Stokes flow through a planar contraction is represented by matching together two series of Papkovich-Fadle eigenfunctions. Each series represents the solution in one of the unbounded rectangular regions upstream and downstream of the contraction plane. The coefficients of the series are obtained by weakly enforcing C3 matching conditions at the contraction plane using the Galerkin method. A post-processing technique is used to improve the appearance of the streamline plots near the singularity in the solution at the re-entrant corner of the channel. The pressure variation along the channel, as well as the excess pressure drop due to the contraction and the size of the upstream recirculating zone versus the contraction ratio, are presented. Channel contraction ratios of between two and six are considered.

Issue Section:
Technical Papers
Topics:
Creeping flow, Eigenfunctions, Corners (Structural elements), Galerkin method, Pressure, Pressure drop
1.
Boger
D. V.
,
1987
, “
Viscoelastic Flows Through Contractions
,”
Annual Review of Fluid Mechanics
, Vol.
19
, pp.
157
–
182
.
2.
Davies
A. R.
,
Lee
S. J.
, and
Webster
M. F.
,
1984
, “
Numerical Simulations of Viscoelastic Flow: The Effect of Mesh Size
,”
Journal of Non-Newtonian Fluid Mechanics
, Vol.
16
, pp.
117
–
139
.
3.
Dennis
S. C. R.
, and
Smith
F. T.
,
1980
, “
Steady Flow Through a Channel with a Symmetrical Constriction in the Form of a Step
,”
Proceedings of the Royal Society London
, Vol.
A372
, pp.
393
–
414
.
4.
Forray, M. J., 1968, Variational Calculus in Science and Engineering, McGraw-Hill, New York.
5.
Ingham, D. B., and Kelmanson, M. A., 1984, Boundary Integral Equation Analyses of Singular, Potential, and Biharmonic Problems (Lecture Notes in Engineering), C. A. Brebbia and S. A. Orszag, eds, Springer-Verlag, Berlin.
6.
Joseph
D. D.
, and
Sturges
L.
,
1978
, “
The Convergence of Biorthogonal Series for Biharmonic and Stokes Flow Edge Problems: Part II
,”
SIAM Journal of Applied Mathematics
, Vol.
34
, No.
I
, pp.
7
–
26
.
7.
Karageorghis
A.
, and
Phillips
T. N.
,
1989
, “
Spectral Collocation Methods for Stokes Flow in Contraction Geometries and Unbounded Domains
,”
Journal of Computational Physics
, Vol.
80
, pp.
314
–
330
.
8.
Karageorghis
A.
, and
Phillips
T. N.
,
1991
, “
Conforming Chebyshev Spectral Collocation Methods for the Solution of Laminar Flow in a Constricted Channel
,”
IMA Journal of Numerical Analysis
, Vol.
11
, pp.
33
–
54
.
9.
Leal, L. G., 1992, Laminar Flow and Convective Transport Processes, Butterworth-Heinemann, London.
10.
Phillips
T. N.
, and
Davies
A. R.
,
1988
, “
On Semi-Infinite Spectral Elements for Poisson Problems With Re-entrant Boundary Singularities
,”
Journal of Computational and Applied Mathematics
, Vol.
21
, pp.
173
–
188
.
11.
Smith
R. C. T.
,
1952
, “
The Bending of a Semi-Infinite Strip
,”
Australian Journal of Scientific Research
, Vol.
5
, pp.
227
–
237
.
12.
Trogdon
S. A.
, and
Joseph
D. D.
,
1982
, “
Matched Eigenfunction Expansions for Slow Flow Over a Slot
,”
Journal of Non-Newtonian Fluid Mechanics
, Vol.
10
, pp.
185
–
213
.
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