Abstract

A numerical study has been carried out for the laminar flow of Newtonian and non-Newtonian power-law fluids through a suddenly expanded axisymmetric geometry. Mathematical correlations are proposed for the prediction of the length of the recirculating eddy in terms of Reynolds number, expansion ratio and rheological parameters. A wide range of expansion ratios (1.25ER8.0) has been covered for the Newtonian fluid and both the shear-thinning and shear-thickening flow characteristic fluids have been considered for the non-Newtonian fluids.

1.
Macagno
,
O. E.
, and
Hung
,
T. K.
, 1967, “
Computational and Experimental Study of Captive Annular Eddy
,”
J. Fluid Mech.
0022-1120,
28
(
1
), pp.
43
64
.
2.
Fletcher
,
D.
,
Maskel
,
S.
, and
Patrick
,
M.
, 1985, “
Heat and Mass Transfer Computations for Laminar Flow in an Axisymmetric Sudden Expansion
,”
Comput. Fluids
0045-7930,
13
, pp.
207
221
.
3.
Back
,
L.
, and
Roshke
,
E.
, 1972, “
Shear Layer Regimes and Wave Instabilities and Reattachment Lengths Downstream of an Abrupt Circular Channel Expansion
,”
ASME J. Appl. Mech.
0021-8936,
94
, pp.
677
681
.
4.
Badekas
,
D.
, and
Knight
,
D. D.
, 1992, “
Eddy Correlations for Laminar Axisymmetric Sudden Expansion Flows
,”
ASME Trans. J. Fluids Eng.
0098-2202,
114
, pp.
119
121
.
5.
Halmos
,
A. L.
,
Boger
,
D. V.
, and
Cabelli
,
A.
, 1975, “
The Behaviour of a Power-law Fluid Flowing Through a Sudden Expansion, Part I: A Numerical Solution
,”
AIChE J.
0001-1541,
21
, pp.
540
549
.
6.
Halmos
,
A. L.
,
Boger
,
D. V.
, and
Cabelli
,
A.
, 1975, “
The Behaviour of a Power-law Fluid Flowing Through a Sudden Expansion, Part II: Experimental Verification
,”
AIChE J.
0001-1541,
21
, pp.
550
553
.
7.
Kahine
,
K.
,
Nguyen
,
V. T.
, and
Lebouché
,
M.
, 1997, “
Ecoulment de Fluides Non-Newtonians a Travers des Elargissements Brusques
,”
Int. Commun. Heat Mass Transfer
0735-1933,
24
, pp.
1103
1112
.
8.
Nguyen
,
V. T.
,
Kahine
,
K.
, and
Lebouché
,
M.
, 1999, “
Étude Numérique de l’Écoulement de Fluides Non Newtoniens à Travers un Élargissement Brusque
,”
Mécanique des Fluides∕Fluid Mechanics
,
327
śerie II b,
91
94
.
9.
Pinho
,
F. T.
,
Oliveira
,
P. J.
, and
Miranda
,
J. P.
, 2003, “
Pressure Losses in the Laminar Flow of Shear-Thinning Power-law Fluids Across a Sudden Axisymmetric Expansion
,”
Int. J. Heat Fluid Flow
0142-727X,
24
, pp.
747
761
.
10.
Neofytou
,
P.
, and
Drikakis
,
D.
, 2003, “
Non-Newtonian Flow Instability in a Channel With a Sudden Expansion
,”
J. Non-Newtonian Fluid Mech.
0377-0257,
111
, pp.
127
150
.
11.
Neofytou
,
P.
, 2006, “
Transition to Asymmetry of Generalized Newtonian Fluid Flows Through a Symmetric Sudden Expansion
,”
J. Non-Newtonian Fluid Mech.
0377-0257,
133
, pp.
132
140
.
12.
Hirt
,
C. W.
, and
Cook
,
J. L.
, 1972, “
Calculating Three-Dimensional Flows Around Structures and Over Rough Terrain
,”
J. Comput. Phys.
0021-9991,
10
, pp.
324
341
.
13.
Leonard
,
B. P.
, 1976, “
A Stable and Accurate Convective Modeling Procedure Based on Quadratic Upstream Interpolation
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
19
, pp.
59
98
.
14.
Bird
,
R. B.
,
Stewart
,
W. E.
, and
Lightfoot
,
E. N.
, 1960,
Transport Phenomena
,
Wiley
,
New York
.
15.
Nataf
,
F.
, 1989, “
An Open Boundary Condition for the Computation of the Steady Incompressible Navier–Stokes Equations
,”
J. Comput. Phys.
0021-9991,
85
, pp.
104
129
.
16.
Hammad
,
K. J.
,
Vradis
,
G. C.
, and
Ötügen
,
M. V.
, 2001, “
Laminar Flow of a Herschel–Bulkeley Fluid Over an Axisymmetric Sudden Expansion
,”
ASME Trans. J. Fluids Eng.
0098-2202,
123
, pp.
588
594
.
17.
Biswas
,
G.
,
Breuer
,
M.
, and
Durst
,
F.
, 2004, “
Backward-Facing Step Flows for Various Expansion Ratios at Low and Moderate Reynolds Numbers
,”
ASME Trans. J. Fluids Eng.
0098-2202,
126
, pp.
362
374
.
You do not currently have access to this content.