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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.

Unsteady viscous crossflow around a rotating circular cylinder is studied in the laminar and turbulent flow regimes. The dependences of drag and lift coefficients of the cylinder on the rotation speed are obtained.

Influence of the turbulence intensity and turbulence length scale on the hydrodynamic characteristics and heat transfer of a circular cylinder, streamlined by a viscous fluid flow, is numerically studied. We take the Reynolds number of the oncoming flow equal to 4×104, the turbulence intensity Tu f and the dimensionless turbulence length scale L f varying from 1.0% to 40% and from 0.25 to 4.0, respectively. We confirmed that the increase of Tu f leads to the suppression of the periodic vortex shedding from the cylinder surface, and as a result the stationary mode of streamlining is formed. Consequently, with the increasing turbulence intensity directly in front of the cylinder Tu*, the amplitude of the lift coefficient decreases monotonically. Nevertheless, the time-averaged drag coefficient of the streamlined cylinder decreases at Tu* 9.0%. The dependence of the average Nusselt number on Tu* is near-linear, and with the increasing turbulence intensity, the Nusselt number rises. However, the change of the average Nusselt number depending on L f is non-monotonic and at L f, the value reaches its maximum.

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.

Results of a numerical investigation of a separation nonisothermal flow of an incompressible viscous fluid around a circular cylinder covered with a permeable porous layer at moderate Reynolds numbers are presented. This flow was defined with the use of Navier–Stokes and energy equations, and the filtration flow in the porous layer was determined by the Forchheimer law. The dependence of the hydrodynamical drag of the indicated cylinder and the length of the vortex region in the flow around it on the Reynolds and Darcy numbers was determined. An analysis of the heat transfer from cylindrical bodies covered with permeable layers of a highly heat-conducting material or a heat-insulating material has been performed.

The motion and heat transfer of water droplets with a swirling air flow is investigated. Flow was considered in a cylindrical chamber in the absence of gravity. We created a mathematical model of this problem and made appropriate calculations. The features of the air flow at a tangential feeding it into the chamber, and the motion of the drops, their thermal behaviour are founded. We presented the recommendations for the rational choice of parameters of the apparatus and rational operation regime.

Mathematical modeling of processes occurring during the spraying of polymer powder compositions on the surface of parts and products is considered. Relations describing the flow around processed bodies, movement of the powder particles in a stream of the carrying medium, dynamics of their deposition on the body surface are presented.