zbMATH — the first resource for mathematics

Three-dimensional stationary flow over a backward-facing step. (English) Zbl 1045.76501
Summary: Three-dimensional stationary structure of the flow over a backward-facing step is studied experimentally. Visualizations and Particle Image Velocimetry (PIV) measurements are investigated. It is shown that the recirculation length is periodically modulated in the spanwise direction with a well-defined wavelength. Visualizations also reveal the presence of longitudinal vortices. In order to understand the origin of this instability, a generalized Rayleigh discriminant is computed from a two-dimensional numerical simulation of the basic flow in the same geometry. This study reveals that actually three regions of the two-dimensional flow are potentially unstable through the centrifugal instability. However, both the experiment and the computation of a local Görtler number suggest that only one of these regions is unstable. It is localized in the vicinity of the reattached flow and outside the recirculation bubble.

76-05 Experimental work for problems pertaining to fluid mechanics
76D99 Incompressible viscous fluids
Full Text: DOI
[1] Armaly, B.F.; Durst, F.; Pereira, J.C.F.; Schönung, B., Experimental and theoretical investigation of backward-facing step flow, J. fluid. mech., 127, 473-496, (1983)
[2] Kaiktsis, L.; Karniadakis, G.E.; Orszag, S.A., Onset of the three-dimensionality, equilibria, and early transition in flow over a backward-facing step, J. fluid. mech., 231, 501-528, (1991) · Zbl 0728.76057
[3] Kaiktsis, L.; Karniadakis, G.E.; Orszag, S.A., Unsteadiness and convective instabilities in two-dimensional flow over a backward-facing step, J. fluid. mech., 321, 157-187, (1996) · Zbl 0875.76111
[4] Kim, J.; Moin, P., Application of a fractional-step method to incompressible navier – stokes equations, J. comput. phys., 59, 308-323, (1985) · Zbl 0582.76038
[5] Lesieur, M.; Begou, P.; Briand, E.; Danet, A.; Delcayre, F.; Aider, J.L., Coherent vortex dynamics in large-eddy simulations of turbulence, J. turbulence, 4, 016, (2003) · Zbl 1083.76540
[6] Williams, P.T.; Baker, A.J., Numerical simulations of laminar flow over a 3D backward-facing step, Int. J. numer. methods fluids, 24, 1159-1183, (1997) · Zbl 0886.76048
[7] Barkley, D.; Gomes, M.G.M.; Henderson, R.D., Three-dimensional instability in flow over a backward-facing step, J. fluid. mech., 473, 167-190, (2002) · Zbl 1026.76019
[8] Cadot, O.; Kumar, S., Experimental characterization of viscoelastic effects on two- and three-dimensional shear instabilities, J. fluid. mech., 416, 151-172, (2000) · Zbl 0948.76521
[9] Adrian, R.J., Particle-imaging techniques for experimental fluid mechanics, Annu. rev. fluid mech., 23, 261-304, (1991)
[10] Rayleigh, J.W.S., On the dynamics of revolving flows, Proc. roy. soc. London ser. A, 93, 148, (1916)
[11] Drazin, P.G.; Reid, W.H., Hydrodynamic stability, (1981), Cambridge University Press · Zbl 0449.76027
[12] Mutabazi, I.; Normand, C.; Wesfreid, J.E., Gap size effects on centrifugally and rotationally driven instability, Phys. fluids A, 4, 1199, (1992) · Zbl 0825.76208
[13] Mutabazi, I.; Wesfreid, J.E., Coriolis force and centrifugal force induced flow instabilities, (), 301-316 · Zbl 0807.76026
[14] Sipp, D.; Jacquin, L., A criterion of centrifugal instabilities in rotating systems, (), 299-308
[15] H. Görtler, On the three-dimensional instability of laminar boundary layers on concave walls, NACA Technical Memorandum 1375, 1954
[16] Albensoeder, S.; Kuhlmann, H.C.; Rath, H.J., Three-dimensional centrifugal-flow instabilities in the lid-driven-cavity problem, Phys. fluids, 13, 1, 121-135, (2001) · Zbl 1184.76025
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.