Problems
of Continuum Mechanics
(scientific seminar and conference)
D.A.Gubaidullin
Institute
of Mechanics and Engineering; Kazan Science Center, RAS, Kazan, RUSSIA
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 2008 and at the
Section of Final Scientific Conference'2008.
D.T.Suyucheva (The
The interaction of a contaminated groundwater flow with the
wells. On materials of the thesis
submitted for Candidate of Sciences Degree, speciality 01.02.05 - mechanics of
liquid, gas and plasma. Scientific chief DrSc E.V. Skvortsov reviewer DrSc A.I.Nikiforov.
The interaction of a contaminated
groundwater flow with the wells was studied. The capture zone boundary was
calculated in the frame of the potential flow scheme. The critical flow rates were
found at which capture zone gaps appeared.
B.G.Gogolashvili (The
Gravity-driven
wetting front instability and fingering in unsaturated porous media. On materials of the thesis
submitted for Candidate of Sciences Degree, speciality 01.02.05 - mechanics of
liquid, gas and plasma. Scientific chief DrSc A.G.Egorov, reviewerDrSc A.I.Nikiforov.
In this work the problem of
unsaturated flow and transport in coarse homogeneous porous media was studied.
The new approach taking into account relaxation and hysteretic effects was
developed for modelling widely known fingering phenomena. The verification of
the proposed model against broad range of experimental data show good agreement
and validity of the model.
A.V.Tsepaev (IME).
The parallel algorithms to solve the three-dimensional flow
problems in porous media. On materials of the thesis
submitted for Candidate of Sciences Degree, speciality 01.02.05 - mechanics of
liquid, gas and plasma. Scientific chief PhD P.A.Mazurov,
reviewer DrSc A.I.Nikiforov.
Two parallel algorithms are developed
to solve the three-dimensional flow problems on a coarse mesh with fine mesh
segments. 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 which grows with increasing number of fine mesh segments.
A.I.Abdullin (IME).
Numerical methods of solution of the filtration inverse
problem in porous-fractured media. On materials of the thesis submitted
for Candidate of Sciences Degree, speciality 01.02.05 - mechanics of liquid,
gas and plasma. Scientific chief DrSc
M.H. Khairullin. Reviewer DrSc V.L.Fedyaev.
In this work the influence of
dependence of fracture permeability from pressure on pressure variation curves
in the fractured-porous layer is investigated. Numerical algorithm for
identification of permeability of fractures in deformable naturally fractured
reservoir by the method of descriptive regularization is developed. Numerical
algorithm for estimation of vertical well bottom zone state in naturally
fractured reservoir is developed. The author researches the influence of
naturally fractured reservoir deformation on change of pressure build-up and
draw-down processes in reservoir, dependence of fracture permeability on
pressure.
T.F.Khalitova (IME).
Strong
compression of no spherical gas bubble 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 DrSc A.A.Aganin, reviewer DrSc P.P.Osipov.
A numerical
technique to study strong compression of a cavitations bubble with an axially symmetric deviations from spherical shape is
proposed. The motion of the vapor in the bubble and surrounding liquid is
governed by equations of a compressible liquid dynamics taking into
consideration heat conductivity, heat-mass exchange, with the realistic
equations of state. Working capacity of the technique and its efficiency is
shown in the large number of problems.
P.G.Velikanov (
Orthotropic plates and shells calculation by the Boundary
Elements Method. On materials of the thesis submitted for Candidate of
Sciences Degree, speciality 01.02.04 - mechanics of a deformable firm body.
Scientific chief DrSc Y.P.Artyukhin,
reviewer PhD V.G.Malakhov.
The work is devoted to the further
development of the Boundary Elements Method (BEM) for the decision of problems
of linear and nonlinear deformation of orthotropic (rectilinearly and curvilinear)
and isotropic multicoherent plates laying on the
complex elastic basis and flat shells with a difficult contour and any boundary
conditions, admitting continuous and step - variable change of rigidity, at the
connected influences of physical (temperature) fields and mechanical (located
and distributed on some area and law) loadings. The technique of the decision
of a contact problem of a bend isotropic plate on the elastic Vinkler's basis under action of a rigid stamp also is
offered. For the decision of the put problems (BEM) matrixes of the fundamental
decisions of systems of the differential equations previously should be known.
The new technique of the decision of the put problem assumes a finding of the
associated differential operator, which reduces a finding of a matrix of the
fundamental decision to simple differentiation of scalar function according to
the associated differential operator.
M.N.Shamsiev (IME).
Investigation of oil and gas reservoirs and wells at unsteady
modes of a filtration.
On materials of the thesis submitted
for Doctor of Sciences Degree in technique, specialty 01.02.05 - mechanics of
liquid, gas and plasma. Scientific consultant DrSc, Prof. M.H.Khairullin, reviewers
DrSc P.G.Danilaev, DrSc A.I.Nikiforov.
Numerical solutions of the inverse
coefficient problems of the filtration theory are considered. The new approach
to interpretation of results of hydrodynamic researches of wells within the
limits of models of elastic, non-linear - elastic modes of a filtration on the
basis of the regularization theory is developed. The method for estimating skin
- effect of vertical wells is offered. The processes of formation and
decomposition of gas hydrates in the porous media and well bore of vertical gas
well are investigated. The process of dissociation of gas hydrates in the
porous media is considered at cyclic thermal influence. The mathematical model
of the process of formation and decomposition of gas hydrate in the system
The following report was presented at
section Sessions of the Final Scientific Conference'2008 of the
D.A.Gubajdullin, R.N.Gafiyatov,
A.A.Nikiforov (IME).
Propagation
of acoustic waves in two-fractional bubble environments of different
composition.
A
closed system of the equations of motion of a two-fractional mixture of liquid
with bubbles of different gases and various initial radiuses which has been reduced
to one differential equation is presented. The dispersion equation determining
propagation of weak perturbations in the given mixture has been received. For a
mixture of water with bubbles of air and helium two local maximums in dependence
of attenuation factor from frequency are revealed. The influence of the account
of two-fractional composition on evolution of pressure impulse has been shown.
A.L.Tukmakov (IME).
Dependence of the
prevailing mechanism of drift of the firm particle in the nonlinear acoustic field
from the parity between the constant of time and wave characteristics. The criterion
allowing depending on a parity between a constant of
time of a particle and wave characteristics to define the prevailing mechanism
and a direction of drift of a firm spherical aerosol particle in a nonlinear
wave field of the closed acoustic resonator is analyzed. As wave
characteristics the time of increase of front of compression and duration of an
acoustic wave are considered. The gas velocity field contains the periodic
nonlinear waves and an acoustic current, movement of particles occurs under the
influence of Stokes, Archimedes and the added mass forces.
P.P.Ossipov (IME).
Impacts of main forces on a particle drift in
one-dimensional periodical field in tube. One-dimensional problem of
solid particle drift in periodic field of velocity with shock is studied
numerically. The impact of the Stocks, Archimedes, Basset, added mass forces,
as well as Oseen-type correction on a drift velocity
is revealed.
D.A.Gubaidullin (IME), R.G.Zaripov (IME), R.G.Galiullin (KSU), L.A.Tkachenko
(IME).
Motion of a spherical particle at forced
longitudinal oscillations of gas in an open tube. The motion of a spherical particle is experimentally investigated at forced
longitudinal oscillations of gas in an open tube near the subharmonic
resonance. The influence of frequency of excitation of gas and lengths of a
tube on an oscillation swing and mean velocity of a motion of a particle is
investigated. The dependence of mean velocity of a particle on frequency of
excitation of gas has the resonant shape. The comparison of the received
results with the experimental data in case of the closed pipe is given.
S.K.Zaripov, A.K.Gilfanov,
D.V.Maklakov (KSU).
Aerosol
sampling at the extended range of ratio of wind and aspiration velocities. The
aerosol aspiration into a thin-walled sampler horizontally oriented in extended
range of ratio of wind and aspiration velocities is numerically investigated.
The velocity field of carrying agent on the basis of Boundary Element and
Finite Volume methods within models of a potential and viscous flow of
incompressible fluid is found. The aspiration efficiency was calculated in the
region of a very small and very large ratio of wind and sampling velocities.
The gravity influence is discussed. The numerical results are compared with
known experimental data and approximate formulas.
V.B.Repin, A.V.Repina
(KSTU), R.G.Zaripov (IME).
Dynamic pressure of a
pulsing jet at nonlinear oscillations of gas in the open tube. At excitation of resonant oscillations of gas in a
tube periodically oscillating piston from the open end of a tube forms a
pulsing jet which dynamic pressure submits to a classical relation with
coefficient 1/7. It is shown, that this relation is true in the case of the
formation of breaks in a profile of a wave. The theoretical relation allowing
calculate a condition of break formation at the first linear resonance well is
received.
A.A.Aganin, A.I.Davletshin
(IME).
Simulation of interaction
of gas bubbles in a liquid with allowing for their small asphericity.
A
mathematical model of interaction of gas bubbles in a liquid with allowing for
small distortions of the bubble surfaces is proposed. It is of the fourth order
of accuracy relative to the ratio of the characteristic radius of the bubbles
to the characteristic distance between them. In the model, the effects of the
liquid viscosity and compressibility are taken into account,
the gas in the bubbles is assumed homobaric. For its
validation, the known solution of the problem of collapse of an empty cavity
near a plane rigid wall, which was obtained by the boundary element method, has
been used.
L.A.Kosolapova, V.G.Malakhov
(IME).
Nonlinear no spherical oscillations of a gas bubble
in liquid with allowing for translation. A mathematical model of
nonlinear no spherical oscillations of a gas bubble in liquid has been
developed. The bubble is considered to be axisymmetric
and its spatial movement to occur along the vertical axis. The shape of the
bubble surface is presented in the form of a series over the spherical
harmonics and the governing equations are written with accuracy of square of
the amplitude of the spherical bubble shape distortion. Viscosity and
compressibility of the liquid are approximately considered. The comparison with
the results of other authors is presented.
T.F.Khalitova, N.A.Khismatullina (IMM).
Strong compression of
ellipsoidal cavitations bubble. The one of possible
scenario of vapor dynamics inside the ellipsoidal cavitations bubble in the
final stage of its strong compression is revealed and described. A no spherical
deformation of the shock wave during its motion from the phase boundary to the
small neighborhood of the bubble center 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 no spherical case can be larger than in spherical
case.
M.H.Hairullin, M.N.Shamsiev,
P.E.Morozov, I.T.Salimyanov
(IME).
Criteria of fitting of wells and estimation of efficiency
of hydraulic rupture of a reservoir bed on the basis of hydrodynamic researches
of wells. Computation algorithms for modelling of liquid inflow into a well with a
fracture of hydraulic rupture of a reservoir bed are offered. The analysis of the
influence of conductivity and the length of a fracture on producing ability of
well is carried out. The method for the definition of conductivity and length
of a fracture of hydraulic rupture of a reservoir bed is created. As the
initial information curves of pressure recovery which have been taken in
vertical wells are used.
P.E.Morozov (IME).
Analytical solutions of fluid flow problems towards
a horizontal well in naturally fractured reservoir. The analysis of
analytical and semi-analytical solutions of fluid flow problems toward a
horizontal well in an infinite reservoir is carried out. The influence of
skin-effect on flux distribution along the well bore face and on dynamics of
the pressure change in a horizontal well is investigated. The analytical and
semi-analytical solution of a steady-state problem for horizontal well in a
circular reservoir is obtained. It is shown that the semi-analytical solution
is in good agreement with the experimental data.
A.I.Abdullin (IME).
Inverse
problem of filtration in a deformable porous-fractured media. A
numerical algorithm for solving the inverse coefficient problem of filtration
in a deformable porous-fractured media is suggested. The algorithm uses a
priori information of the required solution and is based on the method of
descriptive regularization. The dependence of permeability of fractures from
the pressure is taken into account when interpreting hydrodynamic
investigations of vertical and horizontal wells in the petroleum reservoir. The
dependence of permeability is found in the class of monotone and convex
functions.
R.F.Nurullin, A.I.Nikiforov
(IME).
About efficiency of thermogels
use in water flooding of oil reservoirs. The water flooding of oil
reservoir with thermo gel is simulated in the work. Two-phase filtration of
incompressible immiscible fluid into the trilaminar
reservoir is considered. The influence of thermogels
on oil recovery and time of reservoir exploitation is analyzed.
A.I.Nikiforov, R.V.Sadovnikov,
G.A.Nikiforov (IME).
Modeling of fines release by
filtration flow from porous bed. In this work, we
present mathematical model to describe the reductions of porosity and
permeability in two-phase flow in oil reservoirs resulting from migration of
fines in porous media. The model equations describing the release and capture
mechanisms of particle by porous bed have been obtained. Numerical experiments
show that the main mass of particles is carried out to wells by water.
R.V.Sadovnikov, A.I.Nikiphorov
(IME).
Identification
of permeability tensors of blocks and fractures of fractured porous reservoir. This
work is devoted to parallel realization of some algorithms for flow parameters
identification of fractured porous reservoir on hydrodynamic tests results for
system of wells. The work was performed in the framework of Program No 14 for
basic research established by the Presidium of the
G.A.Nikiforov, R.V.Sadovnikov
(IME).
Solution of the two-phase
filtering problem in variable "velocity-saturation". The development of a method of the numerical
modeling of a two-phase filtering problem in variables
"speed-saturation" on the basis of a control volumes method is the
purpose of the present work. Two families of control volumes are used. The
first is used at approximation of the equations for a divergence of speed and
for a saturation, the second is used at approximation
of the equation for a rotor of speed. The equation for saturation is approximated
by WENO scheme. Possibilities of this method are shown on the decision of some
problems.
A.V.Elesin, A.N.Gabidullina,
A.Sh.Kadyrova (IME).
Using
parallel algorithms in problem of hydraulic conductivity identification. A
new algorithm for the minimization of the residual function with consideration
of a priori comparative information on parameter values is proposed. The
algorithm is used for the numerical solution of a model problem of hydraulic
conductivity identification for a three-dimensional anisotropic confined
aquifer. The model task is solved on the multiple processor system with using
parallel calculations.
P.A.Mazurov, A.V.Elesin, A.Sh.Kadyrova (IME).
Quasi-Newton two-step
method of the residual function minimization. Quasi-Newton two-step method is proposed for the
minimization of the residual function taking into account the ravine of
minimizing function. The displacement of the parameters is realized in two steps
on each iteration of this method. This allows to go
round the bends of the ravines bottom and to accelerate the minimization
process. The method is used for the numerical solution of a model problem of
hydraulic conductivity identification for a three-dimensional anisotropic
confined aquifer and for the minimization of test functions. The effectiveness
of two-step method is shown in the comparison with one of the variant of Levenberg-Marquardt method.
V.L.Fedyaev, I.V.Morenko,
B.A.Snigerev (IME).
Optimization of the cooling
tower. The problems of the
structural and parametric optimization are studied. In the present work the
mathematical formulation of the cooling tower basic process is described. The
nozzle height is optimized.
N.K.Galimov, S.N.Yakupov (IME).
Research of mechanical characteristics of spherical membranes. The development
of the experimentally-theoretical approach of definition of mechanical
characteristics of the membranes having the initial spherical form is
described. Theoretical parities are received by Bubnov-Galerkin
method for nonlinear elastic - rubber like materials by Cuppus,
and also plastic materials by Ilyushin. The examples
of definition of mechanical characteristics of spherical rubber membranes with
various quantities of apertures, and also the spherical membranes made of a
plastic material (a plastic ball) are considered. The corresponding conclusions
are made.
N.M.Yakupov, A.A.Abdjushev, I.H.Miftakhutdinov
(IME).
Research of
influence of treating overlays on the vat of panels with system of cracks and
the analysis of mechanical characteristics of overlays at temperature
influence. The results of
researches of pressure intensity distribution in the panel with three parallel
cracks, and also installation for the definition of mechanical characteristics
of strips from the thermofocused material under
temperature influence are described. The installation consists of tightening
elements, a dynamometer, heat source - an air heater. The efficiency of use of "treating overlays>, and also the possibility
of rational placing of such overlays are marked. The conclusions are made.
H.G.Kijamov, N.M.Yakupov (IME).
To calculation of two-dimensional and three-dimensional elements of
designs. It
is noticed, that three-dimensional objects were the first building creations of
mankind. After the millennium thin-walled designs appeared. In the XX-th century thin-walled designs of difficult geometry
appeared. However in the view of the development of modern calculation methods at
first the calculation methods of two-dimensional objects of difficult geometry,
and then three-dimensional have been developed. The calculation of
two-dimensional and three-dimensional objects of difficult geometry is
developed on the basis of the uniform approach based on synthesis of idea of
preliminary parameterization and of a finite-element method, splines variant. The
examples are considered.
N.M.Yakupov, R.R.Ginijatullin, S.N.Yakupov
(IME).
Research of mechanical characteristics of the thin-walled elements
subject to corrosion deterioration at influence of a magnetic field. During corrosion
deterioration, along with geometry changes, a process of material destruction
takes place. Works on studying of magnetic field influence on the process of
corrosion deterioration of thin-walled elements of designs on mechanical
characteristics change of a material began. The samples being in an excited environment
were exposed to the magnetic field influence. For the definition of mechanical
characteristics of a samples material, the experimentally-theoretical approach was
used. The results show, that the magnetic field influences corrosion
deterioration.
A.R.Nurgaliev (IME).
Experimental installation for test of
thin-walled elements of the designs subjected to variable loading and being in the
excited environment. The researches of metal membranes under
static loading in an excited environment that were carried out have shown that
deformations of elements of designs activate corrosion process. The influence
of dynamic loadings on the loaded metal elements of the designs which are being
in an excited environment is practically poorly studied. To study the change of
mechanical characteristics of thin-walled elements during corrosion
deterioration under dynamic loadings experimental installation on the basis of
an internal combustion engine is developed. Debugging works come to the end.
R.I.Shafigullin, N.M.Yakupov (IME).
Experimental installation for keeping the thin-walled elements in the
mixed liquid environment. The
phenomenon of corrosion deterioration of elements of the designs subjected to the
influence of an excited environment with variable density, owing to formation
of vials is considered. Such phenomena are observed in various elements of the
designs subjected to the influence of the mixed liquid, in particular, is
observed in elements of courts near the rowing screws. For research
experimental installation has been created. At installation work the working
environment in which samples are maintained for a preset time is created.
Further tests of samples by an experimentally-theoretical method are carried
out, the conclusions are made.
A.K.Shalabanov (Academy of control <TISBI >).
The analysis of stress-strained
state of the cylindrical shell on the basis of the
specified equations of shells theory.
B.A.Snigerev (IME).
Creeping flow of viscoelastic fluid with free surface at non-isothermal
condition. Numerical
simulation of flow of viscoelastic fluid with free
surface, which is realized in entrance and output flow of polymeric liquid in
extrusion die was performed. The flow of liquid is described by equations of
conservation of mass, momentum and thermal energy with rheological constitutive
equation of Giesekesus. The ratio
of extrusion in dependence of the parameters of rheological model are
received.
I.V.Morenko (IME).
Nonisothermal laminar viscous flow
around a body with built-in vortex cells. Forced convection
heat transfer from an unconfined cylinder with built-in vortex cells in the
steady cross-flow regime has been studied in the range of 1<Re<200. The
influence of the cell depth on the drag, Nusselt
number and other parameters are analyzed in detail.
M.S.Ganeeva, V.E.Moiseeva,
Z.V.Skvortsova (IME).
Computation
of the nonlinear stress-strained state of non-shallow shells of revolution
under a wind loading.
The
effects of wind-like loading on the dome of large reservoir designed as a shell
of revolution with central hole are investigated, in case of intensive loading
when ultimate loads of instability are reached. The algorithm of computation of
geometrically and material nonlinear stress-strained state allowing to receive
critical parameter values of non-axisymmetric loading
is proposed. The results of computations for hemispherical dome are submitted
and analyzed.
A.I.Malikov (IME).
Robust
Control of Electromechanical Systems.
The
matrix comparison systems method is developed for the analysis of robust
stability and ellipsoidal state estimation for electromechanical control
systems with uncertain perturbations and changes of parameters. The conditions
of convergence and bounded ness of ellipsoidal estimations, the conditions of
robust stability, the invariance for continuous and
discrete systems with incomplete description of model are received. The ways of
synthesis of the optimum regulators providing robust stability and quality of
transients are offered.
U.N.Zakirov (IME).
Exact
solution of equation of a controllable motion of concentrated variable mass. For
a broad band of velocities and gravity potential the equations of a
controllable motion of concentrated variable mass (CVM) are obtained on the
basis of generalization of a
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