Two-dimensional laminar incompressible wall jet flow over a backward-facing step is solved numerically to gain insight into the expansion and recirculation of flow processes. Transient streamfunction vorticity formulation of the Navier-Stokes equation is solved with clustered grids on the physical domain. The behavior of the jet has been studied for different step geometry (step length, l, step height, s) and Reynolds number (Re). It is found that the presence of a step in the wall jet flow creates recirculation and the reattachment length follows an almost linear trend within the range considered for both parameters Re and step geometry. Simulations are made to show the effect of entrainment on recirculation eddy. Detailed study of u velocity decay is reported. The velocity profile in the wall jet region shows good agreement with experimental as well as similarity results. The distance where the similarity profile forms is reduced by increasing the step geometry whereas an increment in Re increases this distance. The effects of Re, step length, and step height on wall vorticity are presented. The parametric study is helpful to predict the reattachment location for wall jet flows over step.

1.
Glauert
,
M. B.
, 1956, “
The Wall Jet
,”
J. Fluid Mech.
0022-1120,
1
(
1
), pp.
1
10
.
2.
Schlichting
,
H.
, and
Gersten
,
K.
, 2000,
Boundary Layer Theory
,
8th ed.
Springer
,
New York
.
3.
Amitay
,
M.
, and
Cohen
,
J.
, 1997, “
Instability of a Two-Dimensional Plane Wall Jet
,”
J. Fluid Mech.
0022-1120,
344
, pp.
67
94
.
4.
Cohen
,
J.
,
Amitay
,
M.
, and
Bayly
,
B. J.
, 1992, “
Laminar-Turbulent Transition of Wall-Jet Flows Subjected to Blowing and Suction
,”
Phys. Fluids A
0899-8213,
4
, pp.
283
289
.
5.
Quintana
,
D. L.
,
Amitay
,
M.
,
Ortega
,
A.
, and
Wygnanski
,
I. J.
, 1997, “
Heat Transfer in the Forced Laminar Wall Jet
,”
ASME J. Heat Transfer
0022-1481,
119
, pp.
451
459
.
6.
Seidel
,
J.
, 2001, “
Numerical Investigations of Forced Laminar and Turbulent Wall Jets Over a Heated Surface
,” Ph.D. thesis, Faculty of the Department of Aerospace and Mechanical Engineering. The Graduate College, The University of Arizona, Tucson, AZ.
7.
Bhattacharjee
,
P.
, and
Loth
,
E.
, 2004, “
Simulations of Laminar and Transitional Cold Wall Jets
,”
Int. J. Heat Fluid Flow
0142-727X,
25
, pp.
32
43
.
8.
Sato
,
H.
, 1960, “
The Stability and Transition of a Two-Dimensional Jet
,”
J. Fluid Mech.
0022-1120,
7
, pp.
53
80
.
9.
Sato
,
H.
, and
Sakao
,
F.
, 1964, “
An Experimental Investigation of the Instability of a Two-Dimensional Jet at Low Reynolds Numbers
,”
J. Fluid Mech.
0022-1120,
20
, pp.
337
352
.
10.
Batchelor
,
G. K.
, and
Gill
,
A. E.
, 1962, “
Analysis of the Stability of Axisymmetric Jets
,”
J. Fluid Mech.
0022-1120,
14
, pp.
529
551
.
11.
Cohen
,
J.
, and
Wygnanski
,
I.
, 1987, “
The Evolution Instabilities in the Axisymmetric Jet. Part 1. The Linear Growth of Disturbances Near the Nozzle
,”
J. Fluid Mech.
0022-1120,
176
, pp.
191
219
.
12.
Sarma
,
A. S. R.
,
Sundararajan
,
T.
, and
Ramjee
,
V.
, 2000, “
Numerical Simulation of Confined Laminar Jet Flows
,”
Int. J. Numer. Methods Fluids
0271-2091,
33
, pp.
609
626
.
13.
Barton
,
I. E.
, 1997, “
The Entrance Effect of Laminar Flow Over a Backward-Facing Step Geometry
,”
Int. J. Numer. Methods Fluids
0271-2091,
25
, pp.
633
644
.
14.
Valencia
,
A.
, and
Hinojosa
,
L.
, 1997, “
Numerical Solution of Pulsating Flow and Heat Transfer Characteristics in a Channel With Backward-Facing Step
,”
Heat Mass Transfer
0947-7411,
32
, pp.
143
148
.
15.
Jacob
,
M. C.
,
Louisot
,
A.
,
Juve
,
D.
, and
Guerrand
,
S.
, 2001, “
Experimental Study of Sound Generated by Backward-Facing Steps Under Wall Jet
,”
AIAA J.
0001-1452,
39
(
7
), pp.
1254
1260
.
16.
Roache
,
P. J.
, 1998,
Fundamentals of Computational Fluid Dynamics
,
Hermosa
,
Albuquerque, NM
, Chap. 3.
17.
Napolitano
,
M.
,
Pascazio
,
G.
, and
Quartapelle
,
L.
, 1999, “
A Review of Vorticity Conditions in the Numerical Solution of the ζ-ψ Equations
,”
Comput. Fluids
0045-7930,
28
, pp.
139
185
.
18.
Huang
,
H.
, and
Wetton
,
B. R.
, 1996, “
Discrete Compatibility in Finite Difference Methods for Viscous Incompressible Fluid Flow
,”
J. Comput. Phys.
0021-9991,
126
, pp.
468
478
.
19.
Bajura
,
R. A.
, and
Szewczyk
,
A. A.
, 1970, “
Experimental Investigation of a Laminar Two-Dimensional Plane Wall Jet
,”
Phys. Fluids
0031-9171,
13
, pp.
1653
1664
.
20.
Kang
,
S. H.
, and
Greif
,
R.
, 1992, “
Flow and Heat Transfer to a Circular Cylinder With a Hot Impinging Air Jet
,”
Int. J. Heat Mass Transfer
0017-9310,
35
(
9
), pp.
2173
2183
.
21.
Kanna
,
P. R.
, and
Das
,
M. K.
, 2006, “
A Short Note on the Entrainment and Exit Boundary Conditions
,”
Int. J. Numer. Methods Fluids
0271-2091,
50
(
8
), pp.
973
985
.
22.
Kuyper
,
R. A.
,
Van Der Meer
,
T. H.
,
Hoogendoorn
,
C. J.
, and
Henkes
,
R. A. W. M.
, 1993, “
Numerical Study of Laminar and Turbulent Natural Convection in an Inclined Square Cavity
,”
Int. J. Heat Mass Transfer
0017-9310,
36
(
11
), pp.
2899
2911
.
23.
Comini
,
G.
,
Manzan
,
M.
, and
Nonino
,
C.
, 1994, “
Finite Element Solution of the Streamfunction-Vorticity Equations for Incompressible Two-Dimensional Flows
,”
Int. J. Numer. Methods Fluids
0271-2091,
19
, pp.
513
525
.
24.
Ghia
,
U.
,
Ghia
,
K. N.
, and
Shin
,
C. T.
, 1982, “
High Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and Multigrid Method
,”
J. Comput. Phys.
0021-9991,
48
, pp.
387
411
.
25.
Armaly
,
B. F.
,
Durst
,
F.
,
Pereira
,
J. C. F.
, and
Schonung
,
B.
, 1983, “
Experimental and Theoretical Investigation of Backward-Facing Step Flow
,”
J. Fluid Mech.
0022-1120,
127
, pp.
473
496
.
26.
Gartling
,
D. K.
, 1990, “
A Test Problem for Outflow Boundary Conditions-Flow Over a Backward-Facing Step
,”
Int. J. Numer. Methods Fluids
0271-2091,
11
, pp.
953
967
.
27.
Kanna
,
P. R.
, and
Das
,
M. K.
, 2005, “
Conjugate Forced Convection Heat Transfer From a Flat Plate by Laminar Plane Wall Jet Flow
,”
Int. J. Heat Mass Transfer
0017-9310,
48
, pp.
2896
2910
.
28.
Durst
,
F.
,
Pereira
,
J. C. F.
, and
Tropea
,
C.
, 1993, “
The Plane Symmetric Sudden-Expansion Flow at Low Reynolds Numbers
,”
J. Fluid Mech.
0022-1120,
248
, pp.
567
581
.
29.
Kanna
,
P. R.
, and
Das
,
M. K.
, 2005, “
Numerical Simulation of Two-Dimensional Laminar Incompressible Offset Jet Flows
,”
Int. J. Numer. Methods Fluids
0271-2091,
49
(
4
), pp.
439
464
.
30.
Oosterlee
,
C. W.
,
Wesseling
,
P.
,
Segal
,
A.
, and
Brakkee
,
E.
, 1993, “
Benchmark Solutions for the Incompressible Navies-Stokes Equations in General Co-ordinates on Staggered Grids
,”
Int. J. Numer. Methods Fluids
0271-2091,
17
, pp.
301
321
.
31.
Kondoh
,
T.
,
Nagano
,
Y.
, and
Tsuji
,
T.
, 1993, “
Computational Study of Laminar Heat Transfer Downstream of a Backward-Facing Step
,”
Int. J. Heat Mass Transfer
0017-9310,
36
(
3
), pp.
577
591
.
32.
Thangam
,
S.
, and
Knight
,
D. D.
, 1989, “
Effect of Step Height on the Separated Flow Past to Backward Facing Step
,”
Phys. Fluids A
0899-8213,
1
, pp.
604
606
.
33.
Chiriac
,
V. A.
, and
Ortega
,
A.
, 2002, “
A Numerical Study of the Unsteady Flow and Heat Transfer in a Transitional Confined Slot Jet Impinging on an Isothermal Surface
,”
Int. J. Heat Mass Transfer
0017-9310,
45
, pp.
1237
1248
.
You do not currently have access to this content.