Vibrational Suspension of Two Cylinders in a Rotating Liquid-Filled Cavity with a Time-Varying Rotation Rate

The dynamics of rotating hydrodynamic systems containing phase inclusions are interesting due to the related widespread occurrence in nature and technology.The influence of external force fields on rotating systems can be used to control the dynamics of inclusions of various types.Controlling inclusions is of current interest for space technologies.In low gravity,even a slight vibration effect can lead to the appearance of a force acting on phase inclusions near a solid boundary.When vibrations are applied to multiphase hydrodynamic systems,the oscillating body intensively interacts with the fluid and introduces changes in the related flow structure.Asymmetries in the fluid flow lead to the appearance of an averaged force.As a result,the body is repelled from the cavity boundary and takes a position at a certain distance from it.The vibrationally-induced movement of phase inclusions in liquids can be used to improve various technological processes(for example,when degassing and cleaning liquids from solid inclusions,mixing various components,etc.).This study presents a relevant methodology to study the averaged vibrational force acting on a pair of free cylindrical bodies near the oscillating wall of a cavity.Attention is paid to the region of moderate and low dimensionless frequencies when the size of the inclusion is consistent with the thickness of the Stokes boundary layer.The dynamics of these bodies is considered in a horizontal cylindrical cavity with a fluid undergoing modulated rotation.The average lift force of a vibrational nature is measured by the method of quasi-stationary suspension of bodies whose density differs from the density of the liquid in a static centrifugal force field.The developed technique makes it possible to determine the dependence of the lift force on vibration parameters and the distance from the oscillating boundary at which solid inclusions are located.It is shown that in the region of moderate dimensionless frequencies,the average lift force acting on an inclusion near the boundary undergoing modulated rotation almost linearly depends on the dimensionless frequency.

Oscillatory Dynamics of a Spherical Solid in a Liquid in an Axisymmetric Variable Cross Section Channel

The dynamics of a solid spherical body in an oscillating liquid flow in a vertical axisymmetric channel of variable cross section is experimentally studied.It is shown that the oscillating liquid leads to the generation of intense averaged flows in each of the channel segments.The intensity and direction of these flows depend on the dimensionless oscillating frequency.In the region of studied frequencies,the dynamics of the considered body is examined when the primary vortices emerging in the flow occupy the whole region in each segment.For a fixed frequency,an increase in the oscillation amplitude leads to a phase-inclusion holding effect,i.e.,the body occupies a quasi-stationary position in one of the cells of the vertical channel,while oscillating around its average position.It is also shown that the oscillating motion of a liquid column generates an averaged force acting on the body,the magnitude of which depends on the properties of the body and its position in the channel.The quasi-stationary position is determined by the relative density and size of the body,as well as the dimensionless frequency.The behavior of the body as a function of the amplitude and frequency of fluid oscillation and relative size is discussed in detail.Such findings may be used in the future to control the position of a phase inclusion and/or to strengthen mass transfer effects in a channel of variable cross section by means of fluid oscillations.

Experimental Study of Thermal Convection and Heat Transfer in Rotating Horizontal Annulus

A genuine technological issue–the thermal convection of liquid in a rotating cavity–is investigated experimentally.The experiments are conducted within a horizontal annulus with isothermal boundaries. The inner boundaryof the annulus has a higher temperature, thus exerting a stabilising influence on the system. It is shown that whenthe layer rotation velocity diminishes, two-dimensional azimuthally periodic convective rolls, rotating togetherwith the cavity, emerge in a threshold manner. The development of convection is accompanied by a significantintensification of heat transfer through the layer. It is shown that the averaged thermal convection excitation inthe form of a system of two-dimensional rolls occurs against the background of oscillations of a non-isothermalfluid in the cavity reference frame caused by the gravity field. The excitation threshold and the structure ofconvective rolls are consistent with the results of the earlier theoretical studies by the authors performed usingthe equations of “vibrational” convection obtained by the averaging method. Furthermore, the experiments haverevealed a new type of averaged flow in the form of a spatially periodic system of toroidal vortices. It is shown thata steady streaming, excited by the inertial oscillations of the fluid, is responsible for the generation of the toroidalvortices. These flows develop in a non-threshold manner and are most clearly manifested in a case of resonantexcitation of one of the inertial modes.

Averaged Dynamics of Fluids near the Oscillating Interface in a Hele-Shaw Cell

The steady flow in a Hele-Shaw cell filled with fluids with a high viscosity contrast in the presence of fluid oscillations is experimentally studied.The control of oscillatory dynamics of multiphase systems with interfaces is a challenging technological problem.We consider miscible(water and glycerol)and immiscible(water and high-viscosity silicone oil PMS-1000)fluids under subsonic oscillations perpendicular to the interface.Observations show that the interface shape depends on the amplitude and frequency of oscillations.The interface is undisturbed only in the absence of oscillations.Under small amplitudes,the interface between water and glycerol widens due to mixing.When the critical amplitude is reached,the interface becomes unstable to the fingering instability:Aqueous fingers penetrate the high-viscosity glycerol and induce intensive mixing of miscible fluids and associated decay of the instability.After the disappearance of the fingers,the interface takes a U-shape in the central part of the cell.A similar effect is observed for immiscible fluids:The oscillating interface tends to bend to the side of a high-viscosity fluid.Again,when the critical amplitude is reached,the fingering instability arises at the convex interface.This paper focuses on the causes of bending of the initially undisturbed interface between miscible or immiscible fluids.For this purpose,we measure the steady flow velocity near the interface and in the bulk of a high-viscosity fluid using Particle Image Velocimetry(PIV).

Dynamics of Low-Viscosity Liquids Interface in an Unevenly Rotating Vertical Layer

The behavior of two immiscible low-viscosity liquids differing in density and viscosity in a vertical flat layer undergoing modulated rotation is experimentally studied.The layer has a circular axisymmetric boundary.In the absence of modulation of the rotation speed,the interphase boundary has the shape of a short axisymmetric cylinder.A new effect has been discovered,under the influence of rotation speed modulation,the interface takes on a new dynamic equilibrium state.A more viscous liquid covers the end boundaries of the layer in the form of thin films,which have the shape of round spots of almost constant radius;with increasing amplitude of the velocity modulation,the wetting boundary expands.It is found that upon reaching the critical amplitude of oscillations,the film of a viscous liquid loses stability,and the outer edge of the wetting spot collapses and takes on a feathery structure.It is shown that this threshold is caused by the development of the Kelvin-Helmholtz oscillatory instability of the film.The spreading radius of a spot of light viscous liquid and its stability are studied depending on the rotation rate,amplitude,and frequency of rotation speed modulation.The discovered averaged effects are determined by different oscillatory interaction of fluids with the end-walls of the cell,due to different viscosities.The effect of films forming can find application in technological processes to intensify mass transfer at interphase boundaries.

Linear and Non-Linear Dynamics of Inertial Waves in a Rotating Cylinder with Antiparallel Inclined Ends

This work is devoted to the experimental study of inertial wave regimes in a non-uniform rotating cylinder with antiparallel inclined ends.In this setting,the cross-section of the cylinder is divided into two regions where the fluid depth increases or decreases with radius.Three different regimes are found:inertial wave attractor,global oscillations(the cavity’s resonant modes)and regime of symmetric reflection of wave beams.In linear wave regimes,a steady single vortex elongated along the rotation axis is generated.The location of the wave’s interaction with the sloping ends determines the vortex position and the vorticity sign.In non-linear regimes several pairs of the triadic resonance subharmonics are detected simultaneously.The instability of triadic resonance is accompanied by the periodic generation of mean vortices drifting in the azimuthal direction.Moreover,the appearance frequency of the vortices is consistent with the low-frequency subharmonic of the triadic resonance.The experimental results shed light on the mechanisms of the inertial wave interaction with zonal flow and may be useful for the development of new methods of mixing.

Libration-Generated Average Convection in a Rotating Flat Layer with Horizontal Axis

The study of average convection in a rotating cavity subjected to modulated rotation is an interesting area for the development of both fundamental and applied science.This phenomenon finds application in the field of mass transfer and fluid flow control,relevant examples being crystal growth under reduced gravity and fluid mixing in microfluidic devices for cell cultures.In this study,the averaged flow generated by the oscillating motion of a fluid in a planar layer rotating about a horizontal axis is experimentally investigated.The boundaries of the layer are maintained at constant temperatures,while the lateral cylindrical wall is thermally insulated.It is demonstrated that libration results in intense oscillatory fluid motion,which in turn produces a time-averaged flow.For the first time,quantitative measures for the instantaneous velocity field are obtained using the Particle Image Velocimetry technique.It is revealed that the flow has the form of counter-rotating vortices.The vortex circulations sense changes during a libration cycle.An increase in the rotation rate and amplitude of the cavity libration results in an increase in the flow intensity.The heat transfer and time-averaged velocity are examined accordingly as a function of the dimensionless oscillation frequency,and resonant excitation of heat transfer and average oscillation velocity are revealed.The threshold curve for the onset of the averaged convection is identified in the plane of control parameters(dimensionless rotational velocity and pulsation Reynolds number).It is found that an increase in the dimensionless rotational velocity has a stabilizing effect on the onset of convection.