Science

INSTITUTE OF MECHANICS AND ENGINEERING; KAZAN SCIENCE CENTER; RAS

SCIENTIFIC SEMINAR

Problems of Continuum Mechanics

(Scientific Seminar and Conferences)

D.A.Gubaidullin

Institute of Mechanics and Engineering; Kazan Science Center; RAS

Lobachevsky 2/31, Kazan, 420111 RUSSIA

 

The Scientific Seminar "Problems of Continuum Mechanics" works in the Institute of Mechanics and Engineering, Kazan Science Center RAS. The Chairman of the Seminar is Director of the Institute Corresponding Member of the RAS D.A.Gubaidullin. Problem reports and dissertations of researchers of the Institute and scientists from other organizations are presented and discussed at the Seminar. Main scientific directions for presentation are:

ž       non-linear mechanics of thin-walled constructions, hydroaeroelastic and wave systems;

ž       dynamics of multiphase multicomponent media in porous structures and technological plants;

ž       non-linear stability theory of control systems with changeable structure.

 

The following reports were presented at the Seminar in the second half-year 2006 and at the Section of Final Scientific Conference'2006.

June 29, 2006

D.Yu. Toporkov (IME).

Liquid viscosity effect on variation of a small distortion of the spherical shape of a gas bubble. On materials of thesis submitted for Candidate of Sciences Degree, speciality 01.02.05 - mechanics of liquid, gas and plasma. Scientific chief DrSc A.A.Aganin. Reviewer PhD V.G.Malakhov.

The liquid viscosity effect on variation of a small distortion of the spherical shape of a gas bubble is studied in the course of free decay of a distortion, during periodical radial gas bubble oscillations and in the course of single strong enlargement-compression of a vapor bubble. The exact model of the liquid viscosity influence as well as some approximate ways of its description without non-stationary character of diffusion of the liquid vortex motion is used. An efficient technique of calculation of the viscosity effect within the exact model has been developed. Features of influence of the liquid vorticity have been studied.

August 31, 2006

M.A. Ilgamov (IME, Institute of Mechanics, Ufa Branch RAS).

On stability of the spherical shape of bubbles and cavities.

The spherical shape of a shell under its given material weightš allows the shell to contain inside maximum volume of a liquid, a gas, etc., to bear external and internal pressure differences. These features bring about wide application of the spherical shells in apparatus and structures. In the report, the up-to-date state of the stability problem of the spherical shells andš cavities is presented. The interaction between Euler and Reilay-Tailor instabilities as well as their manifestation in various problem statements of hydroelastic system is considered.

 

The following report was presented at plenary Session of the Final Scientific Conference'2006 of the Kazan Science Center RAS:

February 8, 2007

A.I. Nikiforov (IME).

Modelling of two-phase liquid flow in oil reservoirs with variable pore structure.

The models of flow deviation technologies applied in petroleum industry for enhanced oil recovery are presented in this work. The results of calculations obtained by these models are compared with known experimental data. Some model examples for studying results of stimulation of heterogeneous oil reservoirs are examined.

 

The following reports were presented at section Sessions:

February 14, 2007

D.A. Gubaidullin (IME), R.G. Zaripov (IME), R.G. Galiullin (Kazan State University), L.A.Tkachenko (IME), A.J. Pjaterkin (KSU).

Drift of a particle at longitudinal oscillations of gas in the tube.

Drift of a particle at longitudinal oscillations of gas generated by the plane piston is experimentally investigated in tubes with different conditions at the ends. It is revealed, that the oscillating particle on an axis moves from the closed and open end of a tube to the piston, and near a wall it moves to a reverse side that is caused by acoustic streaming. In a radial direction drift of a particle to a wall of a tube is observed. It is shown, that the increase in frequency of oscillations of gas and lengths of a tube leads to growth of an oscillations swing of a particle and increase of its mean velocity.

D.A. Gubaidullin, A.A. Nikiforov (IME).

Weak waves of different geometry in mixtures of a liquid with bubbles vapor and gas.

Distribution of acoustic waves in liquids with bubbles in the view of phase transitions is theoretically investigated. Dispersive curves are calculated, influence of the maintenance vapor is shown. The calculation of evolution of impulse waves of pressure in liquids with vapor-gas and gas bubbles is led. Nonmonotonic dependence of attenuation of impulse indignation of pressure on initial radius of bubbles in liquids with vapor-gas bubbles is shown.

L.A. Kosolapova, V.G. Malakhov (IME).

A refined model of nonlinear ellipsoidal oscillations of a gas bubble in a liquid.

A refined mathematical model of nonlinear ellipsoidal oscillations of a gas bubble in a liquid has been developed. Variation of the bubble surface shape is presented as the second spherical harmonic. In the equations of the model terms of the third order of smallness relative to the amplitude of the distortion of the spherical shape of the bubble are taken into account. Nonlinear oscillations of an air bubble in water have been studied under the conditions at which the phenomenon of single bubble son luminescence arises. Comparison of the results of the present work with the results of the second order theory has been performed.

T.S. Guseva (IME).

Estimations of change of distortions of spherical form of a bubble during its strong enlargement-compression.

Estimations of change of distortion of sphericity of an air bubble enlarging and then collapsing in water have been obtained numerically. The problem conditions correspond to the known experiments on son luminescence just the amplitude of oscillations of the water pressure was supposed five times more than the static pressure. A wide spectrum of the distortion wave-length has been considered, the moment when the distortion arises has been varied. It has been established that the distortions arising in vicinity of the maximum enlargement are most dangerous. To the moment of collapse their amplitude may increase about hundred thousands times that is two orders more than under conditions of acoustic cavitations of deuterated acetone.

D.Yu. Toporkov (IME).

Vapor density effect on distortion of sphericity of a bubble in deuterated acetone.

Variation of small distortion of the sphericity of the vapor bubble in the course of its single strong enlargement-compression is studied. Spherical component of the liquid and vapor motion is described by the equations of hydrodynamics with allowing for the processes of non-equilibrium evaporation-condensation on the bubble surface. Non-spherical component of the bubble surface motion is described with allowing for the influence of the vapor density. It has been found that the Rayleigh-Taylor instability, which significantly influences the bubble shape in the case of neglecting the vapor density, does nearly not manifest itself when the vapor density is taken into account.

A.A. Aganin, T.F. Khalitova (IME).

Modelling of strong compression of an axially symmetric cavity in a liquid.

A computational technique developed to study strong compression of an axially symmetric cavity in a liquid by direct numerical simulation based on the equations of fluid and gas dynamics is presented. The efficiency of this technique is confirmed by results of computation of several model problems. It has been shown that the suggested technique based on the ENO-scheme is more effective than the TVD-modification of Godunov's scheme and considerably effective than the widely known classic Godunov's scheme of the first order accuracy.

N.V. Sonin (IME).

The aerosol distribution at non-linear oscillations in the open tube.

The experimental results of quick coagulation and precipitation of aerosol in the second nonlinear resonance of oscillations in open tube are given. The non-monotone character of distribution of intensity of a diffused light along the tube, with maximum displaced from the middle of the tube to piston is found. Near an open end the rough decrease of the intensity of a diffused light is found, which is conditioned to throwing out of aerosol into environment. It is found, that aerosol has a final depth of penetration of a beam from open end to piston, which grows monotonously in resonance. The velocity of changing the depth of penetration is more than compared with closed tube.

V.V. Klokov, A.Sh. Taha (Kazan State University).

The definition of the fusion shape border in case of a polygonal heat source.
This research is dealing with some technological problems (to define the fusion border), as for the importance of knowing the decision of the following problem. The one-dimensional thermal field between the heat source and the border of fusion is described the temperature, satisfying as Laplace equation. The field is stationary (convection by making both internal thermal sources and drains are neglected). We assume the temperature distribution along the borders of the field is constant. The fusion shape border is unknown (It is required to determine), on it (in its limiting position) the value of the local thermal stream is known. The decision of this problem found by the theory (which named the functions complex variable methods) and hydro dynamical analogy which formulated task to application of Gukovcki function. Results can be used to studying jet current and mathematical modeling of limit electrochemical generating machining of Metals.

P.P. Ossipov (IME), R.N. Maksudov (Kazan State Technological University).

Mass-transfer simulator in biporouse medium.

In the present work the mass-transfer in biporouse medium with microscopic and macroscopic channels is considered. It is assumed that in macroscopic channels filtration takes place, and in microscopic channels diffusion proceeds. The main conservative laws and phenomenological relations underlying the simulator are presented. The work of simulator is demonstrated on the example of optimization of oil extraction from amaranth milled seeds.

M.Kh. Khairullin, M.N. Shamsiev, P.E. Morozov (IME).

Estimating of limiting pressure gradient by draw down curves.š

M.Kh. Khairullin, P.E. Morozov, M.N. Shamsiev, A.I. Abdullin (IME).

Analysis of pressure transient test in wells.

The influence of reservoir boundaries, well bore storage and skin effect on pressure and pressure derivative curves for basic filtration models has been investigated. The comparison of analytical and numerical solution of transient flow problem towards horizontal well in anisotropy homogenous and naturally fractured reservoir has been studied.

R.V. Sadovnikov (IME).

Application of parallel algorithms for solution of flow problems on high-performance computers.

The results of finite element simulation of single phase 3D wells stream with different well bore trajectory: vertical, inclined, horizontal and others in dual porous media with two tensors of permeability (fractures and blocks) are presented. The system of obtained equations was solved by Aztec library of parallel iterative algorithms that includes a number of Krylov iterative methods.

P.A. Mazurov, A.I. Nikiforov, A.V. Tsepaev (IME).

The parallel algorithms for solving three-phase flow equation with fine grid segments.

At the decision of three-phase flow equation on each time step it is necessary to define fields of pressure and saturations.š Two parallel algorithms have been developed to solve three dimensional three-phase flow equation on a coarse grid with fine grid segments. The solution of the equations for pressure is based on the independent decision of the equations for fine grid segments and the new type of the agreement of these decisions with the decision on a coarse grid. The solution of equations for saturation is based on a combination of elements of explicit and implicit schemes. These algorithms show the efficiency with the increasing number of fine grid segments.

A.N. Gabidullina, A.V. Elesin, A.Sh. Kadyirova, P.A. Mazurov (IME).

Parameters identification with prior information in problems of fluid flow.

The task of identification of the hydraulic conductivity has been studied in the case of three-dimensional confined aquifer with prior information about hydraulic conductivity values. The comparison of solutions with prior information and without prior information has been made.

I.A. Aganin, A.I. Nikiforov (IME).

Some results of numerical simulation of water-flooding of clay-containing oil reservoir.

Two-phase filtration in clay-containing oil reservoir is modeled in this work. Alteration of dynamic porosity and permeability due to swelling of clay material in reservoir is described using the function of the pore sizes distribution. The influence of clay swelling on the oil recovery factor in layered reservoir is analyzed on numerical examples.

 

February 15, 2007

N.M. Yakupov (IME).

Leonard Euler - one of the founders of building mechanics. To three - hundredth anniversary from the date of a birth.

Building business since ancient times was the locomotive of the progress of society. Theš dialectic of development - from massive designs to thin-walled, from simple geometry to complex curvilinear forms. It is marked, that the bases of a modern building science have been incorporated since Renaissance. In the beginning the experimental researches have been led only. Leonard Euler (1707-1783) has made a big contribution in the mathematization of science. He has specified two ways of knowledge of the phenomena: 1) through making reasons; 2) through the final reasons. His developments, in particular, Euler's theorem, Euler's equations, Euler's formula, Euler's corners, a longitudinal bend by Euler have been used till now. Euler's works contain about 850 names.

N.M. Yakupov, A.R. Nurgaliev (IME).

About influence of defects on mechanical characteristics of the membranes working in an excited environment.

Protection against corrosion destruction is one of the major problems. Experimental installation DMK-1 allowing to test the thin-walled samples in the corrosion environment and to define mechanical characteristics in time is developed. The researches of influence of defects on the mechanical characteristics of membranes which are being under loading and in the corrosion environment are started. Samples with scratches and dents are considered. Conditional modules of elasticity at the plastic deformations of samples are calculated.

F.Kh. Akhmetzyanov, N.M. Yakupov (IME).

To an estimation of reliability of bearing ability of the damaged compressed concrete and ferro-concrete elements under mechanical loading.

Various cracks of micro and macro sizes in service of ferro-concrete designs appear. In particular, the results of inspection of the Cooler óë - 1200 demonstrate that. In the work the engineering approach to the definition of bearing ability of the damaged concrete and ferro-concrete building elements is shown. The smallness of deformations is supposed. The model in the form of continuous environment in which under mechanical loading arise and develop the macro cracks, leading the element's division into parts, is accepted.

N.M. Yakupov, Kh.G. Kiyamov, I.Kh. Miftakhutdinov (IME).

To calculation of environments of complex geometry with preliminary experimental parametrization of its surface.

For the calculation of intense-deformed conditions (IDC) of the shells of complex geometry in laboratory NMO a spline variant of the finite-element method, based on the synthesis of idea of parametrization of a median surface of shells and a finite-element method, is developed. The experimentally-theoretical approach to the research of the shells of complex geometry is developed. The concrete examples of parametrization of the shells set on experimental data are considered and the calculation of the IDC of these shells is made.

I.Kh. Miftakhutdinov (IME).

New kinds and forms of the shells of the minimal surface - MS.

In the work the analysis of modern kinds of forms of shells of the minimal surface - MS is made. Leading universities of the Europe and Northern America are seriously engaged in the search of new types of MS - but virtually. The closest scope of such shells in life - small architectural forms for the ornament of a city landscape is certain. In laboratory NMO the manufacturing techniques of real environments of MS are developed. Modern polymeric materials are applied for this purpose with special properties. Patents of the Russian Federation are received.

N.M.Yakupov, A.A.Abdjushev (IME).

Parametrical researches of the form of "treating" overlays and influence of their position on loading-deformed condition of plates with a crack.

If natural designs admire us with their perfection, man-made - are rather far from that. One of the reasons of destruction of designs is the presence of concentrators. The most dangerous concentrator is a crack. One of known ways to stop the crack is use of overlays which create a field of compression (the application for the invention  ¿ 2005130624/06). The question of the rational arrangement of overlays, and also the arising efforts in overlays is considered.

N.K. Galimov (IME).

About an opportunity of application of the equations of flat shells in a problem about balance of the spherical membrane loaded by uniform internal pressure.

By comparison of exact decisions of the linear equations of the specified problem in a wide range of change of parameters the opportunity of application of the equations of flat shells is established. That is possible even for enough high shells. It somewhat facilitates the consideration of the given problem.

N.K. Galimov (IME).

To one problem about definition of a dot skeleton of the minimal surfaces.

The problem about definition of a dot skeleton and surfaces close to them on the basis of Laplace equation is considered. It is shown, that the error of the decision on the basis of the approached way is small and does not exceed 3-4%.

S.N. Yakupov, R.I. Shafigullin, L.N. Shagidullina (IME).

Research of influence of a sunlight on mechanical characteristics polymeric films.

In practice various films and membranes find wide application. In the laboratory ofš nonlinear mechanics of environments the experimentally-theoretical method of research of mechanical characteristics of films and membranes is developed, experimental installation is made. The research of influence ofš sunlight on properties of polymeric films is started. It is noted, that mechanical characteristics are influenced by the geometrical parameters of a film and color of a substrate. The offered approach allows catching the thin processes occurring in the material of a film at a solar irradiation.

A.I. Malikov (IME).

Stability and stabilization of hybrid control systems.

In this report the survey of results in the stability and stabilization of hybrid systems are given. The results of switched linear (stable and unstable) systems are discussed The analog Lyapunov theorems are installed and stability condition for system with phase constraints. The problems of construction of normal functioning domain and regulator design which provide maximal normal functioning domain are solved.

A.I. Malikov (IME), E.E. Vezdenetskiy (Kazan State Technical University), F.I. Yafasov (IME).

Estimate state and functional diagnosis for electromechanical control system.

The Estimate state and functional diagnosis results for system with induction motor on experimental unit. The observer of state are constructed for electromechanical control system. These observers are used for fault detection of sensors and actuators. For the system with induction motor theš fault detection and isolation procedures are suggesting. Its are based on application of guarantied state estimation algorithms. The state estimation and fault diagnosis results are received for the system with induction motor of experimental unit in real time.

U.N. Zakirov (IME).

Geometrical method of research of orbital stability of a test particle.

As a geometrical method, the multidimensional Riemannian space of five measurings is used as a mathematical-physical auxiliary mean, containing a tensor field (gravitation) and a scalar field (perturbation and direction).The present method has allowed for a Lagrangian maintaining phase volume, to take into account the influence of gravitational and scalar fields on orbital stability of a rest particle by Lyapunov, and also to receive function demonstrating a Mach principle - definition of inertia of a body with allowance of all environmental gravitating bodies of Space.

I.V. Morenko (IME), A.B. Mazo (KSU).

Calculation of the flow past the bluff bodies based on various turbulent models.

A numerical investigation of high Reynolds number circular cylinder flow was performed on Spalart-Allmaras model, shear-stress transport model, large eddy simulation. The mean drag and lift force coefficients, the Strouhal numbers and other parameters were obtained. The results were analyzed in detail and compared with experimental and numerical data of other authors.

B.A. Snigerev (IME).

Numerical simulation of viscoelastic flows around rounded bodies in tube.

The discretization of transient equations of flows using finite element method is applied to numerical investigation of negative wakes in viscoelastic fluids. The standard Galerkin finite element method is applied to discretize the governing equation. The single-mode Phan-Thien Tanner non-linear, viscoelastic model is used as a constitutive equation. Numerical results for negative wakes past sphere and rounded rigid bodies in cylindrical tube are presented.

M.S. Ganeeva, V.E. Moiseeva (IME).

The computation technique of large deflections in the non-shallow elastic-plastic shells of revolution under non-axisymmetric loading.

The computation technique of a geometrically and materially non-linear stress-strained state of the non-shallow shells of revolution under non-axisymmetric loading similar to wind force is proposed. The technique is able to find limiting points on the representative curve of loading (lower and top limiting values of the non-axisymmetric load parameter). Calculation results for hemispheric shell with central hole and rigid patching edges in dependence on non-axisymmetric loading, material properties, thickness and problem nonlinearity type are presented.

 

 

Potential participants are kindly invited for the presentation of their results at the Seminar.

Contact address - gubajdullin@mail.knc.ru

 

Damir A. Gubaidullin - Director of IME KazSC RAS; Deputy Chairman of Presidium, Kazan Science Center RAS; Corresponding Member of the RAS; specialist in the area of mechanics and thermophysics of multiphase media.

gubajdullin@mail.knc.ru

 




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