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.     

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).     

Linear problem of a hydrofoil moving under the free surface of a finite-depth fluid

A method of solving the plane linear problem of a steady-state irrotational flow about a body under the free surface of a heavy fluid of finite depth is developed. The boundary-value problem is formulated for a complex perturbed velocity and is reduced to a singular integral equation relative to the intensity of a vortex layer that models the hydrofoil. The kernel of the equation is the exact solution of the corresponding boundary-value problem for a vortex of unit intensity. The equation is solved by the discrete-vortex method. The effect of the parameters of the problem on the hydrodynamic characteristics of the elliptical hydrofoil and the shape of the free surface are estimated numerically. Omsk Division of the Sobolev Institute of Mathematics, Omsk 644099. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 85–90, November–December, 1998.     

Exact solution of the problem of convective heat exchange for a circular cylinder at small Prandtl numbers

The problem of the heat exchange of a circular cylinder in an incompressible flow at small Prandtl numbers Pr ≪ 1 is solved. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 43–48, January–February, 1994.     

Motion of a cylinder below the free surface of a fluid at large froude numbers

A method of solving the problem of the motion of a cylinder of given shape below the free surface of an infinitely deep heavy fluid is perfected for large Froude numbers. The motion of a circular cylinder is investigated at small distances from the free surface. Solutions of the problem are given for cylinders with noncircular cross-sections. Kazan. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 34–45, July–August, 2000. The work was carried out with financial support from the Russian Foundation for Basic Research (projects Nos. 99-01-00169 and 99-01-00173).     

On the stability and extension of reduced-order Galerkin models in incompressible flows

Proper orthogonal decomposition (POD) has been used to develop a reduced-order model of the hydrodynamic forces acting on a circular cylinder. Direct numerical simulations of the incompressible Navier–Stokes equations have been performed using a parallel computational fluid dynamics (CFD) code to simulate the flow past a circular cylinder. Snapshots of the velocity and pressure fields are used to calculate the divergence-free velocity and pressure modes, respectively. We use the dominant of these velocity POD modes (a small number of eigenfunctions or modes) in a Galerkin procedure to project the Navier–Stokes equations onto a low-dimensional space, thereby reducing the distributed-parameter problem into a finite-dimensional nonlinear dynamical system in time. The solution of the reduced dynamical system is a limit cycle corresponding to vortex shedding. We investigate the stability of the limit cycle by using long-time integration and propose to use a shooting technique to home on the system limit cycle. We obtain the pressure-Poisson equation by taking the divergence of the Navier–Stokes equation and then projecting it onto the pressure POD modes. The pressure is then decomposed into lift and drag components and compared with the CFD results.     

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.     

Motion of an airfoil near a flat screen

Omsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 1, pp. 47–52, January–February, 1995.     

Solving the stress problem for solid cylinders with different end conditions

The paper proposes an approach to solving a spatial stress problem for solid circular cylinders under axisymmetric surface loading. Two types of boundary conditions at the ends are examined: simply supported or clamped. The circumferential variable is separated using Fourier series for the former type of boundary conditions, and spline-approximation in longitudinal coordinate is used for the latter type of boundary conditions. The resulting one-dimensional problems are solved by the stable discrete-orthogonalization method, evaluating indeterminate forms on the cylinder axis in the governing equations. Radial displacements and circumferential and longitudinal stresses are plotted __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 6, pp. 24–31, June 2006.     

New exact solution of the problem of rotationally symmetric Couette-Poiseuille flow

An exact solution is obtained for the problem of steady-state viscous incompressible flow under a pressure difference in the gap between coaxial cylinders for the case where the inner cylinder rotates at a constant angular velocity. The solution differs from the classical Couette-Poiseuille result by the presence of radial mass transfer, which provides for interaction between the poloidal and azimuthal circulations. The flow rate is found to depend linearly on the angular velocity of rotation of the inner cylinder. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 71–77, September–October, 2007.     

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.     

Molecular approach in linear polymer dynamics: Theory and numerical experiment

A constitutive equation for polymer solutions and melts is obtained on the basis of the dynamics of noninteracting dumbbells moving in a nonlinear anisotropic fluid. The equation obtained is used to describe nonlinear effects under conditions of simple shear and steady-state flow in a circular tube and for the numerical investigation of a flow in a finite cylinder with a rotating end face. Barnaul. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 3–13, January–February, 2000.     

Quasi-cylindrical figures of equilibrium of a rotating fluid

The problem of the equilibrium shape of a steady rotating rectilinear infinite cord of ideal self-gravitating homogeneous fluid is considered. The question whether, apart from the obvious solution, namely, an infinite circular cylinder, noncylindrical equilibrium figures can exist is investigated. A search is carried out among axisymmetric figures with periodic surface structure (“wavy” cylinders). The period of the wave structure and, in the first approximation, the shape of the surface are found as functions of the angular velocity of rotation. Sankt-Peterburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 22–30, May–June, 2000.     

Hydrodynamic characteristics of a vortex source performing translational motion in a multilayer heavy fluid

The problem of translational motion of a vortex source in a three-layer fluid bounded by a bottom from below is considered. The fluid in each layer is perfect, incompressible, heavy, and homogeneous. Based on the previously developed method, formulas for disturbed complex velocities of the fluid in each layer and the wave drag and lift force of the vortex source are obtained. The vortex motion is considered near the interface of two semi-infinite fluid media and in a two-layer fluid with different conditions at the boundary. In all cases, the hydrodynamic characteristics of the vortex source are given as functions of the Froude number. In a number of problems, these characteristics have discontinuities at the transition through the critical Froude numbers. The character of these discontinuities is studied analytically. Omsk Department of Sobolev Institute of Mathematics, Siberian Division, Russian Academy of Sciences, Omsk 644099. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 140–146, September–October, 2000.     

Experimental Study of the Dynamic Effect of an Internal Solitary Wave on a Submerged Circular Cylinder

The hydrodynamic loads due to the interaction of a small-amplitude internal solitary wave with a submerged circular cylinder in a two-layer system of miscible fluids were studied experimentally. The dependence of the internal-wave transmission coefficient on the position of the center of the cylinder relative to the pycnocline and on the ratio of the cylinder diameter to the fluid-layer thickness was obtained. The effects of the pycnocline thickness and the depth of the center of the cylinder on the value of the hydrodynamic loads were studied. Visualization of the flow structure was performed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 36–44, November–December, 2005.     

Specific features of the nonlinearly elastic behavior of cylindrical compressible bodies in torsion

The torsion problem of a cylinder with a circular transverse cross section twisted by end moments that are equal in magnitude and opposite in direction is considered for various models of nonlinearly elastic compressible media. The problem is solved by the semi-inverse method of elasticity theory. The Poynting effect, which consists of variation in the length of a shaft in torsion, is treated qualitatively and quantitatively. The results of the numerical and asymptotic (only terms that are quadratic relative to the displacement gradient are conserved) solutions for various models of the nonlinearly elastic behavior of materials are compared. An analysis of the results shows that in some cases, the quasilinear model is not applicable for studying the behavior of nonlinearly elastic compressible media. Rostov State Construction University, Rostov-on-Don 344022. Rostov State University, Rostov-on-Don 344090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 188–193, March–April, 2000.     

Nonstationary radial electroelastic vibrations of a piezoceramic cylinder under mechanical loading

The radial nonstationary vibrations of a piezoceramic cylinder polarized across the thickness and subjected to mechanical dynamic loading are studied. To solve the initial–boundary-value problem, mesh approximations and difference schemes are used. The electromechanical state of the cylinder under an instantaneously applied constant force is analyzed in detail     

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).     

Investigation of the flow around a circular cylinder under the influence of an electromagnetic force

An investigation of the effect of the local electromagnetic body force on the flow behavior around a circular cylinder is conducted. The electromagnetic force is applied locally on the cylinder surface in the range of 70–130° from the stagnation point along the cylinder circumference in both clockwise and counterclockwise directions. The numerical results predict that the Lorentz force applied in the circumferential direction on the cylinder moves the separation point rearward, and reduces the drag. To validate the numerical results, an experiment is conducted with a circular cylinder of 5 cm diameter. The electrodes and permanent magnets are flush mounted on the cylinder in such a way that the Lorentz force is generated in the circumferential direction. Flow visualization with polystyrene particles and direct drag measurement using strain gages are made. The fluid used is natural sea water of electric conductivity of about 4 (Ω m)^-1. Induction effect can be neglected in the present investigation due to the low flow speed and the Lorentz force is proportional to E×B where E is an applied electric field and B is a magnetic field. Received: 7 June 1998/Accepted: 28 April 1999     

Buckling of cylinders with cutouts under axial compression

An experimental study was carried out to clarify the effects of circular holes on the buckling of circular cylinders under axial compression. The effect of reinforcements was also examined by placing thin annular plates around the cutouts. Tests were performed on polyester shells with radius-to-thickness ratio of 400 and 100 and with two diametrically opposed circular holes. If a hole is small enough, there are no appreciable effects on the buckling strength of the cylinder. However larger cutouts result in a significant reduction of the buckling load. When doublers are placed around the holes, the buckling load approaches the value for the complete cylinder with no cutouts as the stiffening volume increases. Paper was presented at the 1982 SESA-JSME Joint Conference held in Oahu and Maui, HI on May 23–30, 1982.