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1

Inertial oscillations indeced by propagation of Vistula Lagoon freshwater into the Baltic Sea

Yurov V. A., Yurova A. A.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2017

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Vol. 21, No 2

121--134

EN

A mathematical model of the mechanism of the appearance of antisymmetric vortices during the propagation of freshwater into the seawater which is observed, in particular, at the exit from the Baltic Canal connecting the Vistula Lagoon and the Baltic Sea is constructed in the work. In particular it is shown that the main reason for the vortex formation in this case is the Coriolis force. The exact dependence of the circulation of velocity on time for the three simplest types of the “tongue” of the intrusion of freshwater is calculated analytically in the work as well.

2

Vorticity transport analysis in magnetic viscoelastic fluid

Kumar P., Mohan H., Hoshoudy G.

Journal of Theoretical and Applied Mechanics

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2016

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Vol. 54 nr 1

127--133

EN

Results of investigation on the transport of vorticity in Rivlin-Ericksen viscoelastic fluid in the presence of suspended magnetic particles is presented here. Equations governing the transport of vorticity in Rivlin-Ericksen viscoelastic fluid in the presence of suspended magnetic particles are obtained from the equations of magnetic fluid flow. From these equations it follows that the transport of solid vorticity is coupled with the transport of fluid vorticity. Further, we find that because of thermokinetic process, fluid vorticity may exist in the absence of solid vorticity, but when fluid vorticity is zero, then solid vorticity is necessarily zero. A two-dimensional case is also studied and found that the fluid vorticity is indirectly influenced by the temperature and the magnetic field gradient.

3

Random vortex method in numerical analysis of 2D flow around circular cylinder

Kostecki S.

Studia Geotechnica et Mechanica

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2014

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Vol. 36, nr 4

57--63

EN

A combination of the vortex method and the boundary element method is used here to predict the two-dimensional flow field around a circular cylinder. Cylindrical structures experience strong hydrodynamic loading, due to vortex detachment from the both sides of cylinder during the flow. Thus, the practical meaning of such calculation is significant particularly in offshore oil and gas engineering as well as in the bridge and hydraulic structure engineering. This paper presents the mathematical formulation of the vortex method for the velocity and vorticity field calculation. The calculated velocity and vorticity fields are then used to predict the pressure distribution on the cylinder surface by the boundary element method. The resulting pressure on the cylinder, the Strouhal number and the length of the base recirculation zone are compared with solutions of other numerical methods and experiments, and a good agreement is achieved.

4

Numerical analysis of hydrodynamic forces due to flow instability at lift gate

Kostecki S. W.

Archives of Civil and Mechanical Engineering

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2011

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Vol. 11, no 4

943-961

EN

A numerical method, being a combination of the vortex method and the boundary element method, is used here to predict the two-dimensional flow field in the vicinity of an underflow vertical lift gate. In practice, tunnel-type flat-bottomed lift gates experience strong hydrodynamic loading, due to vortex detachment from the gate bottom edge, and near-wake velocity fluctuations. This paper presents a stream function, and velocity and vorticity distributions for two gate gaps. The vortex detachment mechanism is described and the vortex shedding frequency, expressed as a Strouhal number, is presented. The predicted velocity and vorticity fields are then used to calculate the pressure distribution on the gate surface by the boundary element method. The time histories of the lift and drag coefficients are presented. The proposed numerical method has been validated by the measurements of the downpull coefficient for the flow around the lift gate.

PL

W pracy przedstawiono numeryczną metodę wynikającą z połączenia metody wirów i metody elementów brzegowych do określenia dwuwymiarowego pola prędkości pod zamknięciem zasuwowym. W praktyce, zamknięcia w spustach dennych, pracujące jako ciśnieniowe są poddane silnym obciążeniom dynamicznym, wynikającym z odrywania się wirów od dolnej krawędzi zamknięcia i fluktuacji pola prędkości w strumieniu za zamknięciem. W artykule przedstawiono funkcję prądu, pole prędkości i wirowości dla dwóch poziomów otwarcia zasuwy. Przedstawiono mechanizm odrywania wirów i podano częstość tego zjawiska, wyrażoną za pomocą liczby Strouhala. Obliczone pola prędkości i wirowości zostały następnie wykorzystane do obliczenia rozkładu ciśnienia na powierzchni zamknięcia metodą elementów brzegowych. Zaprezentowano również przykładowe przebiegi czasowe współczynnika siły unoszenia i oporu. Wyniki symulacji numerycznych zweryfikowano na podstawie cytowanych w literaturze pomiarów współczynnika siły ssania działającej na zamknięcie zasuwowe.

5

Numerical analysis of fluid flow in a syringe - test tube

Krasoń W., Łazowski J., Małachowski J.

Journal of KONES

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2010

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Vol. 17, No. 1

233-240

EN

Numerical research in the field of collaboration of basic components and entire constructional solutions is much cheaper than managing a goods production and testing them in actual conditions. Numerical research allows determining essential modifications of a product being prepared from the functional, utilitarian and technological point of view. Considering the problem to be solved, the blood flows through the area limited by the sides of apiston, syringe and needle were analyzed. Pressure arises after the initiation of the piston's move and the blood flows as a result of the difference in pressures. The blood flows from the areas with higher pressure to the ones with lower pressure. The numerical research focused on analysis of the boundary conditions influence on the arrangement of the velocity and blood pressure in a syringe. In order to calculate the blond flow through a syringe the researchers used a model that allows the flow of adhesive fluids - substances with internal friction. Navier-Stokes' equations were used to describe adhesive fluids move mathematically. These equations allowed describing non-stationary flow of incompressible fluids, i.e. including no volumetric changes, however, including figural changes. In last analyzed case, i.e. with flow orifice, fluids dam up in front ofthe orifice and thenflow into the next chamberjust after the orifice. The fluids flow to the chamber as apiled up stream. Then, the fluids hit internal bend sides and rotate again in front of the needle orifice entry. Considering fluids parameters, vorticity process improves fluid mixing process.

6

Fluid theory with asymmetric molecular stresses: Difference between vorticity and spin equations

Teisseyre R.

Acta Geophysica

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2010

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Vol. 58, no. 6

1056-1071

EN

We present a new development in fluid theory, incorporating into it the velocity and spin fields; special attention is given to the structure of transport.The theory includes asymmetric molecular stresses and independent rotation velocity, i.e., spin. Our approach is based on our former studies on the asymmetric continuum theory with the balance and constitutive laws for displacement velocity and independent rotation motion, and points out the role of a related characteristic length unit. It is assumed that the vorticity caused by velocities can induce a spin transport counterpart. Thus, under certain conditions, an additional transport term due to rotational velocity fields may be incorporated to the velocity transport, which may lead to the vortex fields included directly into the theory. The Coriolis effect, important for the vortex processes, is considered and it is demonstrated that the motion equations in our asymmetric theory include this effect automatically. When confinining to 2D case, some compatibilities are found between the relations derived for the rotation motions and the moment formed by the Coriolis forces and applied to such motions. This is an important argument supporting our approach. The obtained nonlinear vortex equations (solitons) are derived and discussed for a stationary case.

7

Numerical modelling of flow through moving water-control gates by vortex method. Part I - problem formulation

Kostecki S. W.

Archives of Civil and Mechanical Engineering

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2008

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Vol. 8, no 3

73-89

EN

A vortex method for simulating a flat flow within moving complex boundaries is presented. Thanks to the use of Lagrange variabies (the trajectories of vortex particles) to determine the evolution of vorticity and velocity fields the method offers the possibility of modelling high Reynolds number flows. A procedure for formulating boundary conditions for flows confined by a moving impervious boundary, consisting in the superposition of three velocity fields: the first originating from the vortex particles, the second being a potential field satisfying the no-through-flow boundary condition and the third one resulting from the fact that the vortex sheet is modelled along the impervious boundaries and satisfying the no-slip-flow condition, is described. The original derivation of,a formula for vortex sheet intensity, based on the single layer potential theory and leading to the formulation a second-kind Fredholm equation for vortex sheet intensity, is presented. This paper is the first part of a work covering the theoretical foundations and general description of the vortex method algorithms and boundary conditions. An example illustrating the computation of the vorticity and velocity fields of the flow through a moving hydraulic gate will be provided in the second part of the work.

PL

Zaprezentowano metodę wirów dyskretnych dla symulacji płaskiego przepływu ograniczonego złożonymi ruchomymi brzegami. Zaletą tej metody jest możliwość modelowania przepływu z dużą liczbą Reynoldsa, dzięki wykorzystaniu zmiennych Lagrange'a - trajektorii cząstek wirowych do wyznaczania ewolucji pól wirowości i prędkości. Przedstawiono sposób formułowania warunków brzegowych dla przepływów ograniczonych nieprzepuszczalnym i ruchomym brzegiem, polegający na superpozycji trzech pół prędkości. Pierwszego, pochodzącego od cząstek wirowych, drugiego potencjalnego spełniającego warunek brzegowy no-through-flow oraz trzeciego wynikającego z modelowania warstwy wirowej wzdłuż brzegów nieprzepuszczalnych spełniającego warunek no-slip-flow. W niniejszej pracy przedstawiono oryginalne wyprowadzenie formuły na wyznaczanie natężenia warstwy wirowej na podstawie teorii potencjału warstwy pojedynczej prowadzące do sformułowania równania Fredholma drugiego rodzaju dla natężenia warstwy wirowej. Niniejsza praca stanowi część pierwszą, obejmującą podstawy teoretyczne i ogólny opis algorytmów metody wirów oraz warunków brzegowych. Przykład obliczenia pól wirowości i prędkości Przepływu przez zamknięcie wodne znajdujące się w ruchu zostanie przedstawiony w drugiej części pracy.

8

Studium konwekcyjnego ruchu powietrza nad powierzchnią ogrzewanej płyty metodą symulacji numerycznej

Trzciński P.

Inżynieria i Aparatura Chemiczna

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2006

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Nr 6s

243-244

EN

Elaboration of a numeric model describing convectional heat transfer in the system consisting of warmed plate source and enclosing air was the aim of this work. The two-dimensional temperature field, vorticity, stream function and velocity distribution were presented. Convectional movement was modelled using the MRS method in the MATLAB environment programme. Key words: convection, MRS, stream function, vorticity

9

Laanemets J., Pavelson J., Lips U., Kononen K.

Oceanological and Hydrobiological Studies

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2005

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Vol. 34, No.2

15--36

EN

Hydrographic (towed CTD) and acoustic Doppler current profiler (ADCP) velocity surveys were conducted daily aboard the RV Aranda from July 15 to 26, 1996 at the entrance to the Gulf of Finland, Baltic Sea. Strong alongshore wind forcing that lasted two days caused an intensive downwelling event north of Hiiumaa Island with an approximate 20 m onshore descent of the thermocline. The associated eastward downwelling jet (~30 cm s-1, width 8-12 km) developed into an anticyclonic eddy with a diameter of ~20 km. A strong jet (~35 cm s-1, width 4-6 km) was observed in the periphery of the anticyclonic eddy, centered at the depth of reversal in baroclinicity. The geostrophic streamfunctions were derived from ADCP data and combined with the CTD density field to study the variations of isopycnal potential vorticity. The variation of relative vorticity from -0.95f to 1.2f and five-fold changes in the thickness of the selected isopycnal band caused up to fifty-fold variation of isopycnal potential vorticity over the survey area. The distribution of isopycnal potential vorticity as a conservative property correlated well with the isopycnal salinity distribution. The maximum upward and downward velocities, 35 and 26 m d-1, correspondingly, were estimated through the divergence of the Q-vector using the ω-equation diagnostic technique.

10

Transport of vorticity in fluid in the presence of suspended magnetic particles in porous medium

Sunil

Applied Mechanics and Engineering

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1999

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Vol. 4, no 1

35-43

EN

Transport of vorticity in a magnetic fluid in a porous medium is considered in this note. Equations governing the transport of vorticity in magnetic fluid in a porous medium are obtained from the equations of magnetic fluid flow proposed by Wagh (1996) by replacing the usual viscous term in the equation of fluid motion by the resistance term __ to discuss the transport of vorticity in magnetic fluid in a porous medium. A two-dimensional case is also studied.