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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.

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.

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.

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.

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.