INSTITUTE OF MECHANICS AND
ENGINEERING; KAZAN SCIENCE CENTER; RAS
SCIENTIFIC SEMINAR
Problems
of Continuum Mechanics
(Scientific Seminar and Final Conference)
Kazan, 2009-2010, Russia
D.A.Gubaidullin
Institute
of Mechanics and Engineering;
Lobachevsky
2/31,
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. The main scientific directions for presentation are:
·
non-linear mechanics of thin-walled constructions,
hydroaeroelastic and wave systems;
·
dynamics of multiphase multicomponent media in porous
structures and technological plants;
·
non-linear stability theory of control systems with
changeable structure.
On
June, 25th, 2009 on the session of academic council and scientific seminar of IME KazSC RAS the following
reports were presented.
A.A.Aganin, T.F.Khalitova,
N.A.Khismatullina (IME).
Strong compression
of a nonspherical cavitation bubble.
Strong compression of an axially-symmetrical cavitation bubble is
considered in conditions close to experimental ones on neutron emission during
acoustic cavitation of deutarated acetone. The investigation is conducted by
direct numerical simulation based on the two-dimensional equations of
compressible fluid dynamics to describe the motion of the gas (vapor) in the
bubble and the flow of the surrounding liquid. Heat conductivity of the vapor
and the liquid, evaporation and condensation on the bubble surface are taken
into account. Realistic equations of state are used for the vapor and liquid.
It has been shown that the maximum values of the pressure, temperature and
density of the bubble content are strongly influenced by the bubble non-sphericity.
N.M.Yakupov (IME).
Mechanics:
a problem - idea - practice.
A.L.Tukmakov (IME).
The numerical simulation of
water flow with vapor bubbles through the nozzle.
D.A.Gubajdullin, P.P.Osipov (IME).
Drift of the
particle under the Stokes, Archimedes and added forces.
L.А.Tkachenko, R.G.Zaripov (IME).
Nonlinear oscillations in the closed
tube at the unstressed-wave regime.
V.G.Malakhov (IME).
Waves in the solid
body under the shock influence of water.
R.N.Gafiyatov (IME).
Acoustic waves in
the two-fractional bubble liquid taking into account interphase diffused mass exchange.
The
following reports were presented at the Seminar in the period from September
2009 till March 2010 and at the Section of Final Scientific Conference'2009.
September 18, 2009
A.I.Davletshin (IME).
Simulation
of interaction of gas bubbles in a liquid.
On materials of the thesis
submitted for Candidate of Sciences Degree in physics and mathematics,
speciality 05.13.18 - Mathematical modeling, numerical methods and complexes of
programs. Scientific chief doctor-of-sciences in physics and mathematics,
professor A.A.Aganin. Reviewer
doctor-of-sciences in physics and mathematics P.P.Osipov.
Mathematical models of close
interaction of slightly non-spherical gas bubbles in a liquid with allowing for
the influence of viscosity and compressibility of the liquid, heat exchange
between the liquid and the bubbles are proposed. Each of the models is a set of
ordinary differential equations of the second order for the radii of the
bubbles, the coordinates of their centers, the amplitudes of the deflections of
their shape from the spherical one and the first order for the gas temperatures
in the bubbles. Verification of the proposed models has been performed and
their applicability has been illustrated. Some new regimes and scenarios of
bubble interaction have been found.
December 9, 2009
O.R.Nurislamov
(Birsk
state social-pedagogical academy).
Some
parietal and filtration self-similar flows with phase transfer.
On materials of the thesis
submitted for Candidate of Sciences Degree, speciality 01.02.05 - Mechanics of
liquid, gas and plasma. Reviewer DrSc A.I.Nikiforov.
The model problems about a
boundary layer for flow past wall by a liquid with a parietal boiling and
injection of a gas-vapor mixture and about hydrate formation in a porous medium
by means of injection gas are reviewed in research work. The self-similar
solutions are obtained and influence of intensity of thermal effect and
intensity of injection of gas on dynamics of hydrodynamic and temperature
fields in a boundary layer and in a porous medium is analyzed. Besides a
problem of a decrease of hydrodynamic resistance on account of a steam-gaseous
"lubrication"; because of a boiling-up of a liquid and injection of a
steam-gaseous mixture from its surface is reviewed for flow past wall by a
liquid. The capability of the appearance of a steam blanket is analyzed only at
the expense of forces of viscosity friction for a case when the liquid is in
boiling point. The modes of injection of gas in a porous medium with hydrate
formation and without it in a temperature dependence of gas injection and
intensity of pump are also detected in this work. It is shown that in the
reason of hydrate formation in volumetric areas due to injection of cold gas
there can be a heating of a porous medium on tens grades.
December 23, 2009
A.Sh.Kadyrova
(IME).
Numerical
solution of hydraulic conductivity identification problems on basis of
two-steps methods of residual function minimization.
On materials of the thesis
submitted for Candidate of Sciences Degree in physics and mathematics,
speciality 05.13.18 - Mathematical modeling, numerical methods and complexes of
programs. Scientific chief PhDr. P.A. Mazurov. Reviewer DrSc M.Kh.Khairullin.
A new two steps methods
Newton, Gauss-Newton and Levenberg-Marquardt of residual function minimization
are proposed. Its efficiency on calculation is shown on the model tasks of
hydraulic conductivity identification and minimization of testing functions.
January 13, 2010
E.R.Teregulova (Kazan State University of Architecture and
Engineering).
Bearing
ability of the plates lying on the deformable basis.
On materials of the thesis
submitted for Candidate of Sciences Degree in physics and mathematics,
speciality 01.02.04 - Mechanics of a deformable firm body. Scientific chiefs
DrSc I.G. Teregulov, Ph.Dr. V.G. Nizameev. Reviewer DrSc Ganeeva M.S.
March 17, 2010
D.E.Igoshin
(Sterlitamak
state pedagogical academy).
Research
of a convective-diffusion mass transfer modes at thermal influence on damp
porous environments.
On materials of the thesis
submitted for Candidate of Sciences Degree, speciality 01.02.05 - Mechanics of
liquid, gas and plasma. Scientific chief, DrSc, prof. V.S.Shagapov. Reviewer
DrSc A.I.Nikiforov. Researches of drying of porous environment sated with a
liquid in convective-diffusion and in pure diffusion approach are carried out. Self-similar
solutions for a semi-infinite layer and numerical solutions for the limited
layer are received. The mathematical model of tape dryer functioning is
offered.
The
following report was presented at section Sessions of the Final Scientific
Conference'2009 of the Kazan Science Center RAS:
February 9, 2010
D.A.Gubaidullin, R.G.Zaripov, L.A.Tkachenko (IME).
Motion of a spherical
particle at nonlinear oscillations of gas in an open tube and in an exterior
wave field.
The motion of a spherical particle inside an open
tube and in an exterior wave field is experimentally investigated at forced
oscillations of gas. Inside a tube, the particle moves from the open end to the
piston, making longitudinal oscillations. Outside of a tube, the particle moves
from the open end to an exterior wave field practically without oscillations
with nonlinear increase of coordinate from time. The oscillation swing and
average velocity of a particle have the maximal values at a subharmonic
resonance.
D.A.Gubajdullin, A.A.Nikiforov, R.N.Gafiyatov (IME).
Weak perturbations in
two-fractional liquid with bubbles of different gases and initial radiuses with
phase transformations.
A closed system of the equations of motion of a
two-fractional mixture of liquid with bubbles of different gases and various
initial radiuses with mass exchange is submitted. The dispersive equation which
determines propagation of weak perturbations in the given mixture has been
received. Dispersive curves for a mixture of water with vapor-gas and helium
bubbles have been constructed. The comparison between mixtures of water with
one and two-fractional composition, also with and without mass exchange has
been shown.
D.A.Gubaidullin, A.A.Nikiforov, E.A.Utkina (IME).
Acoustic waves in
two-fractional mixtures of gas with drops and particles of different materials
and sizes at presence of phase transformations.
Propagation of acoustic waves inside the
two-fractional mixtures of gas with drops and rigid particles of different
materials and sizes with phase transformations is investigated. The
mathematical model is presented, the dispersion relation and a wave equation
are received and dispersion curves are calculated. Dependencies of the relative
velocity of a sound and attenuation decrements upon a wavelength on a frequency are analyzed and calculations of propagation of
impulse perturbations in two-fractional mixtures of air with drops of water and
particles of sand are carried out.
A.L.Tukmakov (IME).
Modeling of nonlinear
fluctuations of an aerosol in the closed channel on the basis of two-speed and
two-temperature model.
Dynamics of a monodisperse aerosol in the
acoustic resonator is numerically modeled. For its description the model of the
two-temperature two-speed environment without phase transitions is applied. We
neglect collisions of particles and their possible coagulation. To describe the
motion of the gas we used the compressible heat-conducting Navier - Stokes
equations. The disperse phase is described by the conservation equations of mass, impulse components and internal
energy. System was written in time-dependent coordinates and was solved by the
explicit MacCormack method with conservative correction scheme. This method is
applied for the research of aerosol nonlinear fluctuations in the flat channel.
A.A. Aganin, A.I.
Davletshin, D.Yu. Toporkov (IME).
Enlargement-compression of
cavitation bubbles in a comet-like streamer.
Deformations of bubbles in the course of their
strong enlargement-compression in the comet-shaped streamers are studied. Due
to interaction, the bubbles in the process of strong compression in such
streamers have been shown to undergo large deformations (more 50%) if the
distance between the bubbles d is less than d = 4 D (D is the diameter of the
bubbles at the moment of their maximum enlargement).
L.A.Kosolapova, V.G.Malakhov (IME).
Spatial displacements of a
non-spherical gas bubble in an acoustic field.
A mathematical model of dynamics of a gas bubble in
a liquid has been constructed for non-small disturbances of its spherical form,
allowing for the spatial motion of the bubble, influences of the gravity and
the speed of the liquid flow. Viscosity and compressibility of the liquid are
approximately taken into account. It has been shown that in particular cases
the equations derived coincide with those obtained by other authors. Solutions
to the problem of oscillations of a moving non-spherical bubble under periodic
change of pressure of the liquid are presented.
T.F.Khalitova, N.A.Khismatullina (IME).
Strong compression of
ellipsoidal cavitation bubble.
The possible scenarios of deformation of shock wave
inside the slightly non-spherical cavitation bubble in the final stage of its
compression are revealed. It is shown that in the case of ellipsoidal
cavitation bubble they are appeared to be very close to the deformations of the
shape of the empty cavity. Changing of pressure and temperature fields inside
the pear-shaped bubble is shown. It is established that on the stage of a
moderate deformation of a shock wave the maximum pressure and temperature
values in the non-spherical case can be larger than in spherical case.
A.I.Davletshin (IME).
Simulation of interaction
of gas bubbles in an acoustic field.
The mathematical model of close-range interaction
of gas bubbles in a liquid with allowing for small distortions of bubble
surfaces has been proposed. As opposed to existing models it is of arbitrary
order of accuracy relative to the ratio of the characteristic radius of the
bubbles to the characteristic distance between them. The possibility of
interaction of non-spherical bubbles with formation of connected pairs and
triplets has been shown.
A.V.Repina, V.B.Repin (The
Kazan State Technical University named after A.N.Tupolev),
R.G.Zaripov (IME).
Research of subharmonic
resonances at periodic excitation of gas in an open tube.
Subharmonic resonances near to the second and third
natural frequencies of gas in an open tube are theoretically investigated. It
is shown, that in decomposition of the real law of motion of the piston with
a connecting rod on the Fourier components it is enough to take into account
only first two Fourier components. Computational data are satisfactorily agreed
with experimental results.
R.V.Sadovnikov, D.A.Gubajdullin, A.I.Nikiphorov (IME).
Realization
of preconditioned iterative Krylov subspace methods for solution of sparse
systems of linear algebraic equations on graphical processors and their
application for flow theory problems.
In this paper the realization of the library of iterative
Krylov subspace methods with preconditioning on modern NVIDIA graphical
processors is presented. Nowadays these methods are one of the most general groups
of methods used in applications for solution of large sparse systems of
algebraic equations. The considered methods are used for symmetrical and
nonsymmetrical sparse matrixes with non regular structure. The library of
iterative methods is intended for users who want to avoid difficulties and
details of parallel programming on graphical processing units, but for those ones
who must solve large sparse linear system of algebraic equations and to use the
effectiveness of parallel architecture of graphical processors.
A.V.Tsepaev (IME).
The solution of
three-dimensional two-phase flow problems on GPU.
Two algorithms have been developed to solve the
three-dimensional two-phase flow equation on graphic computing systems. The
first algorithm has been suggested to solve the equation for pressure, the
second one to solve the equation for saturation. These algorithms show their
efficiency with increasing number of fine grid segments.
A.N.Gabidullina, A.V.Elesin, A.Sh.Kadyrova, P.A.Mazurov (IME).
The multistep
Levenberg-Marquardt methods in hydraulic conductivity identification task.
The multistep Levenberg-Marquardt methods are
proposed for the minimization of a residual function. The proposed methods and
the classical Levenberg-Marquardt method are compared on solving model problem
of hydraulic conductivity identification for a three-dimensional anisotropic
confined aquifer. The numerical results are shown the efficiency of the multistep
Levenberg-Marquardt methods.
P.E.Morozov (IME).
The research of layers and
wells by the filtration waves of pressure.
The numerical and analytical solution of the fluid
flow to the vertical well with a periodic change in flow rate have been
compared. The influence of skin effect and the period of the active well on the
pressure change in the observation wells is investigated.
A.I.Abdullin (IME).
A coefficient inverse
problem of filtration in three-dimensional naturally fractured reservoir.
A computational algorithm for solving inverse
problems of fluid filtration towards horizontal well in the deformable
porous-fractured media. As the initial information the well test data are used.
The algorithm is constructed taking into account the dependence of the
fractures permeability on the pressure, the influence of the wellbore.
V.V.Klokov, D.Е.Sergeev (Kazan State University).
A
method of calculation of anodic boundary at ECM in the case of multivalent hodograph.
A method of calculation of
study electro-chemical machinery (ECM) of anodic boundary with given polygonal
cathode-instrument was developed. It is based on using of hydro-dynamical
analogy of a problem, with application of multivalent hodograph of velocity.
Solutions in cases of two cathode-instruments non-symmetrically placed
referring to vector of feed and in case of cathode-instrument with dielectric
holder were presented. The examples of solutions characterize variants of
broaching and cutting with method of ECM, at manufacturing of swages,
perforators and other detail of machinery.
February 10, 2010
N.M.Yakupov (IME).
Mechanics:
a problem - idea - practice.
Speaking about the major discoveries, John
Gribbin in the book
N.K.Galimov, I.H.Miftakhutdinov
(IME).
To definition of the module
of elasticity catenoids.
In the first part the questions of formation of
covers in a form of catenoids from polymeric materials are considered. The
complexities which have arisen under the testing of such covers from influence
of internal pressure, in particular, a problem of maintenance of tightness of
the examined node are marked. In the second part of the message the received
parities for calculation of covers in a form catenoids are resulted. Knowing
the form of deformation of a cover, it is possible to define the module of
elasticity of a material catenoids.
N.M.Yakupov, H.G.Kiyamov (IME).
Crack
modelling in three-dimensional statement.
The two-dimensional
approach does not allow with necessary accuracy to analyze area of defects,
area of joints of thin-walled elements, areas of fastening, area of the application of the concentrated
loadings. For such analysis it is necessary to use the three-dimensional
approach. In the present work the development of splines variant of МFE for
calculation of designs elements in
three-dimensional statement is described. The considered object is set by
co-ordinates of an individual cube. The decision in each of rectangles is
represented in a form of interpolar Hermitian cubic splines of three variables. On the
basis of the developed program the analysis of the panel with a through and not
through crack is made.
S.N.Yakupov (IME).
To definition of mechanical characteristics
of nanocovers.
The effective way
of research of mechanical characteristics of thin coverings in system
"covering-substrate" is described, without dismembering a covering
from a substrate. The experimentally-theoretical method separately investigates
system and "substrate" and covering
characteristics are defined. The example of definition the module of elasticity
and the conditional module of elasticity of a nanocover from oxide of titan covered
by an ionic-plasma method on a polymeric film is considered. Simplicity of the
approach and absence of necessity to work directly with thin nanocover is
marked. The experimentally-theoretical approach allows receiving of authentic
results.
N.M.Yakupov, R.R.Giniyatullin (IME).
Research
of influence of ultra-violet radiation on corrosion deterioration.
Represents a great
interest influence of various fields on change of mechanical characteristics of
a material in the course of corrosion deterioration. The works on research of
influence of ultra-violet radiation on process of corrosion deterioration are
started. Installation is developed for test of thin-walled elements of designs
in the corrosion environment under the influence of ultra-violet radiation.
Further for definition of mechanical characteristics of a material of samples
the experimentally-theoretical approach is used. Schedules of dependence of a
deflection of a dome of samples from pressure are constructed. The analysis of
results shows influences of ultra-violet radiation on corrosion deterioration.
N.M.Yakupov, R.I.Shafigullin (IME).
Research
of influence of a mixed liquid on corrosion deterioration.
The studying of
corrosion deterioration of the thin-walled metal elements subjected to
influence of a streamline aggressive liquid with vials has begun. Installation
has been developed and experimental researches are spent. For definition of
mechanical characteristics of a material of investigated samples the
experimentally-theoretical approach is used. Schedules of dependence of a
deflection of a dome of samples from pressure are constructed. The influence of
a mixed liquid on corrosion deterioration is established. In particular, it is
shown that at more intensive influence of stream corrosion deterioration is
more considerable.
N.M.Yakupov, A.A.Abdyushev (IME).
Numerical
research of the panel with a crack with "an active" and
"passive" overlay.
An effective way of
treatment of cracks is the way of use of active overlays - the special overlays
made of a material with memory of the form which creates compressing efforts in
the established area. The researches of
influence of active "treating" overlays on the intense-deformed
condition of the panel with one crack by the finite element method are carried
out. Distributions of the pressure intensity in the panel with the central
crack depending on an arrangement of an active overlay are shown. Efficiency of
use of active "treating" overlays, and also possibility of rational
placing of such overlays are marked.
A.R.Nurgaliev (IME).
Definition of mechanical
characteristics of the deformed elements of the designs which are subjected in
an excited environment.
A number of products, designs and constructions
work at intensive mechanical loadings in corrosion environments, thus
mechanical loadings accelerate corrosion process. The installation is
developed, allowing executing of two kinds of researches: research of directly
exemplary with any defects, including corrosion; research of variation of mechanical characteristics of samples, in the
course of corrosion deterioration. On the basis of experimentally-theoretical
approach a number of researches for definition of mechanical properties of the
considered samples with various defects are spent.
A.A.Aganin, M.A.Ilgamov (IME).
Reorganization of harmonics
during dynamic loss of stability in mechanical systems.
Dynamic buckling of a rod under action of a
step-like (in time) compressing force and development of deviations from the
spherical shape during strong compression of a cavity in liquid are considered.
These examples are used to show dependence of dynamics of a system on the
decreasing distribution of amplitudes of harmonics of the initial deviation, in
particular, reorganization of modes in the process of evolution of this
deviation.
A.I.Malikov (IME).
State estimation and performance of control systems
with uncertainties and parametrical perturbations.
At various ways of the
assignment of perturbation set in a matrix of unit (in the form of polyhedral
set in space of matrixes, in the form of an ellipsoid or by means of matrix
inequalities) corresponding ways of construction of matrix comparison system
are offered. On the basis of matrix comparison systems algorithms for finding of an invariant
ellipsoid and an estimation of
performance by local criterion are developed for system with
uncertainties and parametrical perturbations. The conditions of robust
stability, dissipative, invariance, a condition of bounded ness and convergence
of ellipsoidal estimations for continuous and discrete systems are received. In
case of linear autonomous systems with application of matrix comparison systems
and linear matrix inequalities the problem of a finding minimal (by any
criterion) invariant ellipsoid, giving an asymptotic estimation, and findings
suboptimal and locally optimal invariant ellipsoids completely is solved. The developed
algorithms of state estimation and performance are approved on test examples of
dynamic systems.
M.S.Ganeeva, V.E.Moiseeva, Z.V.Skvortsova (IME).
Non-linear bending and
stability of a spherical shell loaded by the pressure of a liquid.
Stability and the non-linear bending of thin
elastic-plastic spherical shells under the pressure of a compressible and
incompressible liquid have been theoretically investigated. Theoretical
relations of the problem, an algorithm and a computational program have been elaborated.
Results of numerical solution have been obtained for a hemispherical shell and
segments depending on experiment arrangement conditions.
V.G.Malakhov (IME).
Impact of a liquid jet on
an elastic body.
Impact of a liquid jet arising during collapse of a
cavitations bubble on linearly-elastic isotropic semi-space is studied. It is
supposed that at the initial moment of time a liquid layer can be between the
boundary of the semi-space and the jet tip. It has been found that the impact
of the jet can result in considerable compressive as well as tensile stresses
in the elastic body. In doing so, compressive stresses in the body can be even
more than the pressure of the liquid on the contact surface. It has been shown
that the maximal compressive stresses can be reached on some distance from the
body surface rather than on the surface itself.
A.N. Shikhranov (IME).
Designing most rigid plates
and shells.
Efficiency of the developed
numerical method and iteration algorithm of searching for most rigid thin
shallow shells of revolution and circular plates in non-axially symmetric and
geometrically non-linear problem statements has been shown. The optimal
projects obtained have better characteristics of rigidity than the initial ones
of constant thickness and the same volume of the material.
B.A. Snigerev (IME).
Flow of viscoelastic liquid
in conforming channel.
This study investigates numerical simulation of
creeping flow of viscoelastic liquids, which is realized at entrance of
extrusion die. The flow of liquids is described by equations of motion and
continuity, together with rheological equation of state, based on molecular
theory of polymers. The results of orientation and deformations of molecules
are received on dependence of parameters of rheological model.
I.V.Morenko (IME).
Influence of the free
stream turbulence on the hydrodynamics and heat transfer of bluff bodies.
The effect of free stream turbulence on drag and
lift coefficients, heat transfer from a circular cylinder is numerically
investigated for free stream Reynolds number 40000, turbulence intensity from
1% to 40% and integral length scale from 0.25 to 4 cylinder diameter.
N.Z.Serazetdinov (IME).
Water purification from
suspended particles (review).
The methods and techniques of water purification
from suspended particles were considered. Different types of filters were
reviewed, correction and improvement of design were offered. Mathematical
models describing the processes occurring in the filters were considered
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