Hostname: page-component-745bb68f8f-kw2vx Total loading time: 0 Render date: 2025-01-09T21:47:13.956Z Has data issue: false hasContentIssue false
  • English
  • Français

Three-dimensional instability of the flow over a forward-facing step

Published online by Cambridge University Press:  21 February 2012

Daniel Lanzerstorfer  and
Hendrik C. Kuhlmann
Daniel Lanzerstorfer
Affiliation:
Institute of Fluid Mechanics and Heat Transfer, Vienna University of Technology, Resselgasse 3, 1040 Vienna, Austria
Hendrik C. Kuhlmann*
Affiliation:
Institute of Fluid Mechanics and Heat Transfer, Vienna University of Technology, Resselgasse 3, 1040 Vienna, Austria
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The global, temporal stability of the two-dimensional, incompressible flow over a forward-facing step in a plane channel is investigated numerically. The geometry is varied systematically covering constriction ratios (step-to-inlet height) from 0.23 to 0.965. A three-dimensional linear stability analysis shows that the stability boundary is a smooth continuous function of the constriction ratio. If the critical Reynolds and wavenumbers are scaled appropriately, they approach a linear asymptotic behaviour for large step heights. The critical mode is found to be stationary and confined to the region of separated flow downstream of the step for all constriction ratios. An energy-transfer analysis reveals that the basic flow becomes unstable due to a combined effect involving lift-up and flow deceleration, leading to a critical mode exhibiting steady streaks. Moreover, the receptivity of the flow to initial as well as to structural perturbations is studied by means of an adjoint analysis.

JFM classification

Instability: Instability Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 695 , 25 March 2012 , pp. 390 - 404
Copyright
Copyright © Cambridge University Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Albensoeder, S., Kuhlmann, H. C. & Rath, H. J. 2001 Three-dimensional centrifugal-flow instabilities in the lid-driven cavity problem. Phys. Fluids 13, 121–135.CrossRefGoogle Scholar
2. 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
3. Chiba, K., Ishida, R. & Nakamura, K. 1995 Mechanism for entry flow instability through a forward-facing step channel. J. Non-Newtonian Fluid Mech. 57, 271–282.CrossRefGoogle Scholar
4. Dennis, S. C. R. & Smith, F. T. 1980 Steady flow through a channel with a symmetrical constriction in the form of a step. Proc. R. Soc. Lond. A 372, 393–414.Google Scholar
5. Giannetti, F. & Luchini, P. 2007 Structural sensitivity of the first instability of the cylinder wake. J. Fluid Mech. 581, 167–197.CrossRefGoogle Scholar
6. Landahl, M. T. 1975 Wave breakdown and turbulence. SIAM J. Appl. Math. 28, 735–756.CrossRefGoogle Scholar
7. Landahl, M. T. 1980 A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98, 243–251.CrossRefGoogle Scholar
8. Lanzerstorfer, D. & Kuhlmann, H. C. 2011 Global stability of the two-dimensional flow over a backward-facing step. J. Fluid Mech. 693, 1–27.CrossRefGoogle Scholar
9. Marino, L. & Luchini, P. 2009 Adjoint analysis of the flow over a forward-facing step. Theor. Comput. Fluid Dyn. 23, 37–54.CrossRefGoogle Scholar
10. Plotkin, A. & Mei, R. W. 1986 Navier–Stokes solutions for laminar incompressible flows in forward-facing step geometries. AIAA J. 24 (7), 1106–1111.Google Scholar
11. Pollard, A., Wakarani, N. & Shaw, J. 1996 Genesis and morphology of erosional shapes associated with turbulent flow over a forward-facing step. In Coherent Flow Structures in Open Channels, pp. 249–265. Wiley.Google Scholar
12. Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows. Springer.CrossRefGoogle Scholar
13. Stüer, H. 1999 Investigation of separation on a forward facing step. PhD thesis, ETH Zürich.CrossRefGoogle Scholar
14. Stüer, H., Gyr, A. & Kinzelbach, W. 1999 Laminar separation on a forward facing step. Eur. J. Mech. B/Fluids 18, 675–692.CrossRefGoogle Scholar
15. Theofilis, V. 2000 Globally unstable basic flows in open cavities. In 6th AIAA/CEAS Aeroacoustics Conference. AIAA 2000-1965.CrossRefGoogle Scholar
16. Theofilis, V. 2003 Advances in global linear instability analysis of nonparallel and three-dimensional flows. Prog. Aerosp. Sci. 39, 249–315.CrossRefGoogle Scholar
17. Theofilis, V. 2011 Global linear instability. Annu. Rev. Fluid Mech. 43, 319–352.CrossRefGoogle Scholar
18. Wilhelm, D. 2000 Numerical investigation of three-dimensional separation in a forward-facing step flow using a spectral element method. PhD thesis, ETH Zürich.Google Scholar
19. Wilhelm, D., Härtel, C. & Kleiser, L. 2003 Computational analysis of the two-dimensional–three-dimensional transition in forward-facing step flow. J. Fluid Mech. 489, 1–27.CrossRefGoogle Scholar