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TECHNICAL PAPERS

Backward-Facing Step Flows for Various Expansion Ratios at Low and Moderate Reynolds Numbers

[+] Author and Article Information
G. Biswas, M. Breuer, F. Durst

Lehrstuhl für Strömungsmechanik, Universität Erlangen-Nürnberg Cauerstr. 4, D-91058 Erlangen, Germanye-mail: breuer@lstm.uni-erlangen.de

J. Fluids Eng 126(3), 362-374 (Jul 12, 2004) (13 pages) doi:10.1115/1.1760532 History: Received March 06, 2003; Revised November 08, 2003; Online July 12, 2004
Copyright © 2004 by ASME
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References

Lee, Y. S. and Smith, L. C., 1986, Analysis of power-law viscous materials using complex stream, potential and stress functions, in Encyclopedia of Fluid Mechanics, vol. 1, Flow Phenomena and Measurement, ed. N. P. Cheremisinoff, pp. 1105–1154.
Moffatt,  H. K., 1964, Viscous and resistive eddies near a sharp corner, J. Fluid Mech., 18, pp. 1–18.
Roache, P. J., 1972, Computational Fluid Dynamics, Hermosa, New Mexico, pp. 139–173.
Taylor,  T. D., and Ndefo,  E., 1971, Computation of viscous flow in a channel by the method of splitting, Proc. of the Second Int. Conf. on Num. Methods in Fluid Dynamics, Lecture Notes in Physics, vol. 8, pp. 356–364, Springer Verlag, New York.
Durst,  F., and Peireira,  J. C. F., 1988, Time-dependent laminar backward-facing step flow in a two-dimensional duct, ASME J. Fluids Eng., 110, pp. 289–296.
Alleborn,  N., Nandakumar,  K., Raszillier,  H., and Durst,  F., 1997, Further contributions on the two-dimensional flow in a sudden expansion, J. Fluid Mech., 330, pp. 169–188.
Brandt,  A., Dendy,  J. E., and Ruppel,  H., 1980, The multigrid method for semi-implicit hydrodynamic codes, J. Comput. Phys., 34, pp. 348–370.
Hackbusch, W., 1985, Multigrid Methods for Applications, Springer, Berlin.
Lange,  C. F., Schäfer,  M., and Durst,  F., 2002, Local block refinement with a multigrid flow solver, Int. J. Numer. Methods Fluids 38, pp. 21–41.
Ladevéze,  J., and Peyret,  R., 1974, Calcul numerique d’une solution avec singularité des equations de Navier-Stokes: écoulement dans un canal avec variation brusque de section, J. Mech., 13, no. 3, pp. 367–396.
Armaly,  B. F., Durst,  F., Peireira,  J. C. F., Schönung,  B., 1983, Experimental and theoretical investigation of backward-facing step flow, J. Fluid Mech., 127, pp. 473–496.
Durst,  F., and Peireira,  J. C. F., and Tropea,  C., 1993, The plane symmetric sudden-expansion flow at low Reynolds numbers, J. Fluid Mech., 248, pp. 567–581.
Kim,  J., and Moin,  P., 1985, Application of a fractional-step method to incompressible Navier-Stokes equations, J. Comput. Phys., 59, pp. 308–323.
Gartling,  D. K., 1990, A test problem for outflow boundary conditions—flow over a backward-facing step, Int. J. Numer. Methods Fluids 11, pp. 953–967.
Lee,  T., and Mateescu,  D., 1998, Experimental and numerical investigation of 2D backward-facing step flow, J. Fluids Struct., 12, pp. 703–716.
Kaiktsis,  L., Karniadakis,  G. E., and Orszag,  S. A., 1991, Onset of three-dimensionality, equilibria, and early transition in flow over a backward-facing step, J. Fluid Mech., 231, pp. 501–528.
Kaiktsis,  L., Karniadakis,  G. E., and Orszag,  S. A., 1996, Unsteadiness and convective instabilities in a two-dimensional flow over a backward-facing step, J. Fluid Mech., 321, pp. 157–187.
Heenan,  A. F., and Morrison,  J. F., 1998, Passive control of backstep flow, Exp. Therm. Fluid Sci., 16, pp. 122–132.
Le,  H., Moin,  P., and Kim,  J., 1997, Direct numerical simulation of turbulent flow over a backward-facing step, J. Fluid Mech., 330, pp. 349–474.
Kaltenbach,  H.-J., and Janke,  G., 2000, Direct numerical simulation of flow separation behind a swept rearward-facing step at Re=3000, Phys. Fluids, 12(9), pp. 2320–2337.
Williams,  P. T., and Baker,  A. J., 1997, Numerical simulations of laminar flow over a 3D backward-facing step, Int. J. Numer. Methods Fluids 24, pp. 1159–1183.
Chiang,  T. P., and Sheu,  T. W. H., 1999, A numerical revisit of backward-facing step flow problem, Phys. Fluids, 11(4), pp. 862–874.
Barkley,  D., Gomes,  M. G. M., and Henderson,  R. D., 2002, Three-dimensional instability in flow over a backward-facing step, J. Fluid Mech., 473, pp. 167–190.
Nie,  J. H., and Armaly,  B. F., 2002, Three-dimensional convective flow adjacent to backward-facing step—effects of step height, Int. J. Heat Mass Transfer, 45, pp. 2431–2438.
White, F. M., 1991, Viscous Fluid Flow, 2nd ed., McGraw-Hill, New York.
Orlanski,  I., 1976, A simple boundary condition for unbounded flows, J. Comput. Phys., 21, pp. 251–269.
Breuer, M., and Rodi, W., 1996, Large-eddy simulation of complex turbulent flows of practical interest, In: Flow Simulation with High-Performance Computers II, ed. E. H. Hirschel, Notes on Numerical Fluid Mechanics, 52 , pp. 258–574, Vieweg Verlag, Braunschweig.
Breuer,  M., 1998, Large-eddy simulation of the sub-critical flow past a circular cylinder: numerical and modeling aspects, Int. J. Numer. Methods Fluids 28, pp. 1281–1302.
Breuer, M., 2002, Direkte Numerische Simulation und Large-Eddy Simulation turbulenter Strömungen auf Hochleistungsrechnern, Habilitationsschrift, Universität Erlangen-Nürnberg, Berichte aus der Strömungstechnik, ISBN 3-8265-9958-6, Shaker Verlag, Aachen.
Demirdžić,  I., and Perić,  M., 1990, Finite-volume method for prediction of fluid flow in arbitrary shaped domains with moving boundaries, Int. J. Numer. Methods Fluids 10, pp. 771–790.
Patankar,  S. V., and Spalding,  D. B., 1972, A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows, Int. J. Heat Mass Transfer, 15, pp. 1787–1806.
Perić,  M., Kessler,  R., and Scheuerer,  G., 1988, Comparison of finite-volume numerical methods with staggered and colocated grids, Comput. Fluids, 16, pp. 389–403.
Durst,  F., and Schäfer,  M., 1996, A parallel blockstructured multigrid method for the prediction of incompressible flows, Int. J. Numer. Methods Fluids 22, pp. 549–565.
Lange,  C. F., Durst,  F., and Breuer,  M., 1998, Momentum and heat transfer from cylinders in laminar flow at 10−4≤Re≤200,Int. J. Heat Mass Transfer, 41, pp. 3409–3430.
Lange,  C. F., Durst,  F., and Breuer,  M., 1999, Wall effects on heat losses from hot-wires, Int. J. Heat Mass Transfer, 20, pp. 34–47.
Durst,  F., Shi,  J. M., and Breuer,  M., 2002, Numerical prediction of hot-wire corrections near walls, J. Fluids Eng., 124, pp. 241–250.
Shi,  J. M., Breuer,  M., and Durst,  F., 2002, Wall effect on heat transfer from a micro cylinder in near-wall shear flow, Int. J. Heat Mass Transfer, 45, pp. 1309–1320.
Hornung,  H., and Perry,  A. E., 1984, Some aspects of three-dimensional separation, part I: streamsurface bifurcations, Z. Flugwiss. Weltraumforsch., 8(2), pp. 77–87.
Oswatitsch, K., 1958, Die Ablösungsbedingung von Grenzschichten, In: Grenzschichtforschung, ed. H. Goertler, pp. 357–367, Springer Verlag Berlin/Göttingen/Heidelberg.

Figures

Grahic Jump Location
Moffatt eddies in a concave corner for 2α=60 deg. The values describe the relative intensities (Moffatt 2).
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Sketch of the flow configuration and definition of length scales
Grahic Jump Location
Flow in the vicinity of the step. Expansion ratio H/h=1.9423; 10−4≤ReD≤102. (a) ReD=0.0001; (b) ReD=0.1; (c) ReD=1; (d) ReD=10; (e) ReD=50; (f) ReD=100.
Grahic Jump Location
Flow in the vicinity of the step. Expansion ratio H/h=1.9423; ReD=1. (a) Zoom of the concave corner showing the first Moffatt eddy; (b) Increased zoom showing additionally the second Moffatt eddy.
Grahic Jump Location
Length x1 of the first corner eddy behind the backward-facing step (expansion ratio H/h=1.9423) normalized by the step height S.
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Flow in the vicinity of the step. Expansion ratio H/h=1.9423; 200≤ReD≤800; two-dimensional simulations; (a) ReD=200; (b) ReD=400; (c) ReD=600; (d) ReD=800.
Grahic Jump Location
Length x1 of the primary recirculation region behind the backward-facing step (expansion ratio H/h=1.9423) normalized by the step height S
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Length x4 and x5 of the secondary recirculation region (on the roof) behind the backward-facing step (expansion ratio H/h=1.9423) n ormalized by the tep height S
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Length of the primary recirculation region behind the backward-facing step x1 for different expansion ratios, H/h=1.9423, 2.5, and 3.0
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Dimensionless pressure loss Δpt/(0.5ρUb,12)⋅ReD in the streamwise direction of the channel. Expansion ratio H/h=1.9423; Reynolds number range 5⋅10−3≤Re=ReD≤5⋅102.
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Pressure loss coefficient ξ in the channel for different Reynolds numbers ReD and expansion ratios H/h
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Comparison of the spanwise location of the reattachment line past the backward-facing step at Re=ReD=397, 648, and 800. Expansion ratio H/h=1.9423; aspect ratio W/h=35; present numerical 3-D simulation and experimental data of Armaly et al. 11.
Grahic Jump Location
Surface streamlines of the backward-facing step flow at ReD=648. Expansion ratio H/h=1.9423; aspect ratio W/h=35; (a) Roof; (b) Bottom Wall; (c) Side Wall; (d) Symmetry Plane.
Grahic Jump Location
Comparison between the boundary of the primary recirculation zone and the line of ∂u/∂y|wall=0. Flow past the backward-facing step at ReD=648. Expansion ratio H/h=1.9423; aspect ratio W/h=35; a) y*=0.046; (b) y*=0.154; (c) y*=0.273; (d) y*=0.402.
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Contours of the velocity component w on various x-z planes. y* denotes the dimensionless distance from the bottom wall; H/h=1.9423; ReD=648
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Velocity vectors at a spanwise location of z=1.05; H/h=1.9423; ReD=648
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Development of a wall jet in streamwise direction near the bottom wall. Spanwise location z=1.05; H/h=1.9423; ReD=648; three-dimensional simulation.
Grahic Jump Location
Cross-stream velocity vectors at a streamwise location of x=6; H/h=1.9423; ReD=648
Grahic Jump Location
Development of a wall jet in spanwise direction near the bottom wall. H/h=1.9423; ReD=648. Steamwise locations: (a) x=6 (b) x=8.

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