Laminar swirling jet with allowance for buoyancy forces

There have been many investigations into swirling immersed viscous jets, and fairly detailed analyses of these studies have been given in monographs [1–3]. Nevertheless, swirling jets with free convection have not been studied. In the present paper, exact and approximate self-similar solutions are found for the problem of a swirling jet produced by a source of viscous fluid propagating vertically upward (or downward) under the influence of Archimedean forces and an initial thrust.     

Motion of a drop with allowance for thermocapillary forces

A study is made of the motion of a drop in a viscous medium of nonuniform temperature when the dependence of the surface tension on the temperature at the interface of the two media gives rise to additional tangential stresses leading to thermocapillary convection in fluids. The motions of a spherical drop and a deformed drop (when the surface of the drop is determined in the process of finding the solution) are considered. The shape of the drop surface is calculated for different values of the parameters of the problem. Dependences are obtained for the Reynolds number of the thermocapillary drift of drops in the absence of body forces.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 80–86, July–August, 1982.     

Convection in a Hele-Shaw cell with allowance for heat exchange on the wide faces

Convection in a Hele-Shaw cell is studied analytically and numerically with allowance for heat exchange on the wide faces according to Newton's law. It is shown that this heat exchange has a considerable effect on the amplitude in the neighborhood of the threshold and explains laboratory experiments in which convection was observed even in the case of heating from above.Perm. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 24–32, March–April, 1995.     

Stability and nonuniqueness of axisymmetric flows in rotating spherical layers (nonlinear theory)

A numerical analysis technique and its results for viscous incompressible flows in the annulus between two concentric coaxial spheres generated by the rotation of the boundary spheres in the same or opposite directions are presented. It is shown that in the course of its development, the main flow passes through three characteristic stages which differ significantly from each other (qualitatively as well as quantitatively) with respect to meridional circulation and azimuthal flow. Depending on the fluid layer thickness, different stages of main flow development may precede the loss of stability; this determines the differences in the mechanisms of loss of stability of the main flow and in the nature of the secondary flows. The calculated results are compared with the experimental data. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 75–86, January–February, 1998.     

Convection and heat transfer in a vertical layer with allowance for radiation from nonisothermic walls

Many studies (for example, [1–5]) consider motion and heat transfer in closed vertical cavities with given different temperatures of the lateral boundaries. The majority of studies cover the case of convection, but of late studies have appeared (for example, [4]) in which joint radiative—convective heat transfer is taken into account. In the present study we consider motion and heat transfer in a rectangular cavity separating two media with given different temperatures. In contrast to [4], the temperature of the lateral boundaries is determined from the condition for interaction with the surrounding medium, and the air in the cavity is assumed to be transparent for the heat radiation of the walls. The problem considered is a mathematical model of the heat transfer through windows, and is necessary for the analysis of methods of improving the heat proofing of buildings.Translated-from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 25–30, 1987.     

Convection in anisotropic inclined porous layers

Two-dimensional convective flow in a system of fluid-saturated porous layers is considered for small fluid velocities. The layers are inclined at an angle to the horizontal and there is a temperature gradient across them. A mathematical model of the system is constructed and the resulting series solution is numerically summed. The unique features of this model include its ability to represent non-symmetric multi-layered systems and materials whose permeabilities are anisotropic.The model is applied to various physical configurations. System aspect ratios, system symmetry and permeablity anisotropies are found to influence the effect that layers of different materials have on the convective flow.     

Instability investigation for rotating thin spherical membrane

A fluid-filled truncated spherical membrane fixed along its truncated edge to a horizontal, rigid and frictionless plane and spinning around a center axis was investigated. A two-parameter Mooney–Rivlin model was used to describe the material of the membrane. The truncated sphere was modeled in 3D using finite element meshes with different symmetry properties. A quadratic function was used for interpolating hydro-static pressure, giving a symmetric tangent stiffness matrix, thereby reproducing the conservative problem. Various problem settings were considered, related to the spinning, and different instability behaviors were observed. Multi-parametric problems were defined, generalized paths including primary and secondary paths were followed. Stability of the multi-parametric problem was evaluated using generalized eigenvalue analysis based on the total differential matrix for the constrained problem. Numerical results showed that mesh symmetry affected the simulated stability behavior. Fold line evaluations showed the parametric effects on critical solutions.     

Nonstationary secondary flows in spherical layers

An experimental study of the change in secondary flow type at the main flow stability limit is presented. For spheres rotating in the same direction, it is found that the passage from the main flow to a three-dimensional secondary flow occurs via a nonstationary transition regime. The paper continues the study [1] in which the three-dimensional stability limit of the main flow in the space of the governing parameters was found. The stability limit consists of regions with specific types of secondary flows. A scheme of the changes in secondary flow type on crossing these regions is considered. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 201–204, May–June, 1998. The work received financial support from the Russian Foundation for Basic Research (project No.96-01-01340).     

Equations of isotropic deformation of gas-saturated materials with allowance for large strains of spherical pores

Translated. from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 120–124, July–August, 1988.     

Excitation of a spherical piezoemitter which generates nonsteady electric signals with allowance for processes in the cable channel

The problem of the excitation of a thin-walled spherical piezoemitter which generates nonsteady electric signals is examined with allowance for processes in a long cable used with the piezoemitter. An analytic method of solving the problem is developed on the basis of the Laplace time transform. Boundary conditions are satisfied in the space of the originals, allowing the problem to be reduced to a system of Volterra integral equations. Numerical results are presented. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 2, pp. 41–46, February, 1999     

Convection of a heat-generating fluid in a rotating horizontal cylinder

Thermal convection of a fluid in a horizontal cylinder rotating about its own axis with uniformly volume-distributed internal heat sources is experimentally investigated. The enclosure boundary temperature was kept constant. The threshold of the excitation of convective flows and their structure are studied as functions of the heat-release intensity and the rotation velocity. The experiments are performed with water and water-glycerin solutions. It is shown that rapidly rotating fluid is in a stable quasiequilibrium state, namely, the temperature distribution is axisymmetric and has a maximum at the center of the enclosure. It is found that with decrease in the rotation velocity a convective flow arises thresholdwise, in the form of vortex cells periodically arranged along the axis. The thermal convection in the rotating enclosure is shown to be determined by the effects of two different mechanisms. One of these is due to the centrifugal force of inertia and plays the stabilizing role, while the other, thermovibrational mechanism is connected with nonisothermal fluid oscillations under the action of gravity in the enclosure-fitted reference frame and is responsible for the occurrence of mean thermal convection. The boundaries of the convection generation are plotted in the plane of the governing dimensionless parameters and the heat transfer in the supercritical region is studied.     

Limit of main flow stability in spherical layers

This paper presents the results of an experimental study of the stability limit for the main flow of an incompressible viscous liquid between two concentric spheres rotating coaxially. In the space of the governing parameters, a three-dimensional surface of the main flow stability is obtained.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 66–70, July–August, 1996. In memory of Yurii Nikolaevich Belyaev     

Convection in a rotating medium above a thermally inhomogeneous horizontal surface

The linear stationary problem of convection in a medium rotating about a vertical axis above a thermally inhomogeneous horizontal surface is theoretically investigated. Attention is mainly focused on the case of a homogeneous medium, but certain stratification effects and especially the convection characteristics in binary mixtures (for example, in saline sea water) are also considered. When the rotation is rapid (large Taylor numbers) the convective cells are strongly elongated in the vertical direction, though they also contain a thin Ekman boundary layer. The importance of the boundary conditions on the horizontal surface (in parallel with the no-slip conditions, more general conditions that may follow from the quadratic turbulent friction model are considered) is shown. In the case of binary mixtures, the differential diffusion and rotation effects may together result in the appearance of “induced salt fingers”, the deep penetration of convection into an arbitrarily stably stratified medium. The convective motions may then have a considerable effect on the background vertical temperature and admixture distributions. Attention is drawn to an original manifestation of the analogy between the rotation and stratification effects: in a non-rotating, stably stratified medium, near a thermally inhomogeneous vertical surface, the convection also penetrates deep into the medium, but in the horizontal direction, so that, when the coordinate system is rotated through 90°, the solution coincides with the case of a rotating non-stratified fluid considered here.