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1
Content available Stokes flow in lid-driven cavity under inclined magnetic field
Gürbüz-Çaldag M., Çelik E.
Archives of Mechanics
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2022
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Vol. 74, nr 6
549--564
EN
Stokes flow in a lid-driven cavity under the effect of an inclined magnetic field is studied. The radial basis function (RBF) approximation is employed to the magnetohydrodynamic (MHD) equations which include Navier-Stokes equations of fluid dynamics and Maxwell’s equations of electromagnetics through Ohm’s law with the Stokes approximation. Numerical results are obtained for the moderate Hartmann number (0 ≤ M ≤ 80) and different angles of a magnetic field (0 ≤ α ≤ π). It is found that the increase in the Hartmann number causes the development of new vortices under the main flow due to the impact of a magnetic field. However, the type of the inclination angle (acute or obtuse) determines the location of the vortices.
2
Content available Slip flow of a sphere in non-concentric spherical hypothetical cell
Krishna-Prasad Madasu
Journal of Applied Mathematics and Computational Mechanics
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2020
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Vol. 19, nr 3
59--70
EN
Slow axisymmetric flow of an incompressible viscous fluid caused by a slip sphere within a non-concentric spherical cell surface is investigated. The uniform velocity (Cunningham’s model) and tangential velocity reaches minimum along a radial direction are imposed conditions at the cell surface (Kvashnin’s model). The general solution of the problem is combined using superposition of the fundamental solution in the two spherical coordinate systems based on the centers of the slip sphere and spherical cell surface. Numerical results for the correction factor on the inner sphere are obtained with good convergence for various values of the relative distance between the centers of the sphere and spherical cell, the slip coefficient, and the volume fraction. The obtained results are in good agreement with the published results. The effect of concentration is more in the Cunningham’s model compared to the Kvashnin’s model. The wall correction factor on the no-slip sphere is more compared to that of a slip sphere. The correction factor on the slip sphere is more than that of a spherical gas bubble.
3
Content available Drag force of a porous particle moving axisymmetrically in a closed cavity of micropolar fluid
Madasu Krishna Prasad
Journal of Applied Mathematics and Computational Mechanics
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2019
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Vol. 18, nr 4
41--51
EN
The present paper deals with the problem of an incompressible axisymmetric creeping flow caused by a porous spherical particle in a spherical cavity filled with micropolar fluid. Depending on the kind of cell model, appropriate boundary conditions are used on the surface of sphere and spherical cavity. Drag force on the porous particle in the presence of a cavity is calculated to determine the correction factor to the Stokes law. A general expression for the hydrodynamic force acting on the porous sphere and, hence, for the wall correction factor of the sphere are obtained. The special cases of the porous sphere in viscous fluid, zero permeability solid sphere in micropolar fluid and viscous fluid are obtained in open and closed cavity respectively.
4
Content available A Comparison of Simplified Two-dimensional Flow Models Exemplified by Water Flow in a Cavern
Prybytak D., Zima P.
Archives of Hydro-Engineering and Environmental Mechanics
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2017
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Vol. 64, nr 3-4
141--154
EN
The paper shows the results of a comparison of simplified models describing a two-dimensional water flow in the example of a water flow through a straight channel sector with a cavern. The following models were tested: the two-dimensional potential flow model, the Stokes model and the Navier-Stokes model. In order to solve the first two, the boundary element method was employed, whereas to solve the Navier-Stokes equations, the open-source code library OpenFOAM was applied. The results of numerical solutions were compared with the results of measurements carried out on a test stand in a hydraulic laboratory. The measurements were taken with an ADV probe (Acoustic Doppler Velocimeter). Finally, differences between the results obtained from the mathematical models and the results of laboratory measurements were analysed.
5
Content available Modelowanie przepływu w układzie niekoncentrycznych obracających się cylindrów metodą elementów brzegowych
Teleszewski T. J., Sorko S. A.
Symulacja w Badaniach i Rozwoju
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2016
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Vol. 7, nr 1-2
67--79
PL
W opracowaniu przedstawiono algorytm rozwiązania zagadnienia przepływowego płaskiego, laminarnego ruchu cieczy lepkiej pomiędzy niekoncentrycznymi wirującymi cylindrami. Przedstawiono matematyczny opis zagadnienia przepływowego i metodę wyznaczania pola prędkości cieczy i pola ciśnienia oraz naprężeń lepkościowych na ściankach struktur ograniczających przepływ.
EN
In the elaboration was presented the algorithm of solution of the problem of two dimensional, laminar flow of viscous fluid between eccentric rotating cylinders. The problem was formulated and solved by using Boundary Element Method. One introduced the mathematical description of the problem of flow and the method of calculating of the velocity and pressure fields, also tensions on sides of structures restrictive the flow.
6
Content available Modelowanie przepływu Taylora-Couetta metodą elementów brzegowych
Teleszewski T. J., Sorko S. A.
Symulacja w Badaniach i Rozwoju
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2016
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Vol. 7, nr 1-2
55--65
PL
W opracowaniu przedstawiono algorytm rozwiązania zagadnienia przepływowego płaskiego, laminarnego ruchu cieczy lepkiej pomiędzy koncentrycznymi wirującymi cylindrami. Przedstawiono matematyczny opis zagadnienia przepływowego i metodę wyznaczania pola prędkości cieczy i pola ciśnienia oraz naprężeń lepkościowych na ściankach struktur ograniczających przepływ.
EN
In the elaboration was presented the algorithm of solution of the problem of two dimensional, laminar flow of viscous fluid between concentric rotating cylinders. The problem was formulated and solved by using Boundary Element Method. One introduced the mathematical description of the problem of flow and the method of calculating of the velocity and pressure fields, also tensions on sides of structures restrictive the flow.
7
Content available remote Method of regularized sources for two-dimensional Stokes flow problems based on rational or exponential blobs
Wen S., Wang K., Zahoor R., Li M., Šarler B.
Computer Assisted Methods in Engineering and Science
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2015
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Vol. 22, no. 3
289--300
EN
The solution of Stokes flow problems with Dirichlet and Neumann boundary conditions is performed by a non-singular method of fundamental solutions (MFS) which does not require artificial boundary, i.e., source points of fundamental solution coincide with the collocation points on the boundary. The fundamental solution of the Stokes pressure and velocity is obtained from the analytical solution due to the action of the Dirac delta- type force. Instead of Dirac delta force, a non-singular function called blob, with a free parameter epsilon is employed, which is limited to Dirac delta function when epsilon is limited to zero. The analytical expressions for related Stokes flow pressure and velocity around such regularized sources have been derived for rational and exponential blobs in an ordered way. The solution of the problem is sought as a linear combination of the fields due to the regularized sources that coincide with the boundary and with their intensities chosen in such a way that the solution complies with the boundary conditions. A numerical example for two-dimensional (2D) driven cavity and a flow between parallel plates are chosen to assess the properties of the method. The results of the posed method of regularized sources (MRS have been compared with the results obtained by the fine-grid second-order classical finite difference method (FDM) and analytical solution. The results converge with finer discretisation; however, they depend on the value of epsilon. The method gives reasonably accurate results for the range of epsilon between 0.1 and 0.5 of the typical nodal distance on the boundary. Exponential blobs give slightly better results than the rational blobs; however, they require slightly more computing time. A robust and efficient strategy to find the optimal value of epsilon is needed in the perspective.
8
Content available Laminar flow past the bottom with obstacles – a suspension approximation
Wojnar R., Bielski W.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2015
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Vol. 63, nr 3
685--695
EN
From Albert Einstein’s study (1905) it is known that suspension introduced to a fluid modifies its viscosity. We propose to describe the influence of obstacles on the Stokesian flow as a such modification. Hence, we treat the fluid flow through small obstacles as a flow with suspension. The flow is developing past the plane bottom under the gravity force. The spatial distribution of suspension concentration is treated as given, and is regarded as an approximation of different obstacles which modify the fluid flow and change its viscosity. The different densities of suspension are considered, beginning of small suspension concentration until 40%. The influence of suspension concentration on fluid viscosity is analyzed, and Brinkman’s formula as fitting best to experimental data is applied.
9
Content available Symulacja pól prędkości i temperatury w przepływie cieczy lepkiej metodą elementów brzegowych
Sorko S. A., Teleszewski T. J.
Symulacja w Badaniach i Rozwoju
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2014
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Vol. 5, nr 2
129--142
PL
W opracowaniu przedstawiono algorytm rozwiązania zagadnienia przepływowego płaskiego, laminarnego ruchu cieczy lepkiej pomiędzy ściankami: płaską i profilowaną, generowanego względnym wzdłużnym ruchem ścianek przy użyciu metody elementów brzegowych. Przedstawiono matematyczny opis zagadnienia przepływowego i metodę wyznaczania pola prędkości cieczy i pola temperatury generowanego w izotermicznym przepływie cieczy lepkiej dyssypacją energii.
EN
In the elaboration was presents the algorithm of solution of the problem of two dimensional, laminar viscous fluid flow between parallel plates: flat and arbitrary profiled, whereat the flow is generated by longitudinal, steady moving of one of the walls. The problem was formulated and solved by using Boundary Element Method. One introduced the mathematical description of the problem of flow and the method of calculating of the velocity field of liquid and of the temperature field generated in the isothermal flow of viscous fluid by dissipation of the energy.
10
Content available Modelowanie oscylacyjnego przepływu cieczy przez przewody prostoosiowe
Sorko S. A.
Symulacja w Badaniach i Rozwoju
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2014
|
Vol. 5, nr 1
29--42
PL
W opracowaniu przedstawiono algorytm rozwiązania zagadnienia przepływowego, laminarnego ruchu cieczy w prostoosiowym przewodzie o dowolnym kształcie przekroju poprzecznego w warunkach oscylacyjnego ruchu wzdłużnego przewodu. Przedstawiono matematyczny opis problemu przy użyciu metody brzegowych równań całkowych. Zaprezentowano rozwiązanie zagadnienia testowego wykazujące poprawność modelu matematycznego i algorytmu obliczeniowego. Przedstawiono przykład wyznaczenia pola prędkości przepływu przez prostoosiowy przewód o przekroju eliptycznym.
EN
In the elaboration was presented the algorithm of solution of the problem of laminar viscous flow through straight pipe of an arbitrary cross-section under conditions of the oscillatory movement of the pipe in longitudinal direction. The mathematical description and solution of the problem was formulated by using integral equations method. One presented solution of the test-problem demonstrative the correctness of the mathematical model and the computational algorithm. The example of the solution of the flow generated by the pressure gradient and the oscillations of the tube of an elliptic cross-section shape was presented.
11
Content available Wyznaczanie przepływów Stokesa w przewodach profilowanych metodą elementów brzegowych
Teleszewski T. J., Sorko S. A.
Symulacja w Badaniach i Rozwoju
|
2013
|
Vol. 4, nr 1
41--50
PL
W opracowaniu przedstawiono zastosowanie metody elementów brzegowych (MEB) do wyznaczania przepływów Stokesa w profilowanych przewodach i kołowym przekroju poprzecznym metodą elementów brzegowych. W celu walidacji metody elementów brzegowych porównano rozwiązania numeryczne zrealizowane metodą elementów brzegowych z rozwiązaniem analitycznym i rezultatami eksperymentalnymi. W prezentowanej pracy przedstawiono graficzne rezultaty obliczeń dla wybranych przykładów, dla których nie są znane rozwiązania analityczne.
EN
The aim of the article is to present a simulation of steady Stokes flow in a circular pipe with changing axisymmetric of radius of the tube using the Boundary Element Method (BEM). Results of this method were compared with experiment result of Taneda and analytical solution. Examples of BEM solution Stokes flow through nozzle, deep caving and rounded caving are also presented. The software was written for a PC computer.
12
Content available Slow extensional flow past a non-homogeneous porous spherical shell
Rajvanshi S. C., Wasu S.
International Journal of Applied Mechanics and Engineering
|
2013
|
Vol. 18, no. 2
491--502
EN
An analytical investigation of extensional flow past a porous spherical shell of finite thickness with velocity slip at the surface is presented. The permeability of the shell varies continuously as a function of the radial distance. The flow in the porous region is assumed to obey Darcy’s Law. The drag has been calculated in terms of normal volume flux rate per unit area of the outer and inner surfaces. Particular cases of flow past a homogeneous sphere and no-slip boundary condition have been deduced.
13
Content available remote Axi-symmetric motion of a porous approximate sphere in an approximate spherical container
Srinivasacharya D., Krishna Prasad M.
Archives of Mechanics
|
2013
|
Vol. 65, nr 6
485--509
EN
The creeping motion of a porous approximate sphere at the instant it passes the center of an approximate spherical container with Ochoa-Tapia and Whitaker’s stress jump boundary condition has been investigated analytically. The Brinkman’s model for the flow inside the porous approximate sphere and the Stokes equation for the flow in an approximate spherical container were used to study the motion. The stream function (and thus the velocity) and pressure (both for the flow inside the porous approximate sphere and inside an approximate spherical container) are calculated. The drag force experienced by the porous approximate spherical particle and wall correction factor are determined in closed forms. The special cases of porous sphere in a spherical container and oblate spheroid in an oblate spheroidal container are obtained from the present analysis. It is observed that drag not only changes with the permeability of the porous region, but as the stress jump coefficient increases, the rate of change in behavior of drag increases.
14
Content available remote Faxén’s law for arbitrary oscillatory Stokes flow past a porous sphere
Prakash J., Raja Sekhar G. P., Kohr M.
Archives of Mechanics
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2012
|
Vol. 64, nr 1
41-41
EN
The present article deals with the study of the hydrodynamics of a porous sphere in an oscillatory viscous flow of an incompressible Newtonian fluid. Unsteady Stokes equations are used for the flow outside the porous sphere and Darcy’s equation is used for the flow inside the porous sphere. Corresponding Faxén’s law for drag and torque acting on the surface of the porous sphere is derived. Also the results are compared with few existing special cases. Examples like uniform flow, oscillating Stokeslet, oscillatory shear flow and quadratic shear flow are discussed.
15
Content available Symulacja linii prądu w przepływach Stokes'a metodą brzegowych równań całkowych
Teleszewski T. J., Rynkowski P.
Symulacja w Badaniach i Rozwoju
|
2011
|
Vol. 2, nr 1
47-54
PL
Opracowanie zawiera zaproponowany algorytm wyznaczania linii prądu w przepływach Stokes’a metodą brzegowych równań całkowych. W celu walidacji metody elementów brzegowych porównano rozwiązania metodą brzegowych równań całkowych ze znanym eksperymentem. Przedstawiony algorytm może być wykorzystany do wyznaczania linii prądu w płaskich przepływach Stokes’a w różnych dziedzinach techniki. W prezentowanej pracy przedstawiono przykładowe graficzne rezultaty obliczeń dla wybranych przykładów, dla których nie są znane rozwiązania analityczne. Algorytm został zaimplementowany w autorskim programie obliczeniowym napisanym w języku Fortran.
EN
In this article it has been introduced the way to calculate streamlines of Stokes flow using Boundary Integral Equation Method. The algorithm was verified using a known experiment S. Taneda. The computer program was written in Fortran programming language. The algorithm BEM enables very effective solving of test and practical problems in engineering and can be alternative to mesh methods like Finite Difference Method, Finite Volume Method or Finite Element Method. A numerical examples were presented.
16
Content available Stokes flow of an incompressible micropolar fluid past a porous spheroidal shell
Iyengar T., Radhika T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2011
|
Vol. 59, nr 1
63-74
EN
Consider a pair of confocal prolate spheroids S0 and S1 where S0 is within S1. Let the spheroid S0 be a solid and the annular region between S0 and S1 be porous. The present investigation deals with a flow of an incompressible micropolar fluid past S1 with a uniform stream at infinity along the common axis of symmetry of the spheroids. The flow outside the spheroid S1 is assumed to follow the linearized version of Eringen’s micropolar fluid flow equations and the flow within the porous region is assumed to be governed by the classical Darcy’s law. The fluid flow variables within the porous and free regions are determined in terms of Legendre functions, prolate spheroidal radial and angular wave functions and a formula for the drag on the spheroid is obtained. Numerical work is undertaken to study the variation of the drag with respect to the geometric parameter, material parameter and the permeability parameter of the porous region. An interesting feature of the investigation deals with the presentation of the streamline pattern.
17
Content available remote Magneto-hydro-dynamic unsteady second-grade fluid flow for Stokes' problem
Mohyuddin M. R., Ali Mirza A., Siddiqui A. M.
International Journal of Applied Mechanics and Engineering
|
2007
|
Vol. 12, no 4
1061-1072
EN
The present note discusses the flow of an unsteady second-grade fluid oscillating on a plate. The magnetic field is applied perpendicular to the flow field in two cases (i) when it is fixed to the fluid, and (ii) when it is fixed to the boundary. The applied magnetic field is found to slow down the flow for the case when it is fixed to the fluid whereas this effect is reversed in the case when it is fixed to the plate. The physical interpretation of the physical parameters is presented graphically and is compared with the already known results.
18
Content available remote Three-particle motion under gravity in Stokes flow: an equilibrium for spheres in contrast to "an end-of-world" for point particles
Ekiel-Jeżewska M. L., Wajnryb E.
Archives of Mechanics
|
2006
|
Vol. 58, nr 4-5
489-494
EN
Evolution of three identical solid spheres falling under gravity in a low-Reynolds number flow is investigated for a symmetric initial configuration. Three spheres aligned horizontally at equal distances evolve towards an equilibrium relative configuration while the point particles collapse onto a single point in a finite time.
19
Content available remote Stokes flow past a porous approximate sphere
Srinivasacharya D., Raghavacharyulu T. K. V., Radhakrishnamacharya G.
International Journal of Applied Mechanics and Engineering
|
2005
|
Vol. 10, no 4
689-697
EN
In this paper, the flow of an incompressible viscous fluid past and within a porous approximate sphere directed along its axis of symmetry is considered. By assuming that Stokes equations for a creeping flow govern the flow outside the body and Darcy's law governs the tluid motion within the porous region of the body, an analytical soIution for the stream function is obtained. The drag experienced by the body is calculated and its variation with respect to the permeability parameter is studied numericaIly. Prom the present analysis, the flow past a porous sphere and spheroid are obtained as special cases.
20
A second kind integral equation formulation for the interaction between a solid particle and a compound drop at low Reynolds number
Kohr M.
Applied Mechanics and Engineering
|
2000
|
Vol. 5, no 3
557-577
EN
In this paper, we determine a boundary integral formulation for the motion and deformation of a compound drop due to its interaction with a solid particle. The problem is reduced to a system of Fredholm integral equations of the second kind. We prove that this system has a unique continous solution when the boundaries of the flow are Lyapunov surfaces and the boundary data are continous.
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