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A numerical study of the Couette–Taylor–Poiseuille two-phase flow is presented in this work. The proposed mathematical model takes into account the nonstationarity and three-dimensionality of the process of medium motion and rotation of the surface of the inner cylinder, as well as surface tension and the action of gravity. The developed numerical technique was tested on the solution of the problem of Couette–Taylor single-phase flow, which is the limiting case of a two-phase flow, when the volume concentration of the gas phase is zero. Two regimes of a two-phase flow are obtained. At low Reynolds numbers, a stratified flow regime is observed. In the second regime of two-phase flow, the gas phase is localized along a helical line along the surface of the inner cylinder. It is shown that the dimensionless torque increases when the gas phase is added to the flow.

The problem of the viscous incompressible fluid flow between two coaxial cylinders is considered in the case when the inner cylinder is rotates and the outer cylinder is stationary. The process of fluid flow is simulated by solving the three-dimensional Navier–Stokes equations. The computational algorithm is based on the finite volume method. The dependences of the dimensionless viscous torque from the Reynolds number and the radius ratio are established.

The results of a numerical study of the implosion of a spherical gas cavity in a cylindrical tank filled with liquid are presented. Under the influence of a pressure drop, the fluid starts to move, and the gas cavity begins to collapse. Mathematical modeling of the nonstationary, nonisothermal, turbulent motion of a compressible fluid is based on the fluid volume method. The focus is on the generation of pressure waves in a fluid during an implosion process. The study involved changes in the initial pressure in the gas cavity. It is shown how the initial pressure in the gas cavity affects the peak pressure recorded at the control point and the time it takes to reach it. An approximation formula is obtained for calculation of the peak pressure of a spherical compression wave.

Numerical simulation of the three-dimensional flow in the laminar and turbulent regimes around of the heated cylinder rotating around its axis was carried out. Laminar flow of the viscous incompressible fluid is described by the Navier-Stokes system of equations in natural variables. The unsteady Reynolds-averaged Navier-Stokes equations together with the Shear-Stress Transport model are chosen for the simulation of the turbulent fluid flow. The results of numerical simulation are compared with experimental and numerical data of other authors in the case of the flow past of the stationary cylinder. The dependences of the drag coefficient of the cylinder and the Nusselt number from the rotation speed are established.

The processes of redox interconversion of Cu and Cu2O sol nanoparticles in the presence of poly(N-vinylpyrrolidone) are studied. Reduction processes are conducted in the presence of tert-butylamine borane, and oxidation processes are carried out using Cu2+ ions. The successive oxidation-reduction of copper-containing nanoparticles is performed successfully several times. Stable Cu and Cu2O sols are obtained during all reduction-oxidation steps. Initially, only isolated spherical nanoparticles are formed; their average diameter increases at each step from 6.5 to 10 nm. With increasing number of interconversions, the associates of nanoparticles with spherical symmetry are first observed and then wormlike nanostructures are registered. At the final steps, the associates of nanoparticles with toroidal symmetry are formed.

Nonisothermal cross flow of a viscous incompressible fluid around a porous cylinder with a square cross section is considered. Main attention is paid when an impermeable core of the cylinder is surrounded with a porous layer. The full system of Navier–Stokes and energy equations is integrated numerically by the finite-volume method. The hydrodynamic interaction between the flow and the matrix of the porous layer is described by Darcy’s law. At moderate Reynolds numbers, the influence of the permeability of the porous layer on the nature of the flow and the heat exchange between the cylinder and the flow is studied. It is shown that, with increasing permeability, heat transfer from the cylinder increases mainly on its front side. From the analysis of the data obtained, an approximate formula for the mean Nusselt number as a function of the Reynolds and Darcy numbers is derived. The results of the calculation of hydrodynamic and thermal characteristics of the cross-flow around an impermeable and a fully permeable cylinder are also presented.

The numerical simulation of the laminar viscous flow past a cylinder performing rotary oscillations around its axis is carried out. The Navier–Stokes equations are solved by finite volume method using the program package OpenFOAM. The values of the amplitude and frequency of forced oscillations are found, at which the maximum reduction of the drag coefficient of the cylinder is achieved.

A viscous incompressible fluid flow with particles past the circular cylinder in a channel and heat transfer was considered. A numerical simulation of unsteady laminar flow of the mixture was carried out using Euler continuum approach. The corresponding boundary value problem is solved numerically using the finite volume method. The influence of the density, specific heat, and thermal conductivity of the particle material, as well as the particle diameter, on the drag and heat transfer of the cylinder was estimated.