Numerical analysis of vortex cell efficiency in laminar and turbulent flows past a circular cylinder with embedded rotating bodies

The effect of flow intensification in small-sized vortex cells on the flow pattern in the near wake downstream of a cylinder and the cylinder drag in laminar and turbulent flows is analyzed on the basis of a numerical simulation of the two-dimensional steady-state flow past a circular cylinder with rotating cylindrical bodies built into the cylinder contour. St. Petersburg, Saratov. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 88–96, July–August, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (projects Nos. 99-01-01115 and 99-01-00772).     

Unsteady nonlinear problem of the horizontal motion of a contour under the interface between two liquids

A method of solving the initial boundary-value problem of the horizontal motion of a circular cylinder under the interface between two liquids is developed within the framework of nonlinear theory and implemented numerically. Profiles of generated waves and hydrodynamic loads are calculated for the problem of the acceleration of a circular cylinder under the free surface of a heavy liquid. The phenomenon of wave breaking is considered in detail. Omsk Department, Sobolev Institute of Mathematics, Siberian Division, Russian Academy of Sciences, Omsk 644099. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 37–43, May–June, 1999.     

Effect of surface and internal waves on the hydrodynamic characteristics of a contour in the linear approximation

A method of solving the problem of the motion of an elliptic contour in a three-layer fluid is developed within the framework of the linear theory. The results of calculating the hydrodynamic contour loads and the shape of the interfaces are presented for the following problems: the motion of a contour beneath an interface between two media and in a two-layer fluid both beneath a rigid lid and a free surface. On the basis of the numerical experiment it is concluded that surface and internal waves have a significant effect on the hydrodynamic characteristics of the contour. Omsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 121–127, May–June, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00093).     

Numerical modeling of the induced vorticity effect on the von Kàrmàn vortex street downstream of a circular cylinder

On the basis of a solution of the time-dependent Navier-Stokes equations on multiblock computational grids, the phenomenon of significant decay of the von Kàrmàn vortex street downstream of a circular cylinder owing to vorticity generation in passive and active vortex cells embedded in the cylinder contour is numerically analyzed. Feodosiya, Sankt-Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 68–74, March–April, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (projects Nos. 99-01-01115 and 99-01-00772).     

Kinetic model of a collisional admixture in dusty gas and its application to calculating flow past bodies

Using the methods of statistical physics, the basic kinetic equation describing the dynamics of a polydisperse admixture of solid particles in a dilute dusty-gas flow is derived. Particle rotation, inelastic collisions, and interaction with the carrier gas are taken into account. The basic kinetic equation is used to obtain a Boltzmann-type equation for the one-particle distribution function, for which the boundary conditions for the problem of dusty-gas flow past a body are formulated. On the basis of the kinetic model developed, using direct statistical modeling, the flow patterns and the fields of the dispersed-phase macroparameters in a uniform crosswise dusty-gas flow past a cylinder are obtained for various free-stream particle sizes and concentrations. Sankt-Peterburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 81–97, May–June, 2000. The work received financial support from the Russian Foundation for Basic Research (projects 96-01-01467 and 99-01-00674).     

On the motion of incompressible-medium particles in a domain with a periodically varying boundary

The motion of incompressible-medium particles in a cavity bounded by a plane bottom, vertical lateral walls, and a top boundary deformed in accordance with an arbitrary periodic law is investigated. The problem is reduced to solving the Hamilton equations with a time-periodic Hamiltonian. To study the system, the Hamilton system averaging method and the KAM (Kolmogorov, Arnold, Mozer) theory are used. A novel modification of the averaging procedure using the Poincaré point map is proposed. Correct to an exponentially small cavity boundary deformation amplitude, the Poincaré map points lie on the closed integral curves of an averaged autonomous Hamiltonian system. An asymptotic expansion of the averaged Hamiltonian in the amplitude is written down. The method is applied to the solution of the following problems: (i) the Stokes problem of mass transfer by a progressive wave on the surface of a heavy finite-depth fluid and (ii) the problems of particle motion in a thin layer of viscous or viscoplastic medium with a deformable boundary. For the case of finite amplitudes, qualitative agreement between the results of the asymptotic theory and the numerical calculations is obtained. The reasons for the appearance of a stochastic regime are discussed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 12–19, July–August, 2000. The work received financial support from the Russian Foundation for Basic Research (project 99-01-00250).     

Optimum clearance of a gas hydrostatic thrust bearing with maximum load capacity

The optimum design of a gas hydrostatic thrust bearing clearance is obtained using the methods of calculus of variations. The variational problem of determining the clearance shape giving the maximum load capacity is solved for a given external pressurization and various journal speeds. The structure of the optimum solution is found on the basis of the gas lubrication approximation with and without constraints on the height of the bearing pad (pocket). The calculation results embrace all possible values of the parameters. A comparison with optimum liquid bearings is carried out. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 68–78, July–August, 2000. The work was carried out with support from the Russian Foundation for Basic Research (projects Nos. 99-01-01211 and 96-15-96158).     

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.     

Perturbations on interfaces between media driven by the vertical ascent of a circular cylinder in a multilayer fluid

The initial-boundary value problem of the vertical ascent of a circular cylinder in a multilayer fluid is considered within the nonlinear theory. In each layer the fluid is ideal, incompressible, heavy, and homogeneous. At the initial instant of time the cylinder is located in the lower layer and begins smoothly to accelerate vertically from zero to a constant velocity. A system of integrodifferential equations of the problem is obtained. As unknowns, this system contains both the intensities of the singularities simulating the fluid and rigid boundaries and the functions describing the shape of the interface between the fluid media. The numerical solution of this system is based on two iteration processes, one of which is associated with time integration using the Runge-Kutta-Felberg scheme, while the other is associated with the solution of a system of linear algebraic equations obtained by discretization of the integral relations in each time step. The problem of the vertical ascent of a cylinder in a three-layer fluid (seawater, fresh water and air) is considered in detail. The results of calculating the perturbations of the fluid interfaces and the distributed and total hydrodynamic contour characteristics are given. The results obtained are compared with the solution of the problem of the ascent of a circular cylinder to the interface between water and air media. It is concluded that the third layer and the Froude number significantly affect the nature of the perturbations induced by the contour. Omsk, e-mail: gorlov@iitam.omsk.net.ru. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 153–159, March–April, 2000. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00093).     

Azimuthal wave motions on the surface of a rotating fluid cylinder

Wave motions in a fluid cylinder rotating about the axis are investigated within the framework of the linear theory. The cylinder is assumed to be fairly long. This makes it possible to restrict attention to the study of the plane oscillation pattern. The fluid is assumed to be ideal and incompressible. The models in which the fluid particles are confined by gravitational (body) or/and capillary forces (surface stress forces) are considered. A mode analysis is carried out and the dispersion relations are constructed. Traveling and steady-state waves on the surface of the fluid cylinder are investigated; qualitative effects ("wave inertia") are established. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 128–133, May–June, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00221). An erratum to this article is available at .     

Investigation of the velocity fluctuation spectrum of a vortex flow of vibrationally excited molecular gas in a glow discharge

The flow velocity fluctuations in a gas laser are measured under non-self-maintained glow discharge conditions. Spectra of the pulsating velocity signal on the frequency interval up to 2 kHz and the time dependence of the signal under glow and neutral flow conditions for pure nitrogen, a mixture of nitrogen and helium, and a trial CO₂-N₂-He mixture are obtained. Deformation (due to the action of the discharge) of the spectra of the transverse velocity component in the wake of a right circular cylinder is observed. In order to analyze the data obtained a model of the dynamic response of the pulsating velocity is constructed and a model of the Kármán vortex street behind a body is generalized with allowance for variations of the oscillation phase in the street. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 81–91, March–April, 2000. The work was carried out with partial financial support from the Russian Foundation for Basic Research (projects Nos. 96-01-00372 and 99-01-01199).     

Two-dimensional problem of a uniform flow of a two-layer fluid of finite depth past a circular cylinder

The linear steady problem of an irrotational uniform flow past a horizontal circular cylinder located in the upper or in the lower layer of a two-layer fluid is solved by the multipole-expansion method. The flow is perpendicular to the axis of the cylinder. The fluid is assumed to be inviscid and incompressible, and the flow in each layer is assumed to be potential. The upper layer can be bounded by a free surface or a solid lid, and the lower layer by a rigid horizontal bottom. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 91–101, November–December, 1998.     

Unsteady motion of an elliptic cylinder under a free surface

A problem of generation of nonlinear unsteady waves on the surface of an ideal liquid in an infinitely deep fluid due to the motion of a submerged elliptic cylinder is considered. The initial formulation of the problem is reduced to an integrodifferential system of equations for the function defining the free surface shape and for the normal and tangential components of velocity on the free surface. The small-time asymptotics of the solution is constructed for the case of cylinder motion with a constant acceleration from the state at rest.     

Nonstationary deformation processes in a multilayer cylinder

The problem of the pulsed loading of a multilayer cylinder has been solved. The simulation is based on the linear elastic theory for homogeneous and isotropic substances. The manner in which the problem is solved guarantees exact fulfillment of motion equations and systems of initial and boundary conditions. The numerical results presented show the wave pattern of the deformation of the inside surface of a multilayer cylinder, and describe the strain state of this cylinder. A. M. Podgornyi Institute of Machine-Building Problems, National Academy of Sciences of Ukraine, Khar'kov, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 8, pp. 10–17, August, 1999.     

Observation of standing waves of large amplitude in harmonic Faraday resonance

Stationary two-dimensional gravity waves on the free surface of a homogeneous fluid in a rectangular vessel in the presence of vertical oscillations excited in harmonic Faraday resonance with identical frequencies are investigated. For the second mode, the dependence of the amplitude on the excitation frequency is found and the wave profiles are obtained. The experimental results are compared with the theoretical model. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 185–188, January–February, 2000. The work was supported by the Russian Foundation for Basic Research (project No. 99-01-01080) and CONACYT (Mexico, Catedra Patrimonial, S. Ya. Sekerzh-Zen’kovich, Ref. 489100-2, Exp. 950060).     

Nonlinear problem of a steady-state flow of a weighable liquid bounded by a free surface about a system of vortices

The problem of a fluid flow with a free surface about a system of two vortices of opposite intensity is considered within the framework of the nonlinear theory. The range of parameters of the problem in which there is no stationary solution is found. Results of the numerical experiment on the effect of vortex intensities and the Froude number on the shape of the free surface and the hydrodynamic reactions of the singularities are given. Omsk Department of the Sobolev Institute of Mathematics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 63–68, November–December, 1999.     

Features of how surface waves form in a cylinder made of a hard material and filled with a fluid

The properties of harmonic surface waves in an elastic cylinder made of a rigid material and filled with a fluid are studied. The problem is solved using the dynamic equations of elasticity and the equations of motion of a perfect compressible fluid. It is shown that two surface (Stoneley and Rayleigh) waves exist in this waveguide system. The first normal wave generates a Stoneley wave on the inner surface of the cylinder. If the material is rigid, no normal wave exists to transform into a Rayleigh wave. The Rayleigh wave on the outer surface forms on certain sections of different dispersion curves. The kinematic and energy characteristics of surface waves are analyzed. As the wave number increases, the phase velocities of all normal waves, except the first one, tend to the sonic velocity in the fluid from above __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 48–62, September 2007.     

Energy analysis of development of kinematic perturbations in weakly inhomogeneous viscous fluids

The deformation stability relative to small perturbations is analyzed for weakly inhomogeneous viscous media on the assumption that both the main flow and perturbation field are three-dimensional. To test the damping or growth of initial perturbations, sufficient estimates based on the use of variational inequalities in different function spaces (energy estimates) are obtained. The choice of function space determines the measures of the parameter deviations, which may be different for the initial and current parameters. The unperturbed process chosen is a fairly arbitrary unsteady flow of homogeneous incompressible viscous fluid in a three-dimensional region of Eulerian space. At the initial instant, not only the kinematics of the motion but also the density and viscosity of the fluid are disturbed and the medium is therefore called weakly inhomogeneous. On the basis of the integral relation methods developed in recent years, sufficient integral estimates are obtained for lack of perturbation growth in the mean-square sense (in theL ₂ space measure). The rate of growth or damping of the kinematic perturbations depends linearly on the initial variations of the kinematics, density and viscosity. Illustrations of the general result are given. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 56–67, March–April, 2000. The work was supported by the Russian Foundation for Basic Research (projects No. 99-01-00125 and No. 99-01-00250) and by the Federal Special “Integration” Program (project No. 426).     

Natural convection from a cylinder in a narrow gap and in a porous medium

The problem of natural convection from a horizontal cylinder in a narrow gap and in a porous medium is solved both theoretically and experimentally. An integral method for calculating heat transfer from the cylinder for constant flux on its surface was suggested. Numerical analysis clarified the role of regime and geometrical factors. It is shown that natural convection from a cylinder in a porous medium can be modeled by a Hele Shaw cell. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 140–150. January–February, 1999.     

Nonlinear problem of a circular cylinder rising vertically to an interface between liquid media

The nonlinear initial-boundary-value problem of a contour approaching an interface between two liquid media is considered. A solution is constructed using a previously developed numerical method that is based on reducing the original problem to a system of integrodifferential equations for singularities simulating liquid and rigid boundaries and a function that describes the interface between the media. Calculation results for the perturbations generated by a circular cylinder approaching a free surface are presented. The dependences of the flows obtained and the hydrodynamic characteristics of the contour on the Froude number are estimated. Omsk Branch of the Sobolev Institute of Mathematics, Siberian Division, Russian Academy of Sciences, Omsk 644099. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 84–89, March–April, 2000.