Problems of continuum mechanics
Scientific Seminar and Final
Scientific Conference'2010
D.A.Gubaidullin
IME
KazSC RAS
Lobachevsky,
2/31,
The Scientific Seminar "Problems of Continuum Mechanics" works in the
In the period from
October 2010 to November 2011 the reports, representing the achievements in the
sphere of non-linear mechanics of thin-walled constructions, hydroaeroelastic
and wave systems; dynamics of multiphase multicomponent media in porous
structures and technological installations; non-linear stability theory of
control systems with changeable structure, were shown on the seminar and
section of the Final scientific conference of 2010.
The theory of
distribution of acoustic waves in two-fractional disperse mixtures of gas and
vapor, drops and solid particles and the mixtures of liquid with gas-vapor
bubbles and bubbles of inert gas of different
composition and size with phase transformations in one of the fraction
is developed in the works of D.A.Gubaidullin with his co-authors. The change of
the part of air-vapor bubbles in monodisperse bubble mixture with phase
transitions to the bubbles with inert helium is detected to lead to considerable
growth of wave attenuations at low frequencies. The drift of spherical
entrainment in acoustic resonator was investigated. Nonlinear oscillations of
homogeneous gas and aerosol in the closed tube in a non shock-wave mode near to
the first natural frequency, dynamic head of jet pulsating were experimentally
investigated in the reports of D.A.Gubaidullin, R.G.Zaripov and etc. The
efficient model of investigation of small sphericity distortion of a cavitations
bubble during its super compression and the comparison of the method of
decomposition in spherical functions and the method of reflections in the
problems of determination of velocity potential of a liquid with gas bubbles
were presented in the works of D.U.Toporkov, T.F.Khalitova, A.I.Davletshin. The
works of A.A.Aganin with co-authors are devoted to the study of the dynamics of
an elastic body under shock loading and jet impact on the rigid wall.
In the articles of D.A.Gubaidullin,
A.I.Nikiforov, R.V.Sadnikov and others the software tools to solve the
filtration problems on hybrid computation system were presented, the problems
of two-phase filtration in the variable "speed-saturation" were
solved. The effective modified two-step
methods of the Levenberg-Marquardt minimization of residual function were
proposed by P.A.Mazurov and others. Methods of decomposition for solving
three-dimensional three-phase flow problems on graphic computing systems were
worked out by A.V.Tzepaev In the works of M.Kh.Khairullin, P.E.Morozov and
others non-isothermal filtration in porous medium saturated with gas, water and
hydrate was modeled; the analytical and
semi-analytic solution of unsteady fluid flow to horizontal well after an
instantaneous sampling or injection was proposed; thermo-hydrodynamic
researches of layers and wells were presented.
Experimentally
theoretical method of determination of mechanical characteristics of membrane,
films and tissue materials, under the different physical influences is
developed and accuracy of the method is defined in the works of N.M.Yakupov, N.K.Galimov,
S.N.Yakupov, R.R.Giniyatullin and others. The reports of N.M.Yakupov, Kh.G.Kiyamov,
A.A.Abdyushev are devoted to the finite element modeling of thin-walled
elements of the complex geometry design, to the research of stress-strained state of the stretched panel with the defects
in the form of cracks without overlays and with overlays. The schemes of devices for
strengthening of operating cooling-towers were presented in the
works of
B.A.Snigerev presented
the research of the field of velocities, position of interface boundary in a
two-layer flow depending on rheological properties of liquid and flow regimes.
The unsteady non isothermal cross flow around a circular cylinder of the viscid
mixture and the fluid flow with particles near the lattice were investigated in
the works of V.L.Fedyaev, I.V.Morenko.
The
matrix comparison method for robust stability analysis of some classes
nonlinear control systems; the approach for local regulators of the synchronous
generator synthesis; the approach control synthesis for the nonlinear
multivariable system, that showed the efficiency for the stabilization of the
double inverted pendulum are developed by A.I.Malikov and co-authors.
Doctoral thesis of
B.A.Snigerev, the dissertations of the postgraduates S.N.Yakupov, E.A.Teregulova,
G.A.Nikiforov, R.N.Gafiyatov were presented. PhD thesis's of M.U.Garnishev,
A.A.Akhtareyev, Kh.A.Abragam were presented, on which the Seminar made a
conclusion of the leading organization.
The reports on the Final conference
D.A.Gubaidullin,
R.G.Zaripov, L.A.Tkachenko (IME).
Resonance oscillations of aerosol and deposition in a closed tube in no
shock-wave mode.
Features of nonlinear
oscillations of homogeneous gas and aerosol in the closed tube in a no
shock-wave mode near to the first natural frequency are experimentally
investigated. Asymmetry of the continuous form of a wave of pressure of gas in
a resonance is shown. Observable resonance frequency has smaller importance,
than calculated under the linear theory and coincides with the frequency
calculated under the nonlinear theory in view of dissipation. Numerical
concentration of drops of an aerosol monotonously decreases in due course. With
increase of amplitude of oscillations of the piston time of coagulation and
deposition of an aerosol decreases.
D.A.Gubajdullin,
A.A.Nikiforov, R.N.Gafiyatov (IME).
Acoustic waves in two-fractional liquid with bubbles with phase
transformations.
Distribution of acoustic
waves in two-fractional mixtures of a liquid with vapor-gas and gas bubbles of
various size and different structure with phase transformations is
investigated. The system of the differential equations of movement of a mixture
is submitted, the dispersive equation is received. Numerical calculations of
evolution of weak impulse indignations of pressure in the given mixture are
executed.
D.A.Gubaidullin,
P.P.Ossipov (IME).
Characteristic
frequencies at the drift of spherical entrainment in acoustical resonator.
A drift of spherical
entrainment in acoustical waves as well as in periodic shock waves is studied
by analytical and approximate methods. The formula for the drift force in
fields like standing waves is derived. The formula of characteristic wave
frequency is obtained, which is crucial for the direction of the drift force. Depending
on this frequency five cases of drift are detected.
D.Yu.Toporkov,
T.F.Khalitova (IME).
Simulation of small sphericity distortion of a
cavitation bubble during its super-compression.
Small distortions of
the spherical shape of a cavitations bubble during its super-compression is
considered. Applicability of relatively simple and very
efficient-in-application model (based on splitting the two-dimensional flow of
the liquid and the vapor into the spherical part and its small non-spherical
perturbation) to estimate maximum growth of the amplitude of such distortions
is studied. It has been shown that the evaluated estimates are quite
satisfactory, which in the case of low-frequency distortions has been supported
by comparison with the results of application of two-dimensional hydrodynamic
model.
A.A.Aganin,
V.G.Malakhov, N.A.Khismatullina (IME).
Dynamics of an elastic body under shock loading.
Axially symmetric
shock impact on an elastic body is studied. The body is simulated by the
isotropic linearly-elastic semi-space. A computational technique has been
developed and two cases of shock impact on the elastic body have been
investigated. In the first case the load in the finite circular domain of the
body surface remains constant while in the second one it varies in the radial
direction as a cubic parabola. It has been shown that in both cases the maximal
stresses appear on the body surface and at the distance from it on the order of
the radius of the loaded domain. The presented results give qualitative estimate
of the stressed state of the elastic body.
A.A.Aganin,
T.F.Khalitova (IME).
The jet impact on the rigid wall.
A mathematical model
and a numerical technique of impact of high-speed ax symmetric liquid jet with
hemispherical end on the rigid wall have been developed. Fluid dynamics in the
jet is described by Euler equations. The problem is solved by the Godunov
method on moving grids with explicit tacking of the jet surface. It is shown
that in the radial profile of loading a maximum is formed on the periphery of
the contact area. The extreme value of this maximum is found to be
approximately two times higher than the extreme value of the liquid pressure in
the center of the contact area and it is attained in the narrow ring region
with the radius approximately 1/5 of the jet radius.
A.I.Davletshin
(IME).
Two methods of evaluation of velocity potential of a
liquid with gas bubbles.
A comparison of
numerical efficiency of two methods of computation of velocity potential of a
liquid with gas bubbles has been performed: the method of decomposition in
spherical functions and the method of reflections. It has been shown that at
relatively large distances between the bubbles the efficiency of both methods
are approximately equal for any number of the interacting bubbles. With
decreasing the distance, the method of decomposition in spherical functions
becomes more efficient, except for the case of two bubbles.
A.V.Repina
(KNRTU), R.G.Zaripov (IME), V.B.Repin
(KNRTU).
Dynamic head of jet pulsating near by open butt-ended
resonator forming.
The results of
experimental investigation of dynamic head of pulsating jet are produced. It is
shown that the presence of shock waves brings to its reduction.
D.A.Gubaidullin, N.A.Nikiforov, R.V.Sadovnikov (IME).
Investigation of scalability of subsurface flow
problem on hybrid computation system.
A gpu_sparse library
of Krylov iterative methods with preconditioning was proposed for hybrid
computing systems based on Nvidia graphics processors (GPU). Primitives of
library are implemented by means of C++, CUDA, CUBLAS and OpenMP. Real 3D
problem of unsteady fluid flow to wells with complex geometry in fractured
porous reservoir were tested on a system with several NVidia GPUs of different
performance. Using GPUs allows to speed up computations of more than 6 times
compared with the 8-processor cluster.
G.A.Nikiforov,
D.A.Gubaidullin, R.V.Sadovnikov (IME).
On the solution of some problems inherent to two-phase filtration in the
variable "speed-saturation".
Set of problems inherent
to two-phase filtration in the variables "velocity-saturation" has been solved
by means of control volume approach. We examine such questions as gravitational
segregation of two-phase fluid and the spreading of contaminating liquid in a
porous medium with impermeable inclusions. The comparison with experimental
results R.A.Dawe, C.A.Grattoni has been carried out.
A.N.Gabidullina,
A.V.Elesin, A.Sh.Kadyrova, P.A.Mazurov (IME).
To the constructing of modifications of residual function two-step
minimization methods.
The analysis of the
Levenberg-Marquardt method with the use of sensitivity storage is carried out
on the solution of model identification task. A modified two-step methods the
Levenberg-Marquardt minimization of residual function are proposed. The results
of the model problems solution are shown the efficiency of the proposed
methods.
A.V.Tsepaev (IME).
Methods of decomposition for solving three-dimensional three-phase flow
problems on graphic computing systems.
Two decomposition
methods have been developed to solve the three-dimensional three-phase flow
equation on GPU. The first algorithm has been suggested to solve the equation
for pressure, the second one to solve the equation for saturation. These
methods show their efficiency with increasing number of fine grid segments.
P.E. Morozov (IME).
Express-methods for well test analysis in low permeability reservoirs.
Analytical
and semi-analytic solution of unsteady fluid flow to horizontal well after an
instantaneous sampling or injection is proposed. Comparison of these solutions
with the results of numerical modeling of fluid flow in an anisotropic
reservoir is carried out. The distribution of fluid flow along the horizontal
well at different moments of time is analyzed.
M.Kh. Khairullin, M.N.
Shamsiev, P.E. Morozov, A.I. Abdullin (IME).
Modeling the dissociation of gas hydrates in porous media.
In this work an ax
symmetric problem of gas production from a vertical well in the reservoir
saturated with thermodynamic equilibrium mixture of gas, water and hydrate is
considered. Based on numerical simulations of non-isothermal two-phase
filtration in porous medium saturated with gas, water and hydrate, the analysis
of depressurization in gas hydrate reservoir is performed.
E.R.Badertdinova (
Thermo-hydrodynamic researches of layers and wells.
N.K.Galimov, S.N.Yakupov (IME).
Estimation of accuracy of the results received
by an experimentally-theoretical method.
Accuracy of received results depends on accuracy
of measurements of experimental data and accuracy of used theoretical parities.
At a theoretical stage the parities received from the nonlinear theory of
covers at the big moving and deformations that provides high accuracy of a
stage are used. At an experimental stage results of measurements are
represented in the form of the sum of directly measured size, for example, a
film or membrane deflection at the given loading, and plus a minus the
approached value of an error of measurement. Thus true value with enough high
probability is in this confidential interval. Results of research of polymeric
films with the distributed apertures are resulted.
N.M.Yakupov, K.G.Kiyamov (IME).
Spline variant of МFE for calculation of elements
of designs of difficult geometry.
In connection with inquiries of practice in the
XX century bases of the theory of plates and covers have been put in pawn and
there are begun works on working out of methods of calculation tensely - the
deformed condition of thin-walled elements of designs. It is developed spline a
variant of a method of final elements for calculation of thin-walled elements
of a design of difficult geometry. There are begun works on development of this
approach for calculation tensely - the deformed condition of three-dimensional
elements of the designs having difficult geometry. Thanks to synthesis of idea
of parameterization and a method of final elements with approximation of
variables Ermit cubic splines, it is possible to receive the co-ordinate final
elements. Calculation examples are considered.
V.I.Pogoreltsev (Policlinic of KazSC of RAS), S.N.Yakupov (IME).
Changing of mechanical characteristics of
bandage in a solution of ximedon.
Tissue materials contacting with the liquid
environment can change their properties. The influence of time and environment
on the mechanical characteristics of bandage is of great interest. Change of
mechanical characteristics of the bandage placed in the liquid environment is
investigated. A solution of furacelin, and also a solution of ximedon were
considered as the liquid environment. The material was placed in liquid
environment for 1 and 5 minutes. Dependence "deflection-pressure" for the
bandage with a polymeric substrate of
N.M.Yakupov, A.A.Abdyushev (IME).
"Treatment" of defects by a film covering.
The stress-stained condition of the stretched
panel with defects in the form of cracks without overlays and with overlays is
investigated by a method of final elements. The passive overlays which don't
create stress of compression, and the active overlays creating the stress of
compression at operation are considered. In particular, the maximum values of
the intensity of pressure decrease in 5,7
times at values of deformation in an overlay е = 0,0004. Choosing position
of active overlays and deformation in them, it is possible to lower the level
of pressure. The intense-deformed condition of the panel with defect of a
passive covering in the form of a film, covering defective area, is
investigated. Efficiency of coverings-films is shown.
N.M.Yakupov, R.R.Giniyatullin, G.G.Gumarov (IME).
Corrosion deterioration of the thin-walled
elements subjected to ionic burning.
The review on processing of
materials surface by the concentrated stream of energy is given. Results of an
experimental research of corrosion deterioration of constructional elements, on
the surface of which the carbon ions were implanted, are presented. The
samples, sustained for the preset time in the aggressive environment, are
processed by an experimentally-theoretical method. The dependence "pressure р - deflection Н", characterizing the degree
of deterioration of the sample is defined in the course of experiment. Using
the parities of the nonlinear theory of covers, curves "intensity of pressure -
intensity of deformations" are under construction. Efficiency of ionic
implantation against corrosion is shown.
N.M.Yakupov, R.G.Nurullin, A.R.Nurgaliev, S.N.Yakupov (IME).
Maintenance of safety of building designs while
in service on an example of large-sized cooling-towers СК 1200.
On an example of surveyed cooling-towers СК1200 the condition of
constructions in the process of operation is analyzed, the most dangerous
defective areas are allocated, schemes of devices for strengthening of
constructions are described. Devices provide rational transfer of efforts.
Realization of schemes allows to prevent technogenic accidents. Ideas of
strengthening can be used for strengthening of other designs and constructions.
Complex working-out is transferred to the Limited Company "NKNH" in order to
use cooling-towers СК1200 at major repairs". Patents for inventions on all schemes of
strengthening are received. Workings out are noted by medals of the International Salons and forums.
M.S.Ganeeva, V.E.Moiseeva,
Z.V.Skvortsova (IME).
Nonlinear bending and stability of ellipsoidal shell under the liquid
pressure.
Ax symmetric bending and
stability of oblate ellipsoidal shell under the liquid pressure on the convex
side of the shell are considered. Geometrical and material nonlinear theory of
shells is used. The liquid pressure is determined by the adiabatic law. Results
have shown that the nonlinear deformation depends on the characteristics of the
loading medium. Particularities of the examined shell stress-strain state are
also determined by the middle surface curvature variability.
B.A.Snigerev (IME).
Two layer nonlinear viscous flow in plane channel.
Numerical simulation of
double-layer nonlinear viscous flow in flat channel was performed. The fluid
motion is described by equations conservation of mass and momentum, supplemented
by the rheological equation of state of nonlinear viscous fluid on the Carreau
model. Results on the field of velocities, position of interface boundary in a
two-layer flow depending on rheological properties of liquid and flow regimes
were received.
I.V.Morenko, V.L.Fedyaev
(IME).
Non-isothermal monodispersed mixture flow around a circular cylinder.
The gas-particle
unsteady non-isothermal cross flow around a circular cylinder is investigated.
Influence of Stokes number, particle concentration and other parameters on the
lift and drag coefficient, Strouhal, Nusselt numbers are analyzed.
N.Z.Serazetdinov,
I.V.Morenko (IME).
Flow of monodisperse mixture in a constrained area.
The goal of this work
was definition of the behavior of fluid with particles near the lattice, as
well as studying of the effect of particles on the hydrodynamic resistance of
the lattice. Several types of cells of periodicity were allocated and
corresponding computational areas were constructed. Then flow of monodisperse
mixture in constructed areas was calculated. Fluid flow and particle behavior
before and after the grill depending on the particle density and shape of the
computational domain were studied. Also the effect of constraint of computation
area on the flow characteristics was shown.
A.I.Malikov (IME).
The Methods of dynamical analysis and synthesis of robust regulators on
the basis of matrix comparison systems.
The matrix comparison
method for robust stability analysis of some classes of nonlinear control
systems is developed. The methods for synthesis of robust regulators for some
classes of nonlinear control systems are offered. It is shown, that for
autonomous nonlinear control systems the synthesis of robust regulators problem
in some cases is reduced to resolvability of optimization problem with linear
matrix inequalities. The received results are applied to synthesis of robust
regulators for electromechanical systems with uncertainties.
Z.M.Ali (
The synthesis of local excitation control method for synchronous
generators in power systems.
The approach for local
regulators of the synchronous generator synthesis, based on reduction of matrix
dimension of simplified model of the single machine system is developed.
Analytical expressions for definition of typical regulator parameters from a
condition of the set arrangement of pair roots of the characteristic equation,
defining quality of a rotor mechanical movement transients and system stability
at small perturbations are received. The offered approach for local excitation
control adjustment in multi-machine power systems provide improvement of
transients quality at the account of influence of various disturbances.
A.E.Evstifeev,
A.I.Malikov (IME).
Synthesis of nonlinear regulators for double inverted pendulum.
The approach control
synthesis for the nonlinear multivariable system is offered, allowing to
receive transients close to transient in reference system. On an example of
system with Double Inverted Pendulum it is shown, that the offered control low
provides stabilization in the top position of balance in a greater range of
initial deviations in comparison with other regulators, in particular with a
linear square-law regulator.
The
reports on the Seminar
S.N.Yakupov (IME).
Mechanical characteristics of flat and spherical films and membranes
with difficult structure.
On materials of thesis
submitted for Candidate of Sciences Degree, specialty 01.02.04 - Mechanics of
deformable solid. Scientific chief PhD N.K.Galimov. Reviewer DrSc
M.N.Serazutdinov.
The
experimentally-theoretical method of research of mechanical characteristics of
flat and spherical films and membranes with difficult structure and with
defects is developed. Settlement dependences for non-linear elastic and plastic
spherical covers are received at the big moving and deformations. The way of
definition of mechanical characteristics of a covering in system is developed.
B.A.Snigerev (IME).
Hydrodynamics and heat transfer of non-Newtonian fluids in molding
products from polymeric materials.
On materials of thesis
submitted for Doctor of Sciences Degree, specialty 01.02.05 - mechanics of
liquid, gas and plasma. Scientific consultant DrSc F.Kh.Tazuykov. Reviewer DrSc
A.L.Tukmakov.
The numerical study of
flow and heat transfer fluids and polymer melts during pressing-out from the
extrusion nozzle for forming fibers and films have been conducted. The
influence of the size and geometry of the capillaries start connection zone,
the rheological properties of formed fluid and heat transfer conditions on the
performance of the extrusion nozzles have been investigated.
March,
4th 2011г.
E.A.Teregulova (IME).
Acoustic waves in two-fractional gas-particle mixture with phase
transformations.
On materials of thesis
submitted for Candidate of Sciences Degree, specialty 01.02.05 - mechanics of
liquid, gas and plasma. Scientific chief Corresponding Member of the RAS
D.A.Gubajdullin. Reviewer DrSc A.A.Aganin.
Propagation of acoustic
waves in two-fractional mixtures of gas with rigid particles of different
materials and sizes and vapor-gas-droplets with rigid particles with phase
transformations is investigated. Dispersion relations and wave equations are
received. Dispersion curves are calculated and analyzed.
G.A.Nikiforov (IME).
Modeling of the two-phase flow in non-homogeneous and multilayered
porous mediums.
On materials of thesis
submitted for Candidate of Sciences Degree, specialty 01.02.05 - mechanics of
liquid, gas and plasma. Scientific chief Corresponding Member of the RAS
D.A.Gubaidullin. Reviewer PhD A.V.Elesin.
The
problem of two-phase filtration in the variables "velocity-saturation" and "pressure-velocity-saturation"
is solved by the control volume method. Filtration flow in non-homo-geneous and
multilayered reservoirs are investigated under capillary and gravitational
forces.
M.U.Garnishev (KFU).
Mathematic simulation of two-phase filtration in the layers interacting
with bottom water.
On the material of the
thesis for Candidate of sciences (Ph.D.) in physics and mathematics with the
specialization 01.02.05- mechanics of fluid, gas and plasma. Scientific chief:
DrSc A.B.Mazo. Reviewer DrSc A.I.Nikiforov.
R.N.Gafiyatov (IME).
Acoustic waves in mixtures of liquid with bubbles of
two different gases and vapor with phase transformations.
On materials of thesis
submitted for Candidate of Sciences Degree, specialty 01.02.05 - mechanics of
liquid, gas and plasma. Scientific chief Corresponding Member RAS D.A.
Gubajdullin. Reviewer DrSc A.A.Aganin.
Distribution of acoustic
waves in two-fractional mixtures of liquid with bubbles of different gases and
sizes without and with phase transformations is investigated. Mathematical
models are submitted, the closed systems of the linear differential equations
of the indignant movement of a mixture are written. Dispersive equations
determining distribution of acoustic indignations are received. With the help
of a method of fast transformation Fourier numerical calculations of
distribution impulse indignations of pressure of small amplitude in
two-fractional mixtures of liquid with vapor-gas bubbles are executed.
A.A.Akhtareyev (
Unbalanced model of fluid filtration in unsaturated porous medium.
On the material of
the thesis for Candidate of sciences (Ph.D.) in physics and mathematics with
the specialization 05.13.18 - mathematic simulation, numerical method and program
system. Scientific chief: DrSc R.Z.Dautov. Reviewer DrSc A.I.Nikiforov.
Kh.A.Abragam (
Simulation and calculation of the framed structures, strengthened in
stress state.
On the material of the
thesis for Candidate of sciences in physics and mathematics with the
specializations: 05.13.18 - mathematic simulation, numerical method and program
systems; 01.02.04 - mechanics of deformable solid. Scientific chief: DrSc
M.N.Serazutdinov. Reviewer
The problems of
strengthening of the framed structures, that are in stress state. Mathematic
simulation and the data of the calculations are for the cases when the
strengthening is achieved due to the increase of the size of cross sections of
frames. The possibility of plastic deformations is permitted.
Potential participants
are kindly invited for the presentation of their results at the Seminar.
Contact address - gubajdullin@mail.knc.ru
© 1995-2008 Kazan State University