INSTITUTE OF MECHANICS AND
ENGINEERING;
SCIENTIFIC SEMINAR
Problems
of Continuum Mechanics
(scientific seminar and conference)
D.A.Gubaidullin
Institute
of Mechanics and Engineering;
Lobachevsky 2/31,
The Scientific
Seminar "Problems of Continuum Mechanics" works in the
·
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.
The
following reports were presented at the Seminar in 2007 and at Final Scientific Conference'2007 (Kazan,
A.A. Nikiforov (IME). Dynamics of spherical and cylindrical waves
of small amplitude in disperse systems. On materials of the thesis
submitted for Candidate of Sciences Degree, speciality
01.02.05 - mechanics of liquid, gas and plasma. Scientific chief Corresponding
Member of the RAS D.A. Gubaidullin. Reviewer DrSc A.A. Aganin.
The distribution of spherical and cylindrical waves of small amplitude in
mixtures of vapor, gas and drops and in liquids with bubbles is theoretically
investigated taking into consideration interphase
mass transfer. The influence of geometry of process and key parameters of
disperse mixtures on evolution of impulse perturbations of pressure is analyzed.
A.O. Syromyasov (The
The flow of viscous fluid through a periodic structure
of particles. On materials of the thesis submitted for Candidate of Sciences Degree, speciality 01.02.05 - mechanics of liquid, gas and plasma. Scientific chief DrSc S.I. Martynov. Reviewer DrSc A.I. Nikiforov.
Uniform and linear flows of
incompressible viscous fluid containing the infinite periodic array of particles
are studied in Stokes approximation. The developed method combines a
lattice-periodic multipole decomposition of solution
and takes into account symmetry groups of lattice and of boundary conditions.
Permeability tensors and effective viscosity tensors are found for suspensions
containing cubic and hexagonal lattices. The evolution of deforming cubic
lattices in shear flows is studied and the average shear viscosity of such
suspensions is calculated. When the average
stress is fixed the lattice oscillates in a complicated manner.
K.A. Potashev (The
Models and problems
of the theory of filtration in weak soils. On the materials of thesis
submitted for Candidate of Sciences Degree, speciality
01.02.05 - mechanics of liquid,
gas and plasma. Scientific chief DrSc
A.V.Kosterin. Reviewer DrSc A.I.Nikiforov.
The
problem of sewage deposits consolidation is solved. The simplified analytical
model of filtrational consolidation of weak soils is
offered. The model of viscoelastic soils
consolidation for the account of their hardening is generalized. The question of initial strain-deformed state of a loaded
saturated peat is considered. The mathematical model of infiltration of liquid
organic contaminants into the ground is developed. The water-saturation jump at
the pollution front is taken into account.
A.G. Gavrilov (The
The
investigation of "oil pool - well" system by high frequency pressure waves
method. On materials of the thesis submitted for Candidate of Sciences Degree, speciality 01.04.03 - radio physics and 25.00.29 -
atmosphere and hydrosphere physics. Scientific chief DrSc M.N.Ovchinnikov. Reviewer DrSc M.Kh.
Khairullin.
The original method to make
hydrodynamic investigations of "oil pool - well" system by the harmonic
pressure waves method using automated control system of hydrodynamic parameters
in wide range of oscillation frequency to affect the oil pool (10-1-10-5Hz),
including millihertz range is worked out.
Khuzina F.R.
(The
Birsk State Social Pedagogical academy)
About the outflow
of the boiling liquid from the tubular canal and the reservoir of finite
volume. On materials of the thesis submitted for Candidate of Sciences Degree, speciality 01.02.05 - mechanics of liquid, gas and plasma.
Scientific chief DrSc V.Sh.
Shagapov. Reviewer DrSc FedyaevV.L.
A.G. Kochenkov (The
The characteristics and structure of low-pressure
two-phase flow in planar nozzles under the outflow of the liquid into rarefied
medium. On materials of the thesis submitted for Candidate of Sciences Degree, speciality 01.02.05 - mechanics of liquid, gas and plasma. Scientific chief DrSc Yu.F.Gortyshov.
Reviewer DrSc A.L.Tukmakov.
The
following report was presented at the plenary Session of the Final Scientific
Conference'2007 of the
N.M. Yakupov (IME).
The experimentally-theoretical method of research of
mechanical characteristics of films and membranes.
Among thin-walled constructions
films and membranes are especially distinguished. Some mechanical
characteristics of nanofilms are resulted. The approach
of research of mechanical characteristics of the thin compositions with
non-uniform structure, defects and damages is stated. Experimental
installations are created. The two-dimensional approach is used: the round
sample is clamped on a contour and loaded with superficial pressure. The monitoring
of the dome form is made. Using ratios of elasticity, plasticity and the
equations of the theory of membranes the mechanical characteristics are
defined. Some results of researches, including films with nanofillings
are resulted. The approach of research of films and membranes with a nonplanar median surface is proposed.
The following
reports were presented at section Sessions:
D.A.Gubaidullin, A.A. Nikiforov (IME).
The influence
of concentration of vapor of disperse phase on distribution of weak waves in
mixes of a liquid with vapor-gas bubbles. The distribution of acoustic
waves in liquids with bubbles taking into account phase transitions is
theoretically investigated. The essential influence of initial vapor
concentration in vapor-gas bubbles on the speed of distribution and attenuation
of waves is shown taking into account phase transformations. It is established,
that the influence of vapor concentration in vapor-gas bubbles on the dynamics
of waves under growth of the initial volumetric maintenance of a bubbles
essentially increases.
D.A. Gubaidullin (IME), R.G. Zaripov (IME), R.G. Galiullin (KSU), L.A. Tkachenko (IME), I.A. Shulga (KSU).
Dynamic of a spherical particle at forced longitudinal
oscillations of gas in a closed tube. Dynamic of a
spherical particle along the axis of a closed
tube at forced longitudinal oscillations of gas is experimentally investigated.
Dependences of the particle coordinate on time for different lengths of a tube
and frequencies of excitation are obtained. Nonmonotonic
character of dependence of mean velocity of a spherical particle from an
oscillation frequency of the gas column at transitions through frequencies of subharmonic resonances is detected. Comparison of the obtained results with the data for a flat
particle is given.
A.L. Tukmakov (IME).
Drift
of firm particles at resonant fluctuations of gas in the open channel. By the numerical modeling
the drift of the firm spherical particles, arising under the action of longitudinal resonant fluctuations of a
gas column, is investigated. The firm spherical particles are being in a
suspension state in the open channel. The field of gas speeds contains periodic
nonlinear waves and acoustic current, the movement of particles occurs under the
action of Stokes force. The distributions of easy and heavy particles in a wave
field of the open channel near to the first, second and third fundamental frequencies
of fluctuations of a gas column are received. It is revealed, that the initial
stage of particles drift in the open channel under the action of acoustic
radiation is accompanied by occurrence in a moving cloud of particles of the
ordered configurations which in process of displacement to a cut of the channel
collapse.
A.A. Aganin, T.S. Guseva (IME).
Dynamics of bubbles in a strong acoustic field. A system of equations of "near" interaction of two
spherical bubbles in a strong acoustic field have been derived in the case when
the liquid region of one bubble with the distance from its center on the order
of the characteristic radius of the bubble is practically the same as the
similar region of the other bubble. The liquid compressibility influence (acoustic
radiation) appears in this system only in equations for the radii of the
bubbles. Some numerical examples are given to illustrate the effect of the
acoustic radiation during the bubble interaction.
D.Yu. Toporkov (IME).
A liquid viscosity effect on distortion of the sphericity of a bubble in deuterated
acetone. The evolution of
small distortion of the sphericity of a vapor bubble
in the course of its single strong enlargement-compression is studied. The spherical
component of the liquid and vapor motion is described by equations of gas
dynamics with realistic equations of state. It has been found that liquid
viscosity effect on evolution of small distortion with the wave length one
sixth of the bubble radius (i < 40) is negligible.
As the wave length decreases within i > 40 the
stability of the sphericity of a bubble rapidly
increases. It turned out that the bubble sphericity
is absolutely unstable if the liquid viscosity is neglected.
T.F. Khalitova, N.A. Khismatullina (IME).
Direct
numerical simulation of a gas cavity collapse in a liquid with
an axially symmetric deviations from spherical shape. The collapse of a
gas cavity in liquid with an axially symmetric deviations
from spherical shape is considered. The liquid and gas motion is described by
the gas dynamics equations with realistic equations of state. The problem is
solved in two stages. In the first stage, the gas dynamics equations are solved
without taking into consideration thermal conductivity, evaporation and
condensation. Godunov method is used for that. In the
second stage, the equation of thermal conductivity is solved with the
appropriate boundary conditions. This allows one to take into consideration
thermal conductivity, evaporation and condensation. Implicit alternating
direction scheme and explicit scheme are used in this stage.
A.A. Aganin, A.I. Davletshin (IME).
Interaction of a spherical gas bubbles
in a liquid. The mathematical model of interaction of two
spherical gas bubbles in a liquid is offered. This model is a system of the second
order ordinary differential equations for the radii of the bubbles and the
spatial position of their centers. It differs from the analogues widely-known
in literature in that it allows one to study considerably smaller distances
between interacting bubbles. Some numerical examples are presented to
illustrate applicability of the model of the present work.
D.A. Gubajdullin,
A.I. Nikiphorov, R.F. Nouroullin,
R.V. Sadovnikov (IME).
Parallel algorithms for identification
of parameters of 3D anisotropic fractured porous reservoir. Some
parallel algorithms for identification tensors of permeability of fractures and
blocks for fractured porous
reservoir were created. The obtained estimations lets one
determine the general values and directions of general axes for tensors of
permeability of fractures and blocks. The influence of errors
of initial data and initial values of estimated parameters on the results of
identification were investigated on model problems.
I.A. Aganin,
A.I. Nikiforov, R.V. Sadovnikov
(IME).
Simulation of
two-phase flow in clay-containing oil reservoirs with allowing for hysteresis
of clay swelling. The
influence of hysteresis of clay swelling on the oil recovery factor during a water
flooding is studied. It has been shown that in practical calculations one
should take into account how the clay material is distributed in the reservoir
and what the rate of irreversibility of the clay material swelling is.
A.V. Elesin,
A.Sh. Kadyrova (IME).
Using a priori
comparative information in hydraulic conductivity identification problems. A new
algorithm for the minimization of the discrepancy function with consideration
of a priori comparative information on parameter values is proposed. The
algorithm is used for the numerical solution of the model problem of hydraulic
conductivity identification for a three-dimensional anisotropic confined
aquifer. Several algorithms constructed with and without using a priori
comparative information are compared.
A.V.Tsepaev, P.A.Mazurov, A.I.Nikiforov (IME).
The solution three-phase flow problems
on fine-grids segments.
The numerical
parallelization algorithm earlier proposed by the authors for solving two-phase
flow problems is applied to solve a three-dimensional three-phase flow problem
on a coarse grid with fine-grid segments. This algorithm shows its efficiency
with an increasing number of fine-grid segments. The numerical approximation of
this problem is based on the control-volume method. The work was performed in
the framework of Program N 14 for the basic
research established by the Presidium of the
M.N. Shamsiev,
M.H. Khairullin,
Modeling of hydrate
formation in the vertical gas well. Mathematical model of gas hydrate formation in a
vertical gas well is suggested. This model allows to forecast
places of hydrate formation in a well under given regimes of well exploitation.
P.E.Morozov, M.Kh.Khairullin, M.N.Shamsiev (IME).
Simulation of
steady- and nonsteady-state fluid flow to the
horizontal well in anisotropic fractured porous reservoir. The numerical
and analytical solutions of the problem of nonsteady-state
fluid flow to the horizontal well in anisotropic fractured porous reservoir have been compared. The asymptotic solution for
horizontal wells in the circular anisotropic reservoir has been obtained.
A.I.Abdullin (IME).
Interpretation of pressure curves in
the deformable fractured porous reservoir. The computing
algorithm for the interpretation of vertical and horizontal well test data in
the deformable fractured porous reservoir has been developed. Diagnostic signs of non-linear elastic mode of filtration has
been discovered. The used mathematical model of the filtration process in a
fractured porous media takes into consideration the dependence of fracture
permeability on pressure. As source information the well test data are used.
V.V.Klokov, A.Sh.Taha
(KSU).
The investigation of the melting problem by the
fluid-flow analogy method.
N.M.Yakupov, A.A.Abdjushev, S.N.Yakupov (IME).
The scheme of
a covering of a sediment bowl. The schemes of coverings are noted. The
constructive-power scheme of the covering of the increased corrosion stability under
the minimal weight is described. The covering consists of the central element
and the lateral membranes, made from extending from the center to the periphery
radial chutes. From the bottom part the filter, which forms with chutes radial scavenge
ports, is established. The strengthening top membrane, made also from chutes, is
fixed on the central element. The central element with the
top membrane forms the additional scavenge ports. The calculation of the
variant of constructions by the finite element method is lead and the evaluating
characteristics of elements of a construction are estimated.
N.K. Galimov
(IME).
About one
approximate method of designing the dotted structure of minimal surfaces. It is known, that
the minimum surface is characterized by equality to zero of mean curvature. The
expression for the mean curvature contains a linear member (
A.R.Nurgaliev, N.M.Yakupov (IME).
The influence of surface scratches on
mechanical characteristics of the membranes which are being under excited
environment. For the research of corrosion deterioration of metal membranes
at the presence of mechanical loadings installation DMK-1 has been created and
the experimentally-theoretical approach of research of their mechanical
characteristics is developed. The researches of influence of superficial
defects on mechanical characteristics of the membranes, subjected to mechanical
influence in the corrosion environment, are carried out. Samples with defects
in the form of scratches with the certain step are considered. For comparison
of the results similar samples with scratches were simultaneously tested
without an excited environment. The character of change of the conditional
module of elasticity of a material is defined, the conclusions are made.
N.M.Yakupov, A.A.Abdjushev, I.H.Miftahutdinov,
S.N.Yakupov (IME).
The way of repair of cracks in
thin-walled casing designs. The knowledge of mechanisms of
destruction allows to develop effective ways of protection
of designs from destruction. One of the reasons of destruction of designs is the
presence of concentrators among which the most dangerous is the crack. For the
suspension of development of a crack it is recommended to use the idea of the
patent for the invention © 2310791.
Overlays from thermo orientation materials paste (attach) to coast of a
crack. The working part of an overlay is subjected to heating to temperature
recover-forming. Thus the coast of a crack are drawn
to each other. The most loaded areas of an overlay,
and also rational geometry of an overlay, and also the scheme of their
accommodation have been studied by the finite element method.
N.K.Galimov, S.N.Yakupov
(IME).
The research of mechanical characteristics of spherical membranes from
rubber-like materials. The module of elasticity of the
rubber spherical membrane loaded by uniform internal pressure is defined by the
theoretic-experimental method. During the process of loading membranes heights
of rise of top of a dome of a spherical segment are measured. Further, using ratios
received from the theory of membranes, calculations of the module of elasticity
of a material of a spherical membrane is made. The factor of cross-section
compression is undertaken equal 0,5. On the basis of the
results of calculation dependence of the module of elasticity on deformation is
constructed.
I.H.Miftahutdinov (IME).
Polycarbonate
- a new effective material for shells. In connection with the forthcoming entry into
operation the plant for the production of polycarbonate, based on "Kazanorgsintez" the author questioned the need for the
issuance of shell structures to the needs of the
R.I.Shafigullin, S.N.Yakupov,
N.M.Yakupov (IME).
The experimental installation for test of thin-walled
elements of constructions in an excited environment. For studying mechanical characteristics of the loaded
thin-walled elements during the periodic influence of corrosion environment
installation DMVK-1 consisting of a working part, a source of the pressure,
submitting and receiving capacities with an excited environment, the block of
management, measuring devices, and also pipelines with armature are created. The
installation allows to fix round samples, to load with
their unilateral pressure and to submit on other surface under some time law an
excited environment, and also to make the gaugings of
deflections of test samples during experiment. Debugging works are lead and the
results which have shown influence of periodicity of the influence of an excited
environment are received.
S.N.Yakupov, N.M.Yakupov (IME).
The influence
of a sunlight at the
frost on mechanical characteristics of polymeric films. Polymeric materials
are sensitive to the influence of conditions and environments in which they are
maintained. The questions of change of mechanical characteristics polymeric
films with white and black substrates under the action of a sunlight
during years and winter time are considered. In addition the effect of
influence of thickness of a snow cover above a film was considered. For research
the experimentally-theoretical method is used. Samples of various thickness were exposed to a solar irradiation during certain
time and then were tested on experimental installation DM-1. The schedules of
dependence "intensity of pressure - intensity of deformations
" for films on the average values are constructed, the analysis of the
results is lead and the conclusions are made.
N.M.Yakupov, H.G.Kiyamov (IME).
To the calculation of an environment of complex
geometry with the variable module of elasticity.
It is possible to use the spline variant of the finite element method for calculation
of thin-walled elements of constructions of complex geometry with the variable
module of elasticity. Thus it is necessary to provide changeability of the
module of elasticity on the elements. For testing a new variant of the program,
comparisons of decisions for round plates are in particular carried out. The
researches of goffered membranes with the variable module of
elasticity are also resulted.
N.M.Yakupov
(IME), R.R.Ginijatullin
(The
Deterioration of metal membranes in a magnetic field. Works on the research of characteristics of a material
of a thin-walled element of a construction during corrosion deterioration in a
magnetic field are begun. The electromagnet, which allows to
create the various intensity of a magnetic field, is used. The
investigated sample in a magnetic field is exposed to unilateral corrosion
deterioration during the certain time. In parallel for the comparison, the
similar sample is exposed to corrosion deterioration without the influence of a
magnetic field. For the definition of mechanical characteristics of a material
of samples the experimentally-theoretical approach is used. The received
results show the influence of a magnetic field on the process of corrosion
deterioration.
I.H.Miftahutdinov
(IME).
The design of a car shell from polycarbonate safe for
the pedestrian. On the roads of the
RF in various accidents annually 36000 people, i.e. 100 people daily, are killed.
According to the statistics of GIBDD of the
The sketches, diagrams and
models are implemented. For more details productions of new, more sophisticated
experiments are needed.
A.A.Abdjushev (IME).
The program ARS ERA-PK2000 to meet the challenges of
construction mechanics. The first part of
the report focuses on four decades of the history and the development of ARS
ERA-PK2000, beginning from highly specialized package of Applied Programs for
the calculation of aircraft fuselages by the finite element method in the form
of forces towards the Automated Solving System for the strength Analysis of
Spatial Structures. In the second part of the report the current status,
structure and the area of application of ARS are briefly described. It's
mentioned that the specified evidence of the possibility of application of ARS
ERA-PK2000, issued by the certification center "TsAGI
TEST." The examples of solving different practical problems in the fields
of aviation, engineering and civil constructions are shown.
N.M.Yakupov (IME).
20
years at the rudder of laboratory of nonlinear mechanics of environments
(1988-2007). The previous heads: H.М. Mushtari (1946-1965), M.S. Kornishin
(1965-1987). The laboratory carries out researches in the framework of 2
programs of the
M.A.Ilgamov, M.S.Ganeeva,
V.E.Moiseeva (IME).
Stability of the spherical segment loaded by the
pressure of compressible liquid. Non-linear bending
and the stability of a thin elastic-plastic spherical segment under the
pressure of compressible liquid are investigated. Problem specification,
algorithm and computer program were developed. The results of numerical
solution for shallow and non-shallow shells depending on the experiment
arrangement conditions for liquid pressure realization were obtained.
M.S.Ganeeva, V.E.Moiseeva (IME).
Particularity of deformation of whole spherical shells
and segments. Stressed-strained
state and non-axisymmetric buckling of whole
spherical shells and segments under external uniform pressure were
investigated. Computation algorithm and computer program based on the
linearization and orthogonal sweep methods were developed. Numerical results
depending on thin-walling and shell camber parameters and material
characteristics were obtained.
A.I.Malikov
(IME).
The control of the hybrid electromechanical systems. The brief review of the results on stability and
stabilization research of hybrid systems is given. The special attention is attended
to the control of double inverted pendulum on the cart in the top (unstable)
position of balance. Synthesis of a two-level regulator is designed: the first
provides translation of a pendulum in the area of small deviations of vertical
equilibrium point due to the movement only of cart, and the second regulator -
stabilization in vertical equilibrium point. The computer program for animation
of the motion of considered object is developed. The results of numerical
modeling are produced.
U.N.Zakirov
(IME).
About
the class of equations of the satellite motion, generated by the induced
energy- momentum (stability, control) tensor. In multivariate affine space
two classes of the equations of a satellite: a class with symmetrical metric
tensors and a class including unsymmetrical metric tensors, being functional
parameters of control and stability are explored. For five-measurement space
the induced energy-momentum tensor allows to take into account a state of an
environment in an equation of motion. For the second class the system of the
algebraic equations for the unknown Christoffel symbols
is solved under known metric tensors (symmetric and asymmetrical). For the
first class for a stability study of a motion it is enough to define the
function of Dirichlet-Lagrange, for the second class
it is necessary to find according to the second method the function of Lijapunov.
V.L.Fedyaev, I.V.Morenko (IME).
Hydrodynamics
of the cartridge filters. The cartridge filters are applied for the water
mechanical purification. New filter construction is invented. The
three-dimensional turbulent flow was calculated on the basis of the model. The
character of fluid flow was analyzed.
B.A.Snigerev
(IME).
Numerical
simulation the structure of viscoelastic flow and heat
transfer around bodies.
The momentum and forced
convection heat transfers characteristics for viscoelastic
flow past a sphere and rounded body have been investigated numerically. The
mass, momentum, constitutive and energy equations are described using the finite
element method. The rheological constitutive equation
of the fluid follows a common form of the PTT model, which embodies both the influence
of elasticity and shear-thinning in viscosity. Drag, lift force and heat
transfer on the bodies and other flow characteristics are predicted.
P.P.Osipov
(IME).
The application
of simulator <ExGrain> in optimizing and scaling of mass
transfer under supercritical extraction in vegetable biporous
mediums. The scheme and the govern equations of mass transfer in vegetable biporous medium under supercritical carbon dioxide
extraction are considered. The suggested nonlinear model is characterized by 9
dimensionless parameters. Using pilot experimental data the model identification
is carried out on simulator. The simulator capabilities in optimizing and
scaling of mass transfer are shown in the example of design of real extractor.
I.V.Morenko (IME).
Calculation of the viscous flow around a body with
built-in vortex cells. A numerical
investigation of laminar and turbulent flow past body with built-in vortex
cells was carried out. The mean drag and lift force coefficients and other
parameters were obtained. The results were analyzed in details.
Potential
participants are kindly invited for the presentation of their results at the
Seminar.
Contact
address - gubajdullin@mail.knc.ru
Damir A. Gubaidullin, the
Director of IME KazSC RAS; the Deputy Chairman of
Presidium, Kazan Science Center RAS; the Corresponding
Member of the RAS; the specialist in the area of mechanics and thermophysics of multiphase media.
© 1995-2008 Kazan State University