Science

INSTITUTE OF MECHANICS AND ENGINEERING; KAZAN SCIENCE CENTER; RAS

SCIENTIFIC SEMINAR

Problems of Continuum Mechanics

(scientific seminar and conference)

Kazan, Russia

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.

The following reports were presented at the Seminar in 2007 and at  Final Scientific Conference'2007 (Kazan, February 8-15, 2008):

April 18, 2007

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.

September 26, 2007

A.O. Syromyasov (The Mordovian State University named after N.P. Ogaryov, Saransk city)

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.

September 26, 2007

K.A. Potashev (The Kazan State University)

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.

 

October 17, 2007.

A.G. Gavrilov (The Kazan State University)

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.

October 31, 2007

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.

November 21, 2007 г.

A.G. Kochenkov (The Kazan State Technical University named after A.N. Tupolev)

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 Kazan Science Center RAS:

February 8, 2008

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:

February 14, 2008

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 Russian Academy of Science under the title "Fundamental problems of computer science and information technologies".

M.N. Shamsiev, M.H. Khairullin, L.A. Tulupov (IME)

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.

February 15, 2008

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 (Laplace operator) and nonlinear members. Several problems of  the  identification of applicate of minimal surfaces in areas limited by rectangles under given on the border area applicates of surfaces are considered by the finite element (triangular elements) method. The comparison with the "exact" solutions of  other authors showed that with the small margin of error (about 5%) for flat surfaces the problem can be considered on the basis of a simplified expression for the mean curvature of the surface that contains the only operator Laplace, without taking into account the nonlinear members.

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 Republic of Tatarstan and the entire country. Polycarbonate is made in the form of flat sheets and solid honeycomb structures. The Tatarstan Republic market is saturated by such polycarbonate manufacture - but only foreign production. Apparently domestic polycarbonate would be cheaper, but we will not be able to sell it abroad because of competition. As an alternative could be the selfmoulding shells, which producing technology is developed in the laboratories of nonlinear mechanics shells IME.

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 Kazan State Architectural-Building University), S.N.Yakupov (IME).

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 Russian Federation, 40% of them are pedestrians. Designers of auto over the world entirely protect the driver and the passengers inside the car - a seat belt and various inflatable air cushions. But designers are absolutely not interested in pedestrians, and for them probably nothing is made. The author proposes the shell of a car from polycarbonate in the form of a minimal surface, the hood of which is convex-concave. The concave part of the shell takes upon itself the men hit by a car.

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 Russian Academy of Science. For the period 1988-2007: 8 books, more than 100 articles and reports have been published, 20 patents of the Russian Federation for inventions are received, the laboratory participated in the work of 2 congresses on the mechanic and 36 scientific conferences. The thesis for a doctor's degree "The statics of elastic thin-walled constructions of complex geometry" was protected in 1995. The developments of laboratory are included in 9 Reports of the Russian Academy of Science, including: the Major results (2001, 2002, 2004), the Basic results in the field of natural, the technical and social studies (2006), the Basic researches and the development of scientific institutes of the Russian Academy of Science, ready to practical application (1999, 2001, 2002, 2004, 2006). The developments of laboratory were rewarded with medals "Brussels-Eureka 2004", "Geneva-2007", <ВТ XXI-2005>,"Geneva-2007", and also the diplomas of FIPS and the Ministry of the Republic of Tatarstan.

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.

 

 

 




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