Vol 40, No 6 (2019)

The influence of the hydrodynamic interaction of cavitation bubbles in acetone on the deformation of their surfaces during their single joint strong expansion and collapse is investigated. The bubbles are initially spherical and are located at the pressure antinode of an ultrasonic standing wave. Two configurations of the relative position of the bubbles are considered. The first configuration (linear) consists of three equally-spaced bubbles. Their centers are located in one straight line. The second configuration (planar) consists of nine bubbles. Their centers are located at the nodes of a uniform square grid located in one plane. The main attention is payed to the dynamics of the central bubbles. It is found that in both configurations, the deformations of the central bubbles in the form of the second spherical harmonic are significantly greater than in the form of other harmonics with higher numbers. In the final high-speed stage of collapse, the interaction between the bubbles becomes insignificant. At the end of collapse, the central bubble in the linear configuration appears flattened along the axis of symmetry, whereas in the planar configuration, it is elongated along the normal to the plane of the bubble centers.

A mathematical model for calculating the thermohydrodynamic situation during film condensation based on the equations of conservation of mass, momentum and energy for the refrigerant in a limited area, the condensate film flowing and the gas phase in a two-dimensional formulation is constructed. The dependence of the viscosity of the working medium on the temperature is taken into account. The boundary conditions of conjugation are specified on the inner wall of the refrigerant flow region, the outer wall through which the condensate film flows, and also at the film-gas interface. The obtained boundary value problem is solved by approximate and numerical methods together with the condition for determining the unknown film thickness, which allows the calculation of all characteristics of the condensation process.

The identification task of the absolute permeability is considered under conditions isothermal three-phase flow in porous medium. The identification process is carried out by known values of the flow rate on a single well. The resulting permeability field is used to calculate the flow rate at the following moments of time. The proposed approach is tested to solve the model problem. The influence of time and number of the flow rate measurements on the identification results is investigated.

The effect of cryogenic and high temperatures on the nonlinear straining processes of the non-shallow spherical shells under external axisymmetric and non-axisymmetric pressure has been numerically investigated. Along with this, the limit loads buckling have been determined. Cases of substantial differences between reached and initial temperatures are considered. According to the calculations, a diversity of the buckling forms in the analyzed problems has been shown. It has been found that the largest critical loads for the deep spherical shell are observed at cryogenic temperatures for the analyzed thermal and force loading and its values decrease considerably at higher temperatures. The calculations have shown a significant dependence of the stress-strain state of the thermo-stressed segments on the accounting completeness of the temperature dependence of the material characteristics.

The results of numerical modeling of hydrodynamics and heat and mass transfer at boiling of subcooled liquids in conditions of forced flow in vertical heated pipes are presented. The mathematical model is based on the use of Euler’s description of mass, motion and energy conservation for liquid and gas phases, recorded within the framework of the theory of interacting continua. The turbulent characteristics of the fluid are calculated using a modified model of transfer of components of the Reynolds stress tensor, taking into account the presence of the gaseous phase in the medium. For an approximate calculation of the heat transfer coefficient for bubble boiling of a liquid near the heat-generating wall, generalized empirical dependences are used, taking into account the various mechanisms of heat transfer in a two-phase vapor-liquid medium. Comparison of the results of numerical modeling with experimental data has shown that the proposed approach allows to simulate bubble boiling modes in a wide range of pressure values, mass flow rates, heating modes of subcooled liquids during forced turbulent fluid flow in vertical pipes.

The liquid compressibility effect during impact of a liquid jet at a speed of 250 m/s on the surface of a solid wall is investigated, depending on the jet shape. The study is conducted by the comparison of the numerical solutions obtained with and without taking into account the liquid compressibility (by the CIP-CUP and BEM methods, respectively). It is shown that the manifestation of the liquid compressibility during impact substantially depends on the jet shape. For example, the neglect of the compressibility in the case of impact of a cylindrical jet with a plane end strongly distorts the impact pattern over a long time. In the case of a cylindrical jet with a hemispherical end, a distorted picture appears only at the short-term initial stage of impact. For a pointed cone-shaped jet with an angle between the cone surface and the wall equal to π/4, the flow patterns obtained with and without allowing for the liquid compressibility are almost identical.

The problem of state and unknown inputs estimation for time-varying nonlinear Lipschitz systems is solving. Methods are proposed to synthesize state and unknown inputs observers that provide finite time boundedness of estimation error with respect to the given sets. In this case the gain of observer depends on time and is determined on the basis of a numerical solution of optimization problem with differential linear matrix inequalities or a numerical solution of the corresponding matrix comparison system. The results are illustrated by the example of a robot manipulator with a DC motor and an elastic links connection.

In this paper the isothermal flow of two non-compressible immiscible fluids through a porous medium is simulated taking into account capillary and gravitational forces. It is supposed that oil has non-Newtonian properties. The deviation from Darcy’s law is modeled by introducing a function depending on the filtration rate into the momentum equation. The problem statement in the variables “velocity-saturation” is used. The influence of non-Newtonian properties of oil in heterogeneous sloping reservoirs is demonstrated on the numerical examples. This influence is manifested in the formation of stagnant and washed zones. It is shown that it is necessary to take into account the geometry of the reservoir for the placement of wells and that producing wells should be placed down the slope of the reservoir.

The paper is devoted to the study of the problem of high-frequency low-amplitude harmonic oscillations of a circular cylinder in a viscous incompressible fluid. The study develops the classical method of successive asymptotic expansions of a solution into internal and outer, steady and oscillating components in terms of a small parameter. The case of finite streaming Reynolds numbers is considered. Using the original method for calculation of the hydrodynamic force components from external flow characteristics, analytical expressions for four terms of the force expansion were found. The obtained results allow to evaluate not only a linear response to perturbations of flow caused by oscillations of the cylinder, but also the effect of the non-linear interaction of harmonics in the boundary layer.

The results of theoretical and experimental studies of thermal secondary effects arising from nonlinear oscillations of gas in an open tube are presented. The heat flow distributions along the tube at the transition through resonance for different amplitudes of the piston displacement are obtained. It is established that the heat flow decreases from the piston to the open end. A good agreement between theoretical calculations and experimental data was obtained.

The work is devoted to the methods of solving three-phase fluid flow problems in the reservoirs. It is assumed that in domain with high velocities Darcy’s law is violated and a nonlinear filtration law is used. The methods for solving three-phase flow problems in porous media with a nonlinear filtration law based on the decomposition methods are proposed. The proposed methods are implemented on the heterogeneous computing systems.

The general goal of this work is to create the mathematical model of the ejector type actuator, which is installed to the wing model. The second goal of this work is to calculate its characteristics. For this purpose the CFD methods (3D RANS) were used. The experimental data obtained by the authors are used for the mathematical model validation. It is shown that this type actuator is an effective device for the wing flow control at subsonic speeds including landing and take-off regime.

Film and membrane elements, which include coatings, are widely used in all industries. The research tools are described. The mechanical properties of the compositions “polymer film + fabric + polymer film” on the size of delamination, on color of the fabric and time of ultraviolet radiation influence were researched. Studies of changes of adhesive properties of the film to steel substrate depending on time of ultraviolet influence, were also carried out.