Abstract
In the paper, we investigate the problem of a symmetric two-dimensional fluid outflow from a vessel bounded by two parallel walls. The outflow is through a filter modeled by a permeable surface. It is assumed that when a liquid passes through such a surface, the local seepage velocity is proportional to the local pressure drops between the input and output sides of the filter. It is also assumed that the filter has a directing effect: the outflowing liquid moves in the direction perpendicular to the plane of the filter. The liquid moves under the action of a given pressure difference at infinity in the vessel and in the outflowing jet. Inside the vessel, the liquid is assumed to be ideal and incompressible, and the flow is assumed to be potential. After passing through the filter, the liquid remains ideal and incompressible, but the unidirectional flow in the outflowing jet is no longer potential and will have a vorticity distribution. We have found an exact analytical solution of the problem using the method of conformal mapping. The proposed formulation modifies that by Joukowsky (Mat. Sbornik 15, 1890), who studied a similar outflow through an open orifice with the formation of a jet bounded by free streamlines.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
N. E. Jukowsky, ‘‘A modification of Kirchhoff’s method of determining two-dimensional motions of a fluid given constant velocity along an unknown streamline,’’ Mat. Sb. 15, 121–278 (1890); in Collected Works of N. E. Joukowsky (Trans. CAHI, 1930), Vol. 3, No. 3.
M. I. Gurevich, The Theory of Jets in an Ideal Fluid (Pergamon, Oxford, 1966).
J. W. Elder, ‘‘Steady flow through non-uniform gauzes of arbitrary shape,’’ J. Fluid Mech. 5, 355–368 (1959).
J.-K. Koo and D. F. James, ‘‘Fluid flow around and through a screen,’’ J. Fluid Mech. 60, 513–538 (1973).
I. P. Castro, ‘‘Some problems concerning the production of a linear shear flow using curved wire-gauze screens,’’ J. Fluid Mech. 76, 689–709 (1976).
D. R. Jenkins and N. G. Barton, ‘‘Computation of the free-furface shape of an invisdd jet incident on a porous wall,’’ IMA J. Appl. Math. 41, 193–206 (1988).
A. C. King, ‘‘A note on the impact of a jet on a porous wall,’’ IMA J. Appl. Math. 45, 139–146 (1990).
Kh. A. Rakhmatulin and S. V. Guvernyuk, ‘‘On formulation of problems of incompressible flows over permeable bodies,’’ Fluid Mech. Sov. Res. 17 (2), 46–71 (1988).
V. A. Buchin, ‘‘Solution of the problem of the flow around a permeable plate with separation of jets,’’ Dokl. Akad. Nauk SSSR 269, 1331–1335 (1983).
V. A. Buchin, S. V. Guvernyuk, and S. A. Feshehenko, ‘‘Solution of the problem of outflow of fluid from a half-space through a partially permeable wall,’’ Fluid Dyn. 20, 815–817 (1985).
P. R. Andronov and S. V. Guvernyuk, ‘‘The streamline flow around a permeable plate in a plane-parallel channel,’’ J. Appl. Math. Mech. 79, 270–280 (2015).
Funding
This paper has been supported by the Russian Science Foundation (grant no. 18-11-00115).
Author information
Authors and Affiliations
Corresponding authors
Additional information
(Submitted by A. M. Elizarov)
Rights and permissions
About this article
Cite this article
Maklakov, D.V., Pichugov, V.A. Symmetric Fluid Outflow from a Vessel Bounded by Two Parallel Walls through a Filter (Modification of Joukowsky’s Problem). Lobachevskii J Math 43, 2961–2969 (2022). https://doi.org/10.1134/S1995080222130297
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995080222130297