INSTITUTE OF MECHANICS AND ENGINEERING; KAZAN SCIENCE CENTER; RAS
SCIENTIFIC SEMINAR
(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
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.
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