Wyniki wyszukiwania - BazTech

1

Mathematical modelling of the process of pipeline deformation through which gas-liquid mixtures with aggressive components are transported

Oliynyk A. P., Feshanych L. I., Grygorchuk G. V.

Journal of Achievements in Materials and Manufacturing Engineering

|

2022

|

Vol. 111, nr 2

57--63

EN

Purpose: Mathematical modelling of the process of deformation of pipeline, transporting gasliquid mixtures with aggressive components and a comparative analysis of the value of the specified velocity depending on the dynamic viscosity of the multicomponent gas mixture is conducted. Design/methodology/approach: A mathematical model of the process of leakage of the transported product due to the loss of tightness of the pipe based on the system of Navier-Stokes equations with boundary conditions with considering the geometry of the leakage zones and the value of the leakage rate is implemented. Findings: Models of the process of deformation of the pipeline due to displacements of a certain set of surface points by specifying different types of functions, describing the geometry of deformed sections are constructed. The method of calculating the tensely deformed state based on the data on the movement of surface points by comparing different ways of setting functions, taking into account the actual configuration of sections and axes is improved. The change of flow characteristics in the pipeline when changing the structure of the mix, transported by studying of influence of change of dynamic viscosity is investigated; The method of calculating the rate of leakage of the mixture in case of loss of tightness due to the occurrence of critical stresses in the pipe material is improved. Research limitations/implications: Building a model of the deformation process, information about the nature, duration of forces and loads affecting the pipeline is not used. The law of the pipeline movement was constructed having taken into account the deformation of the sections in three directions. The necessity to take wind loads into account, estimating the real tensely deformed state was displayed. Practical implications: Using the method of calculating the tensely deformed state based on the data on the movement of surface points by comparing different ways of setting functions, taking into account the actual configuration of sections and axes. Originality/value: According to the computational algorithms created on the basis of the specified models, the calculations of the tense state of the pipelines and the flow rate of the mixture depending on its composition were performed. An analysis of the results of calculations - tense intensity and flow rate depending on the dynamic viscosity of the mixture is performed. The influence on the flow parameters - the flow rate of the mixture and the force of hydraulic resistance - changes in the dynamic viscosity of the mixture is analyzed.

2

Modeling of heat transfer and fluid flow in a rectangular channel with an obstacle

Stryczyński Mikołaj, Majchrzak Ewa

Journal of Applied Mathematics and Computational Mechanics

|

2020

|

Vol. 19, nr 2

121--132

EN

Heat transfer and fluid flow in the rectangular channel with an obstacle are considered. The problem is described by the Fourier-Kirchhoff equation, Navier-Stokes equations and continuity equation supplemented by appropriate boundary and initial conditions. To solve this system of equations the finite difference method with a staggered grid is used. The results of computations obtained using authorial computer program are compared with ANSYS Fluent simulation. Computations are carried out for obstacles of various sizes and positions, and on this basis the conclusions are formulated.

3

A regularity criterion for positive part of radial component in the case of axially symmetric Navier-Stokes equations

Kubica A.

Demonstratio Mathematica

|

2015

|

Vol. 48, nr 1

62--72

EN

We examine the conditional regularity of the solutions of Navier–Stokes equations in the entire three-dimensional space under the assumption that the data are axially symmetric. We show that if positive part of the radial component of velocity satisfies a weighted Serrin type condition and in addition angular component satisfies some condition, then the solution is regular.

4

Navier–Stokes problems with random coefficients by the Weighted Least Squares Technique Stochastic Finite Volume Method

Kamiński M., Ossowski R. L.

Archives of Civil and Mechanical Engineering

|

2014

|

Vol. 14, no. 4

745--756

EN

The main aim of this article is numerical solution to the Navier–Stokes equations for incompressible, non-turbulent and subsonic fluid flows with Gaussian physical random parameters. It is done with the use of the specially adopted Finite Volume Method extended towards probabilistic analysis by the generalized stochastic perturbation technique. The key feature of this approach is the weighted version of the Least Squares Method implemented symbolically in the system MAPLE to recover nodal polynomial response functions of the velocities, pressures and temperatures versus chosen input random variable(s). Such an implementation of the Stochastic Finite Volume Method is applied to model 3D flow problem in the statistically homogeneous fluid with uncertainty in its viscosity and, separately, coefficient of the heat conduction. Probabilistic central moments of up to the fourth order and the additional characteristics are determined and visualized for the cavity lid driven flow owing to the specially adopted graphical environment FEPlot. Further numerical extension of this technique is seen in an application of the Taylor–Newton–Gauss approximation technique, where polynomial approximation may be replaced with the exponential or hyperbolic ones.

5

Solutions of incompressible Navier-Stokes equations with the artificial compressibility method for two- and three-dimensional shear-driven cavity flows

Kosma Z.

International Journal of Applied Mechanics and Engineering

|

2012

|

Vol. 17, no. 1

113-125

EN

An efficient method for simulating laminar flows in complex geometries is presented. The artificial compressibility method was applied to solve two- and three-dimensional Navier-Stokes equations in primitive variables on Cartesian grids. Two numerical approaches were proposed in this work, which are based on the method of lines process in conjunction with transfer of all the variables from the boundaries to the nearest uniform grid knots. Initial value problems for the systems of ordinary differential equations for pressure and velocity components were computed using the one-step backward-differentiation predictor-corrector method or the Galerkin-Runge-Kutta method of third order. Some test calculations for laminar flows in square, half-square, triangular, semicircular, cubic, half-cubic, half-cylinder and hemisphere cavities with one uniform moving wall were reported. The present results were compared with the available data in the literature and the Fluent solver numerical simulations.

6

A mixed, scalable domain decomposition method for incompressible flow

Vergnault E., Allix O., Maison-le-Poëc S.

Computer Assisted Methods in Engineering and Science

|

2012

|

Vol. 19, no. 2

173-190

EN

This work deals with the construction of a mixed and extensible domain decomposition method for incompressible flows. In the scheme proposed here, the solution is sought at the intersection of two spaces, one containing the solution of the Navier–Stokes equations considered separately in each subdomain, and theother one containing the solutions of the compatibility equations on the interfaces. A solution verifying all the equations of the two spaces is achieved iteratively. One di?culty is that the interface problem is large and dense. In order to reduce its cost while maintaining the extensibility of the method, we defined an interface macroproblem in terms of a few interface macro unknowns. The best option takes advantage of the incompressibility condition to prescribe an interface macroproblem which propagates the information to the whole domain by making use of only two unknowns per interface. Several examples are used to illustrate the main properties of the method.

7

Wyznaczanie stacjonarnego ruchu cieczy lepkiej w dwu- i trójwymiarowych zagłębieniach z jedną poruszającą się ścianką

Kosma Z., Kalbarczyk R., Piechnik B.

Logistyka

|

2011

|

nr 6

PL

Prezentowana jest efektywna metoda wyznaczania laminarnego stacjonarnego ruchu cieczy lepkiej w obszarach o skomplikowanych kształtach. Do rozwiązywania dwui trójwymiarowych zagadnień dla równań Naviera-Stokesa zapisanych w zmiennych pierwotnych została zastosowana metoda sztucznej ściśliwości na siatkach kartezjańskich. Zostały zaproponowane dwa numeryczne podejścia - oparte na wykorzystaniu metody prostych w połączeniu z przeniesieniem wszystkich zmiennych z granic obszarów do najbliższych węzłów równomiernych siatek obliczeniowych. Prezentowane są wyniki testowych obliczeń numerycznych dla sześciu zagłębień z jedną poruszającą się ścianką: kwadratowego, półkwadratowego, półkolistego, sześciennego, półsześciennego i półkulistego - porównane z wynikami dostępnymi w literaturze i symulacjami wykonanymi za pomocą programu Fluent.

EN

An efficient method for simulating steady laminar flows in complex geometries is presented. The artificial compressibility method was applied to solve two- and threedimensional Navier-Stokes equations in primitive variables on Cartesian grids. Two numerical approaches were proposed in this work, which are based on the method of lines process in conjunction with transfer of all the variables from the boundaries to the nearest uniform grid knots. Some test numerical calculations for flows in square, half-square, semicircular, cubic, half-cubic and hemisphere cavities with one uniform moving wall were reported. The present results were compared with the available data in the literature and the Fluent solver numerical simulations.

8

Wyznaczanie niestacjonarnego ruchu cieczy lepkiej w dwu- i trójwymiarowych zagłębieniach z jedną poruszającą się ścianką

Kosma Z., Kalbarczyk R., Piechnik B.

Logistyka

|

2011

|

nr 6

PL

Prezentowana jest efektywna metoda wyznaczania laminarno-turbulentnego niestacjonarnego ruchu cieczy lepkiej w obszarach o skomplikowanych kształtach. Do rozwiązywania dwu- i trójwymiarowych zagadnień dla równań Naviera-Stokesa zapisanych w zmiennych pierwotnych została zastosowana zmodyfikowana metoda sztucznej ściśliwości na siatkach kartezjańskich. Zostały zaproponowane dwa numeryczne podejścia - oparte na wykorzystaniu metody prostych w połączeniu z przeniesieniem wszystkich zmiennych z granic obszarów do najbliższych węzłów równomiernych siatek obliczeniowych. Prezentowane są wyniki testowych obliczeń numerycznych dla czterech zagłębień z jedną poruszającą się ścianką: kwadratowego, półkolistego, półsześciennego i półkulistego - porównane z symulacjami numerycznymi wykonanymi za pomocą programu Fluent.

EN

An efficient method for simulating unsteady laminar-turbulent flows in complex geometries is presented. The extension of the artificial compressibility method to unsteady flows was applied to solve two- and three-dimensional Navier-Stokes equations in primitive variables on Cartesian grids. Two numerical approaches were proposed in this work, which are based on the method of lines process in conjunction with transfer of all the variables from the boundaries to the nearest uniform grid knots. Some test numerical calculations for flows in half-square, semicircular, half-cubic and hemisphere cavities with one uniform moving wall were reported. The present results were compared with the Fluent solver numerical simulations.

9

Finite difference schemes and the method of lines for solving incompressible viscous flow problems

Kosma Z., Motyl P.

International Journal of Applied Mechanics and Engineering

|

2011

|

Vol. 16, no 1

15-35

EN

For the determination of viscous incompressible flows a pure stream-function formulation for the fourth-order equation, the artificial compressibility method, and velocity correction method are employed. Test calculations are performed for various flows inside square, triangular, semicircular and cubic cavities with one uniform wall, the backward-facing step, double bent channels, the flow around an aerofoil at large angle of attack and for flows over models of buildings. Some complex geometrical configurations can be decomposed into a set of simpler subdomains. A practical methodology for the computation of the Navier-Stokes equations in arbitrarily complex geometries is also considered. The simplest approach for specifying boundary conditions near curved or irregular boundaries is to transfer all the variables from the boundaries to the nearest grid knots.

10

Numerical simulation of NO production in a pulverized coal fired furnace

Straka R., Makovička J., Beneš M.

Environment Protection Engineering

|

2011

|

Vol. 37, nr 2

13-22

EN

Behaviour of air-coal mixture has been described using the Navier-Stokes equations for the mixture of air and coal particles, accompanied by the turbulence model. The undergoing chemical reactions are described by the Arrhenius kinetics (reaction rate proportional to exp(-E/RT) ). Heat transfer via conduction and radiation has also been considered. The system of partial difference equations is discretized using the finite volume method and the advection upstream splitting method as the Riemann solver. The resulting ordinary differential equations are solved using the 4th order Runge-Kutta method. Results of simulation for typical power production level are presented together with the air staging impact on NO production.

11

Modelowanie przewodów pneumatycznych do symulacji inżynierskich systemów heterogenicznych

Kamiński Z.

Pneumatyka

|

2008

|

nr 2

48-52

PL

Na podstawie równań Naviera-Stokesa dla przepływu jednowymiarowego opracowano równania modelu przewodu pneumatycznego o parametrach skupionych. Model matematyczny oparty na równaniach różniczkowych zwyczajnych może być bez trudności zaimplementowany w większości programów komputerowych do symulacji złożonych systemów inżynierskich. Opracowany model przewodu wykorzystano do symulacji dynamiki prostego obwodu pneumatycznego z siłownikiem tłokowym jednostronnego działania w programie Matlab-Simulink.

EN

The govering Navier-Stokes equations for quasi-one-dimensional flow arę presented and from them the lumped govering equations for modeling pneumatic pipelines are derivated.The mathematical model based entirely on ODEs can readily be implemented in most ODE-based simulator for modelling complex heterogeneous engineering systems. The pipeline model was used to simułate dynamics of simple pneumatic circuit with one-acting cylinder in Matlab-Simulink.

12

Symulacja zjawiska pierścienia wirowego wokół wirnika śmigłowca w oparciu o rozwiązanie równań Naviera-Stokesa z uproszczonym modelem wirnika w postaci powierzchni skoku ciśnienia

Stalewski W., Dziubiński A.

Prace Instytutu Lotnictwa

|

2006

|

Nr 1-2 (184-185)

65-71

PL

W pracy omówiono zjawisko pierścienia wirowego oraz przedstawiono metodę komputerowej symulacji tego zjawiska. Metoda bazuje na rozwiązaniu równań Naviera-Stokesa opisujących niestacjonarny opływ śmigłowca wykonującego manewry. Zastosowano uproszczony model wirnika śmigłowca bazujący na powierzchni skoku ciśnienia. Symulacje przeprowadzono przy wykorzystaniu komercyjnego programu FLUENT rozwiązującego równania Naviera-Stokesa metodą objętości skończonych. Przedstawiono wyniki symulacji typowego lotu śmigłowca wprowadzającego go w stan pierścienia wirowego oraz manewrów umożliwiających wyjście z tego stanu.

EN

This work contains the simulations results of Vortex Ring State appearance and evolution around main rotor of a helicopter. These calculations were based on solution of Navier-Stokes equations using the Fluent code. During this simulation An Actuator Disc model of fan has been used. This model assumes that a fan is a pressure jump generating surface. Two mashes has been used during this simulation: three dimensional and axisymmetrical two-dimensional. The most of the cases has been calculated using steady flow solutions, but unsteady model also has been applied. Main goal of this work was a calibration of model, in terms of simplifications influence on results, and also in comparison with experimental results. Two different conditions of flight has been considered: hover and vertical descent with various velocities along axis of rotor. The results has been analyzed to determinate Vortex Ring State conditions and confirmed, that Actuator Disc model can be used to qualitative analisys of VRS phenomena. It is assumed, that after a proper calibration this model can be used in further flight safety methods of VRS elimination research.

13

Modelling of convective heat explosion

Ducrot A., Volpert V.

Journal of Technical Physics

|

2005

|

Vol. 46, no 3

149-163

EN

A strong temperature dependence of the reaction rate can result, for an exothermic chemical reaction, in heat explosion. In this work we study numerically the influence of natural convection on heat explosion. The model consists of the reaction-diffusion equation coupled with the Navier-Stokes equations under the Boussinesq approximation. A new type of heat explosion, the oscillating heat explosion is found. Critical conditions of explosion and complex nonlinear dynamics of the reaction-diffusion-convection problem are studied.

14

On some issues concerning the modeling of the motion of fluids

Rajagopal K. R., Tao L., Chen G. Q.

International Journal of Applied Mechanics and Engineering

|

2005

|

Vol. 10, no 3

475-487

EN

We address some issues regarding the use of the Lagrangian description and convected frames in describing fluid motions. We also discuss the implications of Brownian motion on modeling the macroscopic motion of fluids and the schemes of filtered simulations. The relevance of these issues to the modeling of turbulence is discussed in detail.

15

Przepływ cieczy lepkiej w obszarze prostokątnym z półwyspem

Kołodziejczyk M.

Zeszyty Naukowe Politechniki Białostockiej. Budowa i Eksploatacja Maszyn

|

2004

|

Z. 12

67-80

PL

Tematem pracy jest wyznaczenie nieustalonego przepływu cieczy lepkiej w obszarze prostokątnym z ruchomą ścianką oraz wewnętrzną przegrodą. Zastosowana w pracy metoda obliczeniowa pełnych, nieuproszczonych równań Naviera-Stokesa oparta jest na sposobie eliminowania ciśnienia drogą wyznaczenia całki po konturze zamkniętym z różniczki zupełnej ciśnienia. W pracy przedstawiono wyniki obliczeń dla Re = 600 przy różnych ustawieniach przegrody wewnątrz obszaru przepływu.

EN

A numerical simulation of the flow of viscous incompressible fluid in a rectangular cavity with a division wall is a subject of this paper (Re = 600). The simulation has been done applying the method of elimination of the pressure from the Navier-Stokes equations by determination of the contour integral of the total differantial of the pressure.

16

Modelling of fluid flow in the steel continuous casting process

Rywotycki M., Malinowski Z.

Metallurgy and Foundry Engineering

|

2004

|

Vol. 30, No 2

99-108

EN

The paper presents the mathematical model describing the fluid flow. The motion of liquid metal in the steel continuous casting mould has been analysed. The solution for the velocity field has been obtained from the Navier-Stockes equation and the continuity condition. The problem has been solved with the use of the finite element method. In the course of numerical calculations, the velocity fields for various dimensions of the casted strip and various casting velocity were obtained. The liquid, mushy and solid zones were taken into consideration in the model.

PL

W pracy przedstawiono model matematyczny opisujący ruch cieczy. Analizie został poddany ruch ciekłego metalu w krystalizatorze COS. Opis pola prędkości otrzymano z rozwiązania równania Naviera-Stokesa z równaniem ciągłości strugi. Przedstawiony problem został rozwiązany z zastosowaniem metody elementów skończonych. W trakcie obliczeń numerycznych otrzymano pola prędkości dla różnych wymiarów pasma COS i różnych prędkości odlewania. Obszar obliczeń podzielono na strefy: ciekłą, przejściową i zakrzepłą.

17

Blood flow in a vessel with asymmetric aneurysm

Kumar B. V. R., Yamaguchi T., Liu H., Himeno R.

International Journal of Applied Mechanics and Engineering

|

2004

|

Vol. 9, no 3

505-521

EN

Blood flow in an asymmetrically dilated fusiform artery has been investigated under pulsatile inflow conditions for a full cycle of period T. The coupled non-linear partial differential equations governing the conservation of mass and momentum of a viscous incompressible fluid flow has been numerically analyzed by a time accurate Finite Volume Scheme in an implicit Euler time marching setting. Roe's flux difference splitting of non-linear terms and the pseudo-compressibility technique in the current numerical scheme makes it robust both in space and time. The combined influence of asymmetric geometry and Reynolds number on the hemodynamic factors like WSS, pressure and velocity has been analyzed. Vortices favoring the thrombogenesis are seen to periodically manifest with 3D shedding in the diastolic phase of the flow cycle. During the whole cycle, relatively high WSS is noticed at the head and toe of the aneurysm. Further for the entire period (T) considerable pressures, with relatively large ones on the distal portion, are noticed on the hull of the aneurysm.

18

The implementation of the Navier - Stokes equations in modelling of ingots casting

Rywotycki M., Malinowski Z.

Metallurgy and Foundry Engineering

|

2003

|

Vol. 29, no. 1

13-20

EN

The Navier-Stokes equation have been employed to model the flow of the liquid steel during ingots casting. A numerical modę! for the solution of the hydrodynamic problem has been presented. The finite element method has been used to solve the problem. Numerical calculation have been performed by using a developed computer program. Numerical tests have been performed in order to test the computer program and the numerical model. The Solutions have been accomplished for the steady state conditions. Computation have been performed for the two tests. The first one consists of the liquid steel flow in the square mould. The results obtained have been typical for this type of the benchmark test. The second test involved the ingot mould filling up. Two stages of the mould filling up have been analyzed. The results obtained confirmed the consistency of the developed model.

PL

Praca przedstawia przykłady zastosowania równań Naviera - Stokesa do symulacji ruchu ciekłego metalu w procesach odlewania stali do wlewnic. Analizie zostały poddane mechanizmy wywołujące i decydujące o ruchu ciekłego metalu w tym procesie - ruch wywołany działaniem strugi wpływającego metalu oraz ruchy konwekcyjne. Przedstawiono model matematyczny opisujący ruch płynu w tym procesie. Opracowano autorski program komputerowy rozwiązujący postawione zadanie metodą elementów skończonych w obszarze płaskim, w stanie ustalonym z zadanymi warunkami brzegowymi. Przedstawiono przykłady symulacji komputerowych.

19

More accurate determination of a pressure function in long hydrodynamical bearings

Zapoměl J.

Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska

|

2002

|

z. 19

173-178

EN

Fluid-film bearings are usually incorporated into computational models by means of nonlinear force couplings. Calculation of components the hydraulical force through which the layer of lubricant acts on the rotor journal and bearing shell requires to determine a pressure distribution ( a pressure function ) in the bearing gap which is described by a set of Navier-Stokes equations. Because their solution (together with the equation of continuity) is considerably time consuming, a new approach to calculation of the pressure function has been developed. It consists in averaging the terms in the Navier-Stokes equation corresponding to the direction of prevailing pressure gradient (in long bearings it is in the circumferential direction ). To perform this manipulation velocity profiles obtained from solving a Reynolds' equation are applied. As the pressure function is 2π-periodic, it is approximated by a finite number of terms of a Fourier series and the Fourier coefficients are calculated by means of a trigonometric collocation method.

20

Modelowanie przepływów cieczy z wykorzystaniem metody elementów skończonych

Węgrzyn-Skrzypczak E., Skrzypczak T.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

|

2002

|

Vol. 1, nr 1

227--233

PL

W pracy zajęto się jednym z aspektów rozwiązania równań Naviera-Stokesa. Jak wiadomo, rozwiązanie numeryczne tych równań stwarza wiele problemów związanych ze stabilnością procesu obliczeniowego. W celu pokonania tych trudności zastosowano metodę elementów skończonych z wykorzystaniem elementów Taylora-Hooda, które dzięki mieszanym funkcjom aproksymacyjnym, innym dla prędkości i ciśnienia, pozwalają na osiągnięcie zbieżności rozwiązania. Zaprezentowano przykład obliczeniowy potwierdzający skuteczność analizowanej metody.