Viscous flow in a partially-filled horizontal cylinder rotating at constant speed

The problem under consideration is that of the stationary shape of the free surface of a viscous fluid in a steadily rotating horizontal cylinder. In the majority of investigations of this problem the thickness of the fluid layer coating the inner surface of the cylinder is assumed to be small [1–3]. The case of a near-horizontal free surface, with the bulk of the fluid at the cylinder bottom, was considered in [4], where, after considerable simplification, the governing equations were reduced to ordinary differential equations. In the present study the behavior of the free surface is investigated using a creeping flow approximation. The controlling parameters vary over a wide range. In the numerical computations a boundary element method was used. The numerical results have been confirmed experimentally.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 25–30, May–June, 1993.     

Drag of porous cylinders in a viscous fluid at low reynolds numbers

The problem of flow past a permeable cylinder at low Reynolds numbers is of interest for the solution of a number of problems in chemical technology in, for example, the design of porous electrodes and porous catalysts and in the calculation of nonstationary filtration of aerosols by fibrous filters. In the present paper, we solve the problem of transverse flow of a viscous fluid past a continuous cylinder in a porous shell and, in particular, in the case of a porous cylinder under conditions of constrained flow (system of cylinders) and an isolated cylinder at arbitrary permeability. The analogous problem of Stokes flow past permeable spheres has been solved in a number of papers [1–3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 122–124, November–December, 1979.     

Establishment of circumfluence (steady-state flow) when a shock wave strikes a cylinder or a sphere

The problem of the diffraction of a shock wave at a stationary sphere or cylinder is considered. The finite-difference method proposed by S. K. Godunov [1, 2] is employed Numerical solutions are obtained for the stage of the diffraction of the shock wave and for the subsequent steady state of flow around the object (circumfluence). Cases of sub-, trans-, and supersonic flow behind the shock wave are considered. When strong shock waves undergo diffraction, zones of reverse flow appear in the neighborhood of the tail part of the obstacle.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 97–103, September–October, 1972.     

Optimization of suction-blowing in a viscous fluid

The problem of drag minimization in a viscous fluid by means of controlled suction (blowing) is considered. In the low Reynolds number approximation matched asymptotic expansions are used to construct the second approximation and analytic solutions of the optimization problem are found for a sphere and a circular cylinder. Transition from unseparated to separated flow is accompanied by a qualitative restructuring of the optimal solution.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 27–32, May–June, 1989.     

Circulating rarefied gas flow in a rotating cylinder with a stationary upper end face

In order to analyze the intensity of the circulating flow in the rarefaction zone near the axis of a rapidly rotating cylinder, the problem of gas flow in a cylinder with a stationary upper end face is solved for intermediate Knudsen numbers by the direct statistical modeling method. The effect of the rarefaction of the gas on the intensity of the secondary flow is investigated. The contribution of the self-excited thermal circulation of the gas to the total circulating flow is analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 186–188, May–June, 1990.     

Plane problem of uniform flow of a two-layer fluid past a circular cylinder

An explicit solution is found for the problem of uniform horizontal flow of a two-layer fluid of infinite depth past a circular cylinder. The cylinder axis is perpendicular to the flow. The problem is solved within a linear formulation. The solution of the problem is expressed in the form of rapidly converging series with coefficients determined from a recurrence relation. The first seven terms of the series yield the values of the hydrodynamic loads with a relative accuracy of 10^–6. The results are in good agreement with the known values for similar problems in a homogeneous fluid. Tables of the lift and wave drag are given for homogeneous and two-layer fluids.Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 91–97, January–February, 1996.     

Detached flows past a cylinder with a flat end

In the framework of the Navier-Stokes equations, a numerical solution is found to the problem of longitudinal (axisymmetric) flow of a viscous perfect heat conducting gas past a cylinder with a flat front end at subsonic and transonic velocities of the oncoming flow. The flow in the neighborhood of the corner of the cylinder is investigated and a study made of the occurrence and development of detached flow along the side of the cylinder. Tie heat fluxes to the surface of the cylinder are determined, and the influence of the temperature of the wall of the cylinder on the development of the separation is found. The investigations yield the critical Reynolds number Re₀ for the occurrence of a detached flow as a function of the Mach number of the oncoming flow for the investigated bodies.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 3–10, March–April, 1979.I am grateful to Yu. A. Dem'yanov for discussing the work and for a number of valuable comments.     

Direct Statistical Simulation of a Supersonic Flow of a Binary Mixture of Rarefied Gases around a Transversely Positioned Cylinder

A supersonic flow of a binary mixture of gases in a wide range of rarefaction (from a flow with a Knudsen number K _n = 0.1 to a free-molecular flow) around a cylinder is studied by means of direct statistical Monte Carlo simulations (DSMC method). The influence of a small fraction of heavy particles in a light gas flow on the region of significant nonequilibrium near the cylinder and on the heat flux is considered.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 53–59, September–October, 2005.     

Transverse subsonic flow past a cylinder

At around the critical Reynolds number Re = (1.5–4.0)·10⁵ there is an abrupt change in the pattern of transverse subsonic flow past a circular cylinder, and the drag coefficient C_x decreases sharply [1]. A large body of both experimental and computational investigations has now been made into subsonic flow past a cylinder [1–4]. A significant contribution to a deeper understanding of the phenomenon was made by [4], which gives a physical interpretation of a number of theoretical and experimental results obtained in a wide range of Re. Nevertheless, the complicated nonstationary nature of flow past a cylinder with separation and the occurrence of three-dimensional flows when two-dimensional flow is simulated in wind tunnels do not permit one to regard the problem as fully studied. The aim of the present work was to make additional experimental investigations into transverse subsonic flow past a cylinder and, in particular, to study the possible asymmetric stable flow regimes near the critical Reynolds number.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 154–157, March–April, 1980.     

A class of exact solutions of a nonlinear boundary-value problem for fluid flow in a rotating cylinder

The flow of an ideal incompressible weightless fluid that fills a rotating cylinder is investigated. The rotation axis of the cylinder is outside it and parallel to the cylinder generator, and the form of the cylinder section is determined in the process of solution of the problem. In the paper, a class of exact solutions of the problem is obtained in terms of elementary functions for different angular velocities of the cylinder. In these solutions, the flow field is formed by two straight vortex filaments parallel to the cylinder generator. The intensities of the vortex filaments are determined by the angular velocity . Investigations of ideal fluid flow in rotating vessels were begun already in the last century by Stokes and Zhukovskii [1]. The subject has been reviewed in monographs [2, 3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No, 1, pp. 71–75, January–February, 1984.     

Numerical investigation of separated flow in front of a spiked cylinder

The problem of axisymmetric flow of a perfect heat conducting gas over a cylinder from the front of which a spike projects is solved at subsonic and supersonic velocities of the oncoming flow in the model of a viscous fluid. The formation and development of the flow separation due to the spike ahead of the front surface of the cylinder is investigated. The change in the gas-dynamic and geometrical parameters of the separated flow is studied as a function of the Mach and Reynolds numbers of the oncoming flow. The obtained results are compared with the available experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 162–166, October–December, 1981.     

Translational motion of a cylinder below the free surface of a fluid

A method of solving the problem of the translational motion of a cylinder of given shape below the free surface of an infinitely deep heavy fluid is developed. As distinct from existing techniques, the method permits the obtaining of a solution which becomes exact as the Froude number increases without bound. The solution of the problem of the motion of a circular cylinder is considered in detail. Suggestions are made concerning the characteristic properties of an exact solution of the general problem.Kazan'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 9–22, November–December, 1996.     

Interaction of an internal gravity current with a submerged circular cylinder

The problem of hydrodynamic loads due to the interaction of a gravity current propagating over a bottom channel with a submerged circular cylinder is studied experimentally. It was shown that in the examined range of parameters, the hydrodynamic loads are simulated after Froude. The hydrodynamic loads are maximal if the cylinder lies on the bottom, and they decrease rapidly with increase in the distance from the cylinder to the channel bottom. The effects of mixing and entrainment on the nature of the hydrodynamic loads are considered.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 81–90, March–April, 2005.     

Influence of general rotation on the transfer of torsional vibrations through axisymmetric layers of viscous liquid

A study is made of the motion of a viscous incompressible liquid in a gap between a cylinder of finite length and a jacket that contains it. The motion is due to small torsional vibrations of the jacket, whereas the complete system rotates uniformly around the common symmetry axis. The equation is linearized under the assumption that the Rossby number is small. Three problems are considered: the one-dimensional problem of vibrational motion in the cylindrical gap, the self-similar problem for the flow in the end interdisk gaps, and the two-dimensional problem that describes the flow in the corner region. It is established that the superposition of the general rotation makes the damping properties of the liquid layers between the jacket and the ends of the cylinder much less good. The influence of boundary effects is clarified.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 26–31, May–June, 1991.     

Some problems of centrally symmetrical percolation of a gas

A solution is considered for the centrally symmetrical problem of unsteady inflow of gas to a stratum sampler on a logging cable in a thick stratum with constant pressure at the discharge and variable pressure when filling the closed cylinder of the sampler with gas.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 117–121, November–December, 1971.     

Diffusion toward a cylinder in the case of an arbitrary viscous flow. Diffusive boundary layer approximation

Steady convective diffusion of a dissolved substance toward the surface of a cylinder (optionally circular) in a viscous flow is examined. An analytical solution is obtained in [1, 2] for the case of laminar flow around a curved cylinder when the freestream flow is straight and uniform. More complex hydrodynamical problems are examined in [3, 4]. In the present work an approximate analytical expression is obtained for diffusive flow of a substance toward the surface of a solid cylinder in the case of an arbitrary two-dimensional flow. Formulas are given for calculating the mass transfer at a circular cylinder in some shear flows of a viscous, incompressible fluid.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 163–166, September–October, 1976.The authors thank Yu. P. Gupalo and Yu. S. Ryazantseva for formulating the problem and their attention to the work.     

Magnetic fluid motion driven by a high-frequency rotating magnetic field

The problem of the circulating flow of a nonisothermal magnetic fluid in a long vertical cylinder placed in a rotating magnetic field is solved in the weak vorticity approximation.Perm'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 18–22, January–February, 1996.     

Cavitation flow around a plate in a channel by a stream of heavy liquid

The nonlinear problem of cavitation flow around a plate by a stream of heavy liquid is investigated in precise formulation; the plate is located on the horizontal floor of a channel when the gravity vector is directed perpendicular to the wall of the channel. Two flow systems are considered-Ryabushinskii's and Kuznetsov's system [1]. This problem was investigated in linear formulation in [2], Similar problems were considered earlier in [3–7] for unrestricted flow. Below, on the basis of a method proposed by Birkhoff [8, 9], all the principal hydrodynamic and geometric characteristics are calculated for the problem being considered.Translated from Ivestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 3, pp. 3–9, May–June, 1973.     

Charging of disperse particles in two-phase media with unipolar charge

Charging of disperse particles with good conduction in two-phase media with unipolar charge is considered in the case when the volume concentration of the particles is low. For this, in the framework of electrohydro-dynamics [1, 2], a study is made of the charge of one perfectly conducting liquid particle in a gas (or liquid) with unipolar charge in a fairly strong electric field. The influence of the inertial and electric forces on the motion of the gas is ignored, and the velocities are found by solving the Hadamard—Rybczynski problem. We consider the axisymmetric case when the gas velocity and electric field intensity far from the particle are parallel to a straight line. The analogous problem for a solid spherical particle was solved in [3–6] (in [3], the relative motion of the gas was ignored, while in [4–6] Stokes flow around the particle was considered). The two-dimensional problem of the charge of a solid circular, perfectly conducting cylinder in an irrotational flow of gas with unipolar charge was studied in [7].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 108–115, November–December, 1980.We thank L. I. Sedov and V. V. Gogosov for a helpful discussion of the present work.     

Thermoelastic Contact of a Shroud Ring and a Cylinder under Unsteady Friction-Induced Heat Release

Mathematical formulation is performed and a solution is found for a quasi-static thermoelastic problem of contact interaction of an elastic shroud ring and a hollow circular cylinder inserted into this ring, which are compressed by a load varied along the axis of the system, under the condition of an unloaded contact over the ring surface or over the circumference contour. The radial displacements of the contact surface of the shroud ring are approximated by displacements of the surface of a long circular hollow cylinder. Unsteady friction-induced heat release caused by the action of friction forces owing to shroud ring rotation over the cylinder with a time-dependent low angular velocity is taken into account. The problem is reduced to a system of integral equations whose structure is determined by the form of thermophysical contact conditions. A numerical algorithm of the solution is proposed, and the influence of the problem parameters on the contact pressure and temperature distributions is considered. Based on an analysis of results, a conclusion is made that the character of axial variation of the compressing load has a significant effect on the distribution of contact pressure in describing the kinematic condition of interaction of bodies in accordance with Hertz’s theory.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 4, pp. 161–178, July– August, 2005.