This paper is concerned with the behavior of flows over a backward-facing step geometry for various expansion ratios $H/h=1.9423,$ 2.5 and 3.0. A literature survey was carried out and it was found that the flow shows a strong two-dimensional behavior, on the plane of symmetry, for Reynolds numbers $ReD=ρUbD/μ$ below approximately 400 $(Ub=bulk$ velocity and $D=hydraulic$ diameter). In this Reynolds number range, two-dimensional predictions were carried out to provide information on the general integral properties of backward-facing step flows, on mean velocity distributions and streamlines. Information on characteristic flow patterns is provided for a wide Reynolds number range, $10−4⩽ReD⩽800.$ In the limiting case of $ReD→0,$ a sequence of Moffatt eddies of decreasing size and intensity is verified to exist in the concave corner also at $ReD=1.$ The irreversible pressure losses are determined for various Reynolds numbers as a function of the expansion ratio. The two-dimensional simulations are known to underpredict the primary reattachment length for Reynolds numbers beyond which the actual flow is observed to be three-dimensional. The spatial evolution of jet-like flows in both the streamwise and the spanwise direction and transition to three-dimensionality were studied at a Reynolds number $ReD=648.$ This three-dimensional analysis with the same geometry and flow conditions as reported by Armaly et al. (1983) reveals the formation of wall jets at the side wall within the separating shear layer. The wall jets formed by the spanwise component of the velocity move towards the symmetry plane of the channel. A self-similar wall-jet profile emerges at different spanwise locations starting with the vicinity of the side wall. These results complement information on backward-facing step flows that is available in the literature.

1.
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.
2.
Moffatt
,
H. K.
,
1964
,
Viscous and resistive eddies near a sharp corner
,
J. Fluid Mech.
,
18
, pp.
1
18
.
3.
Roache, P. J., 1972, Computational Fluid Dynamics, Hermosa, New Mexico, pp. 139–173.
4.
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.
5.
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
.
6.
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
.
7.
Brandt
,
A.
,
Dendy
,
J. E.
, and
Ruppel
,
H.
,
1980
,
The multigrid method for semi-implicit hydrodynamic codes
,
J. Comput. Phys.
,
34
, pp.
348
370
.
8.
Hackbusch, W., 1985, Multigrid Methods for Applications, Springer, Berlin.
9.
Lange
,
C. F.
,
Scha¨fer
,
M.
, and
Durst
,
F.
,
2002
,
Local block refinement with a multigrid flow solver
,
Int. J. Numer. Methods Fluids
38
, pp.
21
41
.
10.
Ladeve´ze
,
J.
, and
Peyret
,
R.
,
1974
,
Calcul numerique d’une solution avec singularite´ des equations de Navier-Stokes: e´coulement dans un canal avec variation brusque de section
,
J. Mech.
,
13
, no.
3
, pp.
367
396
.
11.
Armaly
,
B. F.
,
Durst
,
F.
,
Peireira
,
J. C. F.
,
Scho¨nung
,
B.
,
1983
,
Experimental and theoretical investigation of backward-facing step flow
,
J. Fluid Mech.
,
127
, pp.
473
496
.
12.
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
.
13.
Kim
,
J.
, and
Moin
,
P.
,
1985
,
Application of a fractional-step method to incompressible Navier-Stokes equations
,
J. Comput. Phys.
,
59
, pp.
308
323
.
14.
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
.
15.
Lee
,
T.
, and
Mateescu
,
D.
,
1998
,
Experimental and numerical investigation of 2D backward-facing step flow
,
J. Fluids Struct.
,
12
, pp.
703
716
.
16.
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
.
17.
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
.
18.
Heenan
,
A. F.
, and
Morrison
,
J. F.
,
1998
,
Passive control of backstep flow
,
Exp. Therm. Fluid Sci.
,
16
, pp.
122
132
.
19.
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
.
20.
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
.
21.
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
.
22.
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
.
23.
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
.
24.
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
.
25.
White, F. M., 1991, Viscous Fluid Flow, 2nd ed., McGraw-Hill, New York.
26.
Orlanski
,
I.
,
1976
,
A simple boundary condition for unbounded flows
,
J. Comput. Phys.
,
21
, pp.
251
269
.
27.
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.
28.
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
.
29.
Breuer, M., 2002, Direkte Numerische Simulation und Large-Eddy Simulation turbulenter Stro¨mungen auf Hochleistungsrechnern, Habilitationsschrift, Universita¨t Erlangen-Nu¨rnberg, Berichte aus der Stro¨mungstechnik, ISBN 3-8265-9958-6, Shaker Verlag, Aachen.
30.
Demirdzˇic´
,
I.
, and
Peric´
,
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
.
31.
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
.
32.
Peric´
,
M.
,
Kessler
,
R.
, and
Scheuerer
,
G.
,
1988
,
Comparison of finite-volume numerical methods with staggered and colocated grids
,
Comput. Fluids
,
16
, pp.
389
403
.
33.
Durst
,
F.
, and
Scha¨fer
,
M.
,
1996
,
A parallel blockstructured multigrid method for the prediction of incompressible flows
,
Int. J. Numer. Methods Fluids
22
, pp.
549
565
.
34.
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
.
35.
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
.
36.
Durst
,
F.
,
Shi
,
J. M.
, and
Breuer
,
M.
,
2002
,
Numerical prediction of hot-wire corrections near walls
,
J. Fluids Eng.
,
124
, pp.
241
250
.
37.
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
.
38.
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
.
39.
Oswatitsch, K., 1958, Die Ablo¨sungsbedingung von Grenzschichten, In: Grenzschichtforschung, ed. H. Goertler, pp. 357–367, Springer Verlag Berlin/Go¨ttingen/Heidelberg.
You do not currently have access to this content.