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:
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.
Here it is given the
papers survey in accordance with Program of Seminar and final scientific
Conferences.
The following reports were presented
at the Seminar in 2004-2005 and at the Final Scientific Conference (February
8-11, 2005), dedicated to the 60-th Anniversary of the Kazan Science Center of
the RAS.
May 14, 2004
M.N.Galimzianov (The Institute of Mechanics of RAS).
Two-dimensional waves in
bubble liquid. On materials of thesis for Candidate of
Sciences Degree, speciality: 01.02.05 - Mechanics of liquid, gas and plasma.
Reviewer DrSc A.A.Aganin.
The
report is devoted to the wave processes in bubble liquid mediums. The results
of analytic and numerical solution of acoustic nonlinear shock waves in liquid
containing the bubbles are presented. In particular, the special features of
wave propagation in "pure" liquid, containing bubble zones of finite size are
considered. The evolution of waves of pressure in partially-inhomogeneous
water-air mixture is investigated.
June
9, 2004
I.V.Kostolomov (The Tyumen State Architectural Academy).
Mathematical modeling of
processes heat- and -air transfer in premises. On
materials of thesis for a degree of physical and mathematical sciences,
speciality 01.04.14 - thermophysics and theoretical heating engineering. Reviewer PhD A.L.Tukmakov. The processes of
isothermal and non- isothermal movement of air in premises are investigated.
The influence of numbers of Reynolds, Grasgof and non-dimensional geometrical
parameters are analyzed. The influence of the given parameters on average and
maximal speeds and the temperature of air in premises is considered.
June 9, 2004.
I.E.Timoshenko (IME).
Modeling "polymer-disperse"
action on oil reservoir. On materials of a thesis on
depending scientific degree PhD (physics and mathematics), speciality: 01.02.05
- Mechanics of liquid, gas and plasma. Scientific chief PhD A.I.Nikiforov. Reviewer
DrSc M.Kh.Hajrullin. The mathematical model flooding of oil reservoir with
applying "polymer-disperse" systems is presented. The pore and particle size
distribution functions and model introducing of a porous medium as a bundle of
parallel capillaries are used in the model. The algorithm of a numerical
solution is based on the finite element method of control volumes. The
comparison of the experimental data and the results of numerical modeling for
pore and particle size distribution functions is carried out. The results of
calculations for several models of inhomogeneous oil reservoir are given.
October
27, 2004
P.E.Morozov (IME).
Estimation of reservoir flow
parameters on results of hydrodynamic researches of wells on the basis of
regularization methods. On materials of thesis for
Doctor of Sciences Degree, speciality 01.02.05 - Mechanics of liquid, gas and
plasma. Scientific chief prof. M.Kh.Khairullin. Reviewer DrSc. A.I.Nikiforov.
In this thesis computing algorithms were developed on the basis of
regularization methods for estimation of reservoir flow parameters on results
of hydrodynamic researches of vertical and horizontal wells.
November
3, 2004
A.V.Elesin (IME).
The hydraulic conductivity
identification of anisotropic confined aquifer. On
materials of thesis for Candidate of Science Degree, speciality 01.02.05 -
Mechanics of liquid, gas and plasma. Scientific chief PhD P.A.Mazurov. Reviewer
PhD A.I.Nikiforov. The using of the sensitivity storages in the tasks of the
hydraulic conductivity identification of three-dimensional aquifer is
considered in this work. The sensitivity storages show the potential
possibility of parameters for minimization of the residual function. The
approach for constructing of the new minimization algorithms of the residual
function was considered. It is based on analysis of the sensitivity storages
distributions in parameter space along main directions receiving
SVD-decomposition of matrix H = AtA,
where A is the sensitivity matrix.
One of the fundamental problems of the solution of identification tasks is the
constructing of the stopping criteria of the residual function minimization
process. The new stopping criterion of minimization process is proposed. The
efficiency of observation locations which ones are situated along the rivers
and rills is showed.
January
19, 2005
V.E.Moiseeva (IME).
Numerical modeling of
nonlinear deformation of compound shells of revolution affected by
nonaxisymmetric thermoforce loading. On
materials of thesis for Candidate of Science Degree, speciality: 05.13.18 -
Mathematical modeling, numerical methods and program complexes. Scientific
chief DrSc M.S.Ganeeva. Reviewer PhD N.K.Galimov. The computation technique of
geometrically and materially nonlinear
stress-strain state of non-shallow shells of revolution with branching
meridian affected by nonaxisymmetric
thermoforce loading has been proposed taking into account that the physical -
mechanical characteristics of the
material depend on temperature. The technique has been realized as a
FORTRAN program complex. Solution results of some new problems have been
obtained.
June
14, 2005
A.I.Nikiforov (IME).
Modeling of two-phase liquid
motion in reservoir under changing of pore space structure. On materials of thesis for Doctor of Science Degree, speciality:
01.02.05 - Mechanics of liquid, gas and plasma. Reviewer DrSc A.N.Salamatin.
Work is dedicated to study of the carrying interacting dispersion of the
admixtures by filtration flow and modeling of declinator flow technologies in
oil recovery. For the first time from united positions different filtration
processes, being accompanied by changes of filtration-capacitive features layer
are described. Closure equations to law of the conservation of mass and pulse
are built using the functions of the pore and particle sizes distribution.
The
following report was presented at plenary Session of the Final Scientific
Conference of the Kazan Science Center RAS:
February 8, 2005
N.M.Yakupov (IME).
The mechanics of films and
membranes of non-uniform structure. The
effective experimental - theoretical approach of research of films and membranes of non-uniform structure
is considered. Circuits of experimental plants, and also some parities
necessary at theoretical processing of results are given. The substantiation of
influence of deformation on corrosion process is given. The information on some
practical workings, executed in laboratory is given. It is marked about the
rewarding of this complex working by the Diploma and the Silver medal on the
53-rd World Interior Salon of innovations, scientific researches and new
technologies "Brussels - Eurika-2004".
The
following reports were presented at section Sessions:
February 10, 2005
D.A.Gubaidullin, R.G.Zaripov (IME), R.G.Galiullin (KSU), L.A.Tkachenko (IME).
Coagulation and
sedimentation of an aerosol of different initial concentration at nonlinear
oscillations in a closed tube. The results of
experiments on nonlinear oscillations of an aerosol of different initial
concentration in a closed tube near the first nonlinear resonance are given. It
was discovered that for various concentration of an aerosol with increase of
frequency or intensity of oscillations time of a coagulation decreases. The
nonlinear dependence of increment of time of coagulation with increase of
initial concentration of an aerosol is established. At imposing nonlinear
oscillations on the process of coagulation of nonindignant aerosol the general
time of coagulation and sedimentation decreases.
α.L.Tukmakov (IME).
Distribution of firm
particles in the acoustic field of the resonant pipe at various modes of excitation. On the basis of the numerical decision of viscous compressed heat -conductive gas dynamics equations, the
process of drift of firm spherical particles in the closed pipe is
investigated. The movement of particles arises under the influence of
fluctuations of a gas column, which are raised by the flat piston, moving under
the harmonic law. The particles distributions along an axis, characteristic for the first and the second
linear and the first nonlinear resonances, received in the assumption of Stouks
character of a particle flow by gas, are given. It is shown, that average speed of drift is defined by asymmetry
of the wave form and grows near the
resonances where there are explosive fluctuations.
D.A.Gubaidullin,
A.A.Nikiforov (IME).
Spherical and cylindrical
waves in disperse environments. Systems of the
equations of movement to polydispersed mixtures of vapor, gas and drops, in view of interphase heat and mass
transfer, and to monodispersed mixtures of a liquid with bubbles of insoluble
gas are presented, in view of acoustic unloading bubbles, are presented.
Existence of decisions at the presented systems in the form of indignations for
potentials of speeds of phases for flat, spherical and cylindrical cases is
established. Dispersion equation is received. Numerical calculations on
distribution of pulse indignations are executed. Influence of geometry of
process and defining parameters of two-phase environments is shown.
A.A.Aganin, T.S.Guseva (IME).
Distortions of the spherical
shape of a bubble during its strong expansion-compression with account of the
liquid compressibility and the non-uniform gas pressure in the bubble. The evolution of a small initial distortion of the spherical shape of a
gas bubble during its single expansion-compression under harmonic pressure
variation of the surrounding liquid with the amplitude of 1.4-5 bar is
considered. The liquid viscosity is taken into account without allowing for the
liquid vorticity. During expansion and the most part of the compression stage
the radial dynamics of the bubble is described by Rayleigh-Plesset equation,
while in the final stage of compression by gas dynamics equations in the gas
and liquid. Estimates of the maximum distortion amplitude at the moment of the
bubble collapse are obtained.
A.A.Aganin, D.Yu.Toporkov (IME).
Liquid viscosity effect on
distortion of the spherical shape of the vapor bubble. Influence of liquid viscosity on variation of small distortions of the
spherical shape of a vapor bubble in the course of its single strong
enlargement-compression is studied. The liquid near the bubble is assumed
incompressible, the vapor in the bubble being ideal with uniform pressure
distribution. The processes of non-equilibrium evaporation-condensation and
non-stationary heat conduction in the vapor and the liquid are taken into
account. 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 are used.
N.V.Sonin (IME).
Light transmission of
small-dispersible aerosol at passage of a laser beam. The results of experiments of nonlinear oscillations of small-dispersible
aerosol in the closed tube for the third nonlinear resonance are given. It is
found, that in a resonance the amplitude of pressure at the piston is lower,
than at the closed end. By the method of a past and scatter laser beam, the dependences
of its intensity in various sections along the tube on time are received. The
distribution of intensity of a diffused light in an aerosol along a tube is
given. The non-monotone character of distribution of intensity of a diffused
light along a tube with a maximum displaced from the middle of a tube to the
piston is found. The depth of penetration of a beam along a tube is incremented
in due course.
M.V.Taldykin (IME).
The model of transformation
of gravity surface waves on water. For
the planar steady periodic waves on a surface of an ideal incompressible fluid
with infinite depth the analytical equation in a dimensionless aspect with two
independent parameters is given: relative amplitude (steepness) and relative
removal on a normal from a base wave profile. The equation allows to receive
the set of curves circumscribing a modification of a wave contour at magnification
of amplitude from sine (small amplitudes) up to a highest wave of the Stokes
which is characterized by presence of an angular point on a wave crest. The
equation takes into account, as a minimum, a wave contour of the Stokes up to
the second degrees of amplitude. In a parametric aspect trajectories of orbital motion of points on
the surface of a wave for phase are reduced.
A.B.Mazo, I.V.Morenko (IME).
Numerical simulation of the
viscous flowing around the two cylinders in a channel.
V.L.Fedyaev, A.B.Mazo,
V.I.Malov, I.V.Morenko (IME).
Calculation of the hydraulic
networks.
B.A.Snigerev (IME), Phillips T.N. (UK).
Numerical simulation of the
diluted polymers solutions flows.
A.I.Malikov, F.I.Yafasov (IME).
Methods and algorithms for
ellipsoidal guaranteed state estimation of discrete control systems. The new approach for guaranteed state estimation of discrete control
systems with uncertainties and structural changes is presented. Approach is
based on matrix comparison system method and uses the measurement results.
Algorithms are implemented to state the estimation of electromechanical system
with induction motor. The Real-time transient process estimations, taking into
account measurement results from experimental unit, are presented.
U.N.Zakirov (IME)
The relativistic allowances
to property of a rotationally symmetric bundle of hyperbolic trajectories. At a precision determination of a trajectory of space vehicles the
definition of the relativistic allowances to property of axially symmetric
bundle of hyperbolic trajectories is possible: the direction of velocity vector
for a surface of a celestial body (star) for
tnough broad bundle of a trajectory coincides with a direction on centre
of a body (star) on some fixed distance from centre. In the article on the
basis of expanded metrics it became possible for the first time to take into
account perturbation and variation of mass-energy of a close pair. The effects
can be utilised at precision navigating and in a celestia mechanics.
February
11, 2005
M.Kh.Khairullin, M.N.Shamsiev, R.V.Sadovnikov,
P.E.Morozov (IME).
Estimation of the filtration
parameters of a reservoir by the results of hydrodynamic researches of the
wells. In this work we propose methods for
interpretation of hydrodynamic researches of horizontal wells on the basis of
regularizing iterative methods. The various types of horizontal wells profiles:
horizontal, deviated, sinusoidal are considered. The finite elements method is
used for solving the problem of inflow to horizontal well. The preconditioned
Krylov subspace methods are used for solving linear systems.
M.Kh.Khairullin,
M.N.Shamsiev, L.A.Tulupov (IME).
Mathematical modeling of the
processes of formation and dissociation of hydrates. The results of numerical researches of the problem of formation and
dissociation hydrates in porous media with depressurization and heating
influence on the stratum are presented. The numerical analysis of the dissociation depending on filtration and
thermal characteristics has been produced.
S.V.Anohin, A.I.Nikiforov (IME).
Some results of numerical
modeling of gel action on oil pools.
A.R.Zakirova, A.I.Nikiforov (IME).
Numerical simulation of motion
of diphasic fluid in a narrow gap. The
problem of motion of two unblended fluids in a gap between parallel flats in a
case when the presence of a capillary difference of pressure on interface is
taken into account, is solved by the numerical finite difference method. The
case of statement of the contact angle formed by interface and a solid wall is
considered. Graphs of the velocity and pressure fields are plotted. It is
shown, that the presence of the contact border in a diphase stream leads to
redistribution both of pressure and fields of velocity.
A.V.Elesin, P.A.Mazurov (IME).
The influence of location of
observation points on the stability in the problems of hydraulic conductivity
identification. The influence of location of observation points
on the stability of the hydraulic conductivity identification process is
considered in the case of a three-dimensional heterogeneous aquifer. The dependence
of identification result on such a location is studied under boundary
conditions of the first and second types.
A.N.Gabidullina, P.A.Mazurov (IME).
The solution of
identification task with a priori comparative information of values of the
parameters. A new algorithm is proposed for solution tasks
of identification of the hydraulic conductivity of three-dimensional aquifer.
The algorithm takes into account a comparative information about parameters
values.
A.Sh.Kadyirova, P.A.Mazurov (IME).
Constructing of quasi-Newton
algorithms of residual function minimization using the sensitivity storage in
identification tasks. The new algorithm of
residual function minimization is proposed for identification tasks. This algorithm
takes into account the distribution of the sensitivity storages in parameter
space along main directions.
P.A.Mazurov, A.V.Tsepaev (IME).
The solution algorithm of
confined and unconfined filtration task on the coarse grid with the
concentration of grid near the wells on multiprocessoring system. A new algorithm has been proposed to solve flow equation for unconfined
and confined filtration on the coarse grid with the concentration of grid near
the wells. The algorithm is based on the method of division of domain on
subdomains.
E.A.Shirokova (IME).
Interpolation problem for
the 2-d basic problem of the dynamics of elastic solids. We search for the particular solution of the problem for an elastic
plane domain: given the boundary displacements at n moments of the time
interval it should be possible to find the displacements at any point of the
domain at any moment of the time interval. The
interpolation problem is reduced to solution of n boundary value
problems in a given area.
F.Kh.Ahmetzjanov,
N.M.Yakupov (IME).
To an estimation of the
damageability of concrete and ferro-concrete designs of cooling towers. The technical condition is determined, kinds and parameters of damages
on presence of interstices and cracks, a degree of decrease of strength to
compression in ferro-concrete racks of cooling towers σλ-1200
are established. The parameter of an estimation of damageability, as the
relation of residual strength to initial strength is offered. The geometrical
parameter as the relation of the area of cross-section profile of an element
net to the initial area is considered.
M.S.Ganeeva, V.E.Moiseeva,
Z.V.Skvortsova (IME).
The nonlinear bending of the
non-thin shell of revolution with a branching meridian under the influence of
non-axis-symmetrical thermo-force loading. The
nonlinear relations and the numerical computation technique of the
stress-strained state (SSS) of the non-thin shell of revolution with a
branching meridian under the influence of non-axis-symmetrical thermo-force
loading have been obtained. The computation results obtained by using the
developed technique coincide with the known linear analytical solution in the
case of thin shells. The computation results of the elastic-plastic SSS of the
cylindrical pipe with an external transversal
ribbing are presented. It has been shown, that the choice of the
computation theory has important influence on results of computation of the
non-thin pipe SSS.
N.K.Galimov (IME).
About a bend of the jammed
round plates. The bend of the round plates jammed on edge
which are taking place under action of uniform external pressure is studied.
The material of a plate is supposed isotropic. The big deflections of a plate
are taken into account. The decision is received by method of Bubnov-Galerkin
in four approximation. Results of the decision were comparison with results of
other authors. Their good concurrence is marked.
N.K.Galimov, R.G.Nurullin (IME).
To durability of spherical
membranes. Elastic balance of the thin spherical membranes
fixed on edge and loaded with homogeneous internal pressure is considered. The
big deflections of membranes are taken into account. The decision is received
by method of Bubnov-Galerkin in three approximation. Deflections and stress of
a membrane are determined. Comparison of results with the data of other authors
is made. Good concurrence of results is marked.
I.Kh.Miftakhutdinov (IME).
Shells with minimal surface
in nature and architecture. On the base of study natural
bioanalogy, the author has installed a new principle of molded and fabrications
of transparency shells in the form of minimum surfaces. The given principle -
self-molded shells is realized in the process of heat processing oriented
(beforehand two-axis sprained) thermoplastic materials, bolted to the hard
spatial supporting sidebar.
N.M.Yakupov, A.R.Nurgaliev,
R.G.Nurullin, S.N.Yakupov (IME).
The corrosion deterioration:
approaches of research and some results. Various
approaches to research of the process of corrosion deterioration of metal
elements of designs are considered. The factor of definition of a degree of
corrosion deterioration is entered. The polarizing curve of change of a current
from potential in the center of corrosion is analysed at the account of
deformation. The scheme of experimental plant is submitted. Some results in
definition of a degree of corrosion deterioration are received.
A.N.Shikhranov (IME).
Optimal design of most rigid
shells and plates. An efficient numerical
algorithm of optimization of flexible elastic shallow shells of revolution of
prescribed volume with respect to rigidity criterion in non-axially-symmetric
statement is presented. The additional work of deformation is taken as rigidity
characteristic. The thickness function is chosen as the control one. The
stress-strained state of the shell is described in account with geometric
non-linearity. By using the variation problem statement and the method of
Lagrange multipliers, the necessary conditions of optimum design are written.
The algorithm of computing optimal distribution of thickness is based on the
iteration procedure. Some numerical examples are given.
The following reports were presented at the Seminar in 2005-2006 and at
the Final Scientific Conference (February 8-14, 2006), dedicated to the 15-th
Anniversary of the Institute of
Mechanics and Engineering of KazSσ
RAS.
October 18,
2005.
I.K. Gimaltdinov (Sterlitamak State Pedagogical Academy, Sterlitamak).
Dynamics of 2-dimensional
nonlinear and detonational waves in nonuniform bubbly liquid. On materials of the thesis submitted for Doctor of Sciences Degree in
physics and mathematics, speciality 01.02.05 - Fluid and Plasma Mechanics.
Reviewer doctor-of-sciences in physics
and mathematics A.A. Aganin.
February
9, 2006
D.M. Zaripov (Institute of Mechanics of Ufa Science Center of RAS, Ufa).
Mathematical simulation of
the dynamics of a pipeline under the action of pressure waves in transported
fluid. 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 corresponding member of the
RAS M.A. Ilgamov. Reviewer
doctor-of-sciences in physics and mathematics A.A. Aganin.
Investigations of the dynamic behavior of
pipelines allowing for the mass and variable pressure of transported fluid have
been conducted. The mechanism of excitation of transversal oscillations of the
pipe is due to interaction between temporal variations in the internal pressure
and the curvature of the elastic line of the pipe.
March
6, 2006
T.S. Guseva (IME).
Evolution of the distortion
of the spherical shape of Α gas bubble in a liquid under its strong
enlargement-compression. On materials of the thesis
submitted for Candidate of Sciences Degree in physics and mathematics,
speciality 01.02.05 - Fluid and Plasma Mechanics. Scientific chief
doctor-of-sciences in physics and mathematics A.A. Aganin. Reviewer PhD V.G. Malahov.
Qualitative
and quantitative features of the evolution of small distortions of the
spherical shape of Α gas bubble in a liquid under its strong
enlargement-compression have been revealed, regularities of influence of
parameters of the gas in the bubble and surrounding liquid have been determined.
A new equation for description of development of a small distortion of
sphericity with more exact regard to the influence of gradients of velocity and
pressure of the gas and the liquid on the bubble surface at the stage of strong
compression of the bubble has been proposed. Analysis of applicability of
simplified models has been carried out.
The
following report was presented at plenary Session of the Final Scientific
Conference of the Kazan Science Center RAS:
February 8, 2006
D.A. Gubaidullin (IME).
Dynamics and acoustics of
dispersed media. The results of theoretical and experimental
investigations of wave dynamics for two-phase gas-liquid systems are presented.
Some effects and peculiarities of acoustics for gas-drops
media and mixture of liquid with gas bubbles were taken in account. The equations of movement are presented, dispersion ratious are received, evolution of pulse waves is performed, influence of geometry of
process, heat and mass transfer and
basic parameters of mixtures are analysed. On the experimental investigations
of nonlinear oscillations of an aerosol
in closed and open tubes the non-monotone dependence of the drop sedimention
time on the minimum at the frequency of resonance has been revealed. A drift of
alone particles under oscillating of viscous contracted heat-conducting
gas in the closed tube is explored. It
is shown that eventually particles are displaced to nodes of a standing wave
for a field of velocities which allocation is defined by type of a resonance.
The
following reports were presented at section Sessions:
February
13, 2006
D.A. Gubaidullin, A.L. Tukmakov (IME).
Influence of the particles
diameter on their motion in a closed tube at nonlinear gas oscillations.
By
means of a numerical decision of
Navier- Stokes equations, that were solved by MacCormak method of second-order
accuracy, we investigate the influence of the diameter of aerosol particles on their behavior in wave pole of acoustic resonator. Nonlinear oscillations of the gas column in
a closed tube are excited by oscillating piston, driven at the fundamental
resonance frequency. The Numerical studies revealed the distributions
of the particles in the closed tube under nonlinear gas oscillations from their
diameter.
D.A. Gubaidullin, A.A.
Nikiforov (IME).
Acoustic waves in the
mixtures of a liquid with gas bubbles.
Comparison between theory and experiment. Distribution of acoustic
perturbations in liquids with bubbles is theoretically explored in view of
acoustic unloading of bubbles. Comparison of the theory with known experimental
data on a velocity of distribution and damping of waves in mixtures of water
with air bubbles is carried out. Calculation of evolution of impulse waves of
pressure in liquids with bubbles with various values of initial radius of
bubbles is lead. Nonmonotonic dependence of damping of an impulsive disturbance
of pressure on initial radius of bubbles is shown.
D.A. Gubaidullin (IME), R.G. Zaripov (IME), R.G. Galiullin (KSU), L.A. Tkachenko (IME), A.J.Pjaterkin (KSU).
Motion of the particle at
nonlinear oscillations of gas in the closed tube.
Drift of a solid particle at nonlinear oscillations of gas in the closed tube
is experimentally investigated. In up to-resonant modes the particle goes from
the closed end of a tube to the piston, making longitudinal oscillations with
magnification of an oscillations swing. The increase of the excitation
frequency of gas leads to the growth of an oscillations swing of a particle and
increase of its medial velocity for all explored lengths of tubes. With
magnification of length of a tube for the given gas excitation frequency the medial
velocity of a motion of a particle grows, as frequency comes nearer to
resonant.
L.A. Kosolapova, V.G.
Malakhov (IME).
Nonlinear nonspherical
oscillations of a gas bubble under periodic variation of the surrounding liquid
pressure. A mathematical model of nonlinear nonspherical
oscillations of a bubble in the viscous incompressible liquid has been
developed. In this model, the bubble shape variation is presented in the form
of a series over the spherical harmonics. The governing equations are written with
accuracy of square of the amplitude of the spherical bubble shape distortion.
It has been shown that at some values of the initial radius of the bubble and
the liquid pressure amplitude the inclusion of the highest harmonics can lead
to the change in the regime of oscillations but it insignificantly influences
the bubble surface shape.
D.Yu. Toporkov (IME).
Distortion of the sphericity
of the vapor bubble in deuterated acetone.
Evolution of small distortion of the spherical shape of a vapor bubble in the
course of its single strong enlargement-compression in deuterated acetone is
studied. Spherical component of the liquid and vapor motion is described by the
equations of hydrodynamics with taking into account the processes of
non-equilibrium evaporation-condensation on the bubble surface. It was found
that distortion of the sphericity of the bubble decreases up to several orders
if the distortion arises in the stage of the bubble enlargement when the radius
is much less than its maximum and the distortion increases up to several
hundred times if it arises when the radius is close to its maximum.
T.S. Guseva (IME).
A model of nonspherical
dynamics of Α gas bubble in a liquid under its strong compression. A new equation for description of development of a small distortion of
sphericity with more exact regard to the influence of gradients of velocity and
pressure of the gas and the liquid on the bubble surface at the stage of strong
compression of the bubble has been proposed. With its use the most rapid increase
of the bubble sphericity distortion is observed in that part of compression
stage where the radial acceleration is directed from the liquid to the gas.
Analysis of applicability of simplified models has been carried out.
R.V. Sadovnikov (IME).
Estimation of flow and
storage parameters of fractured porous reservoir on the results of hydrodynamic
tests of vertical wells. The numerical technique based on the Levenberg-Marquardt method
is developed in this report to aid the analysis of hydrodynamic tests of
vertical wells for flow and storage parameters identification in a fractured
porous reservoir. Sensitivity coefficients with respect to parameters are
calculated by sensitivity equation method. The fluid flow in fractured porous
reservoir is simulated by the dual porosity model. The results of parameters
estimations are given.
P.A. Mazurov, A.V. Tsepaev (IME).
The parallel algorithms of
solving the two-phase filtration tasks on a coarse grid with fine grid
segments. An algorithm for multiprocessor computing
systems has been developed to solve the two-phase filtration tasks for a
confined aquifer on a coarse grid with fine grid segments near wells. The
efficiency of this algorithm increases with the increasing number of fine grid
segments.
A.N. Gabidullina, A.V.
Elesin, A.Sh. Kadyirova, P.A. Mazurov
(IME).
A new stopping criteria of
minimization process of residual function in inverse problems. The new stopping criteria of minimization process of residual function
has been proposed. This criteria is based on estimation of distance to point of
residual function minimum in parameter space.
M.Kh. Khairullin, M.N.
Shamsiev, L.A. Tulupov (IME).
Mathematical modelling of
gas hydrates formation and dissociation.
A.I. Nikiforov, I.A. Aganin (IME).
About closure correlations
for two-phase filtration model in clay-containing oil reservoirs. The paper presents mathematical model of isothermal filtration of
twophase mixture of incompressible liquids. The influence of clay swelling on
dynamic porocity and permeability with alteration of mineralization of
injection fluid is taken into account without hysteresis of clay swelling. The
pore size distribution function was used in the description of
filtration-capacitive features of reservoir.
February
14, 2006
M.S. Ganeeva, V.E. Moiseeva,
Z.V. Skvortsova (IME).
Deformation of non-thin
cylindrical and conic orthotropic shells under action of the wind loading. The stress-strained state (SSS) of the non-thin cylindrical and conic
orthotropic shells under action of non-axisymmetric loading such as a wind load
is studied. Equations of the shells theory by S.P.Timoshenko are used.
Numerical results about dependence of the SSS of shells on their geometry,
material properties, boundary conditions, type of loading are presented. The results
obtained under the non-thin shells theory and the thin shells theory are
compared. For isotropic shells the results of solving of geometrically and
physically nonlinear problem are presented, influence of parameters of the
numerical methods on results of calculation is studied.
N.M. Yakupov (IME).
About some developments of
laboratory NME for the last years. 60 years ago the
base of laboratory "Nonlinear mechanics of Shells" has been
incorporated. The basic three stages of development are marked. The information
on the development of laboratory for the period 1996-2005 is resulted. The line
of developments "Reports of the Russian Academy of Science" has come
in "The Major results in 2001, 2002 and 2004". Developments are
awarded with Silver medals and Diplomas on the 53-d World Interior of
innovations "Brussels - Eureka - 2004" and on the 33-d International
Interior of inventions "Geneva - 2005", and also the Medal and the
Diploma at the 6-th International forum " High technologies: "Hτ
XXI-2005".
S.N. Yakupov, R.G. Nurullin,
R.I. Shafigullin, N.M. Yakupov (IME).
Device for testing of film
compositions and some results of films research with defects. The device for testing various films is developed and made. A series of
tests from various films is lead and curve deformations are constructed. The
effect of secondary formation of a dome in polymeric films, and also the effect
of hardening of the two-layer membrane having local air cavities is marked.
I.Kh. Miftahutdinov (IME).
Environments of the minimal
surface on the basis of icosahedron. Icosahedron concerns to platons bodies and consists of 15 identical
equilateral triangles. The further development of this body is truncated
icosahedron. (The truncated icosahedron is the modern football). The construction on truncated and on the
core icosahedron of additional pyramids allows to receive forms of the new environments
with folded surfaces. However the replacement of folded elements by elements
from the minimal surfaces leads to absolutely new kinds of environments, as it
shown in the report of the author.
A.R. Nurgaliev (IME).
Experimental construction
and some results of research of membranes in the corrosion environment under
loading. The description of the experimental
construction is given, allowing to carry out the corrosion tests of membranes
under pressure. The difficulties which have arisen at manufacturing and
debugging of construction are marked. Some experimental results are given.
F.Kh. Akhmetzjanov, N.M.
Yakupov (IME).
The new approach to
definition of resistibility of concrete to mechanical influence. The analysis of destruction of samples from fine-grained concrete is
resulted. The approach of an estimation of residual bearing ability of samples
is described in view of damages. Criteria of damageability for the stretched
and compressed concrete elements are considered at short-term simple loading.
Kh.G. Kiyamov, I. Kh.
Miftakhutdinov, N.M. Yakupov (IME).
The experimental way of
parametrization of shells of complex geometry. The
experimental approach of parametrization of surfaces of complex geometry and
algorithm of calculation on experimental data of parameters of surfaces are
developed. Examples of construction of surfaces of complex geometry are
considered.
A.I. Malikov, F.I. Yafasov (IME).
Functional diagnosis of
electromechanical system with induction motor. The
algorithm approach to functional diagnosis of electromechanical system is
considered. Algorithms for guaranteed state estimation of induction motor by
measurement results were received using matrix inequalities and developed for
technical state control, faults detection and identification. Proposed algorithm
and method for functional diagnosis of induction motor were
software-programmable on PC and approved on-line real time processing on
experimental assembly.
U.N. Zakirov (IME).
About the first domestic
article of prof. K.P.Stanykovish on generalization of the formulas of
Ziolkovsky. Further
development of his theory. In 1958 after the start of the first Satellite,
series of operations on the solution (disregarding gravitations) of
relativistic dynamical equation of a center of mass "of an ideal rocket"
appeared abroad. They differed from the results of Ziolkovsky. The series
belonged to the German physic E.Zenger, Dutch ballistics M.Kooj, Bulgarian
explorer N.Kalizin. In these operations the equation obtained in 1930 by
Eno-Peltri is analyzed. In a limit of low speeds of a motion we have the
formula of Ziolkovsky. Prof. K.P.Stanykovish paid attention to relativistic
generalization of effluxion velocity.
P.P. Ossipov (IME), R.N. Maksudov (Kazan
state technological institute).
Mass-transfer modeling of
oil extraction from vegetable substrates with supercritical CO2. In present work the
B.A.Snigerev (IME).
The features of viscoelastic
flows around round-up bodies in flat channel.
The flow of viscoelastic fluid around round-up bodies in flat channel is
investigated. The feature of this flow is developing of the wake behind the
body, which is characterized by the property, that the velocity of fluid here
is higher than in middle of channel. The size of wake and the drag coefficient
of the bodies are investigated in dependence of viscoelactic properties of
fluid.
I.V. Morenko (IME), A.B. Mazo (KSU).
Unsteady flow interference
between two circular cylinders in tandem.
Flow past two cylinders in tandem is numerically simulated. The simulations are
performed for a Reynolds number equal 100 and 200. The influence of the
distance between the cylinder centers on the drag and lift coefficients,
Strouhal number is studied.
Potential
participants are kindly invited for the presentation of their results at the
Seminar.
Contact
address - gubajdullin@mail.knc.ru
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