March 13, 2002

Khadiev M.B. (Kazan State Technological University). Hydrodynamic, thermal and deformational characteristics of oil films of turbomachine bearing-and-thickening units. On material of thesis for Doctor of Sciences Degree, speciality: 01.02.05 - mechanics of fluids and plasma. Reviewer: DSc (Techn.) Fedyaev V.L. Mathematical models of hydrodynamic and thermal processes of fluid flows in thin oil films of bearing-and-thickening units of turbomachines are presented. Mathematical models take into account variations of density and viscosity of the fluid as functions of the temperature, the temperature deformation of carrying surfaces as well as their mutual influence. Radial and axial liquid friction slide bearings, radial unloading devices for high pressure screw compressors and floating thickening units tightening compressors are considered as supports. Parametric analysis has been made and hydrodynamic, thermal and deformational characteristics of oil films of turbomachine bearing-and-thickening units are built. Problems of optimization of slide bearings and thickenings are considered. Algorithm and example of calculation of optimization of a one-side thrust sliding bearing is presented.

September 12, 2002

Ilgamov M.A., Aganin A.A., Guseva T.S. Distortion of the spherical shape of a gas bubble in a liquid under large enlargement-compression. Variation of a small initial distortion of the shape of a spherical gas bubble in a liquid during its large one-time enlargement-compression has been studied. The gas pressure in the bubble is assumed uniform, the liquid around it being viscous incompressible. Initial distortions in the form of single spherical harmonics of numbers i=2-5 have been considered. It has been found that the distortion of the spherical shape of the bubble at its collapse increases with the increase of the number of the harmonic. Disregard of the viscosity effect can lead to considerable overstating of the value of distortion of the spherical shape of the bubble at the time of its collapse.

September 20, 2002

Malov V.I. Computation of two-dimensional flow of non-Newtonian fluid in channels of complicated form and in porous media. Approximate methods of computation of the stationary flow of non-Newtonian fluid in cylindrical channels with arbitrary cross-section and in axially symmetric channels of complex geometry under the action of the pressure difference have been proposed. The formulas of the flow velocity and input-output characteristics have been obtained.

September 27, 2002

Aganin A.A., Kosolapova L.A., Malakhov V.G., Toporkov D.Yu. Comparison of liquid viscosity models in dynamics of a gas bubble. Comparison of the solutions of two problems of dynamics of a gas bubble in liquid (decay of a small initial distortion of the spherical bubble shape and stability shape of a bubble under its periodic radial oscillations) with account of the liquid viscosity by the model of Prosperetti (1977) and a number of others (known in the literature and proposed by the authors), approximate relative to that of Prosperetti has been performed. It has been found that in both problems none of the approximate models can be estimated as more preferable over a wide range of the liquid viscosity: one model proves to be better for one values of the viscosity while another one for the other.

October 11 2002

Aganin A.A., Guseva T.S. Distortion of the spherical shape of a gas bubble in a liquid under strong enlargement-compression. Distortion of the spherical shape of a gas bubble is studied under strong enlargement-compression due to one-time harmonic variation of the pressure in the surrounding liquid. Before beginning the enlargement, the bubble surface oscillates about the spherical shape periodically without decaying with small deviation amplitude. A mathematical model is used, in which the liquid near the bubble is assumed incompressible while the pressure inside the bubble being the same everywhere. Strong dependence of the bubble shape variation in the course of the enlargement-compression on the initial phase of oscillation of the bubble surface has been found. Influence of the problem parameters on the distortion of the shape of the bubble at the instant of its maximum compression has been investigated. Possibility of using a number of simplified ways of allowing for the liquid viscosity known in the literature has been explored.

October 25, 2002

Aganin A.A., Malakhov V.G., Kosolapova L.A. Dynamics of a bubble in a liquid under non-small distortions of its spherical shape. Nonspherical oscillations of a gas bubble in a liquid are considered. The liquid flow velocity field is assumed irrotational. Liquid viscosity influence is taken into account via the dynamic boundary condition along the normal to the bubble surface. The pressure of the gas in the bubble is assumed uniform. Governing equations include nonlinear terms of the second order of magnitude relative to the amplitude of distortion of the spherical shape. Influence of this nonlinearity on the process of the bubble oscillations is investigated in dependence on the initial deflection from the spherical shape in problems with different variation of the liquid pressure far from the bubble.

January 5, 2003

Gilmanov A.N., Sotiropoulos F. (School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, USA). Numerical simulation of fluid/structure interaction problems in 3D incompressible viscous flows. A numerical method is developed for solving the 3D unsteady incompressible Navier-Stokes equations in a Cartesian domain containing geometrically complex flexible immersed boundaries. An extensive study of various features of the method is carried out using the case of laminar flow past a sphere for Reynolds numbers in the range of 50 to 300. The applicability of the method to fluid/structure interaction problems is demonstrated by results of simulation of the flow induced by a fish-like flexible object at Re=300.

The following report was presented at plenary Session of the Final Scientific Conference'2002 of the Kazan Science Center RAS:

February 7, 2003

Yakupov N.M. Some problems of mechanics of deformable bodies, materials and structures. In the field of mechanics of deformable bodies, an effective spline version of the finite element method for definition of stress-strained state of thin-walled structures of complex geometry has been elaborated and is being developed. In the field of mechanics of materials, an experimental-theoretical method of testing of strength properties of film materials has been worked out. A patent of the Russian Federation for the invention has been obtained. The directions of further development have been outlined. In the field of mechanics of structures and buildings, new designs of some parts of cooling towers and their ventilators have been developed. Corresponding patents of the Russian Federation for the inventions have been obtained.

The following reports were presented at section Sessions:

February 4, 2003

Gubaidullin D.A., Laptev S.A., Nikiforov A.A. Features of wave dynamics of dispersed media. Features of propagation of weak waves of different form in two-phase vapour-gas-droplets suspensions and liquid-bubbles mixtures have been investigated. Within the framework of dynamics of heterogeneous media the differential equations of motion of two-phase mixtures are presented. The corresponding dispersion relations have been obtained. Dynamics of weak pressure pulses of various shape in polydispersed air fogs and the mixtures of water with monodispersed air bubbles with the use of the fast Fourier transform algorithm has been studied. It has been found that the amplitude attenuation and change in the form in the case of spherical and cylindrical perturbations are stronger than they are in the case of plane ones.

Aganin A.A., Malakhov V.G., Kosolapova L.A. Nonlinear oscillations of a gas bubble in a liquid under non-small distortions of its spherical shape. In the work some relations have been derived and a number of problems of nonlinear oscillations of a gas bubble in a viscous incompressible liquid have been solved. In the relations, the terms of the second order of smallness relative to the amplitude of the distortion of the spherical shape of the bubble are taken into account. Bubble oscillations have been investigeted under jump and periodic variation of the pressure far off the bubble depending on the value of the initial deflection from the spherical shape of the bubble. Comparison of the solutions obtained in linear and nonlinear problem statements has been made.

Aganin A.A., Guseva T.S. Influence of the liquid viscosity under single enlargement-compression of a bubble. Distortion of the spherical shape of a gas bubble is studied under strong enlargement-compression due to one-time harmonic variation of the pressure in the surrounding liquid. Distortions in the form of single spherical harmonics have been considered. Before beginning the enlargement, the bubble surface oscillates about the spherical shape periodically without decaying with small deviation amplitude. A mathematical model is used, in which the liquid near the bubble is assumed viscous incompressible while the pressure inside the bubble being the same everywhere. Influence of the problem parameters on the distortion of the shape of the bubble at the instant of its maximum compression has been investigated.

Aganin A.A., Toporkov D.Yu. Influence of the liquid viscosity under forced aspherical oscillations of a gas bubble. An opinion is widely-distributed in the literature that distortion of the spherical shape of a bubble always decreases under its enlargement. The reason for that seems to be due to the fact that up to not long ago in investigating the bubble dynamics the influence of the vorticity field of a liquid was mainly approximated by its boundary value. In the present work, using more exact model of allowing for features of the surface deformation of a bubble in a viscous liquid it is shown that under some specified conditions the distortion of the spherical shape of the bubble during its enlargement can not only decrease but also increase.

Tukmakov A.L. Synchronization of oscillations of thin plates with aeroelastic interaction. Synchronization of oscillations of thin elastic plates making up the walls of a gas?filled channel is considered. The gas motion is described by the system of Navier?Stokes equations, which is solved using the second?order Mac?Cormack method with time splitting. The motion of the channel walls is described by a system of geometrically nonlinear dynamic equations of the theory of thin plates. The system is solved by the finite?difference method. Kinematic and dynamic contact conditions are imposed at the interface between the media. A number of numerical experiments has been performed to determine typical dynamic regimes and to study the transition of the aeroelastic system to in?phase oscillations.

Gubaidullin D.A., Zaripov R.G., Galiullin R.G. (KSU), Galiullina E.R. (KSU). Nonlinear oscillations of an aerosol in a closed tube. The results of experimental investigation of nonlinear oscillations of an aerosol contained in a long closed tube are presented. The longitudinal aerosol oscillations are generated by plane piston at one end of the tube. The tube has a quartz section with photo-transducer to measure droplet concentration of the medium. Dependences of coagulation time of droplets on frequency and dimensionless velocity of the piston for several frequency values including subharmonic resonance have been obtained. Non-monotonous nature of the dependence of coagulation time of droplets on the excitation frequency with the minimum at the frequency of subharmonic resonance has been found. It has been shown that as the dimensionless velocity of the piston oscillations increases the coagulation time of droplets decreases.

Galiullin R.G. (KSU), Tkachenko L.A., Philipov S.E., Galiullina E.R. (KSU). Resonance oscillations of a gas in an open-ended tube in the turbulent regime. Theory of oscillating flows in a tube has been considered in the case when the turbulence is developed monotonously, reaching the axis of the tube in a certain time interval after beginning the acceleration from the rest. Mathematical model has been built describing resonant oscillations of such a kind in a half-open tube. It has been shown that the dependence of dimensionless oscillation amplitude on a tube length is nearly inversely proportional and satisfactorily corresponds to the experimental data.

Sonin N.V. Oscillations of an aerosol in a closed tube near nonlinear resonances. The results of experimental investigations of nonlinear oscillations of an aerosol in a closed quarts tube with plane piston are presented for the frequency which is a quarter of the fundamental one. The set up is of low vertical-horizontal unbalance, being stable to vibrations. It has a mechanism of stabilizing rotation velocity of the shaft. It has been found that at resonance the amplitude of the pressure near the piston is lower than that near the closed end and that the pressure distribution has four maximums. The distributions of light intensify in different sections of the tube and along its axis have been obtained by the method of the past and diffused laser light. Non-homogeneous volume distribution of the aerosol concentration has been found. This effect is more appreciable at high frequencies. The ordered structures are clearer at low frequencies of the aerosol excitation. Physical explanation of the aerosol coagulation mechanism is proposed.

Morenko I.V., Mazo A.B. Computation of the drag of the gauze composed of bluff bodies at the moderate Reynolds number. Numerical simulation of the external separated flow past the gauze of various form has been performed at the moderate Reynolds number when a laminar eddy forms past each element of the gauze. Navier-Stokes equations are solved by the finite element method in the flow function-vortex-pressure variables. The influence of the Reynolds number and the gauze step on the drag coefficients, separation length and the separation point location is investigated. The results agree well with available experimental data and numerical solutions obtained by other researchers.

Fedjaev V.L., Sharafutdinova A.B. (Kazan State Architectural-Building Academy), Sharafutdinov V.F. (KSU). Modeling of processes of removing mechanical impurities from liquid using filter partition. The process of removing the contaminated liquids from the mechanical impurities with the help of filter partition is considered. To solve the problem, the whole flow space is divided into three subregions. The first subregion is considered to be occupied by suspension, the second one by the forming sediment, and the third one by the filter partition. The corresponding governing equations are written for every subregion. To close the systems of the equations the conditions of equality of pressures and velocity of the liquid and solid phases at the separation boundaries are used. The solution has been constructed which allows one to calculate the time-dependent mass of impurity kept on the filter partition and the time-dependent volume of the filtered pure liquid as functions of concentration of the impurity in the suspension, interaction of the solid and liquid phases in the suspension, the degree of the sediment compressibility.

Malov V.I., Sharafutdinov V.F. (KSU). Modeling and calculation of non-Newtonian fluid in the cylinder tube with the arbitrary cross-section. The problem of stationary flow of non-Newtonian fluid in the cylinder tube with the arbitrary cross-section at a given pressure drop is considered. An approximate method of evaluation has been proposed, according to which the curvilinear orthogonal system of coordinates q2,q3 is constructed in the tube cross-section, such that the point of maximum velocity and contour of the space are the lines q2=const.The solution is presented as a series containing the basic coordinate functions becoming zero on the symmetry lines and the boundary of the domain. The coefficients of the series are found from the condition of consistency of the rheological equations. The comparison of the exact solution of the problem of the flow of non-Newtonian fluid in the channel with triangular and square cross-sections with the results obtained by the approximate method has been made. The relative error in the consumption did not exceed 1%.

February 5, 2003

Yegorov A.G. (Institute of Mathematics and Mechanics, KSU). Gravitational instability of fronts of permeating in porous media.

Berezinsky D.A. (IMM, KSU), Kosterin A.V. (IMM, KSU). Calendering of polymeric solutions as a problem of the mechanics of the saturated porous media.

Nikiforov A.I., Anokhin S.V. On modeling of some technologies of influence on oil reservoirs. Within framework of academician RAS R.I. Nigmatulin's philosophy the unified approach to modeling of various technological processes in oil recovery accompanied by changes of porous media is presented. In particular, the processes of influence on oil reservoirs with polymer-dispersed and gel-forming systems are simulated. The models allow one to predict the place of changes in collector's properties of an oil reservoir, the time of those changes and their influence on the oil recovery.

Khairullin M.Kh., Shamsiyev M.N., Sadovnikov R.V., Soultanov R.A. Non-isothermal filtration of the gas in reservoir-well system. Numerical analysis of influence of the temperature factor on the estimates of filtration parameters of a reservoir has been performed. New mathematical model of gas hydrate growth and dissociation in gas pipelines and in reservoir-well system is are suggested.

Gabidullina A.N., Elesin A.V., Kadyirova A.Sh., Mazurov P.A. On constructing new algorithms of residual function minimization along the slope. A new algorithm of minimization along the slope has been developed. New criterion of stopping the minimization process with using the sensitivity storage has been derived.. The minimization along the slope is applied to identification of the hydraulic conductivity in the case of 3Dl non-isotropic confined aquifer.

Mazurov P.A., Tsepaev A.V. A method for solving problems with nonlinear law of liquid filtration. A new algorithm of solving problem of determining the field of heads of 3D aquifer with large number of wells has been proposed. The nonlinear filtration law is taken in the areas near the wells at the rapid rate of filtration. The algorithm is based on a new method of dividing the domain into subdomains.

Ganeeva M.S., Skvortsova Z.V. The membrane stress-strained state of the orthotropic ellipsoidal shells of revolution under thermal and force loading. The membrane orthotropic ellipsoidal shell of revolution under action of uniform heating and pressure has been considered. The problem relations are reduced to the differential equation in a function depending on tangential displacement. The equation has been solved analytically. The expressions of displacements in the general form have been derived. The variable thickness of ellipsoidal shells of equal strength was found. The formulas for the approximate evaluation of total stresses of constant thickness shells are derived in the case of force loading. The data obtained for various geometrical parameters are in good agreement with the results of the numerical solution of the problem in complete statement.

Ganeeva M.S., Moiseeva V.E. Numerical investigation of shells of revolution with negatives Gauss curvature under the action of non-axially symmetric loading. Stress-strained state of thin shells of revolution with negative Gauss curvature under non-axially symmetric loading has been numerically investigated. The problem is solved in linear approach and with account of geometrical and material nonlinearities . The stress concentration areas of the hyperboloidal shell depending on a series of boundary conditions have been established. Some ways of reducing the stress concentration have been proposed. The boundary conditions corresponding to appearance of nearly membrane stressed states in the shell considered have been established. It has been shown that in the nonlinear problem the dependence of stresses on the loading parameter is close to linear.

Golovanov А.I. (KSU), Тjuleneva О.N. (KSU), Yakushin S.А. (KSU). Finite element analysis of geometrically and physically nonlinear multi-layered shells. The present report is devoted to development and implementation of numerical technique of investigation of geometrically and physically nonlinear multi-layered anisotropic thin and moderately thick shells. The quadratic isoparametric finite element of multi-layered shell is introduced. In the formulation for geometric nonlinearity, the updated Lagrangian approach is adopted. In order to take into account physical nonlinearity the plastic flow theory is used. In the inelastic range, the material is assumed to obey the Huber-Mises yield criterion generalized by Hill for anisotropic materials.

Golovanov А.I. (KSU), Sennikova A.S. (KSU), Sultanov L.U. (KSU). Problem statement and numerical algorithm to study large deformations of elastic bodies. The work is devoted to a technique of investigation of deformed state with large displacements, rotations and strains. The Eulerian finite element formulation is used. The equation is derived from a current configuration version of the variational principle for incremental deformations. The eight-nodes 3D isoparametric element is used.

Yakupov N.M., Nurullin R.G., Shishkin A.A. (Nizhnekamskneftekhim Company). Analysis of operation and new structural force schemes of blades of ventilators of cooling towers. New structural force schemes of ventilators have been designed: а) spars of blades diverge in a fan-like manner from a hub with bending in places of reinforced ribs; b) blades and hub are designed as a unified structure; c) blades are supplied with pylons. The implementation of such schemes of ventilators allows one to increase their safety, to improve aerodynamic properties, to achieve more uniformity of the flow ejected by the ventilator over the cross-section of a diffuser of a cooling tower and to lower the volume of exhausts of harmful substances together with vapours and drops of water. The engineering solutions are protected by the corresponding documents of the Russian Federation for the inventions verifying their novelty.

Yakupov N.M., Galimov N.K., Nurullin R.,G., Nurgaliev A.R. A method of determination of strength of films. An effective method of determination of mechanical characteristics of films and diaphragms based on synthesis of experimental and theoretical approaches has been developed. The method was protected in 2002 by the patent of the Russian Federation №2184361 for the invention "Method of determination of strength properties of film materials". In the experimental part, the pressure dependence of rising the cupola is constructed. Based on relation of the non-linear theory of shells for large deformations and relations of the plasticity theory, the values of stretching stresses operating in the cupola of a sample are determined. The values of tensile stresses are evaluated using known pressure of destruction of a sample.