Creeping flow through an annular stenosis in a pipe
Author:
A. M. J. Davis
Journal:
Quart. Appl. Math. 49 (1991), 507-520
MSC:
Primary 76D07
DOI:
https://doi.org/10.1090/qam/1121683
MathSciNet review:
MR1121683
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Abstract: The creeping flow disturbance of Poiseuille flow due to a disk can be determined by the use of a distribution of “ringlet” force singularities but the method does not readily adapt to the complementary problem involving an annular constriction. Here it is shown that a solvable Fredholm integral equation of the second kind with bounded kernel can be obtained for an Abel transform of the density function. The exponential decay associated with the biorthogonal eigenfunctions ensures that the flow adjusts to the presence of the constriction in at most a pipe length of half a radius on either side. Methods that depend on matching series at the plane of the constriction appear doomed to failure. The physical quantities of interest are the additional pressure drop and the maximum velocity. The lubricating effect of inlets is demonstrated by extending the analysis to a periodic array of constrictions.
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R. A. Ross, Fluid flow in a stenotic tube, Seventh Canadian Symposium on Fluid Dynamics, 1986
R. Shail and D. J. Norton, On the slow broadside motion of a thin disc along the axis of a fluid-filled circular duct, Proc. Cambridge Philos. Soc. 65, 793–802 (1969)
A. M. J. Davis, Stokes drag on a disk sedimenting towards a plane or with other disks; additional effects of a side wall or free surface, Phys. Fluids A2, 301–312 (1990)
A. M. J. Davis, Stokes drag on a narrow annular disk sedimenting in the presence of fixed boundaries or other disks, Phys. Fluids A3, 249–257 (1991)
Z. Dagan, S. Weinbaum, and R. Pfeffer, An infinite series solution for the creeping motion through an orifice of finite length, J. Fluid Mech. 115, 505–523 (1982)
J. S. Vrentas and J. L. Duda, Flow of a Newtonian fluid through a sudden contraction, Appl. Sci. Res. 28, 241–260 (1973)
T. N. Phillips, Singular matched eigenfunction expansions for Stokes flow around a corner, IMA J. Appl. Math. 42, 13–26 (1989)
I. N. Sneddon, Mixed Boundary Value Problems in Potential Theory, North-Holland, Amsterdam, 1966
S. E. El-Gendi, Chebyshev solution of differential, integral and integro-differential equations, Comput. J. 12, 282–287 (1969)
J. M. Dorrepaal, M. E. O’Neill, and K. B. Ranger, Axisymmetric Stokes flow past a spherical cap, J. Fluid. Mech. 75, 273–286 (1976)
J. Y. Yoo and D. D. Joseph, Stokes flow in a trench between concentric cylinders, SIAM J. Appl. Math. 34, 247–285 (1978)
R. A. Ross, Fluid flow in a stenotic tube, Seventh Canadian Symposium on Fluid Dynamics, 1986
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© Copyright 1991
American Mathematical Society