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1
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.
2
Content available remote A functionally-analytic method for modeling axial-symmetric flows of ideal fluid
Plaksa Sergiy A.
Demonstratio Mathematica
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2019
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Vol. 52, nr 1
213--224
EN
We consider axial-symmetric stationary flows of the ideal incompressible fluid as an important case of potential solenoid fields. We use an integral expression of the Stokes flow function via the corresponding complex analytic function for solving a boundary value problem with respect to a steady streamline of the ideal incompressible fluid along an axial-symmetric body. We describe the solvability of the problem in terms of the singularities of the mentioned complex analytic function. The obtained results are illustrated by concrete examples of modelling of steady axial-symmetric flows.
3
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.
4
Content available Modelowanie przepływu Taylora-Couetta metodą elementów brzegowych
Teleszewski T. J., Sorko S. A.
Symulacja w Badaniach i Rozwoju
|
2016
|
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.
5
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.
6
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.
7
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.
8
Content available Modelowanie oscylacyjnego przepływu cieczy przez przewody prostoosiowe
Sorko S. A.
Symulacja w Badaniach i Rozwoju
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2014
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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.
9
Content available Wyznaczanie przepływów Stokesa w przewodach profilowanych metodą elementów brzegowych
Teleszewski T. J., Sorko S. A.
Symulacja w Badaniach i Rozwoju
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2013
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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.
10
Content available Slow extensional flow past a non-homogeneous porous spherical shell
Rajvanshi S. C., Wasu S.
International Journal of Applied Mechanics and Engineering
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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.
11
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.
12
Content available remote Boundary integral method for an oscillatory Stokes flow past a solid particle
Kohr M., Pop I.
International Journal of Applied Mechanics and Engineering
|
2003
|
Vol. 8, no 4
603-620
EN
In this paper, we present a boundary integral method in order to determine the oscillatory Stokes flow due to translational or rotational oscillations of a solid particle in an unbounded viscous incompressible fluid. As an application of this method, we study both cases of small-and high-frequency oscillations. Finally, we give some numerical results in the case of transverse oscillations of a prolate spheroid.
13
Stokes flow past a cylindrical interface and a rigid obstacle in a tunnel
Kohr M.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
|
1998
|
z. 22 [170]
79-99
EN
A direct integral equation method for the creeping flow of a viscous incompressible fluid in the presence of a solid particle and a cylindrical interface is developed. The rigid obstacle and the cylindrical interface are immersed in another fluid, which is located in a domain bounded by two rigid walls. The integral formulation uses a combination between single-layer and the double-layer potentials, with the densities defined on the boundary of the rigid obstacle and the interface, respectively. The problem is reduced to the study of the existence and the uniqueness for a second-kind integral system of Fredholm equations.
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