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.     

Flow due to parallel disks rotating about non-coincident axis with one of them oscillating in its plane

An exact solution of the Navier–Stokes equations is obtained for the flow between two eccentric disks rotating with the same angular velocity and one of them executing non-torsional oscillations. An analytical solution describing the flow at large and small times after the start is given. The solutions depend on the ratio of the frequency of oscillation to the angular velocity of the disks and the ratio of the amplitude of oscillation to the angular velocity of the disks and to the distance between the axes of rotation, and the Reynolds number based on the distance between the disks and the angular velocity of the disks. The solutions for three cases when the angular velocity is greater than the frequency of oscillation or it is smaller than the frequency or it is equal to the frequency are discussed.     

Lift Force Acting on a Heavy Solid in a Rotating Liquid-Filled Cavity with a Time-Varying Rotation Rate

The dynamics of a heavy cylindrical body in a liquid-filled horizontal cylindrical cavity with a time-varying rotation rate is experimentally investigated. The body is near the cavity boundary under a centrifugal force and undergoes solid-body rotation together with the liquid and the cavity at a fixed rotation rate. The dependence of the body dynamics on the amplitude and frequency of modulation of the rotation rate is investigated. It is found that at a critical amplitude of modulation (at definite frequency), the heavy body repulses from the cavity boundary and comes into a steady state at some distance from the wall. It is found that the average lift force (repulsive one) is generated by the azimuthal oscillation of the body in the rotating frame of reference and manifests itself at a distance comparable to the thickness of the viscous boundary layer. In the experiments, we observed azimuthal drift of the body due to asymmetric azimuthal oscillations of the body. In the limit of high frequency of the rotation rate modulation, the dependence of the lift force coefficient on the gap between the body and the wall is determined.     

Gas bubble oscillations in a fluid in the presence of 2:1 resonance between the radial and deformation oscillation frequencies

Small nonlinear oscillations of an ellipsoidal bubble in a fluid in the presence of 2:1 frequency resonance between the radial and ellipsoidal modes are considered. The equations of motion are reduced to Hamiltonian form. The quadratic and cubic terms are taken into account in the expansion of the Hamiltonian. The Hamilton function is transformed to the normal form using the invariant normalization method in the first approximation. This makes it possible to construct an analogy between the system considered and the well-known problem of a pendulous spring. The radial and ellipsoidal bubble oscillation modes correspond to the vertical and horizontal coordinates of a material point, respectively. In the absence of resonance the solution of the nonlinear equations differs from the solution of the linear equations by only a small (quadratic in the amplitude) change in the oscillation frequency. In the resonance case the radial and ellipsoidal oscillation modes periodically change places and the energy of one mode is converted into that of the other. The interest in the system in resonance is associated with precisely this fact. The question of the dissipation effect in real media is considered. The decay rate depends significantly on the physical properties of the material and, in certain special cases, can be small enough for the energy transfer effect to manifest itself.     

Oscillation of an elastic bar rigidly linked to a kinematically excited pendulum

The oscillation of a mechanical system consisting of an elastic bar rigidly linked at the middle to a kinematically excited pendulum is studied. A system of integro-differential equations with appropriate boundary and initial conditions for the deflections of the bar axis and the rotation angle of the pendulum is derived using the Hamilton-Ostrogradsky principle. Given kinematic excitation conditions, the rotation angle is found as a solution to an inhomogeneous Hill equation in the form of a double power series in the amplitude of kinematic excitation. It is shown that the oscillation of the bar is the linear superposition of three oscillations __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 10, pp. 107–115, October 2006.     

受径向振荡激励的黏弹性液滴稳定性分析

当液滴受到外部周期性的径向激励时, 在其表面会形成驻波模式的不稳定, 这就是在球面上的Faraday不稳定问题. 不稳定的表面波的振荡频率根据流体物性参数和所施加激励条件的不同呈现为谐波或是亚谐波模式的振荡. 本文基于线性小扰动理论, 研究了受径向振荡体积力的黏弹性液滴表面波的不稳定性. 振荡的体积力导致动量方程为含有时间周期系数的Mathieu方程, 系统因此变成参数不稳定问题, 采用Floquet理论进行求解. 本模型中将黏弹性的特征处理为与流变模型参数相关的等效黏度, 从而简化了问题的求解. 基于对中性稳定曲线及增长率的分析, 研究了黏弹性参数对液滴稳定性的影响. 结果表明零剪切黏度和应变驰豫时间的增加具有抑制液滴表面波增长的作用, 提高了使液滴表面发生谐波不稳定的激励幅值. 随着振荡幅值的增加, 增长率不稳定的区域减少, 且随着振荡频率的增加, 液滴表面波增长率减小. 通过对增长率的分析可以得出, 应力松弛时间的增加使得增长率增加, 从而促进了液滴表面波的增长.      

VORTEX SHEDDING RESONANCE FROM A ROTATIONALLY OSCILLATING CYLINDER

Vortex shedding resonance of a circular cylinder wake to a forced rotational oscillation has been investigated experimentally by measuring the velocity fluctuations in the wake, pressure distributions over the cylinder surface, and visualizing the flow field with respect to cylinder oscillations. The vortex shedding resonance occurs near the natural shedding frequency at small amplitude of cylinder oscillations, while the peak resonance frequency shifts to a lower value with an increase in oscillation amplitude. The drag and lift forces acting on the cylinder at fixed forcing Strouhal number indicate that the phase lag of fluid forces to the cylinder oscillations increases with an increase in oscillation amplitude, supporting the variation of resonance frequency with oscillation amplitude. The comparative study of the measured pressure distributions and the simultaneous flow visualizations with respect to cylinder rotation shows the mechanisms of phase lag, which is due to the strengthened vortex formation and the modification of the surface pressure distributions.     

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).     

Magnetic field effects on the nonlinear vibration of a rotor

The nonlinear vibration of a rotor operated in a magnetic field with geometric and inertia nonlinearity is investigated. An asymmetric magnetic flux density is generated,resulting in the production of a load on the rotor since the air-gap distribution between the rotor and the stator is not uniform. This electromagnetic load is a nonlinear function of the distance between the geometric centers of the rotor and the stator. The nonlinear equation of motion is obtained by the inclusion of the nonli...     

Heat and mass transfer of a fuel droplet evaporating in oscillatory flow

A numerical study of the heat and mass transfer from an evaporating fuel droplet in oscillatory flow was performed. The flow was assumed to be laminar and axisymmetric, and the droplet was assumed to maintain its spherical shape during its lifetime. Based on these assumptions, the conservation equations in a general curvilinear coordinate were solved numerically. The behaviors of droplet evaporation in the oscillatory flow were investigated by analyzing the effects of flow oscillation on the evaporation process of a n-heptane fuel droplet at high pressure.The response of the time history of the square of droplet diameter and space-averaged Nusselt numbers to the main flow oscillation were investigated in frequency band of 1–75 Hz with various oscillation amplitudes. Results showed that, depending on the frequency and amplitude of the oscillation, there are different modes of response of the evaporation process to the flow oscillation. One response mode is synchronous with the main flow oscillation, and thus the quasi-steady condition is attained. Another mode is asynchronous with the flow oscillation and is highly unsteady. As for the evaporation rate, however, in all conditions is more greatly enhanced in oscillatory flow than in quiescent air.To quantify the conditions of the transition from quasi-steady to unsteady, the response of the boundary layer around the droplet surface to the flow oscillation was investigated. The results led to including the oscillation Strouhal number as a criteria for the transition. The numerical results showed that at a low Strouhal number, a quasi-steady boundary layer is formed in response to the flow oscillation, whereas by increasing the oscillation Strouhal number, the phenomena become unsteady.     

An Analysis of Journal Orbits for Nonlinear Dynamic Bearing Systems

An analysis of journal centre orbits is presented in this paper based on a non-isothermal non-Newtonian fluid model for dynamically loaded bearing systems. A spectral element approach is used to solve a full set of coupled equations (kinematics and constitutive) governing the flow of the lubricant, and an operator-splitting spectral element technique is used to evaluate the dynamic energy equation. The motion of the journal is calculated on the basis of Newtonian mechanics incorporated with a simple cavitation model. The stability of the journal orbits is investigated under a wide range of the rotation speeds of journal. The unstable orbits arise as a sub-harmonic motion when the journal rotation speed is increased beyond a critical value. The influences of the oscillation speeds of the applied loads on the journal orbits are examined. The numerical simulations demonstrate that both the rotation speed of the journal and the oscillation speed of the applied load play an important role in determining the pattern of the journal orbits. The effects of square-wave and rotating applied loads on the journal orbits are also investigated. Received 22 April 1998 and accepted 26 May 1999     

On Self-Oscillations during the Outflow of a Swirled Jet

It is shown that the core of a swirled helical flow can be described using a novel exact nonstationary solution of the hydrodynamic equations for a viscous incompressible fluid, which generalizes the rigid-body asymptotics for the Burgers and Sullivan vortices in the form of rigid-body rotation with a finite helicity. An estimate of the pressure fluctuations corresponding to this nonstationary vortex regime, which is proportional to the frequency of the swirled-jet core rotation as a rigid body and also depends on the parameters of the initial velocity field structure, is obtained. It is noted that this frequency may correspond to the frequency observed in the pressure fluctuation spectrum, which is almost proportional to the swirled flow rate in vortex acoustic emitters.     

A NUMERICAL SIMULATION OF VORTEX SHEDDING FROM AN OSCILLATING CIRCULAR CYLINDER

Vortex shedding from an oscillating circular cylinder is studied by numerical solutions of the two-dimensional unsteady Navier–Stokes equations. A physically consistent method is used for the reconstruction of velocity fluxes which arise from discrete equations for the mass and momentum balances. This method ensures a second-order accuracy. Two phenomena are investigated and, in both cases, the cylinder oscillation is forced. The first is the flow induced by the harmonic in-line oscillation of cylinder in water at rest. The Reynolds number is equal to 100 and the Keulegan–Carpenter number is equal to 5. A comparison of phase-averaged velocity vectors between measurements and predictions is presented. Applying the widely used model of Morison to the computed in-line force history, the drag and the inertia coefficients are calculated and compared for different grid levels. Using these to reproduce the force functions, deviations from those originally computed are revealed. The second problem is an investigation of a transversely oscillating cylinder in a uniform flow at fixed Reynolds number equal to 185. The cylinder oscillation frequency ranges between 0·80 and 1·20 of the natural vortex-shedding frequency, and the oscillation amplitude is 20% of the cylinder diameter. As the frequency of excitation of the cylinder increases relative to the inherent vortex formation frequency, the initially formed concentration of vorticity moves closer to the cylinder until a limiting position is reached. At this point, the vorticity concentration abruptly switches to the opposite side of the cylinder. This process induces distinct changes of the topology of the corresponding streamline patterns.     

Unsteady heat and mass transfer in MHD flow over an oscillatory stretching surface with Soret and Dufour effects

In this paper, we study the unsteady coupled heat and mass transfer of two-dimensional MHD fluid over a moving oscillatory stretching surface with Soret and Dufour effects. Viscous dissipation effects are adopted in the energy equation. A uniform magnetic field is applied vertically to the flow direction. The governing equations are reduced to non-linear coupled partial differential equations and solved by means of homotopy analysis method （HAM）. The effects of some physical parameters such as magnetic parameter, Dufour number, Soret number, the Prandtl num- ber and the ratio of the oscillation frequency of the sheet to its stretching rate on the flow and heat transfer characteristics are illustrated and analyzed.     

镓铟锡液滴撞击泡沫金属表面的运动学特性研究

常温下为液态的镓铟锡合金以其优异的导热性能在具有特殊要求的传热领域有着重要的应用价值,与传统流动介质相比较大的表面张力使得其产生的流动现象必有所区别.本文研究镓铟锡所形成的液滴撞击泡沫金属表面后所产生的铺展、回缩及回弹现象.采用高速相机拍摄液滴投影轮廓随液滴运动的变化过程,并通过图像处理获得不同撞击速度、底板表面孔径下的液滴铺展系数、中心位置轮廓高度以及液滴回弹后在空中的振动特性.研究结果表明:具有较高表面张力的镓铟锡液滴的铺展系数随无量纲时间的变化在铺展初始阶段仍满足常规流体的1/2次幂关系,只在铺展后期与底板的无量纲孔径有关系;液滴的最大铺展系数在较小无量纲孔径底板大于在光滑镍板,且随底板无量纲孔径增大而逐渐减小;在回弹过程,由于底板孔隙结构的存在使得液滴回弹后在空中的振动呈现3种形态:规则的横向和纵向振动、带旋转的横向和纵向振动以及旋转振动;最后,通过对振动频率的拟合和分析,进一步拓展了传统振动频率理论公式在非规则振动过程预测中的应用.      

A calculating method of shock wave oscillating frequency due to turbulent shear layer fluctuations in supersonic flow

One of the more severe fluctuating pressure environments encountered in supersonic orhypersonic flows is the shock wave oscillation driven by interaction of a shock wave withboundary layer.The high intensity oscillating shock wave may induce structure resonanceof a high speed vehicle.The research for the shock oscillation used to adopt empirical orsemiempirical methods because the phenomenon is very complex.In this paper atheoretical solution on shock oscillating frequency due to turbulent shear layer fluctuationshas been obtained from basic conservation equations.Moreover,we have attained theregularity of the frequency of oscillating shock varying with incoming flow Mach numbersM_∞and turning angleθ.The calculating results indicate excellent agreement withmeasurements.This paper has supplied a valuable analytical method to study aeroelasticproblems produced by shock wave oscillation.     

NUMERICAL STUDY OF THE FLOW PAST A CYLINDER EXCITED TRANSVERSELY TO THE INCIDENT STREAM. PART 1: LOCK-IN ZONE,HYDRODYNAMIC FORCES AND WAKE GEOMETRY

The numerical study of the flow past a circular cylinder forced to oscillate transversely to the incident stream is presented herein, at a fixed Reynolds number equal to 106. The finite element technique was favoured for the solution of the Navier–Stokes equations, in the formulation where the stream function and the vorticity are the field variables. The cylinder oscillation frequency ranged between 0·80 and 1·20 of the natural vortex-shedding frequency, and the oscillation amplitude extended up to 50% of the cylinder diameter. Since the resolution of the characteristics of synchronized wakes is the focus of the study, the first task is the determination of the boundary of the lock-in region. The computation revealed that, when the cylinder oscillation frequency exceeds the frequency of the natural shedding of vortices, the flow is not absolutely periodic at subsequent cycles but a quasiperiodic flow pattern occurs, which creates difficulty in the determination of the lock-in boundary. The time histories of the drag and lift forces for various oscillation parameters are presented, while the vorticity contours were favoured for the numerical flow visualization. The hydrodynamic forces, the phase angle between the lift force and the cylinder displacement, and the parameters of the wake geometry when steady state was reached, are presented in cumulative diagrams. These diagrams indicate the effect of the oscillation parameters on the hydrodynamic forces and on the wake geometry.     

Rotation sensitivity of waves propagating in a rotating piezoelectric plate

The rotation effect on the characteristics of waves propagating in a piezoelectric plate is studied in the framework of linear piezoelectricity including Coriolis and centrifugal forces. The rotation sensitivity of the wave dispersion relations is analyzed in details for polarized ceramic plates and for the lowest thickness-shear and the lowest thickness-twist waves because of the particular importance of these modes for gyroscope applications. The analysis shows that the frequency shifts monotonically with the increasing rotation rate and the rotation sensitivity of long waves is substantially greater than that of short waves. Generally, plates with shorted electrode surfaces have higher rotation sensitivity than plates with free-charge surfaces. For long waves and for small rotation rate relative to the wave frequency, the frequency shifts with rotation rate, linearly for plates with shorted electrode surfaces and nonlinearly with a nearly flat initial tangent for plates with free-charge surfaces. These rotation sensitivity characteristics are of interest for the development of rotation sensors and other piezoelectric devices for which frequency insensitivity to rotation is desired.     

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.