In this paper, we consider the stratified turbulent flow of a two-phase medium in inclined pipes. Based on the new turbulence model [1], a program code for calculating two-dimensional flows for the study of twophase stratified flows in pipes was developed, including taking into account the rough of the pipeline wall. The technique for calculating two-phase flows in extended pipelines is described. The problem of stationary stratified two-phase flow in a pipe of constant cross section in the case of turbulent regime is numerically solved. Calculations of the resistance of a rough pipe are carried out and the results on the influence of roughness on pipe resistance and velocity distribution are presented.

The work is devoted to the study of the features of the behavior of a group of droplets of one viscous liquid in another under the influence of various physical fields. When considering the dynamics of two drops under the action of an electric field, it is assumed that a drop in the form of a sphere with radius а will be placed in an electric field with an intensity , investigates how droplets will react to each other under the influence of an electric field. A mathematical model has been built and a computer program has been developed for the numerical solution of this problem. The behavior of several drops in an electric field is studied for different physical parameters of the material of the drops and the environment, as well as for different initial distributions of drops and the strength of the electric field. It is shown for the first time that emulsion droplets distributed in space, under the action of an electric field, begin to move and after a certain time a new stationary structure of droplets is formed. It was found that the relaxation time depends on the electric field strength, the size of the droplets and their initial distribution.

The heating of oil and oil products is widely used to reduce energy losses during transportation. An approach is developed to determine the effective length of the heat exchanger and the temperature of the cold coolant (oil) at its outlet in the case of a strong dependence of oil viscosity on temperature. Oil from the Uzen field (Kazakhstan) is considered as a heated coolant, and water is considered as a heating component. The method of the log–mean temperature difference, modified for the case of variable viscosity, and the methods of computational fluid dynamics (CFD) are used for calculations. The results of the numerical calculations are compared with the data obtained on the basis of a theoretical approach at a constant viscosity. When using a theoretical approach with a constant or variable viscosity, the heat transfer coefficients to cold and hot coolants are found using criterion dependencies. The Reynolds-averaged Navier–Stokes (RANS) and a turbulence model that takes into account the laminar–turbulent transition are applied. In the case of variable oil viscosity, a transition from the laminar flow regime to the turbulent one is manifested, which has a significant effect on the effective length of the heat exchanger. The obtained results of the CFD calculations are of interest for the design of heat exchangers of a new type, for example, helicoid ones.

A mathematical model of turbulent motion of a non-homogeneous flow is constructed. Based on the pulsation energy balance method, a closed system of equations is obtained for calculating the average velocity and turbidity of a non-uniform flow. The calculation of the pulsation characteristics of the flow with a transverse shift is carried out and the analysis of the effect of the impurity on the pulsation structure of the turbulent flow and its effect on the motion of an unmanned aircraft is carried out. Since the safety assessment and service lifetime of an unmanned aerial vehicle cannot exclude the influence of disturbances in the atmosphere when calculating characteristics.

In the present paper the formation of Liesegang structures, i.e. the process of periodic deposition with the mutual diffusion of two reacting chemicals in the presence of an external constant electric field, is studied using numerical modeling. The mathematical model of the process consists of three differential equations of diffusion-reaction for the concentrations of the initial components and the resulting precipitate. The kinetics of sedimentation is described in accordance with the Ostwald’s supersaturation theory. The equations of the mathematical model in one-dimensional and two-dimensional statements were solved numerically using the control volume method using computer code written by the authors in the C ++ language. As a result of numerical simulation in the absence of an electric field, periodic structures were obtained formed of the precipitate, which qualitatively corresponds to the patterns observed in the experiments. It is shown that numerically obtained Liesegang rings satisfy the well-known laws: the ratio of the distances to neighbouring rings remains constant and there is a power dependence between the distances to the rings and the time of their formation. The influence of the ratio of the concentration of the starting substances and the electric field strength on the nature of the structures formed is investigated. It also has been shown that an increase in the electric field strength leads to an increase in the number of structures formed.