Simulation of the instability of axisymmetric vortices using the contour dynamics method

The two-dimensional problem of the stability of the circular motion of an ideal incompressible fluid with given radial vorticity distribution is studied.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 33–39, January–February, 1985.     

Quasi-three-dimensional calculation of flow in blade passages of turbines

The flow in turbomachines is currently calculated either on the basis of a single successive solution of an axisymmetric problem (see, for example, [1-A]) and the problem of flow past cascades of blades in a layer of variable thickness [1, 5], or by solution of a quasi-three-dimensional problem [6–8], or on the basis of three-dimensional models of the motion [9–11]. In this paper, we derive equations of a three-dimensional model of the flow of an ideal incompressible fluid for an arbitrary curvilinear system of coordinates based on averaging the equations of motion in the Gromek–Lamb form in the azimuthal direction; the pulsation terms are taken into account in the equations of the quasi-three-dimensional motion. An algorithm for numerical solution of the problem is described. The results of calculations are given and compared with experimental data for flows in the blade passages of an axial pump and a rotating-blade turbine. The obtained results are analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 69–76, March–April, 1991.I thank A. I. Kuzin and A. V. Gol'din for supplying the results of the experimental investigations.     

Influence of an acoustic wave on a system of two spheres in a viscous fluid

In this article we formulate and solve the problem of the influence of radiation forces (forces created by the radiation pressure) on two spheres in a viscous fluid during the transmission of an acoustic wave. On the basis of these forces we investigate the nature of the interaction between the spheres as determined by the mutual disturbance of the flow fields around them as a result of interference between the primary and secondary waves reflected from the spheres. A previously proposed [2] approach is used in the investigations. The radiation force acting on one of the spheres is filtered by averaging the convolution of the stress tensor in the fluid with the unit normal to the surface of the sphere over a time interval and over the surface of the sphere. The stresses in the fluid are represented, to within second-order quantities in the parameters of the wave field, in terms of the velocity potentials obtained from the solution of the linear problem of the diffraction of the primary wave by the free spheres. The diffraction problem is formulated and solved within the framework of the theory of linear viscoelastic solids [6]. The case of an ideal fluid has been studied previously [3–5, 7]. Radiation forces are one of the causes of the relative drift of solid particles situated in a fluid in an acoustic field.S. P. Timoshenko Institute of Mechanics, Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 2, pp. 33–40, February, 1994.     

Internal waves generated in an exponentially stratified fluid by an arbitrarily moving source

A theoretical investigation is made into the development of linear internal waves in an exponentially stratified flow of an ideal incompressible fluid in the Boussinesq approximation. The waves are generated by an arbitrarily moving point mass source. The obtained solution is used to investigate three special cases of motion: uniform motion at an angle to the horizontal, nonstationary motion during a finite interval of time, and uniform motion in a circular path. The method of solution of this problem is similar to that used by Wolfe and Lewis [1], who studied the generation of acoustic waves.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 67–74, May–June, 1980.I thank V. V. Sazonov for assistance in the calculations.     

Impact of a figure of revolution in a stream of incompressible fluid with separation of a jet

The impact interaction of bodies with a fluid in a flow with jet separation has been considered in [1–3], for example. This investigation was in the two-dimensional formulation. The present paper considers the three-dimensional problem of impact of a figure of revolution in a stream of an ideal incompressible fluid with separation of a jet in accordance with Kirchhoff's scheme. A boundary-value problem is formulated for the impact flow potential and solved by the Green's function method. A method for constructing the Green's function is described. Expressions are given for the coefficients of the apparent masses. The results are given of computer calculations of these coefficients in the case of a cone using the flow geometry of the corresponding two-dimensional problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 176–180, November–December, 1980.     

Force acting on a deformable contour moving in an arbitary fluid stream

A solution is given for the plane nonstationary motion of an arbitary deformable contour in the potential flow of an ideal incompressible fluid. The problem was solved by conformal mapping. A simple formula is obtained for the force acting on a small size contour.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 4–8, January–February, 1973.The author is grateful to L. I. Sedov and Yu. L. Yakimov for formulating the problem and supervising the research.     

Motion of a spherical solid particle in a nonuniform flow of a viscous incompressible liquid

The effect of a particle on the basic flow is studied, and the equations of motion of the particle are formulated. The problem is solved in the Stokes approximation with an accuracy up to the cube of the ratio of the radius of the sphere to the distance from the center of the sphere to peculiarities in the basic flow. An analogous problem concerning the motion of a sphere in a nonuniform flow of an ideal liquid has been discussed in [1]. We note that the solution is known in the case of flow around two spheres by a uniform flow of a viscous incompressible liquid [2], and we also note the papers [3, 4] on the motion of a small particle in a cylindrical tube.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 71–74, July–August, 1976.     

Unsteady motion of a profile near a wavy shield

The investigation of the motion of a profile near a plane shield and near a wavy shield is one of the ways of approximately taking into account the effect of the surface of a fluid on the characteristics of surface wings. The steady-state characteristics of the profiles near a plane shield have been investigated in a number of theoretical and experimental studies [1, 2]. In the present study we consider the unsteady motion of a thin profile near plane and wavy shields in an ideal incompressible fluid at rest at infinity, and when there is a fluid flow.Translated from Izvestiya Akadeinii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 3, pp. 10–16, May–June, 1973.     

Solution of a problem of flow in a porous medium with limiting gradient

For the law of flow in a porous medium with limiting gradient studied previously in [1], an exact solution is found for the problem formulated in [2] of the plane steady motion of an incompressible fluid in a channel with a rectangular step. Particular cases of the solution obtained are given; these represent the solutions of the problem of flow past a broken wall and of motion from a point source in a strip.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 76–78, January–February, 1985.     

Rayleigh stability of shear flow in relaxing media

The stability of steady-state flow is considered in a medium with a nonlocal coupling between pressure and density. The equations for perturbations in such a medium are derived in the linear approximation. The results of numerical integration are given for shear motion. The stability of parallel layered flow in an inviscid homogeneous fluid has been studied for a hundred years. The mathematics for investigating an inviscid instability has been developed, and it has been given a physical interpretation. The first important results in flow stability of an incompressible fluid were obtained in the papers of Helmholtz, Rayleigh, and Kelvin [1] in the last century. Heisenberg [2] worked on this problem in the 1920's, and a series of interesting papers by Tollmien [3] appeared subsequently. Apparently one of the first problems in the stability of a compressible fluid was solved by Landau [4]. The first investigations on the boundary-layer stability of an ideal gas were carried out by Lees and Lin [5], and Dunn and Lin [6]. Mention should be made of a series of papers which have appeared quite recently [7–9]. In all the papers mentioned flow stability is investigated in the framework of classical single-phase hydrodynamics. Meanwhile, in recent years, the processes by which perturbations propagate in media with relaxation have been intensively studied [10–12].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 87–93, May–June, 1976.     

Separationless flow past a flexible shell

This paper based on the author's work [6] makes a detailed examination of the two-dimensional problem of separationless flow past a shell filled with gas, fixed at one point and at two points. It is assumed that the fluid is ideal, incompressible, and weightless and that the shell cannot be stretched.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 15–20, September–October, 1984.     

Turbulent mixing of accompanying and opposing flows

The solution of the problem of the edge of a turbulent jet, obtained in [1] starting from a model of the vortical motion of an ideal liquid, is generalized for the case of the turbulent mixing of two plane semibounded (accompanying or opposing) flows of an incompressible liquid. It is shown that the results of calculation are in qualitative agreement with experimental data and that they are close to them quantitatively. Some of the special characteristics of the method are discussed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 92–101, November–December, 1973.     

Motion of two circular cylinders in an ideal fluid

A solution of the problem concerning the motion of two circular cylinders in an ideal fluid was given earlier using approximate methods; the error made in this treatment of the problem increased with approach of the cylinders to one another [1, 2]. In this paper we give an exact solution of the problem for arbitrary motion of the cylinders. We define a velocity potential, the kinetic energy, and the forces acting on the cylinders from the fluid side.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 80–84, November–December, 1970.The author wishes to thank N. S. Storozhuk for his aid in preparing this paper.     

Impact of a circular disk and washer on a fluid in a cylindrical vessel

The solution of the problem of the axisymmetric motion of an ideal incompressible fluid in a cylindrical vessel of finite depth is obtained for small vibrations of a flexible circular disk and washer (disk with centered hole) on the surface of the fluid. On the basis of this solution the virtual mass is determined as a function of the dimensions of the vessel, disk and washer for the special case of a rigid nondeformable disk and washer.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 103–111, January–February, 1995.     

Numerical solution of a nonlinear problem of the motion of a plane hydrofoil beneath the free surface of an ideal incompressible fluid

A nonlinear problem of the motion of a hydrofoil of infinite span beneath the free surface of an ideal incompressible fluid with gravity is studied. The stream function is used as the dependent variable. Iterative algorithms for small and large Froude numbers based upon solving a linear boundary value problem in each step with subsequent updating of the shape of the free boundary are proposed. Typical predictions are given for a symmetric profile at different values of the submersion depth, the Froude number and the angle of attack. The free surface and streamlines shapes are shown. The dependence of the lift on the submersion depth for motion through fluid layers of different thickness is presented.Dnepropetrovsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 100–107, July–August, 1995.     

Interaction of two spherical particles in a steady flow of viscous fluid when the Reynolds number is not small

The problem of the interaction of two or more particles moving in a viscous incompressible fluid at small Reynolds numbers (Re 1) has been well studied. The linearity of the Stokes equations makes it possible to develop effective methods of solution of the problem for two and many particles [1]. If the Reynolds number is not small, the inertia forces in the Navier-Stokes equations cannot be ignored, and the problem becomes nonlinear, i.e., much more complicated. The present note is devoted to the problem of the interaction of two spherical particles in a steady uniform flow of a viscous incompressible fluid when the Reynolds number is not small. Asymptotic expressions are obtained for the interaction forces between the particles when the distances between them are large compared with their radius.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 142–144, May–June, 1983.     

Oblique entry of a slender body in an incompressible fluid

The plane problem of oblique penetration of a slender semiinfinite body in an ideal, weightless, and incompressible fluid is examined. Detailed numerical computations are performed for a wedge with rectilinear sides. The formulas obtained are applicable also for the calculation of the hydrodynamic reactions during emergence of a body from a fluid or during transverse motion of a half-blunt body with a low relative velocity. Moreover, the results of the present paper can be used to evaluate the hydrodynamic forces acting on underwater wings or propeller blades during intersection with a free surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 16–24, September–October, 1977.     

Effect of proximity of barrier on lifting force produced by vertical solid jets

The effect of proximity to the ground on the lifting force generated by a vertical solid jet is studied in connection with development of vertical takeoff and landing devices and of air cushion devices. Such a study was made in [1 ] for planar flow by an incompressible ideal fluid. There a generalization of the results obtained on a compressible fluid was made by the approximation method. In the present work the planar problem of streamline flow past a dihedral barrier of a gas jet emerging from a channel with parallel walls was solved by the Chaplygin-Fal'kovich method [2, 3], The results of [1, 4–9] follow as a particular case from the solution obtained. Calculations were carried out clarifying the effect of the proximity of a barrier and the lifting effect of a fluid on flow characteristics at subsonic speeds.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 123–131, September–October, 1971.     

Gromeka-beltrami flow in a semiinfinite cylindrical pipe

The two-parameter homogeneous helical motion of an ideal incompressible fluid in a circular cylindrical pipe is investigated. It is shown that there may be various flow conditions defined by the value of the relative intensity of rotation of the flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 117–120, March–April 1971.     

Control of the motion of a vessel with a heavy inhomogeneous liquid

The problem of controlling the internal waves inside a closed rectangular cavity filled with a heavy two-layer fluid is considered in the linear approximation. The fluid is assumed to be stably stratified, ideal, and incompressible. The controlling horizontal force is applied to the body containing the cavity. It is assumed that at the initial moment there are no oscillations of the fluid and the interface is horizontal. The problem is to bring the vessel as a whole into a prescribed state of linear motion without relative wave motion of the fluid. The Cauchy-Poisson problem and the self-consistent integro-differential equation of the vessel motion are solved using the Fourier method and taking into account the reaction of the internal waves. On the basis of an analysis of the corresponding generalized momentum problem, approaches are proposed for solving the problem of control. It is shown that a control action with a sufficiently high order of Steklov smoothness ensures the approximate solution of the control problem with the required accuracy for all the characteristics of the motion of the hybrid oscillating system under consideration.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 11–22, May–June, 1995.The study was performed with financial support from the Russian Foundation for Fundamental Research (project No. 94-01-01368).