Vibrational hydrodynamic interaction between a sphere and the boundaries of a cavity

A new type of vibrational lift force [1] acting on a spherical body oscillating in a viscous fluid near a rigid boundary is experimentally investigated. The interaction between the body and the cavity boundary creates a repulsion force which is capable of holding a heavy body in the gravity field at a certain distance from the floor and a light body at a certain distance from the ceiling. The repulsion force appears at a distance comparable with the Stokesian boundary layer thickness and increases as the surface is approached. Outside the viscous interaction range, the repulsion force is replaced by an attraction force which decays with distance. Dimensionless parameters governing the vibrational interaction are found and threshold curves, corresponding to the transition of bodies of different densities to the “suspended” state, are plotted as functions of a dimensionless frequency. The dependence of the repulsion and attraction forces on the distance between the body and the wall is studied.     

Vibrational dynamics of a light spherical body in a rotating cylinder filled with a fluid

The behavior of a light spherical body in a rotating horizontal cylindrical cavity filled with a low-viscosity fluid is experimentally investigated both in the absence and in the presence of transverse vibrations. The system is in a centrifuged state. Mean rotation of the sphere relative to the cavity is found to exist. In the absence of the vibrations slow lagging rotation of the body is due to the gravity field. With increase in the cavity rotation velocity the intensity of differential rotation reduces. The vibrations lead to the excitation of differential rotation of the body, either anticipating or lagging, due to the resonance excitation of its inertial oscillations. The differential rotation of the body leads to the formation of the cylindrical Taylor-Proudman column. With increase in the column rotation velocity the instability of its boundary manifests itself as an azimuthal two-dimensional wave.     

A light cylinder under horizontal vibration in a cavity filled with a fluid

The behavior of a light cylindrical body of circular cross-section under horizontal vibration in a rectangular cavity filled with a fluid is experimentally investigated. At critical vibration intensity the body is repelled from the upper side of the cavity and takes up a stable suspended position, in which the gravity field is balanced by the vibrational repulsive force, executing longitudinal oscillations. As the vibrations are intensified, the gap between the cylinder and the wall widens. A new form of instability, namely, the excitation of the tangential motion of the body along the vibration axis, is found to exist on the supercritical range. The cylinder is at a finite distance from the upper side of the cavity and the tangential motion is due to the loss of symmetry of the oscillating motion. The transition of the cylinder to the suspended state and its return to the wall, as well as the excitation of the average longitudinal motion and its cessation, occur thresholdwise and have a hysteresis. The body dynamics are studied as a function of the dimensionless vibration frequency.     

Vibrational dynamics of a light body in a liquid-filled rotating cylinder

The behavior of a light free cylindrical body in a rapidly rotating horizontal cylinder containing a liquid under vibrational action (the vibration direction is perpendicular to the rotation axis) is investigated. An intense rotation of the body relative to the cavity is detected. Depending on the vibration frequency, the body rotation velocity in the laboratory reference system may be higher or lower than the cavity rotation velocity and in the resonance region they may differ by several times. The mechanism of motion generation is theoretically described. It is shown that the motion is related with the excitation of inertial oscillations of the body: the cause of the motion is an average vibrational force generated due to nonlinear effects in the Stokes boundary layer near the oscillating body. The formation of large-scale axisymmetric vortex structures periodic along the rotation axis, which appear under conditions of inertial oscillation of the body during its motion, both leading and lagging, is detected.     

Wall proximity effects on the effectiveness of upstream control rod

Two dimensional flow over a circular cylinder with an upstream control rod of same diameter is simulated in unbound condition and in wall bounded conditions. The cylinders are placed at various heights from the wall and the inter-distance between cylinders is also varied. The control rod is subjected to different rotation rates. It is found that, in unbound condition, rotating the control rod decreases the critical pitch length (S/D_cr) and increases the drag and Strouhal number of the main cylinder. In presence of plane wall, the shielding provided by the separated shear layers from the control rod in cavity regime is deteriorated due to deflection of shear layers which results in higher drag and large fluctuation of lift coefficient. However, in wake impingement regime, the binary vortices from the control rod are weakened due to diffusion of vorticity and hence, the main cylinder experiences a lower drag and small lift fluctuations than that of unbound condition. The critical height of vortex suppression (H/D_cr) is higher in cavity regime than that of wake impingement regime due to the single extended-bluff body like configuration. The rotation of control rod energizes the wall boundary layer and increases the critical height of vortex suppression. Increasing the rotational rate of control rod decreases the drag force and reduces the amplitude of lift fluctuation. Analysis of the wall shear stress distribution reveals that it suffers a sudden drop at moderate height where the normal Karman vortex shedding changes to irregular shedding consisting of single row of negative vortices. Modal structures obtained from dynamic mode decomposition (DMD) reveal that the flow structures behind the main cylinder are suppressed due to wall and the flow is dominated by the wake of control rod.     

Dynamics of a Spherical Body in a Liquid with Rotational Vibration of the Cavity

The average dynamics of a single solid sphere in a liquid-filled cylindrical cavity in the presence of high-frequency rotational oscillation about the axis of symmetry is studied experimentally. In the cavity there is an impermeable membrane which forces the liquid as a whole to vibrates together with the cavity. Various orientations of the vessel in the gravity force field are considered. The action of an average force of vibrational nature on the sphere and the dependence of this force on the vibration parameters and the body dimensions and density are studied. The force is measured with respect to the floating threshold for the heavy body, when the average vibrational force balances or exceeds the action of the gravity force.     

Influence of the boundary of a column of incompressible liquid in investigating axisymmetric oscillations of a solid sphere in a cavity

Axisymmetric oscillations of a rigid spherical body in a column of ideal incompressible liquid with a plane boundary in the form of a free liquid surface or a rigid wall within a round cylindrical cavity are considered. The potential and pressure fields are plotted; expressions are obtained for the kinetic energy of the system and the hydrodynamic forces acting on the body. The resistance of the liquid to accelerated movement of the body is determined as a function of the distance to the boundary, for various parameter values. For specified oscillations of the body, the results obtained for axisymmetric conditions in a halfspace are compared with those obtained in an infinite cylindrical cavity. Translated from Prikladnaya Mekhanika, Vol. 35, No. 12, pp. 11–18, December, 1999.     

Diffraction of a plane acoustic wave by a rigid sphere in a cylindrical cavity: An axisymmetric problem

The paper studies the interaction of a rigid spherical body and a cylindrical cavity filled with an ideal compressible fluid in which a plane acoustic wave of unit amplitude propagates. The solution is based on the possibility of transforming partial solutions of the Helmholtz equation between cylindrical and spherical coordinates. Satisfying the interface conditions between the cavity and the acoustic medium and the boundary conditions on the spherical surface yields an infinite system of algebraic equations with indefinite integrals of cylindrical functions as coefficients. This system of equations is solved by reduction. The behavior of the system is studied depending on the frequency of the plane wave     

Steady Flow Generated by a Core Oscillating in a Rotating Spherical Cavity

Steady flow generated by oscillations of an inner solid core in a fluid-filled rotating spherical cavity is experimentally studied. The core with density less than the fluid density is located near the center of the cavity and is acted upon by a centrifugal force. The gravity field directed perpendicular to the rotation axis leads to a stationary displacement of the core from the rotation axis. As a result, in the frame of reference attached to the cavity, the core performs circular oscillation with frequency equal to the rotation frequency, and its center moves along a circular trajectory in the equatorial plane around the center of the cavity. For the differential rotation of the core to be absent, one of the poles of the core is connected to the nearest pole of the cavity with a torsionally elastic, flexible fishing line. It is found that the oscillation of the core generates axisymmetric azimuthal fluid flow in the cavity which has the form of nested liquid columns rotating with different angular velocities. Comparison with the case of a free oscillating core which performs mean differential rotation suggests the existence of two mechanisms of flow generation (due to the differential rotation of the core in the Ekman layer and due to the oscillation of the core in the oscillating boundary layers).     

封闭圆柱腔内旋转点声源声压的近场频域解

在圆柱腔壁面为声学硬壁面的假定下，利用圆柱腔体空间内的格林函数导出了圆柱腔内旋转运动点声源空间声压的近场频域解；进而利用该频域解计算分析了旋转简谐单极子点源的声学特性。计算分析表明：由于考虑了壁面的影响，在圆柱腔体内，点声源旋转频率和源频率的变化将改变声压的空间指向性；源频率和旋转频率的增加伴随明显的多普勒效应，同时基频声压沿圆柱腔体轴线的分布从比较平缓变为明显波动；沿半径方向基频声压也波动变化。     

Self-oscillatory regimes of cavitation interaction between counter-streaming fluid flows

The effects of unsteady cavitation interaction between a coaxial system of a continuous water jet and a surrounding annular gas jet and a counter-streaming water flow in a cylindrical tube is investigated both experimentally and numerically. The distinctive features of the mechanism of the formation of regular self-oscillatory interaction regimes and their salient features are studied. The dependence of the mean self-oscillation frequency on the ratio of the counter-streaming water flows is determined at different gas jet flow rates. The Froude number effect on the self-oscillation frequency is analyzed. The dependence of the maximum value of the longitudinal displacement of the nose of a developed oscillating cavity penetrating into the counter stream and of the displacement amplitude on the flow rate of the supplied gas is determined. The idea on the pressure distribution in the cavity in different stages of flow development is obtained. The nature of the dependence of the self-oscillation frequency on the degree of tube flow blockage by the cavity is established.     

Some Aspects of the Lift Force on a Spherical Bubble

Several situations in which a spherical bubble experiences a lift force are examined, especially through the use of computational results obtained by solving the full Navier–Stokes equations. The lift force is computed over a wide range of Reynolds number for the case of pure shear flow, pure strain and solid body rotation. Using these results, the validity of asymptotic solutions derived in the limit of low Reynolds number or inviscid flow is discussed. A general expression of the lift force valid for low to moderate shears is proposed. It is shown that for such shears, the lift force in a complex flow can be predicted by superposing the results obtained in pure strain flow and solid body rotation flow. Finally, the interaction force experienced by two bubbles rising side-by-side is studied. The computational results reveal that, at variance with the predictions of potential theory, the sign of this force changes when the Reynolds number or the separation distance between the bubbles decreases below a critical value. All these results are discussed in terms of vorticity. The respective role played by the vorticity generated at the bubble surface and by the one that is eventually present in the unperturbed flow is emphasized.     

Axial acoustic radiation force on a rigid cylinder near an impedance boundary for on-axis Gaussian beam

This work presents a theoretical model to calculate the acoustic radiation force on a rigid cylindrical particle immersed in an ideal fluid near a boundary for an on-axis Gaussian beam. An exact solution of the axial acoustic radiation force function is derived for a cylindrical particle by applying the translation addition theorem of cylindrical Bessel function. We analyzed the effects of the impedance boundary on acoustic radiation force of a rigid cylinder immersed in water near an impedance boundary with particular emphasis on the radius of the rigid cylinder and the distance from the cylinder center to impedance boundary. Simulation results reveal that the existence of particle trapping behavior depends on the choice of nondimensional frequency as well as the offset distance from the impedance boundary. The value of the radiation force function varies when the cylinder lies at the different position of the on-axis Gaussian beam. For the particle with different radius, the acoustic radiation force functions vary significantly with frequency. This study provides a theoretical basis for acoustic manipulation, which may benefit to the improvement and development of the acoustic control technology.     

Vibrational Dynamics of a Centrifuged Fluid Layer

The dynamics of a low-viscosity fluid layer inside a rotating cylinder under transverse translational vibration relative to the rotation axis is investigated experimentally. A novel vibrational effect, the generation of intense azimuthal fluid flows with velocities comparable with the cavity rotation velocity, is revealed. The structure and intensity of the vibrational flows and the flow transformation with variation of the determining dimensionless parameters (frequency and vibrational acceleration) are studied.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 147–156.Original Russian Text Copyright © 2005 by Ivanova, Kozlov, and Polezhaev.     

Dynamics of a cylindrical body in a liquid-filled sector of a cylindrical layer under rotational vibration

The dynamics of a rigid cylindrical body subjected to high-frequency rotational vibration about its own axis in a liquid-filled sector of a horizontal cylindrical layer are investigated experimentally and theoretically. It is found that the vibrations generate an average force on the body which in the case of a body denser than the fluid is directed toward the axis of rotation. Under certain conditions this force exceeds the gravity force, causing the body to float. This effect is analyzed theoretically in the high-frequency low-amplitude vibration approximation. It is shown that the force detected acts on the body over the entire fluid volume. Perm’. Paris. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 29–39, July–August, 1998. The work partially supported by the Russian Foundation for Basic Research (project No. 96-01-00932) and Grant No. 920-5208/95 of the US National Aviation and Space Administration (US NASA).     

Numerical study of the lift force influence on two-phase shock tube boundary layer characteristics

The importance of the lift force acting on the dispersed phase in the boundary layer of a laminar gas-particle dilute mixture flow generated by a shock wave is investigated numerically. The particle phase is supposed to form a continuum and is described by an Eulerian approach. The ability of the Eulerian model to simulate particle flows and the importance of the two-way coupling are proven by comparison with experimental data as well as with the numerical results from schemes based on a Lagrangian approach. The models used for the lift force are discussed through comparisons between numerical and experimental results found in the literature. Some results about the formation of a dust cloud are numerically reproduced and show the major role of the lift force. Simulations of two-dimensional two-phase shock tube flows are also performed including the lift force effects. Although the wave propagation is weakly influenced by the lift force, the force modifies substantially the dynamics of the flow near the wall. Received 17 February 2000 / Accepted 30 November 2000     

Thermal Convection in a Plane Layer Rotating About a Horizontal Axis

The thermal convection of a fluid in a plane vertical layer with a cylindrical lateral boundary, which rotates uniformly about a horizontal symmetry axis, is investigated experimentally. The structure and excitation limit of the convective flows are studied as functions of the rotation frequency, the temperature difference between the layer boundaries, and the layer thickness. The determining dimensionless parameters are found. It is shown that the period-average gravity action produces convection in the form of hexagonally distributed cells stationary in the reference system tied to the cavity.     

Effect of Thermal Modulation on the Onset of Convection in a Porous Medium Layer Saturated by a Nanofluid

The effect of time-periodic temperature modulation at the onset of convection in a Boussinesq porous medium saturated by a nanofluid is studied analytically. The model used for the nanofluid incorporates the effects of Brownian motion. Three types of boundary temperature modulations are considered namely, symmetric, asymmetric, and only the lower wall temperature is modulated while the upper wall is held at constant temperature. The perturbation method is applied for computing the critical Rayleigh and wave numbers for small amplitude temperature modulation. The shift in the critical Rayleigh number is calculated as a function of frequency of modulation, concentration Rayleigh number, porosity, Lewis number, and thermal capacity ratio. It has been shown that it is possible to advance or delay the onset of convection by time-periodic modulation of the wall temperature. The nanofluid is found to have more stabilizing effect when compared to regular fluid. Low frequency is destabilizing, while high frequency is always stabilizing for symmetric modulation. Asymmetric modulation and only lower wall temperature modulation is stabilizing for all frequencies when concentration Rayleigh number is greater than one.     

Hydrodynamics of flow over a transversely oscillating circular cylinder beneath a free surface

In this paper, hydrodynamic force coefficients and wake vortex structures of uniform flow over a transversely oscillating circular cylinder beneath a free surface were numerically investigated by an adaptive Cartesian cut-cell/level-set method. At a fixed Reynolds number, 100, a series of simulations covering three Froude numbers, two submergence depths, and three oscillation amplitudes were performed over a wide range of oscillation frequency. Results show that, for a deeply submerged cylinder with sufficiently large oscillation amplitudes, both the lift amplitude jump and the lift phase sharp drop exist, not accompanied by significant changes of vortex shedding timing. The near-cylinder vortex structure changes when the lift amplitude jump occurs. For a cylinder oscillating beneath a free surface, larger oscillation amplitude or submergence depth causes higher time-averaged drag for frequency ratio (=oscillation frequency/natural vortex shedding frequency) greater than 1.25. All near-free-surface cases exhibit negative time-averaged lift the magnitude of which increases with decreasing submergence depth. In contrast to a deeply submerged cylinder, occurrences of beating in the temporal variation of lift are fewer for a cylinder oscillating beneath a free surface, especially for small submergence depth. For the highest Froude number investigated, the lift frequency is locked to the cylinder oscillation frequency for frequency ratios higher than one. The vortex shedding mode tends to be double-row for deep and single-row for shallow submergence. Proximity to the free surface would change or destroy the near-cylinder vortex structure characteristic of deep-submergence cases. The lift amplitude jump is smoother for smaller submergence depth. Similar to deep-submergence cases, the vortex shedding frequency is not necessarily the same as the primary-mode frequency of the lift coefficient. The frequency of the induced free surface wave is exactly the cylinder oscillation frequency. The trends of wave length variation with the Froude number and frequency ratio agree with those predicted by the linear theory of small-amplitude free surface waves.