Thermal Vibrational Convection in Rotating Cavities

The average vibrational motion of a nonisothermal fluid in a uniformly rotating cavity is described theoretically. Equations are obtained using the averaging technique in the high-frequency vibration approximation. It is found that the rotation significantly affects both the intensity of the average flows and the structure of the pulsatory velocity field generating resonance amplification of the fluid vibrations ar certain ratios of the rotation frequency and the force field oscillation frequency. This makes rotation an important controlling factor ensuring a strong averaged effect under relatively weak vibrational action. The problem of excitation of vibrational convection in a plane rotating layer is considered on the basis of the equations obtained when the vibration frequency substantially exceeds the rotation frequency.     

Effect of rotation on the vibroconvective stability of a fluid layer with internal heat release

The equilibrium stability of a horizontal fluid layer with homogeneous internal heat release is investigated theoretically for the case in which the layer simultaneously undergoes high-frequency circular vibration in a horizontal plane and rotates about a vertical axis. The rotation frequency is assumed to be small as compared with the vibration frequency. It is found that the rotation has a stabilizing effect on the vibrational-gravitational convection. At the high-frequency limit the dependence of the critical values of the controlling parameters (gravitational and vibrational Rayleigh numbers) and the wave number on the rotation frequency is obtained.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 53–61. Original Russian Text Copyright © 2005 by Ivanova, Kozlov, and Kolesnikov.     

Development and instability of steady convective flows in a square cavity heated from below and a field of vertically directed vibrational forces

The present paper is devoted to numerical investigation of the spatial structure and stability of secondary vibrational convective flows resulting from instability of the equilibrium of a fluid heated from below. Vibrations parallel to the vector of the gravitational force (vertical vibrations) are considered. As in earlier work [7–9], a region of finite size is used — a square cavity heated from below. It is shown that enhancement of the vibrational disturbance of the natural convective flow may either stabilize or destabilize flows with different spatial structures; it may also stabilize certain solutions of the system of convection equations that are unstable in the absence of vibrational forces. In addition, increase of the vibrational Rayleigh number can lead to a change of the mechanisms responsible for equilibrium instability and oscillatory instability of the secondary steady flows.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 9–18, March–April, 1991.I thank G. Z. Gershuni for assistance and extremely fruitful discussions of the results of the paper.     

Convective stability of a nonisothermal fluid in a rotating horizontal coaxial gap

The thermal fluid convection in a coaxial horizontal gap uniformly rotating about its axis is investigated. The threshold above which convective flows are excited and the structure of these flows are studied. It is found that convection ensues irrespective of whether the inner or outer boundary temperature is higher. Convection manifests itself in the threshold development of rolls elongated in the direction of the rotation axis and is determined by two different mechanisms. If the layer is heated from outside, the centrifugal convection mechanism plays a leading part and the diameter of the convective rolls is comparable with the layer thickness. If the higher is the temperature of the inner boundary of the layer, the centrifugal inertia force has a stabilizing effect and convection development is related with the action of thermal vibrational mechanism. The latter is determined by gravity-generated oscillations of the nonisothermal fluid relative to the cavity. The wave number of the vibrational convective structures is several times smaller than under centrifugal convection. The results obtained broaden our understanding of thermal convection in systems rotating in external static force fields.     

Experimental investigation of the displacement of viscous fluids from porous media

The results of experimental investigations of different-viscosity and immiscible Newtonian fluid flows through porous media are presented. The investigations were carried out for a Hele-Shaw cell occupied by a porous medium. The basic difference from the previous studies is the observation of the flow after break-through of the displacing fluid into the sink. A series of qualitative and quantitative results which clarify the physics of immiscible fluid flows through capillaries and porous media were obtained in the course of the experimental investigations.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 124–131. Original Russian Text Copyright © 2005 by Baryshnikov, Belyaev, and Turuntaev.     

Average Fluid Flow in the End Regions of a Long Channel Subjected to Rotational Vibration

The average isothermal fluid flow in an elongated parallelepiped that performs rotational vibration is studied experimentally. The structure and intensity of the average flows and the regularities of their transformation with variation of the vibration frequency are investigated. The dimensionless frequency is varied over a wide interval: from extremely low values where the fluid vibration is largely determined by the viscous forces up to high frequencies where the viscosity is important only in relatively thin Stokes boundary layers. The dimensionless complexes that determine the intensity of the average flows over the entire frequency range are found.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, 2005, pp. 37–44.Original Russian Text Copyright © 2005 by Ivanova, Kozlov, and Selin.     

Magnetovibrational flows in a magnetic fluid

A new type of flow in a magnetic fluid has been experimentally detected and investigated. The interaction between an alternating nonuniform magnetic field and a magnetic fluid leads to the parametric excitation of traveling capillary-gravitational waves which are the direct cause of the average flow. A necessary condition of formation of hydrodynamic flows in an alternating field is also the presence of time-dependent harmonics with multiple frequencies synchronized with the first harmonic, so that the time dependence of the ponderomotive force is generally pulsed. It is shown that for plane vibrational flows the classical theory cannot explain the high intensity of the average flows observed. It is suggested that the high intensity of magnetovibrational flows is related to the violation of the cylindrical symmetry of the traveling capillary-gravitational waves and the transition to a three-dimensional motion. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 124–133, January–February, 1998.     

Convection in an oscillating force field and microgravity

Convective flows in a plane layer of viscous fluid in the presence of an oscillating external force are investigated numerically [1 – 8]. The layer is assumed to be placed in a gravitational field. The cases in which the external field oscillations are generated by rotation about the horizontal axis or by vibration in the longitudinal direction are considered. The Navier-Stokes equations and the Boussinesq approximation are used for describing the fluid motion. The flows developing in the layer in the presence of a transverse temperature gradient are determined, the stability boundaries of these flows are found, and the supercritical motion regimes are studied. These investigations are carried out using the averaging method (in order to find the stability limits for high rotation velocities and vibration frequencies) and the Galerkin method.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 99–106, September–October, 1994.     

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.     

Convective flows in a cylindrical fluid zone in a high-frequency vibration field

Convective flows of a nonuniformly heated fluid in a cylindrical fluid zone in a high-frequency longitudinal vibration field are studied. Vibration frequencies which are high as compared with dissipative decrements and capillary frequencies, but small as compared with acoustic frequencies are considered. The general method formulated earlier for describing the behavior of inhomogeneous fluids under the influence of high-frequency vibrations is used. The interaction between the vibrational flow mechanisms and thermocapillary effects on a free surface is analyzed.Perm'. Marseilles (France). Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 53–61, September–October, 1994.     

Universal Velocity Defect Law for the Turbulent Boundary Layer

Turbulent plane boundary layer flows of an incompressible fluid are considered. A refinement of the known Coles wake law is proposed. This refinement makes it possible to ensure the smooth matching of the turbulent boundary layer velocity profile with the outer flow and to extend the range of validity of the law to the case of large positive pressure gradients. The accuracy of the analytical approximation obtained is verified by comparison with the known experimental equilibrium velocity profiles. Using the approximation proposed, a relation for calculating the cross-sectional distribution of the Reynolds stress in the equilibrium boundary layer is derived. The pressure distributions for which the equilibrium turbulent boundary layer flows are single- and two-valued are distinguished.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 89–101.Original Russian Text Copyright © 2005 by Mikhailov.     

Numerical modelling of rotating tangential layers (jets) in shells under strong uniform magnetic field

A numerical study of tangential layers in steady‐state magnetohydrodynamic rotating flows is presented using CFD to solve the inductionless governing equations. The analysis considers two basic flow configurations. In the first, a fluid is enclosed in a cylinder with electrically perfect conducting walls and the flow is driven by a small rotating, conducting disk. In the second, a flow is considered in a spherical shell with an inner rotating sphere. The fluid in both cases is subjected to an external axial uniform magnetic field. The results show that these flows exhibit two different types of flow cores separated from each other by a tangential layer parallel to the axis of rotation. The inner core follows a solid‐body rotation while the outer is quasistagnant. A counter‐rotating jet is developed in the tangential layer between the cores. The characteristics of the tangential layer and the properties of the meridional motion are determined for a wide range of Hartmann numbers. Distributions of angular velocity of circumferential flow and electric potential are obtained and the results are compared with those of analytic methods. Copyright © 2009 John Wiley & Sons, Ltd.     

Measured Reynolds stress distributions and energy budgets of a fully pulsed round air jet

 Most particle-tracking velocimetry (PTV) algorithms are not suitable for calculating the velocity vectors of a fluid flow subjected to strong deformation, because these algorithms deal only with flows due to translation. Accordingly, it is necessary to develop a novel algorithm applicable to flows subjected to strong deformations such as rotation, shear, expansion and compression. This paper proposes a novel particle tracking algorithm using the velocity gradient tensor (VGT) which can deal with strong deformations and demonstrates that this algorithm is applicable to some basic fluid motions (rigidly rotating flow, Couette flow, and expansion flow). Furthermore, the performance of this algorithm is compared with the binary image cross-correlation method (BICC), the four-consecutive-time-step particle tracking method (4-PTV), and the spring model particle tracking algorithm (SPG) using simulations and experimental data. As a result, it is shown that this novel algorithm is useful and applicable for the highly accurate measurement and analysis of fluid flows subjected to strong deformations. Received: 9 February 1999/Accepted: 22 November 1999     

Unsteady flows of an inhomogeneous incompressible viscous fluid

This paper deals with a theoretical analysis of the transfer of reactive impurities by open and filtration flows of an incompressible viscous fluid. The first section of the paper studies the model of an inhomogeneous incompressible viscous fluid, which is widely used in meteorology and oceanology, with additional allowance for the drag of the magnetic field or porous medium. Another object of research in this paper is the model of filtration of an inhomogeneous incompressible fluid in porous media proposed by V. N. Monakhov (1977) (Section 2). In both models, hydrodynamic flows determine the motion of the mixture as a whole and the temperature and concentration distributions of the components of an inhomogeneous fluid are described by a common nonlinear system of equations of diffusive heat and mass transfer.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 44–51, March–April, 2005.     

Rotating incompressible flow with a pressure Neumann condition

This work considers the internal flow of an incompressible viscous fluid contained in a rectangular duct subject to a rotation. A direct velocity–pressure algorithm in primitive variables with a Neumann condition for the pressure is employed. The spatial discretization is made with finite central differences on a staggered grid. The pressure and velocity fields are directly updated without any iteration. Numerical simulations with several Reynolds numbers and rotation rates were performed for ducts of aspect ratios 2:1 and 8:1. Copyright © 2005 John Wiley & Sons, Ltd.     

Bifurcation of self-similar solutions describing a thermocapillary flow of a fluid in a thin layer

Thermocapillary flows of a fluid in a lamina with a rigid lower wall and a free upper surface, along which the temperature gradient is given in the radial direction, are investigated for large Marangoni numbers. Self-similar solutions which describe the axisymmetric flow regimes of a fluid without the circumferential velocity component are constructed numerically and asymptotically for a system of Prandtl equations. It is shown that a pair of new self-similar flow regimes of a fluid with rotation branches off from the regimes obtained. The new regimes ere calculated numerically and asymptotically. Rostov State University, Rostov-on-Don 344090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 137–142, May–June, 1999.     

The \vec\omega-\vec{D} fluid: general theory with special emphasis on stationary two dimensional flows

In this paper a theory is presented in which the extra stress tensor is allowed to depend not only on the rate of strain tensor but also on the relative vorticity of the fluid, i.e. on the vorticity relative to the rate of rotation of the principal straining directions. This theory has its origin in an expansion of in terms of kinematic tensors in the limit of stationarity in a material sense (constant stretch history flows). For two dimensional flows of an incompressible fluid three tensors suffice to completely specify . The three material functions which appear can depend only on two invariants, namely the second invariant of and on . Using the predictions of an Oldroyd 8 constant fluid in a homogeneous planar flow of constant stretch history, the three material functions are studied in detail. For the special case of a quasi-Newtonian fluid shear thinning and extension thickening can directly be accounted for in the “viscosity” function. Received: September 26, 1996     

Thermocapillary Vortices Induced by a Light Beam near a Bubble Surface in a Hele-Shaw Cell

This paper studies thermocapillary vortices induced by local heating of a bubble surface in a Hele-Shaw cell by a light beam. It is found that the vortex rotation frequency and its depth depend on the distance from the light-beam projection onto the layer to the bubble boundary. The surface velocity of the thermocapillary flow is calculated using the balance of the near-surface and return flows of the thermocapillary vortex and the equality of capillary and dynamic pressures. It is shown that a decrease in the surface velocity and the vortex rotation frequency with increase in the distance from the light beam to the bubble surface is due to a decrease in the temperature gradient between the illuminated and cold poles of the bubble.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 93–99, September–October, 2005.     

Motion of a fluid between rotating cones

A study is made of the steady axisymmetric flow of a viscous fluid between two cones rotating in opposite ways round a common axis. It is shown that as in the case of the flow of fluid swirled by plane disks rotating at different speeds [1], there can be two regimes of motion in the system: a Batchelor regime with quasirigid rotation of the fluid outside the boundary layers [2] and a Stewartson regime in which the azimuthal flow is concentrated only in the boundary layers [3]. In the Stewartson regime, a boundary layer analogous to that in the single disk problem (see, for example, [4–6]) forms in the region of each cone far from the apex. For the flows outside the boundary layers, simple expressions are found which make it possible to obtain a conception of the circulation of the fluid as a whole. With minor alterations, the results can be applied to the case of the rotation of other curved surfaces.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 58–64, March–April, 1985.The author thanks A. M. Obukhov for suggesting the subject and for his interest in the work, and A. V. Danilov and S. V. Nesterov for useful discussions.     

Rayleigh-Benard Convection in a Near-Critical Fluid in the Neighborhood of the Stability Threshold

Steady-state Rayleigh-Benard convection in a medium with parameters close to the thermodynamic critical point is simulated within the framework of the complete Navier-Stokes equations with a two-scale representation of the pressure and the Van-der-Waals equation of state. A calibration relation is obtained for a realistic Rayleigh number in a compressible stratified medium. The parameters of the numerical simulation are determined from experimental data for near-critical helium on the basis of the calibration relation. The threshold Rayleigh numbers are found without and with allowance for stratification and a comparison with the experimental and theoretical data is carried out. The effect of compressibility of the near-critical fluid on steady-state convection flows is investigated beyond the stability threshold and the effect of adiabatic compression of the medium is analyzed.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 48–61.Original Russian Text Copyright © 2005 by Polezhaev and Soboleva.