May 8, 2003
Aganin A.A., Khismatullina N.A. (IME).
Computation of liquid vorticity in non-spherical bubble dynamics. The purpose of this work is to compare the efficiency of a number of numerical techniques with respect to their computational time costs. The techniques based on the finite-difference method (the FDM technique), the collocation method (the technique with differentiating the integral boundary condition and the one without it) and the Bubnov-Galerkin method (the BGM technique) have been considered. The central differences are used as approximations for the derivatives in FDM. Harmonics are chosen as basic functions in BGM. Problems of decaying a small distortion of the spherical surface of a bubble and dynamics of a bubble under harmonic liquid pressure variation are used for comparison. The FDM technique has been shown to be the most efficient one in all the cases.

April 10, 2003
Malakhov V.G. (IME).
Nonlinear problems of computation and optimization of shells of revolution. On materials of thesis for Candidate of Science Degree, speciality: 01.02.04 - Mechanics of deformable solid. Reviewer: D. Sc. Gribov A.P. The techniques of computation and optimization of a compound shell of revolution including the thin-walled shell elements connected to one another with elastic rings have been proposed. Physical and geometrical nonlinearities are taken into account in the equations of shells. Parameters of optimization are the shell thickness and dimensions of the cross-sections of the rings. Problems of weight optimization under bounds on strength and the problems of optimal material distribution in the compound shell of revolution of maximum stiffness have been considered. The results of solution of some new problems are presented.

October 22, 2003
Seminar, dedicated to U.N.Zakirov on his 70th Birthday
Zakirov U.N. (IME).
Life, technique, science. I had to communicate with the astrophisical group of academician J.B.Zeldovish. I have understood, that in theoretical mechanics there is no relativistic mechanics of jet propulsion; the theory of prompt flights in far space on the basis of non-chemical power sources. Let's introduce according to Sing - the English mechanical engineer and physicist three patterns: M1 - pattern of Newton mechanics, M2 - pattern of Einstein mechanics. The theories of Newton and Einstein are so closely related, that sometimes it is difficult to make a distinguish between them. They differ by representation about Newtonian time and terrain clearance hardness (M1). In conclusion, within 30 years, it is possible to state, that the relativistic mechanics of jet propulsion (L.I.Sedov, U.N.Zakirov) has been established. As for the theory of stability, the generalization of the theorems of Lyapunov in pattern M2 is possible.

Oktober 30, 2003
Tukmakov A.L. (IME).
Nonlinear dynamics of thin-walled elements of the designs cooperating with gas and diagnostics of nonlinear fluctuations. On materials of thesis for Doctor of Science Degree, specialities: 01.02.04 - Mechanics of deformable solid and 01.02.05 - Mechanics of liquid, gas and plasma. Reviewers: D. Sc. (Phys. & Math.) Aganin A.A., D. Sc. (Phys. & Math.) Golovanov A.I. The work is devoted to the research of nonlinear dynamics of aeroelastic systems. The mechanisms of aeroelastic interaction are investigated by the methods of numerical modelling and the nonlinear effects accompanying dynamics of environments are analyzed. A new method of diagnostics of the nonlinear fluctuations allowing to identify dynamic processes is presented.

March 25, 2004
Morenko I.V. (IME).
Hydrodynamics of the inertial separators and filters. On materials of thesis 01.02.05 - Mechanics of liquid, gas and plasma. Research manager: D. Sc. Fedyaev V.L. Reviwer: PhD Osipov P.P. The gauze drag of the various cross-section cylinders are investigated. The turn ability of the circular cylinder gauze is studied at the small and intermediate Reynolds number. A new forms of the separator profile and filters for water purification from the carry-over are suggested. The efficiency of the work is acknowledge of the calculation.

The following report was presented at plenary Session of the Final Scientific Conference'2003 of the Kazan Science Center RAS:

February 9, 2004
Fedyaev V.L. (IME).
Modernization of the industrial cooling towers. The objects of these investigations are the industrial cooling towers. These installations are widespread in energetics, as well as in chemical and metallurgical works. New systems of the water-supply, fills, traps of the drops, ventilators are proposed. Robust quality of the suggested constructions has been confirmed by math modeling.

The following reports were presented at section Sessions:

February 12, 2004
Gubaidullin D.A., Nikiforov A.A. (IME).
Peculiarities of acoustics of vapor-gas-liquid media. Linear theory of propagation of the plane, spherical and cylindrical perturbations in the polydispersed vapor-gas-drops systems and in mix of a fluid with gas or vapor bubbles is developed. The equations of movement are presented, the dispersion ratious are obtained, the evolution of pulse waves is performed, the influence of processes geometry, heat and mass transfer and the basic parameters of mixtures are analysed. The character of the harmonical waves propagation in spherical and cylindrical cases is the same as for the plane waves. The strongest attenuation and change of the form of pulse spherical perturbations in contrast to the cylindrical and plane cases as well as the strongest dependence of spherical and cylindrical wave propagation from the initial radius of perturbations have been estabilished.

Gubaidullin D.A. (IME), Zaripov R.G. (IME), Galiullin R.G. (Kazan State University), Tkachenko L.A. (IME).
Nonlinear oscillations of aerosol in an open tube nearby a sub-harmonic resonance. Nonlinear oscillations of a small-dispersible aerosol in an open tube close to a half of fundamental frequency are considered. Aerosol oscillations were generated by a plane piston; a tube included a quartz section with photo-transducer for registration of light-penetrability of a medium that governs particle concentration. The concentration of aerosol monotonously decreases in due course and with growth of frequency of excitation. Dependences of time of an enlightenment of an aerosol on frequency have non-monotonic character with a minimum at transition through a resonance. It is revealed, that reduction of length of a tube results in decrease of an enlightenment time of an aerosol.

Zaripov S.K. (KSU, Institute of Mathematics and Mechanics), Hollander W. (Fraunhofer Institute Toxikologie und Experimentelle Medizin, Hannover, Germany).
Hydrodynamically interacting droplets at small finite Reynolds numbers. Droplets moving at close distances interact hydrodynamically. Here we present the experimental and theoretical results of the study with monodisperse 73 µm diameter droplets with initial velocities between 1.5 and 2.5 m/s and variable generation rate (ranging from 125 to 1000 s-1 emitted horizontally and vertically). The hydrodynamic interactions depend on the spatial distance, and we observed a considerable increase of the stopping distance with increasing generation rate. Reviewing the various approaches for the description of hydrodynamic interactions, we adapted a theory for stationary Stokes flow past a linear array of spheres to our situation and found a surprisingly good agreement between our experiments and the above model. Even better agreement was obtained by additionally taking the Basset force into account. This work was supported by the German Academic Exchange Service DAAD (N 325-2002) and partially by Russian Foundation for Basic Research under grant number 02-01-00836 as well as by German Space Agency DLR under grant 50WM0037.

Aganin A.A, Kosolapova L.A., Malakhov V.G. (IME).
Nonlinear dynamics of a bubble in a liquid at axisymmetric distortion of its spherical shape. Nonlinear axisymmetric oscillations of a gas bubble in a liquid are considered. Distortion of the spherical shape of the bubble is presented in the form of spherical harmonic power series. Mathematical model equations include nonlinear terms of second order of smallness with respect to the amplitudes of the harmonics. Nonlinearity influence on the bubble oscillations under periodic variation of the liquid pressure is investigated under various values of the initial distortion and the number of harmonics used to present the distortion of the spherical shape of the bubble.

Aganin A.A., Guseva T.S. (IME).
Spherical shape stability of a gas bubble in a liquid during its strong enlargement-compression. Spherical shape stability of a gas bubble in a liquid during its strong single enlargement-compression has been studied with allowing for its shape oscillations before beginning the expansion. Distortions of the bubble spherical shape are assumed small axisymmetric in the form of single spherical harmonics. The liquid near the bubble is considered to be viscous incompressible, the pressure inside the bubble being the same everywhere. Strong dependence of distortion value during the bubble enlargement-compression on the bubble shape oscillation phase at the moment of the expansion beginning (initial phase) has been found. Spherical shape stability was analyzed by using the worst scenario defined by distortions maximal with respect to the initial phase.

Aganin A.A., Toporkov D.Yu. (IME).
Liquid viscosity effect in nonspherical gas bubble oscillations. The liquid viscosity effect on variation of a small distortion of the spherical bubble shape is studied during bubble oscillations under periodically varying liquid pressure. The model with exact account of viscosity effect is used along with approximate ways. All the approximate ways do not take into account unsteady diffusion effects of vortex motion of the liquid. Parametric areas of the problem have been outlined in which these effects do (and do not) introduce qualitative changes in the shape oscillations. Features of influence of complex vortex motion of the liquid on variation of the distortion of the bubble shape have been studied.

Sharafutdinov V.F. (KSU), Malov V.I. (IME).
The peculiarities of rheological models of non-newtonian fluids constructed on the basis of the experimental s-shaped curves. IT is known that for many newtonian fluids the experimental flow curves have the S-shaped form. In transition from the experimental S-shaped curve to the rheological one in variables: stress and velocity of shift, it is suggested to introduce two rheological dependences. In this case two-phase medium behaves as non-newtonian fluid until the velocity of shift on the tube wall reaches some critical value; after reaching this critical value it behaves as newtonian fluid.

Mazo A.B. (IME).
On boundary conditions in Navier-Stokes stream function-vorticity problem for the set of bodies flow modelling. The method for calculation of stream function value as well as vorticity on the surface of bodies is developed.

Morenko I.V., Mazo A.B. (IME).
A numerical simulation of the drag and turn ability of the gauze at the small and intermediate Reynolds number. The gauze drag of the various cross-section cylinders are investigated. The turn ability of the circular cylinder gauze is studied at the small and intermediate Reynolds number.

Khairullin M.Kh., Soultanov R.A., Shamsiev M.N., Sadovnikov R.V., Tulupov L.A., Morozov P.E. (IME).
Interpretation of hydrodynamic investigations of horizontal wells. The problems of estimation of flow parameters of oil reservoir are considered on the basis of the regularization methods. The results of the hydrodynamic investigations of horizontal wells are used as the initial data. Fluid inflow to horizontal well with horizontal and wave profile is simulated using the finite-difference and finite element methods.

Elesin A.V., Mazurov P.A. (IME).
The quasi-gradient minimization method for solution of the inverse problems. The identification problem of the hydraulic conductivity in the three-dimensional anisotropic confined aquifer in case of one-phase filtration according to the head values in observation locations is solved. A new quasi-gradient algorithm for minimization of a residual function has been proposed. The sensitivity storage distribution for constructing this algorithm is used. The properties of a residual function in minimum point have been analysed. These properties are the basis of a new stopping criterion. In this criterion the knowledge of errors in head data is not required.

Mazurov P.A., Tsepaev A.V. (IME).
The solution of three-dimensional flow equation in confined aquifer with a large number of wells on multiprocessoring systems. A new algorithm has been proposed to solve the flow equation in confined aquifer on the coarse grid with concentration of grid near the wells. The algorithm is based on the method of division of domain on subdomains. The results of solution on multiprocessering systems MVS 1000/16 have been presented.

Timoshenko I.E. (IME).
On the change of pore and particles sizes distribution functions during waterflooding of the oil reservoir "polymer-disperse" systems (PDS). The results of modeling of change of pore and particles sizes distribution functions for waterflooding of oil reservoir "polymer-disperse" systems are presented. The comparison of numerical results with the available experimental data is carried out. Their qualitative concurrence is shown.

Usmanov I.T. (KSU, Institute of Mathematics and Mechanics).
3D-Modification of the multigrid method for numerical calculation of a pressure field in the multilayered oilfilds. 3D-modification of the multigrid method for numerical calculation of a pressure field in the multilayered petroleum layer model is developed within the framework of two-phase filtration. The iterative process was constructed with taking into account that thickness of a petroleum layer many times less than its sizes on spread. All calculations were made for vertical vectors. The grid is coarsed only in the plan. The operators of restriction and prolongation remain the same, as in a two-dimensional case. The way of coefficients modernization for multigrid technology used in case of a given bottom-hole pressure is elaborated. On the large grids the convergence speed of this algorithm is shown to be much more than the earlier known ones.

February 13, 2004
Zakirov U.N. (IME).
Motion and stability of the concentrated variable rest mass in gravitational field of a charged radiative body. The equations of motion of the concentrated variable mass in gravitational field of the massive electrified body (solution of Vaidya-Bonner ) in the context of the five-dimensional theory of Kaluza-Klein are studied at an assumption of proportionality of the five-dimensional and four-dimensional intervals. In studied system the change of the rest mass (energy) of particles is compensated by the change of radiation energy of the gravitating body; it is demonstrated that in the equation deviation of the nonlinear terms depend on the factor, bound with parameters of the change of the rest mass and change of a specific charge. The generalized criterion of orbital stability of particle according to L.Kaplan is analysed.

Ganeeva M.S., Moiseeva V.E. (IME).
The carrying capacity of a reservoir for cryogenic liquid under the nonaxisymmetric loading. We numerically investigate the behaviour of the construction in the form of shells of revolution with the branching meridian under the nonaxisymmetric thermo-force loading. As a rule, the carrying capacity of the construction is estimated on the basis of the achieved level of stresses. In the present work we study the carrying capacity of a tank for cryogenic liquid, which is subjected to windlike loading, on the basis of achieving the material yield strength and (or) the critical level of compressive stress resultants. We have considered means of improving the carrying capacity of the construction. The problem is solved with regard to the geometric and material nonlinearities.

Shirokova E.A. (KSU).
Particular solution of the 3d analog of the second basic problem of the theory of elasticity for cylindrical elastic solids. The method of construction of the particular solution of the following problem is found: given the displacements at n+1 level of the cylindrical surface of a cylindrical solid, the stresses in the solid should be found. The solution has the form of a polynomial over the corresponding coordinate and can be obtained via solution of the boundary value problems. One can find the exact solution for the case when the cross section of the cylindrical solid is the image of the unite disk under the rational function. For the case of circular hollow cylinder together with the displacements at n+1 level of the external cylindrical surface the constant pressure and the sliding condition on the internal surface are given. The examples are constructed.

Sekaeva L.R., Berezhnoi D.V., Konoplev Yu.G. (KSU).
Three-dimensional problem of interaction of the dry and water-saturated continua. The technique of the stress-strained station analysis of the dry and water-saturated grounds, interacting with deformable constructions, based on the finite element method is presented. Static and dynamic interaction of the underground industrial constructions with a ground is considered.

Golovanov A.I., Chigaboutdinov A.F. (KSU).
Natural and forced shell vibrations. FEM technique. The article is devoted to realization of the numerical investigation and simulation of dynamic process for the complex shell constructions. Numerical results based on the finite element method are presented.

Yakupov N.M., Nurullin R.G., Nurgaliev A.R. (IME).
Films and membranes: application and methods of computation. In films and membranes there can be various defects. A small review of the used methods of computation is presented. It is noted, that the works devoted to construction of curves of deformation with the use of two-dimensional approach, as well as the experimental works on the research of durability of films are few. The work is devoted to development of the effective experimental - theoretical method of research of the strength and deformation characteristics of films and membranes with defects. The results of computation for samples with corrosion deterioration are given.

Akhmetzyanov F.H. (Kazan State Architectural-Building Academy), Yakupov N.M. (IME).
An estimation of parameters damages of microstructure of cements stone. The analysis of experimental works is carried out in the area of microstructure of cements stone. From fraktogramm of destruction of cements stone both the length and width of disclosing of the microcrack as well as the distance between them are established. The applicability of the concept of the destruction mechanics of for the description of microcracking of cements stone is shown.

Kayumov R.A. (Kazan State Architectural-Building Academy), Konoplev Yu.G. (KSU), Tazioukov B.F. (KSU).
Identification of mechanical data of an elastic composite on the basis of results of a solution of problems of constructions stability. The procedure of definition stiffness coefficients of a composite fillet is proposed, of which beforehand curved thin elastic plate or cylindrical panel is made. The problem is reduced to a problem of nonlinear programming about minimization of a discrepancy between values of the calculated and experimental values of a critical loading. The approach permitting to gain good coordination of the calculated and experimental data by introduction of expansion of function of the purpose is proposed.

Galimov N.K., Nurullin R.G., Leontiev A.A. (IME).
On elastic balance of round membranes and flat spherical shells under the action of uniform pressure. The solution of a task in three approximations and their comparison with the exact solution is given. It is noted, that the solution of a task within the limits of elasticity of a material in the second approximation gives quite acceptable result.