIC S. F. TSAI
Affiliation:
Department of Marine Engineering, National Taiwan Ocean University, Taiwan
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Abstract

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In the present study, flow simulation has been carried out in a backward-facing step channel defined by an expansion ratio of 2.02 and a spanwise aspect ratio of 8 to provide the physical insight into the longitudinal and spanwise flow motions and to identify the presence of Taylor–Görtler-like vortices. The Reynolds numbers have been taken as 1000 and 2000, which fall in the category of transitional flow. The present simulated results were validated against the experimental and numerical data and the comparison was found to be satisfactory. The simulated results show that the flow becomes unsteady and exhibits a three-dimensional nature with the Kelvin–Helmholtz instability oscillations and Taylor–Görtler-Like longitudinal vortices. The simulated data were analysed to give an in-depth knowledge of the complex interactions among the floor and roof eddies, and the spiralling spanwise flow motion. Destabilization of the present incompressible flow system, with the amplified Reynolds number due to the Kelvin–Helmholtz and Taylor–Görtler instabilities, is also highlighted. A movie is available with the online version of the paper.

JFM classification

Wakes/Jets: Separated flowsVortex Flows: Vortex interactions

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 588 , 10 October 2007, pp. 43 - 58
Copyright
Copyright © Cambridge University Press 2007

References

REFERENCES

Aidun, C. K., Triantafillopoulos, N. G. & Benson, J. D. 1991 Global stability of a lid-driven cavity with throughflow: flow visualization studies. Phys. Fluids A 3, 2081–2091.CrossRefGoogle Scholar
Armaly, B. F., Durst, F., Pereira, J. C. F. & Schónung, B. 1983 Experimental and theoretical investigation of backward-facing step flow. J. Fluid Mech. 127, 473–496.CrossRefGoogle Scholar
Barkley, D., Gomes, M. G. M. & Henderson, R. D. 2002 Three-dimensional instability in flow over a backward-facing step. J. Fluid Mech. 473, 167–190.CrossRefGoogle Scholar
Beaudoin, J. F., Cadot, O., Aider, J. L. & Wesfreid, J. E. 2004 Three-dimensional stationary flow over a backward-facing step. Eur. J. Mech. B/Fluids 23, 147–155.CrossRefGoogle Scholar
CFDRC, Manual 2003 CFD Research Corporation, 216 Wynn Drive Huntsville, AL 35805, USA. www.cfdrc.com.Google Scholar
Chiang, T. P., Hwang, R. R. & Sheu, W. H. 1997 On end-wall corner vortices in a lid-driven cavity. Trans. ASMEI: J. Fluids Engng. 119, 201–204.Google Scholar
Freitas, C. J. & Street, R. L. 1988 Non-linear transport phenomena in a complex recirculating flow: a numerical investigation. Intl J. Numer. Meth. Fluids 8, 769–802.CrossRefGoogle Scholar
Fortin, A., Jardak, M., Gervais, J. J. & Pierre, R. 1997 Localization of Hopf bifurcations in fluid flow problems. Intl J. Numer. Meth. Fluids, 24, 1185–1210.3.0.CO;2-X>CrossRefGoogle Scholar
Gartling, D. K. 1990 A test problem for outflow boundary conditions – flow over a backward-facing step. Intl. J. Numer. Meth. Fluids 11, 953–967.CrossRefGoogle Scholar
Ghia, K. N., Osswald, G. A. & Ghia, U. 1989 Analysis of incompressible massively separated viscous flows using unsteady Navier–Stokes equations. Intl J. Numer. Meth. Fluids 9, 1025–1050.CrossRefGoogle Scholar
Gresho, P. M., Gartling, D. K., Torczynski, J. R., Cliffe, K. A., Winters, K. H., Garrat, T. J., Spence, A. & Goodrich, J. W. 1993 Is the steady viscous incompressible two-dimensional flow over a backward-facing step at Re = 800 stable? Intl J. Numer. Meth. Fluids 17, 501–541.CrossRefGoogle Scholar
Guyon, E., Hulin, J. P., Petit, L. & Mitescu, C. D. 2001 Physical Hydrodynamics. Oxford University Press.CrossRefGoogle Scholar
Jiang, B.-N., Hou, L.-J. & Lin, T.-L. 1993 Least-squares finite element solutions for three-dimensional backward-facing step flow. NASA TM 106353.Google Scholar
Kaiktsis, L., Karniadakis, G. E. & Orszag, S. A. 1991 Onset of three-dimensionality, equilibria, and early transition in flow over a backward-facing step. J. Fluid Mech. 231, 501–528CrossRefGoogle Scholar
Kaiktsis, L., Karniadakis, G. E. & Orszag, S. A. 1996 Unsteadiness and convective instabilities in two-dimensional flow over a backward-facing step. J. Fluid Mech. 321, 157–187.CrossRefGoogle Scholar
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308–323.CrossRefGoogle Scholar
Komerath, N. M., Ahuja, K. K. & Chambers, F. W. 1987 Prediction and measurement of flows over cavities – a survey. AIAA Paper 87-0166.CrossRefGoogle Scholar
Ku, H. C., Hirsch, R. S., Taylor, T. D. & Rosenberg, A. P. 1989 A pseudospectral matrix element method for solution of three dimensional incompressible flows and its parallel implementation. J. Comput. Phys. 83, 260–291.CrossRefGoogle Scholar
Lee, I., Ahn, S. K. & Sung, H. J. 2004 Three-dimensional coherent structure in a separated and reattaching flow over a backward-facing step. Exps. Fluids 36, 373–383.Google Scholar
Nie, J. H. & Armaly, B. F. 2004 Reverse flow regions in three-dimensional backward-facing step flow. Intl J. Heat Mass Transfer 47, 4713–4720.CrossRefGoogle Scholar
Shih, C. & Ho, C. M. 1994 Three-dimensional recirculation flow in a backward facing step. Trans. ASMEI: J. Fluids Engng 116, 228–232.Google Scholar
Silveira Neto, A., Grand, D., Metais, O. & Lesieur, M. 1993 A numerical investigation of the coherent vortices in turbulence behind a backward-facing step. J. Fluid Mech. 256, 1–25.CrossRefGoogle Scholar
Williams, P. T. & Baker, A. J. 1997 Numerical simulations of laminar flow over a 3D backward-facing step. Intl J. Numer. Meth. Fluids 24, 1159–1183.3.0.CO;2-R>CrossRefGoogle Scholar
Wissink, J. G. & Rodi, W. 2003 DNS of a laminar separation bubble in the presence of oscillating flow. Flow, Turbulence Combust. 71, 311–331.CrossRefGoogle Scholar
Wissink, J. G., Michelassi, V. & Rodi, W. 2004 Heat transfer in a laminar separation bubble affected by oscillating external flow. Intl J. Heat Fluid Flow 25, 729–740.CrossRefGoogle Scholar
Yao, H. Cooper, R. K. & Raghunathan, S. 2004 Numerical simulation of incompressible laminar flow over three-dimensional rectangular cavities. J. Fluids Engng 126, 919–927.CrossRefGoogle Scholar

Rani et al. supplementary movie

Movie. Illustration of the spiralling particles for Re = 1000 using streamlines.  A, B, C, D denote the particle seeding points at (x/S, y/S, z/S) = (1, 1.975, 1), (1,1.9, 1), (0, 1, 4) and (1, 1, 4), respectively.

Download Rani et al. supplementary movie(Video)
Video 1.4 MB

Rani et al. supplementary movie

Movie. Illustration of the spiralling particles for Re = 1000 using streamlines.  A, B, C, D denote the particle seeding points at (x/S, y/S, z/S) = (1, 1.975, 1), (1,1.9, 1), (0, 1, 4) and (1, 1, 4), respectively.

Download Rani et al. supplementary movie(Video)
Video 1.8 MB