Flow around a sphere with material cross flow at low reynolds numbers

An analytical solution is carried out for the problem of the flow around a sphere with material cross flow at Reynolds numbers less than 1 and a blowing velocity less than the free stream velocity. The method of asymptotic expansions of Pearson and Proudman is used for the solution. Expressions are obtained for the distribution of the current and velocity component functions as well as for the aerodynamic drag coefficient of the sphere. It is shown that blowing diminishes the sphere drag, where its influence will increase as the Reynolds number grows.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 103–109, May–June, 1972.     

Stress Analysis of Rotating Inhomogeneous Transversely Isotropic Hollow Spheres

An approach is proposed to the stress–strain analysis of hollow, arbitrarily inhomogeneous, transversely isotropic, either closed or open spheres that rotate about the axis of symmetry with a constant angular velocity. The stress problem for a rotating single-layer sphere and a segment of a sphere is solved as an example. The distribution of radial stresses and displacements along the radius of the sphere is analyzed depending on thickness variation at arbitrary points of the sphere     

Slow motion of a permeable sphere in a viscous fluid

Flow of a viscous fluid past a permeable sphere is investigated in the Stokes approximation. An example of such a flow is flow past a perforated or meshed spherical surface. The elements of the sphere contain rigid impermeable sections and openings through which the fluid can flow. The interaction of the sphere with the flow is described by two drag coefficients, which established the connection between the flow velocity of the fluid at the sphere and the stress tensor on it. The dependence of the flow pattern and also the drag and flow rate of the fluid on these coefficients is investigated. In special cases, the obtained solution describes flow past solid and liquid spheres.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 165–167, September–October, 1982.     

Motion of a viscous liquid between two rotating spheres

An analysis is presented of the steady-state asymmetric motion of an incompressible viscous liquid between two concentric spheres rotating with constant angular velocities about various axes passing through their common center. The reaction force of the liquid on the inner sphere is determined; this force reduces to a resistive torque.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 179–180, May–June, 1974.     

Radiation of waves by a sphere harmonically oscillating to-and-fro in a viscous medium

The theory of the radiation of sound by a sphere in an ideal medium is presented in detail in [1–3]. The emission of waves by a sphere oscillating to-and-fro in a viscous incompressible liquid is analyzed in [4, 5]. The present paper gives a precise solution to the problem of the radiation of sound by a sphere oscillating in a viscous medium.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 101–106, September–October, 1970.     

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.     

Heat exchange of sphere with blowing for slow flows

An analytic solution is given for the problem of convective heat- and mass-exchange of a sphere with transverse flow of matter along the surface for values of Peclet numbers smaller than one and for blowing velocity smaller than that of the incoming gas flow. The solution for velocity field obtained by the authors in a previously published publication is employed on flow past a sphere with blowing; the method of asymptotic expansions of Acrivos and Taylor is also used. Expressions to the second approximation are determined for temperature field and for the values of local and averaged Nusselt numbers. It is shown that blowing reduces the temperature gradient or the concentrations at the surface.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 89–94, July–August, 1972.     

Sphere scattering of nonlinearly interacting acoustic waves

Sphere scattering of the field of nonlinearly interacting plane acoustic waves when the sphere is located in the region of nonlinear interaction between the primary pumping waves of a parametric antenna is considered. An analytic expression for the secondary field pressure at the difference frequency is obtained. This expression describes the process of nonlinear interaction of the incident and scattered waves. The secondary-field total pressure components, which characterize the interaction between the incident plane waves and scattered spherical waves are analyzed. The numerical results and experimental data are given.Taganrog. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 4–12, March–April, 1995.     

Flow induced by a vibrating heated sphere

Mean flows induced by a heated or cold sphere vibrating in a liquid are studied. The cases of a sphere immersed in an unbounded liquid and a liquid layer of finite thickness, bounded by two rigid coaxial spheres, are considered. An analytical solution is obtained in the creeping flow approximation for small values of the governing parameters. The vibrating flow structure is shown to depend to a considerable extent on the clearance and to be fairly complex for small clearances. For a fixed clearance, the creeping flow structure is determined by a single parameter, the ratio of the vibrating Grashof number to the pulsating Reynolds number (Schlichting parameter). For large values of the parameters, the vibrating flow structure is determined by the vibrating Grashof number and the Schlichting parameter separately. The changes in the flow structure with increase in the values of the governing parameters are studied numerically by a finite difference method.Krasnoyarsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 31–39, January–February, 1996.     

Viscous fluid flow created by the helical motion of a body of revolution

An investigation is made into the flow created by the helical, exponentially damped motion of a body of revolution in a viscous incompressible fluid stationary at points remote from the body. The forces exerted by the fluid on a body moving in this way are studied. It is shown that the induced flow is uniformly helical. The exposition is illustrated with reference to the example of the motion of a spherical surface. The exact and approximate (in the Stokes sense) solutions are compared. The classical results for the steady-state slow motions of a sphere (both translational and rotational) follow as particular cases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 47–52, March–April, 1985.     

Measurements of the velocity field of a hypersonic flow by a laser Doppler velocimeter

An experimental apparatus is described for measuring the local velocities of gas flows in the range from 100 to 10,000 m/sec by means of the Doppler effect. The results of investigations of a free flow and of the same flow over a sphere in a hypersonic wind tunnel at M = 5 are cited and are compared with measurements of velocity using temperature and pressure probes and with theoretical calculations. The behavior of light scattering-particles in the flow is also investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 69–73, July–August, 1974.     

Experimental investigation of the separation of flow around a sphere

The results of an experimental investigation of the flow around a sphere over a broad range of Mach numbers M=0.3–3 and Reynolds numbers Re=3·10⁴–3·10⁷ are presented. The experiments were carried out on a ballistic test stand and in a wind tunnel. Flow patterns and pressure distributions were obtained. In particular, the effect of the Mach and Reynolds numbers on the position of the separation point and the edge shock was studied; the pressure distribution on the sphere was measured; and a nonmonotonic displacement of the flow separation point upon passage through the speed of sound was established.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 152–156, January–February, 1991.     

Flow of rarefied gas past a sphere in the presence of blowing from its surface

Flow of a rarefied gas past a sphere with various conditions of blowing on the surface is considered. The investigation is based on numerical solution of model kinetic equations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 182–185, September–October, 1982.     

Motion of a variable-volume sphere in an ideal fluid near a plane surface

The motion of a spherical cavity in a fluid is investigated. The radius of the sphere varies under the action of a constant pressure at infinity. The problems of the collapse of a cavity moving in an unbounded fluid and of the collapse of a cavity near a plane are solved in the exact formulation. The occurrence of an initial translational velocity or the presence of a solid surface, by contrast with the collapse of a sphere at rest in an unbounded fluid [1], yields a limiting radius at which the process of collapse ceases. A sphere initially at rest near a plane always comes into contact with the plane as a result of collapse. The radius and velocities at which the sphere arrives the plane are calculated for various initial distances from the latter. The possible mechanism of the action of a cavitation bubble on a solid surface is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 94–103, September–October, 1971.     

Parameters of the atmosphere of an outgassing sphere

A method of calculating the parameters of the cloud formed in connection with free-molecule gas release from the surface of a sphere is described. Analytic solutions are obtained for steady gas release.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 185–187, March–April, 1991.     

Dynamics of vorticity at a sphere

The article discusses the two-dimensional flow of an incompressible liquid between two infinitely close concentric spheres, due to an initial distribution of the vorticity differing from zero. The concept of point singularities (vortices, sources, and sinks) at a sphere is introduced. Equations of motion are obtained for point vortices, as well as invariants of the motion, known for the plane case [1]. The simplest case of the mutual motion of a pair of vortices is considered. Equations are obtained for the motion of point vortices at a rotating sphere. Integral invariants for the continuous distribution of the vorticity are obtained, having the dynamic sense of the total kinetic energy and the momentum of the liquid at the sphere. The effect of the topology of the sphere on the dynamics of the vorticity is noted, and a comparison is made with the plane case.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 57–65, November–December, 1977.     

Slow flow of gas around a strongly heated or cooled sphere

Problems similar to those considered in [1, 2] are studied, namely, slow flow over a uniformly heated (or cooled) spherical particle and flow past a weakly nonuniformly heated sphere in the absence of external body forces and with allowance for thermal stresses in the gas. The use of an improved method of numerical solution [3] has made it possible to advance into the region of large temperature differences. A new effect is found: allowance for the thermal stresses in the case of flow around a strongly heated sphere leads to the appearance of a suction force instead of a drag. In the case of flow around a nonuniformly heated sphere the influence of thermal stresses is unimportant. The problems are considered for two temperature dependences of the transport coefficients.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 170–175, October–December, 1981.     

Distribution of radiant thermal flux over the surface of a sphere for hypersonic flow of a nonviscous radiating gas past the sphere

In the present study using the Newtonian approximation [1] we obtain an analytical solution to the problem of flow of a steady, uniform, hypersonic, nonviscous, radiating gas past a sphere. The three-dimensional radiative-loss approximation is used. A distribution is found for the gasdynamic parameters in the shock layer, the withdrawal of the shock wave and the radiant thermal flux to the surface of the sphere. The Newtonian approximation was used earlier in [2, 3] to analyze a gas flow with radiation near the critical line. In [2] the radiation field was considered in the differential approximation, with the optical absorption coefficient being assumed constant. In [3] the integrodifferential energy equation with account of radiation was solved numerically for a gray gas. In [4–7] the problem of the flow of a nonviscous, nonheat-conducting gas behind a shock wave with account of radiation was solved numerically. To calculate the radiation field in [4, 7] the three-dimensional radiative-loss approximation was used; in [5, 6] the self-absorption of the gas was taken into account. A comparison of the equations obtained in the present study for radiant flow from radiating air to a sphere with the numerical calculations [4–7] shows them to have satisfactory accuracy.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 44–49, November–December, 1972.In conclusion the author thanks G. A. Tirskii and É. A. Gershbein for discussion and valuable remarks.     

Shear flow over a porous particle

Linear axisymmetric Stokes flow over a porous spherical particle is investigated. An exact analytic solution for the fluid velocity components and the pressure inside and outside the porous particle is obtained. The solution is generalized to include the cases of arbitrary three-dimensional linear shear flow as well as translational-shear Stokes flow. As the permeability of the particle tends to zero, the solutions obtained go over into the corresponding solutions for an impermeable particle. The problem of translational Stokes flow around a spherical drop (in the limit a gas bubble or an impermeable sphere) was considered, for example, in [1,2]. A solution of the problem of translational Stokes flow over a porous spherical particle was given in [3]. Linear shear-strain Stokes flow over a spherical drop was investigated in [2].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 113–120, May–June, 1995.     

Flow around and heat and mass transfer of a sphere with blowing at medium reynolds numbers

The Navier-Stokes and heat- and mass-transfer equations are solved numerically for a sphere with uniform blowing over the surface in the Reynolds number range up to 20. A method of refining the boundary conditions far from the sphere is proposed in both problems. A difference scheme from other authors is used to solve the hydrodynamic problem, and an explicit difference scheme with a second order of approximation is used for the heat problem. It is shown that blowing diminishes the aerodynamic drag of the sphere and the temperature or concentration gradient at its surface, i.e., the heat- and mass-transfer intensity.Translated from Zhurnal Priladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 148–156, July–August, 1975.