Flows of viscoplastic fluids through sudden, conical axisymmetric contraction are studied. A finite-element numerical simulation is performed using a biviscosity approximation. Inertia is neglected. The effects of yield stress are analyzed, as are those of shear-thinning, contraction angle, and contraction ratio. The pressure losses, detailed structure of the flow such as the rigid static and moving zones, and the vortex are given in relation to these parameters. Consistent comparisons are also made with the experimental results obtained in the laboratory.

1.
Prager, W., 1961, Introduction to Mechanics of Continua, Ginn, Boston.
2.
Nguyen
,
Q. D.
, and
Boger
,
D. V.
,
1992
, “
Measuring the Flow Properties of Yield Stress Fluids
,”
Annu. Rev. Fluid Mech.
,
24
, pp.
47
88
.
3.
Wilson
,
S. D. R.
,
1993
, “
Squeezing Flow of Bingham Material
,”
J. Fluid Mech.
,
47
, pp.
211
219
.
4.
Piau
,
J. M.
,
1996
, “
Flow of a Yield Stress Fluid in a Long Domain. Application to Flow on an Inclined Plane
,”
J. Rheol.
,
40
, pp.
711
723
.
5.
Piau, J. M., 1998, “Crucial Elements of Yield Stress Fluid Rheology,” Dynamic Complex Fluids, Royal Society and Imperial Press, M. Adams, ed., pp. 353–374.
6.
Barnes
,
H. A.
,
1999
, “
The Yield Stress—a Review or παντα ρει—Everything Flows?
J. Non-Newtonian Fluid Mech.
,
81
, pp.
133
178
.
7.
Coupez, T., Zine, M. A., and Agassant, J. F., 1994, “Numerical Simulation of Bingham Fluid Flow,” Proceedings of the 4th European Rheology Conference, Seville, pp. 341–343.
8.
Isayev
,
A. I.
, and
Huang
,
Y. H.
,
1993
, “
Two-Dimensional Planar Flow of a Viscoelastic Plastic Medium
,”
Rheol. Acta
,
32
, pp.
181
191
.
9.
Gans
,
R. F.
,
1999
, “
On the Flow of a Yield Strength Fluid Through a Contraction
,”
J. Non-Newtonian Fluid Mech.
,
81
, pp.
184
195
.
10.
Magnin, A., and Piau, J. M., 1992, “Flow of Yield Stress Fluids Through a Sudden Change of Section,” Theoretical and Applied Rheology, P. Moldenaers and R. Keunings, eds., Elsevier, Amsterdam pp. 195–197.
11.
Mitsoulis
,
E.
,
Abdali
,
S. S.
, and
Markatos
,
N. C.
,
1993
, “
Flow Simulation of Herschel-Bulkley Fluids Through Extrusion Dies
,”
Can. J. Chem. Eng.
,
71
, pp.
147
160
.
12.
Abdali
,
S. S.
,
Mitsoulis
,
E.
, and
Markatos
,
N. C.
,
1992
, “
Entry and Exit Flows of Bingham Fluids
,”
J. Rheol.
,
36
, pp.
389
407
.
13.
Crochet, M. J., Davies, A. R., and Walters, K., 1984, “Numerical Simulation of Non-Newtonian Flows,” Elsevier, Amsterdam.
14.
Papanastasiou
,
T. C.
,
1987
, “
Flow of Material With Yield
,”
J. Rheol.
,
31
, pp.
385
404
.
15.
Loest
,
H.
,
Lipp
,
R.
, and
Mitsoulis
,
E.
,
1994
, “
Numerical Flow Simulation of Viscoplastic Slurries and Design Criteria for a Tape Casting Unit
,”
J. Am. Ceram. Soc.
,
77
, pp.
254
262
.
16.
Beaulne
,
M.
, and
Mitsoulis
,
E.
,
1997
, “
Creeping Motion of a Sphere in Tubes Filled With Herschel-Bulkley Fluids
,”
J. Non-Newtonian Fluid Mech.
,
72
, pp.
55
71
.
17.
Burgos
,
G. R.
,
Alexandrou
,
A. N.
, and
Entov
,
V.
,
1999
, “
On the Determination of Yield Surfaces in Herschel-Bulkley Fluids
,”
J. Rheol.
,
43
, pp.
463
483
.
18.
Burgos
,
G. R.
, and
Alexandrou
,
A. N.
,
1999
, “
Flow Development of Herschel-Bulkley Fluids in a Sudden Three-Dimensional Square Expansion
,”
J. Rheol.
,
43
, pp.
485
498
.
19.
Alexandrou
,
A. N.
,
McGilvreay
,
T. M.
, and
Burgos
,
G.
,
2001
, “
Steady Herschel-Bulkley Fluid Flow in Three-Dimensional Expansions
,”
J. Non-Newtonian Fluid Mech.
,
100
, pp.
77
96
.
20.
Lipscomb
,
G. G.
, and
Denn
,
M. M.
,
1984
, “
Flow of Bingham Fluids in Complex Geometries
,”
J. Non-Newtonian Fluid Mech.
,
14
, pp.
337
346
.
21.
O’Donovan
,
E. J.
, and
Tanner
,
R. I.
,
1984
, “
Numerical Study of the Bingham Squeeze Film Problem
,”
J. Non-Newtonian Fluid Mech.
,
15
, pp.
75
83
.
22.
Vradis
,
G. C.
, and
Otugen
,
M. V.
,
1997
, “
The Axisymmetric Sudden Expansion Flow of a Non-Newtonian Viscoplastic Fluid
,”
ASME J. Fluids Eng.
,
119
, pp.
193
199
.
23.
Jay
,
P.
,
Magnin
,
A.
, and
Piau
,
J. M.
,
2001
, “
Viscoplastic Fluid Flow Through a Sudden Axisymmetric Expansion
,”
AIChE J.
,
47
(
10
), pp.
2155
2166
.
24.
Belhadri, M., Magnin, A., and Piau, J. M., 1994, Actes du 8em´e Colloque TIFAN, Toulouse, 7, pp. 29–38.
25.
Magnin
,
A.
, and
Piau
,
J. M.
,
1990
, “
Cone Plate Rheometry of a Yield Stress Fluid. Measurement of an Aqueous Gel
,”
J. Non-Newtonian Fluid Mech.
,
36
, pp.
85
108
.
26.
Kim-E
,
M. E.
,
Brown
,
R. A.
, and
Armstrong
,
R. C.
,
1983
, “
The Roles of Inertia and Shear Thinning in Flow of Inelastic Liquid Through an Axisymmetric Contraction
,”
J. Non-Newtonian Fluid Mech.
,
13
, pp.
41
63
.
27.
Nguyen
,
H.
, and
Boger
,
D. V.
,
1979
, “
The Kinematics and Stability of Die Entry Flows
,”
J. Non-Newtonian Fluid Mech.
,
5
, pp.
353
368
.
28.
Boger
,
D. V.
,
1987
, “
Viscoelastic Flows Through Contractions
,”
Annu. Rev. Fluid Mech.
,
19
, pp.
157
182
.
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