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The problem of evolution of an axisymmetric vortex generated by an infinitely elongated cylinder rotating around its axis in a compressible viscous fluid is considered. The asymptotic solution is constructed for large times. The conditions under which the velocity circulation at long distances is higher than in the incompressible fluid case are determined.

Supersonic laminar flow past a sphere and a cylinder placed perpendicular to the freestream is investigated on the basis of the numerical solution of the Navier—Stokes equations. The gas is assumed to be perfect, with a constant specific heat ratio, and the surface temperature is fixed and taken to be the same as to the recovery temperature. The calculations are carried out at the Mach number 3 (cylinder) and 5 (sphere) in the Reynolds number range from 1 to 3000. The effect of the boundary slip and no-slip conditions imposed on the body surface on the flow parameters is investigated. Emphasis is placed on the determination of the aerodynamic characteristics. The results obtained are compared with the available experimental and calculated data.

The formation of three-phase cavitation bubbles in hydrophobic liquid when a cylindrical body slides along a rigid surface is experimentally investigated. The structure of cavitation bubbles is determined. Condensed–steam microdroplets with a positive electric surface charge are revealed on the gas–hydrophobic liquid interface, the cavitation bubble sheath having a negative charge. Each of such cavitation bubbles induces the self-electric field due to the surface charges of the interfaces. The effect of the electric fields of neighboring bubbles on the movement of water microdroplets is established. The presence of the electric field induced by bubbles can lead to their repulsion or integrating. Electroluminescence appearing in coalescence of bubbles is first recorded.

A structural bifurcation analysis of an incompressible two-dimensional (2D) shear flow past an inclined square cylinder by considering topological properties of flow is done in this paper. We have shown how the flow separation leads to complex structure at a time from a point by using this analysis. The streamfunction–vorticity ($$\Psi $$−$$\zeta $$) formulation of Navier–Stokes (N–S) equations in Cartesian coordinates is solved using a higher order compact (HOC) finite difference scheme. Through this analysis, we capture the exact locations of first and second bifurcation points with appropriate non-dimensional time of their occurrences for initial stages as well as fully developed flow. The flow field is mainly influenced by Reynolds number, Re, and shear rate, $$\kappa $$. It is shown that the first and second bifurcations developed within a very small time difference from the upper and lower downstream edges of the cylinder up to $$\kappa $$ = 0.1. Numerical simulations are carried out for Re = 100, 185 with $$\kappa $$ values range from 0 to 0.4. The purpose of the present study is to elaborate on the influence of shear parameter on flow properties. The temporal behavior of vortex formation and relevant streakline patterns are scrutinized for all parameter values. Occurrence of multiple separations is demonstrated in detail by varying $$\kappa $$ for both initial and fully developed flows. Comparisons with previous results in the literature clearly verify the accuracy and validity of the present work.

The problem of one-dimensional intense evaporation waves is considered. It concerns with unsteady instantaneous expansion of overheated material vapors into a vacuum or a low-density medium from a plate, a cylinder, or a sphere, whereupon constant (“sonic”) boundary conditions are imposed on the surfaces of these bodies.

The stability of a moving cylinder in a circulation flow of an ideal incompressible fluid with constant vorticity inside a stationary outer cylinder is investigated using Lagrangian mechanics methods. The Lagrange function in the form of a series expansion by a small displacement of the cylinder and the stability condition in the nonlinear approximation are obtained.

The stability of a cylinder in circulation flow of an inviscid incompressible fluid is considered. The investigation of stability in the simple two-dimensional system is of considerable interest since in this problem the analytical solution can be obtained in both spectral and initial problems. The investigation of the critical layer region in which the phase perturbation velocity coincides with the velocity of mean flow is of particular interest since just in this region the perturbations are concentrated and grow indefinitely.

An analytical model for calculating a viscous incompressible fluid flow in a rotating cylinder with a braking lid and the formation of turbulent boundary layers on the end surfaces is presented. The analysis is made with account for all nonlinear inertial terms in the equations of motion, within the framework of Loitsyanskii's integral relations. The approximate velocity profiles in the boundary layers are preassigned in accordance with the empirical 1/7 law. The main flow is subdivided into an inviscid quasisolid core and a lateral layer, where almost the entire upward part of a circulatory flow is concentrated. The unknown angular velocity of the core and its radial boundary are evaluated from the balance between the moments of the friction forces acting on the main rotating flow and the continuity condition for the circulatory flow.

Heat transfer in the subsonic high-enthalpy air flow in the VGU-4 induction plasmatron is experimentally and numerically investigated for three versions of the sectional discharge channel with the exit section diameters of 30, 40, and 50 mm. The model was a flat-nosed cylinder, 20 mm in diameter. Using a Gamma code the enthalpy he and the velocity at the jet axis are numerically reconstructed from the experimental data. The method for approximately determine the enthalpy he on the basis of the experimental data and the Fay—Riddell formula for the heat flux is proposed. The effective dimensionless model radius reff is introduced, which makes it possible to take account for the dependence of the flow at the outer edge of the boundary layer on the model and discharge channel geometries and the plasmatron operation regime. The value of reff is calculated for the VGU-4 operation regimes with a simple cylindrical discharge channel and a sectional channel. The values of the enthalpy he calculated using the “exact” and approximate methods are compared: the greatest difference in the he values amounts to 6%.

A plane isothermal problem of the internal contact between elastic cylindrical bodies separated by a thin layer of a viscous lubricating fluid under constant load and reverse motion is considered. To determine the deformations of the contacting bodies, solutions of the plane problems of the elasticity theory for a cylinder and a space with a cylindrical cut are used. Extreme cases of low load, high load, small and long periods of reverse motion are considered. The dependences of lubricant layer thickness and pressure on the angular coordinate at different times, as well as the dependence of the eccentricity and the minimum lubricant layer thickness on time are presented. It is shown that the minimum lubricant layer thickness as a function of time exhibits a decrease when braking the cylinder and continues to decrease for some time after a change in the direction of rotation and an increase in speed. It has been established that at the times when the speed is low, under high loads, the gap has narrow spots at the boundaries of the high-pressure area, preventing the lubricant from leaking out of the gap. At a low load and a long period of reverse motion, the maximum pressure in the lubricant layer can increase more than twice.

The problem of constructing an axisymmetric forebody with minimal wave drag with given constraints on volume and dimensions has been solved within the framework of the local linearization of the relationship between the geometric parameters and the gas-dynamic functions. The optimal fore-body has been determined by varying the shape of the cone with equivalent elongation, for which the approximation for the objective function (wave drag related with volume) has been determined on the basis of the known exact values of the flow parameters. Characteristic features of the optimal shape are bluntness of the nose across the front face and a smooth conjugation with closing cylinder for bodies with sufficiently large volume, the latter exceeding the value depending on the elongation and the Mach number. Comparison with the results of direct numerical optimization in the framework of Euler’s model has shown that the proposed analytical solution provides a near-minimum wave drag.

For the purpose of taking the internal degrees of freedom into account, threetemperature approximating model equations, which are a generalization of the R- and ES–BGKmodels, are proposed for a diatomic gas. The surface pressure, friction, and heat transfer coefficients are compared with the direct simulation Monte Carlo (DSMC) solution in the problem of flow past a cylinder in the super- and hypersonic flow regimes. The dependence of the surface coefficients on the rotational collision number is analyzed.

The supersonic (M∞ = 4.85) flow past a cylinder with a forward insertmade of a highlyporous cellular material is numerically modeled within the framework of the Reynolds-averaged Navier–Stokes equations. The air flow in the gas-permeable insert is described on the basis of a skeleton model of a highly-porous medium, whose determining parameters are the porosity coefficient (95%) and the pore dimensions (1 mm) of the actual cellular material. The aerodynamic drag coefficients of the model with different lengths of the porous forward insert are calculated on the unit Reynolds number range from 6.9 × 105 to 13.8 × 106 m−1. They are in agreement with the available experimental data, which indicates the adequacy of the proposed skeleton model in describing the actual properties of highly-porous materials.

The time-dependent mathematical model describing the vortex motion of an incompressible polymeric liquid is discussed. In the steady-state case certain particular solutions are found. In the case of the steady-state pressure along the axis of cylinder, a version of deriving this model for both fixed and free boundaries is given.

The problem of small perturbations of the equilibriumstate of a viscous, heat-conducting fluid in a cylindrical container with a deformable free upper boundary, on which heat exchange with the ambient medium is preassigned, is studied. The mathematical modeling of convection is based on Oberbeck–Boussinesq equations. The spectral problem thus obtained is solved using the tau method. As a result, the dependence of the imaginary part of the complex decrement on the Marangoni number is obtained. In the case of monotonic perturbations the neutral curves are plotted as functions of a geometrical parameter, namely, the cylinder height-to-radius ratio. The dependence of the Marangoni number on the physical parameters of the fluid is also obtained.

The fields of turbulent near-wall pressure fluctuations in the vicinities of cylindrical bodies mounted orthogonal to the surface in a flow are experimentally investigated. The considerable inhomogeneity and three-dimensionality of the pressure fluctuation field in the measurement area is shown. The dependence of the main characteristics of the inhomogeneous pressure fluctuation field on geometric parameters is presented. A weak influence of the boundary layer thickness and the obstacle height, when greater than the cylinder diameter, is demonstrated.

The results of an experimental investigation and calculations of the location of the minimum pressure point are presented for the case, when a cylindrical body moves along a wall in the presence of a small gap. The pressure on the cylindrical body surface is measured in the confusor and diffuser regions. It is shown that with decrease in the gap the minimum pressure point is displaced toward the minimum gap line, with increase in the pressure drop. An increase in the velocity of the motion at a constant gap leads only to a pressure increase in the diffuser region, while the location of the minimum pressure point remains the same. It is established that an increase in the inner cylinder radius moves the minimum pressure location away from the minimum gap line. The formation of two return flow regions in the confusor and diffuser regions near the cylindrical surface is detected. It is shown that the return flow in the pressure drop region reaches the stage of incipient cavitation bubbles. The results obtained can be useful in lubrication theory, as well as in medicine and biology.

A vortex structure consisting of two concentric vortex rings located in a circular cylinder is studied. The rings touch each other and have a uniform vorticity. The geometric and dynamic parameters of the rings satisfy the condition of zero total intensity. A linear stability analysis of this structure is performed, including the limiting cases when the inner ring transforms into a circle or the outer ring is adjacent to the boundary of the cylinder. The results of numerical simulation of the evolution of unsteady flows are presented for a wide range of variation of governing parameters of the problem. It is established that the evolution of unstable vortex flows results in the formation of several types of quasistationary structures, the topology of which depends mainly on the dominant disturbance mode.

Basing upon the ideal inviscid perfect gas model the aerodynamic characteristics and the gasdynamic function distributions over the surface of a cylinder in a steady supersonic three-dimensional flow are studied in the absence and the presence of combined intense air injection from the flat-ended nose and the lateral surface of the body into the shock layer. The purpose of the study is to investigate the influence of gas injection from different regions of the cylinder surface on supersonic flow past the cylinder at different angles of attack.

Three-dimensional laminar flows of a viscous conducting gas in the neighborhood of a rotating disk are considered. The simultaneous impact of an external magnetic field, suction from the disk surface, and the axial temperature gradient as well as the action of the external axial magnetic field on three-dimensional flows in the neighborhood of rigid permeable surfaces are first studied. An exact analytic solution of the system of the boundary layer equations is obtained. It is found that the direction of the radial flow initiated in the boundary layer can be varied by changing the temperature ratio in the external flow and on the disk for various Prandtl numbers Pr. An approximate solution of the problem of flow in the rotating cylinder in the presence of a retarding cover is constructed on the basis of the approach developed for extended disks.

The aerodynamic parameters and the pressure distribution over the surface of a cylinder in a steady axisymmetric supersonic flow is studied within the framework of the inviscid perfect gas model in the absence and the presence of combined intense air injection fromthe flat face and the lateral surface into the shock layer. The purpose of the study is to investigate the effect of gas blowing from different regions of the cylindrical surface on the supersonic axisymmetric flow past the body.

Within the framework of the magnetohydrodynamic approach, the rotational flow of an electrically conducting fluid within a rectangular circular dielectric cylinder in the presence of an asynchronously rotating upper end surface and external axial magnetic field B is investigated. The radial profiles of the azimuthal and axial medium velocity components inside the rotating volume bounded in the axial and radial directions are calculated approximately, using the analytical solutions of the system of nonlinear differentialMHD equations for boundary layers on an unbounded disk.

The results of an experimental investigation of cavitation in the case of the motion of a cylindrical body along a wall at a small gap are presented. The pressure measurements are performed in both confusor and diffuser regions of the cylinder surface. It is shown that under cavitation conditions the pressure in the cavitation region remains constant, does not depend on the cylinder velocity, and is determined by the pressure of the gases dissolved in the liquid. The pressure measurements in the cavitation region show that with decrease in the gap width the pressure drops to the value determined by the pressure of the gases dissolved in the liquid and then remains constant.

A visual investigation of the flow structure in the near wake behind a transverse cylinder in a fluctuating flow is carried out. The experiments were performed on a special setup, on wide ranges of the frequencies and amplitudes of superimposed fluctuations. Characteristic flow patterns are revealed and the corresponding wake flow structures are described. On the basis of the generalization of the information obtained the flow pattern map is constructed.

The results of solving the linear problem of steady-state oscillations of a horizontal cylinder submerged in fluid on whose upper boundary a semi-infinite elastic plate with free edge floats are given. The remaining part of the fluid surface is free. The contour-distributed mass source method is used. The corresponding Green's function is constructed using eigenfunction expansions. The hydrodynamic load and the amplitudes of vertical displacements of the free surface and elastic plate are calculated. Equivalence relations which demonstrate both symmetry of the apparent mass and damping factors and connection of the damping factors with the wave amplitudes in the far field are derived.

The problem of jet impingement on a wall of arbitrary configuration is studied. A curvilinear wall is approximated by a polygonal line with a fairly large number of links and a method based on the classical approach of Joukowski and Michell is applied to solve the problem. By successive displacement of the jet it is established that at a certain wall configuration the problem can have two solutions, one of which is multivalent. The limiting flow regimes characterized by the total disappearance of one of the jets formed after the division of the main impinging jet are revealed. An attempt to model the well-known experiment on the stable position of a small sphere lying on the horizontal bottom, when a slender water jet falls on it, is made. In the modeling the sphere is replaced by a circular cylinder in a separationless flow. It is numerically shown that any jet displacement to the right or to the left from the position corresponding to zero horizontal force acting on the cylinder leads to the generation of an oppositely directed nonzero force which indicates the absolute instability of the cylinder in the separationless jet flow.

Five basic flow regimes between coaxial cylinders are analyzed for a fluid with solidification effect. The dependences of the angular velocity of the inner cylinder on the torque applied to it are obtained. It is shown that this dependence does not increase monotonically. As the torque exceeds a certain critical value, the angular velocity decreases.

Exact analytical solutions of the problem of flow past a sphere and a cylinder in a porous medium are derived within the framework of the Brinkman equationwith the Navier boundary condition. Attention is drawn to the fact that the no-slip condition imposed on the interface between the porous medium and a solid, used, in particular, in the case of the Brinkman equation, must be in the general case replaced by a condition that admits nonzero flow velocity at the boundary.

The problem of non-uniqueness of steady-state modes of hypersonic flow past bodies with a cylindrical frontal bluntness is investigated using the direct numerical simulation by means of the “FLUENT” software. The principal aim of the study is to confirm the fact that three-dimensional wave structures developed on the frontal surface of bodies in a homogeneous hypersonic stream represent one of the steady-state modes of the solutions of the Navier-Stokes equations and do not result from the calculation grid roughness or the exciting action of the boundary conditions.

The study of rotating flows is of interest due to both the development of the centrifugal method of separation of gas and isotope mixtures and the possibility of astrophysical applications. An analytical nonlinear model for calculating the hydrodynamic characteristics of the viscous incompressible fluid flow in a rotating cylinder in the presence of a retarding cover is presented. The cases of stationary and rotating covers are considered. The analysis is performed on the basis of the system of hydrodynamic Navier-Stokes equations. The flow domain is divided up into the main flow and end boundary layers at the cylinder bottom and at the rotating cover. In its turn, the main flow is divided up into an inviscid quasi-rigid core and a lateral layer within which almost the entire upward circulatory flow is concentrated. The equations of the boundary layers at the end surfaces are analyzed by the approximate Slezkin-Targ method. The solutions in the boundary and lateral layers are “stitched” together with the velocity distribution in the main flow core. The unknown angular velocity ω1 and radial boundary R1 of the core are determined from the balance of the moments of the friction forces acting on the main rotating flow and the continuity condition for the circulatory flow. The experimental and calculated data are compared.

The behavior of a light spherical body in a rotating horizontal cylindrical cavity filled with a low-viscosity fluid is experimentally investigated both in the absence and in the presence of transverse vibrations. The system is in a centrifuged state. Mean rotation of the sphere relative to the cavity is found to exist. In the absence of the vibrations slow lagging rotation of the body is due to the gravity field. With increase in the cavity rotation velocity the intensity of differential rotation reduces. The vibrations lead to the excitation of differential rotation of the body, either anticipating or lagging, due to the resonance excitation of its inertial oscillations. The differential rotation of the body leads to the formation of the cylindrical Taylor-Proudman column. With increase in the column rotation velocity the instability of its boundary manifests itself as an azimuthal two-dimensional wave.

The oscillatory instability of advective conducting fluid flow in a horizontal circular cylinder in the presence of a rotating magnetic field is investigated. For Prandtl numbers Pr = 0 and 0.01 calculations showed that in both cases the monotonic instability observed in the absence of a field and in weak fields transforms into oscillatory instability at sufficiently large magnetic Taylor numbers. At Pr ≠ 0, oscillatory instability appears at substantially higher magnetic Taylor numbers.

The joint motion of an ideal fluid and a submerged circular cylinder is considered in the initial stage after an impact. The dynamics of separation points on the inner free boundary (cavity boundary) and the shapes of the inner and outer free boundaries of the fluid are determined. An asymptotic analysis of the inner free boundary near the separation points is made. The effects of the Froude number, the pressure difference, and the cylinder immersion depth are investigated.

Three-dimensional advective flows in a horizontal cylinder of square section are numerically investigated under thermally insulated lateral boundaries and in the presence of a uniform longitudinal temperature gradient. The flow structure is shown to considerably depend on the Grashof number, the channel length, and the Prandtl number; depending on these parameters, the flow symmetrymode and its temporal behavior may be different. It is established that different cases of transition to oscillatory flow regimes are possible, namely, either with a preliminary violation of the flow symmetry (fork bifurcation) or without a change in the type of symmetry. The parameter range on which only the fork bifurcation is observable, while oscillatory flow patterns do not appear, is also determined.

The behavior of a system of two immiscible isothermal fluids in a cylindrical reservoir under circularly polarized vibrations orthogonal to the cylinder axis is considered. The fluctuating flow is studied with account for dissipation in the near-interface vortex layer. Different mean flow generation mechanisms are discussed. It is shown that the main role in the generation is played by nonlinear processes in the near-interface boundary layer, which can be taken into accounted by applying effective boundary conditions. The mean flow structure and intensity are studied. The results obtained are compared with experimental data.

Thermocapillary flows in an infinitely long liquid cylinder surrounded by a coaxial gas layer with a controlled flow rate and the stability of such flows are investigated. In the layers a constant axial temperature gradient is maintained. An exact solution of the equations of motion describing the steady-state flow in this two-phase system is derived. Possible flow regimes and their stability in the linear approximation are studied. It is shown that in the liquid phase the thermocapillary flow can be completely stopped by the gas flow at the expense of the interaction between mechanical stresses at the interface. The results obtained indicate the possibility of controlling thermocapillary flows and their stability by means of gas flows.

The behavior of a light cylindrical body of circular cross-section under horizontal vibration in a rectangular cavity filled with a fluid is experimentally investigated. At critical vibration intensity the body is repelled from the upper side of the cavity and takes up a stable suspended position, in which the gravity field is balanced by the vibrational repulsive force, executing longitudinal oscillations. As the vibrations are intensified, the gap between the cylinder and the wall widens. A new form of instability, namely, the excitation of the tangential motion of the body along the vibration axis, is found to exist on the supercritical range. The cylinder is at a finite distance from the upper side of the cavity and the tangential motion is due to the loss of symmetry of the oscillating motion. The transition of the cylinder to the suspended state and its return to the wall, as well as the excitation of the average longitudinal motion and its cessation, occur thresholdwise and have a hysteresis. The body dynamics are studied as a function of the dimensionless vibration frequency.

A new mechanism of the formation of spatially periodic structures on the nose surfaces of cylindrically blunted bodies in a hypersonic transverse flow is investigated. According to this mechanism, a curved shock wave produces a vortex flow, while the vortex, which is conserved in the presence of weak dissipation, acts on the shock and maintains its curved shape. The realizability of this vortex formation mechanism is verified by direct numerical simulation using the FLUENT software package. It is confirmed that in the case of uniform hypersonic freestream both plane and three-dimensional modes of the steady flow past the cylinder nose can exist. The three-dimensional mode is characterized by periodic-in-span vortex structures and considerable heat flux peaks on the nose surface. The calculated results are compared with the experimental data.

For studying unsteady flow past a rotating circular cylinder the Navier-Stokes equations are used. The numerical algorithm is based on an artificial-compressibility method, an implicit three-layer second-order scheme with subiterations with respect to time, a third-order scheme with splitting of the flux vectors for the convective terms, and a central-difference scheme for integrating the viscous terms. The calculated velocity profiles, the vorticity fields, the Strouhal numbers, the distribution of the pressure and friction coefficients over the cylinder surface, and the coefficients of the drag and lift forces for the laminar flow regime are analyzed.

Two-dimensional viscous flow with a free surface in a horizontal cylinder rotating at a constant speed is investigated numerically using the boundary element method. It is shown that in the initial stage of rotation of the cylinder four different variants of the behavior of the free surface can be realized in the stage of transition from horizontal to steady-state form.

The flow of a hydrogen-oxygen mixture diluted with argon in a supersonic axisymmetric nozzle consisting of an inlet cylinder, a convergent region, a cylindrical throat, and a divergent region is considered. The supersonic flow enters the channel along the axis of symmetry. The flow structure is calculated with allowance for hydrogen ignition. A possibility of stabilizing the combustion zone is studied and the forces acting on the nozzle from the flow are determined. The problem is solved in the two-dimensional approximation with account for detailed combustion kinetics.

The method of nonlinear integral equations of the Hammerstein type is applied to numerically analyze the problem of the separating impact on an elliptic cylinder floating on the surface of an ideal incompressible finite-depth fluid. The bottom effect and the influence of the kinematic and geometric parameters on the zone of fluid particle separation from the cylinder surface are studied.