ROTARY VIBRATIONS OF A POROUS SPHERICAL SHELL WITH AN IMPERMEABLE CORE IN A VISCOUS LIQUID
Background. The investigation of the viscous liquid flows in contact with the oscillating submerged porous bodies of various configurations is of a considerable interest for hydrodynamics in the connection with a great theoretical importance and various practical applications. The aim of the prese...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Penza State University Publishing House
2020-03-01
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| Series: | Известия высших учебных заведений. Поволжский регион: Физико-математические науки |
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| Summary: | Background. The investigation of the viscous liquid flows in contact with the oscillating
submerged porous bodies of various configurations is of a considerable interest for hydrodynamics in the connection with a great theoretical importance and
various practical applications. The aim of the present paper is to determine the fields
of filtration velocities and free liquid velocities respectively inside and outside the
porous spherical shell with the impermeable spherical core which performs rotational-
oscillatory motion in a viscous liquid.
Materials and methods. To solve the problem of the viscous liquid flow induced
by rotational-oscillatory motion of the submerged porous spherical shell with the
impermeable spherical core we used methods of mathematical physics, vector analysis
and ordinary differential equations solving. To describe the viscous liquid flows
in the porous medium the nonstationary Brinkman equation is used. The motion of
the viscous liquid outside the porous medium with the Navier-Stokes equation is described.
Results. Exact analytical solutions for the nonstationary Brinkman equation in the
region inside the porous medium and for the Navier-Stokes equation outside the porous
medium respectively are obtained. The fields of the filtration velocity and the free
liquid velocity inside and outside the porous medium respectively are determined.
Conclusions. It is shown that the liquid velocity fields in the cases of the spherical
porous shell with an impermeable core and a porous sphere without the core differs
considerable. It is shown also that the results obtained earlier for particular case
of the viscous fluid flows induced by a rotational-oscillatory motion of a submerged
porous sphere can be obtained from the solution presented in this paper. |
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| ISSN: | 2072-3040 |