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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.

A numerical study has been made of the wave process in the casing string of the well, which is initiated by the difference of pressures in the imposition device and the well fluid surrounding it. To describe the implosion process, a mathematical model has been proposed that takes account of the presence of two phases, viscous effects, the compressibility of the gas, nonstationarity, heat transfer, turbulence, and other factors. The basic parameters of the implosion process have been calculated. The influence of the implosion-device length on generated rarefaction and compression waves in the well fluid has been established.

Average heat transfer in a turbulent flow on a plate with a system of double-cavity diffuser-type dimples is studied experimentally. The regime of turbulent flow almost reproduces the airflow in a cooling system of a turbine blade. Physical and numerical simulation of flow in a double-cavity diffuser-type dimple is performed. Two self-organizing vortices emerging in the dimple were documented. They provide continuous mass transfer between the dimple and the flow. Numerical simulation results agree well with the physical experiment.

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.

Hydrodynamic processes in a vertical well casing during implosion are considered. Mathematical modeling of the motion of a two-phase medium with a free surface is based on the volume of fluid method. Unsteady Reynolds-Averaged Navier-Stokes equations are supplemented by the Menter’s Shear Stress Transport turbulence model. Numerical calculations were performed by the finite volume method using the open integrated platform OpenFOAM. It was found that the depression period is 1 s, and the maximum pressure at the control point is 1.8 times higher than the hydrostatic pressure at the given input parameters.

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.

No isothermal viscous incompressible fluid flow past a porous permeable balk of square cross section was investigated. The equations of the conservation of the momentum and energy are solved numerically using the finite volume method. The flow pattern, the dependence of the drag and the cylinder Nusselt number on the Reynolds number, Darcy was analyzed.

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 Couette-Taylor flow is considered in a wide gap between coaxial cylinders in the case when the outer cylinder is at rest and the inner one rotates at a constant speed. Unsteady motion of a viscous fluid is described by the system of Navier-Stokes equations. The problem is solved by the control volume method in the OpenFOAM software. Two stable states were obtained depending on the surface rotation speed: the cylindrical Couette flow and the Taylor vortex flow. The calculation results are compared with the known data of other authors. The dependence of the dimensionless shear rate on the Taylor number is obtained.

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.

Nonisothermal flow past a circular cylinder of the fluid with spherical gas inclusions is studied. It has been established that as the volume concentration of the dispersed phase increases, the drag force of the cylinder reduces and its heat transfer with the medium decreases.

Unsteady nonisothermal traverse flow of an impurity-containing viscous fluid past a rotating circular cylinder has been investigated with account of the mechanical and thermal interaction of the carrier and dispersed phases. The processes occurring have been described mathematically with the Lagrange approach. The influence of the impurity on the flow pattern has been analyzed; the dependences of the drag coefficient, the lifting-force amplitude, and the Nusselt number of the cylinder on the relative rotational velocity of its surface have been determined.

The problem of the collapse of a spherical gas cavity in a fluid under non-isothermal conditions is considered. Numerical simulation of the motion of a two-phase medium is based on the volume of fluid method (VOF). The numerical results of fluid pressure history at control points located at different distances from the center of the cavity during the process are obtained.

The process of underwater implosion of the air sphere in the cylindrical reservoir is considered. Numerical simulation of the two-phase flow is based on the volume of fluid approach. Both air and water are considered compressible. Menter's Shear Stress Transport turbulence model is chosen for the closure of Unsteady Reynolds-averaged Navier-Stokes equations. The solution of the problem is carried out by the finite volume method. The implosion event is on the order of milliseconds. The simulation results demonstrate that the pressure wave with high peak pressure moves from centre of the gas volume to reservoir wall. A comparison of pressure time histories were made between experimental data and numerical simulation results.

Results of numerical solution of Navier-Stokes equations in stream function-vortex variables for a nonstationary laminar flow around a circular cylinder with a rotational degree of freedom are presented. The cases of definite, free, and inertial rotation of the indicated cylinder were considered.

An iteration method of calculating pressure by solving Navier–Stokes equations in stream function–vortex variables is proposed. A numerical investigation of the drag and the rotational properties of cascades of circular cylinders at small and moderate Reynolds numbers has been carried out.

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.

Non-isothermal flow around the porous permeable cylinder of square cross section by a viscous incompressible fluid is considered. The motion and energy equations is solved numerically using the finite volume method. The character of the fluid flow, change of the cylinder drag coefficient and Nusselt number as a function of Reynolds and Darcy numbers is analyzed.

Heating and melting of particles of polymeric powder in the central flow channel of spraying gun is investigated. Mathematical models of these processes taking into account convective and radiative-convective heat interaction of particles with environment is represented. Relations for calculating the temperature of the particles depending on the longitudinal coordinate, time of flight, operating and design parameters as well as thermophysical characteristics of the particles material and environment are given.

The influence of mechanical impurities in the fluid on the structure of the flow near a stationary, rotating cylinder, on its hydrodynamic characteristics and the heat exchange with the stream was investigated numerically. It was shown that the presence of impurities in the liquid leads to a significant change in the pattern of the flow, to increase in the resistance and heat transfer of a stationary cylinder, reducing the lifting force. The emissivity of the rotating cylinder in a fluid flow with an admixture of substantially depends on the dimensionless velocity of the surface. If the speed is less critical, equal to 3.0, the heat is intensified. At higher values, on the contrary, the heat transfer deteriorates. The necessity of considering these circumstances when developing technologies for deposition of functional coatings is evidential.