Hostname: page-component-745bb68f8f-d8cs5 Total loading time: 0 Render date: 2025-02-11T12:07:36.888Z Has data issue: false hasContentIssue false
  • English
  • Français

A numerical investigation of the coherent vortices in turbulence behind a backward-facing step

Published online by Cambridge University Press:  26 April 2006

Aristeu Silveira Neto ,
Dominique Grand ,
Olivier Métais  and
Marcel Lesieur
Aristeu Silveira Neto
Affiliation:
Departamento de Engenharia Mecânica, UFU, Uberlândia, M.G. 38400, Brazil Commissariat à l'Energie Atomique, D.R.N., Centre d'Etudes Nucléaires de Grenoble, Service des Transferts Thermiques/LPML, BP 85 X, 38041 Grenoble Cedex, France Institut de Mécanique de Grenoble/LEGI (URA CNRS 1509), Institut National Polytechnique de GrenobleandUniversité Joseph Fourier, Grenoble, BP 53 X, 38041 Grenoble Cedex, France
Dominique Grand
Affiliation:
Commissariat à l'Energie Atomique, D.R.N., Centre d'Etudes Nucléaires de Grenoble, Service des Transferts Thermiques/LPML, BP 85 X, 38041 Grenoble Cedex, France
Olivier Métais
Affiliation:
Institut de Mécanique de Grenoble/LEGI (URA CNRS 1509), Institut National Polytechnique de GrenobleandUniversité Joseph Fourier, Grenoble, BP 53 X, 38041 Grenoble Cedex, France
Marcel Lesieur
Affiliation:
Institut de Mécanique de Grenoble/LEGI (URA CNRS 1509), Institut National Polytechnique de GrenobleandUniversité Joseph Fourier, Grenoble, BP 53 X, 38041 Grenoble Cedex, France
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper presents a statistical and topological study of a complex turbulent flow over a backward-facing step by means of direct and large-eddy simulations. Direct simulations are first performed for an isothermal two-dimensional case. In this case, shedding of coherent vortices in the mixing layer is demonstrated. Both direct and large-eddy simulations are then carried out in three dimensions. The subgrid-scale model used is the structure-function model proposed by Métais & Lesieur (1992). Lowstep computations corresponding to the geometry of Eaton & Johnston's (1980) laboratory experiment give turbulence statistics in better agreement with the experimental data than both Smagorinsky's method and K-ε modelling. Furthermore, calculations for a high step show that the eddy structure of the flow presents striking analogies with forced plane mixing layers: large billows are shed behind the step with intense longitudinal vortices strained between them.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 256 , November 1993 , pp. 1 - 25
Copyright
© 1993 Cambridge University Press

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

Antonopoulos-Domis, M. 1981 Large-eddy simulation of a passive scalar in isotropic turbulence. J. Fluid Mech. 104, 55–79.Google Scholar
Armaly, B. F., Durst, F., Pereira, J. C. & Schönung, B. 1983 Experimental and theoretical investigation of backward-facing step flow. J. Fluid Mech. 127, 423–496.Google Scholar
Arnal, M. & Friedrich, R. 1993 Large-eddy simulation of a turbulent flow with separation. In Turbulent Shear Flows 8 (ed. F. Durst, R. Friedrich, B. E. Launder et al.), p. 169. Springer.
Avva, R. K., Kline, S. J. & FERZIGER, J. H. 1988 Computation of a turbulent flow over a backward-facing step using the zonal modeling approach. Dept. of Mech. Engng, Stanford University, Rep. TF-33.
Bandyopadhyay, P. R. 1991 Instabilities and large structures in re-attaching boundary layers. AIAA J. 29, 1149–1155.Google Scholar
Bernal, L. P. & Roshko, A. 1986 Streamwise vortex structure in plane mixing layers. J. Fluid Mech. 170, 499–525.Google Scholar
Breidenthal, R. 1981 Structure in turbulent mixing layers and wakes using a chemical reaction. J. Fluid Mech. 109, 1–24.Google Scholar
Brown, G. L. & Roshko, A. 1974 On the density effects and large structure in two-dimensional mixing layers. J. Fluid Mech. 64, 775–816.Google Scholar
Buell, J. C. & Huerre, P. 1988 Inflow/outflow boundary conditions and global dynamics of spatial mixing layers. In Proc. 1988 Summer Program - Rep. CTR-S88, pp. 19–27. Stanford University.
Ciofalo, M. & Collins, M. W. 1989 k-ε predictions of heat transfer in turbulent recirculation flows using an improved wall-treatment. Numer. Heat Transfer B 15, 21–47.Google Scholar
Clark, R. A., Ferziger, J. H. & Reynolds, W. C. 1979 Evaluation of subgrid models using an accurately simulated turbulent flow. J. Fluid Mech. 91, 1–16.Google Scholar
Comte, P., Lesieur, M. & Lamballais, E. 1992 Large- and small-scale stirring of vorticity and passive scalar in a three-dimensional temporal mixing layer. Phys. Fluids A 4, 2761–2778.Google Scholar
Deardorff, J. W. 1970 A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J. Fluid Mech. 41, 453–480.Google Scholar
Eaton, J. K. & Johnston, J. P. 1980 Turbulent flow re-attachment: an experimental study of the flow and structure behind a backward-facing step. Stanford University, Rep. MD-39.
Findikakis, A. & Street, R. L. 1979 An algebraic model for subgrid turbulence in stratified flows. J. Atmos. Sci. 36, 1934–1949.Google Scholar
Friedrich, R. & Arnal, M. 1990 Analysing turbulent backward-facing step flow with the lowpassfiltered Navier–Stokes equations. J. Wind Engng Ind. Aerodyn. 35, 101–128.Google Scholar
Gaskel, P. H. & Lau, A. C. K. 1988 Curvature-compensated convective transport: SMART, a new boundedness-preserving transport algorithm. Intl J. Numer. Meth. Fluids 8, 617–641.Google Scholar
Gharib, M. & Derango, P. 1989 A liquid film (soap film) tunnel to study two-dimensional laminar and turbulent shear flows. Physica D 37, 406–416.Google Scholar
Grand, D., Coulon, N., Magnaud, J. P. & Villand, M. 1988 Computation of flow with distributed resistance and heat sources. In Proc. Third Intl Symp. on Refined Flow Modeling and Turbulence Measurements, Nipon Toshi Center Tokyo (ed. Y. Iwasa), pp. 487–494.
Herring, J. R., Schertzer, D., Lesieur, M., Newman, G. R., Chollet, J. P. & Larcheveque, M. 1982 A comparative assessment of spectral closures as applied to passive scalar diffusion. J. Fluid Mech. 124, 411–437.Google Scholar
Hirt, C. W., Nichols, B. D. & Romero, N. C. 1975 SOLA – Numerical solution algorithm for transient fluid flows. LASL Rep., Los Alamos, LA 5852.
Huang, L. S. & Ho, C. M. 1990 Small-scale transition in a plane mixing layer. J. Fluid Mech. 210, 475–500.Google Scholar
Jimenez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213–240.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, 501–528.Google Scholar
Kiya, M. 1989 Separation bubbles. In Theoretical and Applied Mechanics (ed. P. Germain, M. Piau & D. Caillerie), pp. 173–191. North-Holland Elsevier.
Kraichnan, R. H. 1976 Eddy-viscosity in two and three dimensions. J. Atmos. Sci, 33, 1521–1536.Google Scholar
Lasheras, J. C. & Choi, H. 1988 Three-dimensional instability of a plane free shear layer: an experimental study of the formation and evolution of streamwise vortices. J. Fluid Mech. 189, 53–86.Google Scholar
Leonard, A. 1974 On the energy cascade in large-eddy simulations of turbulent fluid flows. Adv. Geophys. 18A, 237–248.Google Scholar
Lesieur, M. 1990 Turbulence in Fluids. Kluwer.
Lesieur, M. & Rogallo, R. 1989 Large-eddy simulation of passive scalar diffusion in isotropic turbulence. Phys. Fluids A 1, 718–722.Google Scholar
Lesieur, M., Staquet, C., Le Roy, P. & Comte, P. 1988 The mixing layer and its coherence examined from the point of view of two-dimensional turbulence. J. Fluid Mech. 192, 511–534.Google Scholar
Lilly, D. K. 1967 The representation of small-scale turbulence in numerical experiments. Proc. IBM Sci. Comput. Symp. Environ. Sci., IBM Data Process. Div., White Plains, NY, pp. 195–210.
Métais, O. & Lesieur, M. 1992 Spectral large-eddy simulation of isotropic and stably stratified turbulence. J. Fluid Mech. 239, 157–194.Google Scholar
Metcalfe, R. W., Orszag, S. A., Brachet, M. E., Menon, S. & Riley, J. J. 1987 Secondary instability of a temporally growing mixing layer. J. Fluid Mech. 184, 207–243.Google Scholar
Moin, P. & Kim, J. 1982 Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341–377.Google Scholar
Müller, A. & Gyr, A. 1986 On the vortex formation in the mixing layer behind dunes. J. Hydraul. Res. 24, 359–375.Google Scholar
Normand, X. & Lesieur, M. 1992 Numerical experiments on transition in the compressible boundary layer over an insulated flat plate. Theor. Comput. Fluid Dyn. 3, 231–252.Google Scholar
Orlanski, I. 1976 A simple boundary condition for unbounded hyperbolic flows. J. Comput. Phys. 21, 251–269.Google Scholar
Pierrehumbert, R. T. & Widnall, S. E. 1982 Two- and three-dimensional instabilities of a spatially periodic shear layer. J. Fluid Mech. 114, 59–82.Google Scholar
Piomelli, U. 1988 Models for large-eddy simulations of turbulent channel flows including transpiration. Doctoral thesis, Stanford University.
Rodi, W. 1982 Examples of turbulence models for incompressible flows. AIAA J. 20, 872–879.Google Scholar
Silveira Neto, A., Grand, D. & Lesieur, M. 1991 Simulation numérique bidimensionnelle d’un écoulement turbulent stratifié derrière une marche. Intl J. Heat Mass Transfer 34, 1999–2011.Google Scholar
Smagorinsky, J. 1963 General circulation experiment with the primitive equations, I. The basic experiment. Mon. Weath. Rev. 91, 99–164.Google Scholar
Werner, H. & Wengle, G. 1993 Large-eddy simulation of turbulent flow over and around a cube in a plate channel. In Turbulent Shear Flows 8 (ed. F. Durst, R. Friedrich, B. E. Launder et al.), p. 155. Springer.
Winant, C. D. & Browand, F. K. 1974 Vortex pairing: the mechanism of turbulent mixing-layer growth at moderate Reynolds number. J. Fluid Mech. 63, 237–255.Google Scholar
Wygnanski, I. & Fiedler, H. E. 1970 The two-dimensional mixing region. J. Fluid Mech. 41, 327–361.Google Scholar