Oscillations of cylinders in a linearly stratified fluid

The paper studies theoretically and experimentally hydrodynamic loads that act on horizontally placed cylinders of rhombic and square cross sections, oscillating harmonically in a linearly stratified fluid. An analytical solution is found with the use of affine similitude. Hydrodynamic force coefficients were evaluated experimentally from Fourier transforms of records of damped oscillations in a time—frequency region. It is shown that for polygonal contours, hydrodynamic loads change abruptly if the slope of the polygon sides coincides with the slope of the internalwave group velocity vector.     

Forces on oscillating bodies in viscous fluid

This paper describes a method for determining the fluid forces on oscillating bodies in viscous fluid when the corresponding flow problem has been solved using the finite element method. These forces are characterized by the concept of added mass, added damping and added force. Numerical results are obtained for several example body shapes. Comparison is made with exact analytical results and other finite element results for the limiting cases of Stoke's flow and inviscid flow, and good agreement is obtained. The results for finite values of the body amplitude parameter β show the appearance of added force from the steady streaming component of the flow for asymmetric bodies. Results are also obtained for the associated flow where the fluid remote from a fixed body is oscillating.     

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.     

A Pressure Field in an Acoustic Medium Containing a Cylindrical Solid and a Sphere Oscillating in a Predetermined Manner

A problem on the interaction of a spherical body oscillating in a predetermined fashion and a rigid cylinder is formulated. The bodies do not intersect, are immersed into an ideal compressible liquid, and their centers are in one plane. The solution is based on the possibility of representing the partial solution of the Helmholtz equation, written in cylindrical coordinates, in terms of partial solutions in spherical coordinates, and vice versa. An infinite system of linear algebraic equations is obtained by satisfying the boundary conditions on the sphere and cylinder surfaces. The system is intended for determining the coefficients of the expansion of the velocity potential into a series in terms of spherical and trigonometric functions. The system obtained is solved by the reduction method. The appropriateness of this method is substantiated. The hydrodynamic characteristics of the liquid surrounding the spherical and cylindrical bodies are determined. A comparison is made with the problem on a sphere oscillating in an infinite incompressible liquid that contains also a cylinder and in a compressible liquid that contains nothing more. Two types of motion of the sphere — pulsation and oscillation — are considered     

Comparison of the drag coefficients of bodies moving in liquids with various stratification profiles

For bodies moving in liquids with various stratification profiles, the relation between the drag coefficients considered as functions of the Froude number is investigated. The problems of stratified liquid dynamics have not previously been studied from this viewpoint, either experimentally or theoretically. On the range of the Froude numbers F₁-1, the drag force coefficients obtained from bench measurements of the towing resistance to the uniform horizontal motion of models in two-layer and continuously stratified liquids are compared. The experimental data obtained in a thermocline are then compared with the results of [1,2] for linearly stratified and two-layer liquids.Nizhnii Novgorod. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 4–11, July–August, 1996.     

On the applicability of some approximate similitude laws in hypersonic aerodynamics

The range of applicability of some similitude laws for heat transfer, friction and drag coefficients is discussed on the basis of numerical solutions of the complete viscous shock layer equations describing hypersonic flow past blunt bodies. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 121–130, March–April, 1994.     

Tomographic reconstruction of internal wave patterns in a paraboloid

Using tomographic synthetic schlieren, we are able to reconstruct the three-dimensional density field of internal waves. In this study, the waves are radiating from an oscillating sphere positioned eccentrically at the surface of a paraboloidal domain filled with a uniformly stratified fluid. We find that the prediction by ray tracing corresponds well with the observed intensities of the wave field. Remarkably, for a specific value of the forcing frequency, we observe convergence of internal wave energy to an internal wave attractor. The attractor is found to dominate fluid motion in the plane perpendicular to the plane spanned by the symmetry axis and the oscillator position.     

A stability analysis of an oscillating body located in fluid flow using automatic differentiation

This paper presents a stability analysis of an oscillating body subjected to fluid forces located in a transient incompressible viscous flow. If the body is supported by elastic springs, oscillation will begin. If the characteristic period of the body and the excited oscillating period due to fluid forces match each other, resonance can occur. Stability analysis is therefore needed to determine the nonlinear behavior of the body. This paper presents an analysis of the changing stability of bodies by the numerical computation. To implement the computation, the motion of fluid around a body is expressed by the Navier–Stokes equation described in the arbitrary Lagrangian–Eulerian form. The fluid influence on the body is discretized by the finite element method based on a mixed interpolation by the bubble function in space. The motion of the body is assumed to be expressed by the equations of motion. To evaluate stability, stability function is defined by the total energy of the oscillating body. The stability is judged according to a stability index, obtained by the use of the automatic differentiation (AD) of the stability function. AD is a derivative computation method that gives high accuracy. By the use of AD, the second‐order derivative matrix, which is needed to compute the stability index, can be obtained exactly. For the numerical studies, analyses of one degree of freedom and two degrees of freedom (2DOF) for a circular cylinder and 2DOF for a rectangular cylinder are carried out. A combination of a cylinder and supporting elastic spring can produce stable, neutral and unstable states. It is shown that the stability of the cylinder can be determined by the stability index. This paper shows new possibilities for stability analysis of bodies located in a fluid flow. Copyright © 2008 John Wiley & Sons, Ltd.     

基于浸入边界算法的振动钝体绕流模拟研究

传统CFD方法在振动钝体绕流计算中常借助动网格技术,网格再生任务繁重。针对于此,本文利用可在静止网格中计算动边界绕流问题的浸入边界算法(IBM),编写数值模拟程序,分别对竖向强迫正弦振动方柱(Re=UD/v=103、振幅恒定、振动频率变化)以及桥梁断面(Re=UB/v=7.5×103、振幅、振动频率均变化)展开气动特性和流场特征结构分析。初步研究结果表明,振幅恒定为方柱高度的14%时,其涡脱锁定区长度为0.06~0.2,锁定区后端(Stc0.2)振动方柱涡脱频率回归静止涡脱频率;不同振幅下的桥梁断面阻力系数均在静止涡脱频率处产生峰值,桥梁断面升力系数则在此处均出现归零效应,且振幅越大,归零效应愈明显。     

Example of motion of a cylindrical solid in a viscous liquid

The problem of motion of a pulsating solid (an infinitely long circular cylinder) in an oscillating viscous liquid in the presence (or absence) of an external stationary force is considered. The perturbation method is applied. It is found that the solution of the time-average motion of a body exists if and only if body pulsations, liquid vibrations, and external forces satisfy a certain relation. The presence of a plane analog of the phenomenon of predominantly unidirectional motion of a compressible solid in an oscillating liquid is established.     

Vibration of beams with general boundary conditions due to a moving random load

Summary  The transverse vibrations of elastic homogeneous isotropic beams with general boundary conditions due to a moving random force with constant mean value are analyzed. The boundary conditions considered are: pinned–pinned, fixed–fixed, pinned–fixed, and fixed–free. Based on the Bernoulli beam theory, the problem is described by means of a partial differential equation. Closed-form solutions for the variance and the coefficient of variation of the beam deflection are obtained and compared for three types of force motion: accelerated, decelerated and uniform. The effects of beam damping and speed of the moving force on the dynamic response of beams are studied in detail. Received 3 December 2001; accepted for publication 30 April 2002     

Instability of vibrations of a moving two-mass oscillator on a flexibly supported Timoshenko beam

Summary  Transversal vibrations of a uniformly moving two-mass oscillator on a Timoshenko beam of infinite length supported by a viscoelastic foundation are studied. By using integral transforms, the characteristic equation for the oscillator's vibrations is obtained. It is shown that the equation may have a root with a positive real part. The existence of such a root leads to the exponential increase of the amplitude of the oscillator vibrations, i.e. to instability. The reasons for the instability to occur are discussed. By employing the method of D-decomposition, the instability domains are found in the space of the system parameters. Received 30 October 2000; accepted for publication 28 March 2001     

A CFD study of the interaction of oscillatory flows with a pair of side-by-side cylinders

The behavior of vortices induced by a pair of side-by-side square cylinders in an oscillating flow is investigated using an in-house numerical model. The study is carried out for various Keulegan–Carpenter numbers, Reynolds numbers, and cylinder gap spacings. For an oscillating flow past a pair of side-by-side cylinders, the gap ratio plays a vital role in the flow pattern. A jet-like structure is observed when fluid flows through the gap. Moreover, the gap promotes the earlier appearance of asymmetric vortex shedding. In-line force and lift force coefficients of two square cylinders are analyzed using spectral analysis. An autocorrelation function is used to determine the relation between flow patterns around two cylinders. These results demonstrate the transition of the flow field from the periodic state to the chaotic state.     

A GENERAL FORMULA FOR CALCULATING FORCES ON A 2-D ARBITRARY BODY IN INCOMPRESSIBLE FLOW

In the present paper, a general integral equation is presented to calculate the forces exerted on a two-dimensional (2-D) body of arbitrary shape immersed in unsteady, incompressible flows. By finding the general solutions of a set of Laplace equations with particular boundary conditions, the equation can be simplified to produce a simplified formula for calculating the forces. The simplified formula consists of three parts, representing contributions from different physical phenomena: added mass force and/or inertial force in inviscid flow, the force caused by the deformation of fluid and viscosity and the force caused by the convection of fluid with nonzero circulation. It can be applied to any 2-D arbitrary body in viscous or inviscid, steady or unsteady incompressible flow. As the formula excludes either temporal derivatives of velocity or spatial derivatives of vorticity in the flow field, the numerical errors contained in the numerical solution of velocity and vorticity fields will not be magnified, and therefore the resulting force calculated is more accurate. Most importantly, the formula presents an alternative method for obtaining the added mass of a 2-D body of arbitrary shape accelerating in a fluid. For bodies of simple shape, such as a circle, ellipse and plate, the added masses predicted using the present method are in agreement with that obtained by conventional methods. For bodies of complex shape, the present method only requires the calculation of the first two coefficients of the conformal transformation and cross-sectional area.     

Influence of the Coefficients of Thermal Expansion on the Nature of Stresses and Local Effects in a Uniformly Heated Sandwich Plate

Thermal stresses are determined in a sandwich plate uniformly heated under plane-strain conditions. Linearly elastic isotropic bodies model the plate components. An approximate solution is found by the finite-difference approach. The influence of the coefficients of thermal expansion on the nature of stress concentration regions is studied.     

Application of Differing Forcing Function Models on Simulated Flow Past an Oscillating Cylinder in a Uniform Low Reynolds Number Flow

A Computational Fluid Dynamics (CFD) model is presented for the uniform viscous two dimensional flow past an oscillating cylinder at low Reynolds number. Numerical simulations are made to study the effect of differing forced induced oscillation mechanisms with a large range of cylinder forcing frequencies. In the first case sinusoidal velocity slip boundary conditions are adopted for the cylinder surface to simulate cylinder oscillation. The implication suggests that no modification or additional term need to be added to the Navier-Stokes equations. In the second case this time extra body force terms which are assumed to account for velocity effects due to cylinder movement are included in the Navier-Stokes equations with the imposition of same boundary conditions. Drag and lift coefficients are extracted from present numerical results and other detailed computations of these coefficients are made at a Reynolds number of 80 and an amplitude-to diameter ratio 0.14. The results are found to be in agreement with each other at low force driving frequencies below and near lock-in. However, differences are found at higher frequencies above lock-in. Agreement are also found with experimental results at some frequency ranges.     

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.     

Slow flow of gas around a strongly heated or cooled sphere

Problems similar to those considered in [1, 2] are studied, namely, slow flow over a uniformly heated (or cooled) spherical particle and flow past a weakly nonuniformly heated sphere in the absence of external body forces and with allowance for thermal stresses in the gas. The use of an improved method of numerical solution [3] has made it possible to advance into the region of large temperature differences. A new effect is found: allowance for the thermal stresses in the case of flow around a strongly heated sphere leads to the appearance of a suction force instead of a drag. In the case of flow around a nonuniformly heated sphere the influence of thermal stresses is unimportant. The problems are considered for two temperature dependences of the transport coefficients.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 170–175, October–December, 1981.     

Forces on oscillating foils for propulsion and maneuvering

Experiments were performed on an oscillating foil to assess its performance in producing large forces for propulsion and effective maneuvering. First, experiments on a harmonically heaving and pitching foil were performed to determine its propulsive efficiency under conditions of significant thrust production, as function of the principal parameters: the heave amplitude, Strouhal number, angle of attack, and phase angle between heave and pitch. Planform area thrust coefficients of 2.4 were recorded for 35° maximum angle of attack and efficiencies of up to 71.5% were recorded for 15° maximum angle of attack. A plateau of good efficiency, in the range of 50–60%, is noted. A phase angle of 90–100° between pitch and heave is found to produce the best thrust performance. Also, the introduction of higher harmonics in the heave motion, so as to ensure a sinusoidal variation in the angle of attack produced much higher thrust coefficient at high Strouhal numbers. Second, experiments on a harmonically oscillating foil with a superposed pitch bias, as well as experiments on impulsively moving foils in still water, were conducted to assess the capability of the foil to produce large lateral forces for maneuvering. Mean side force coefficients of up to 5.5, and instantaneous lift coefficients of up to 15 were recorded, demonstrating an outstanding capability for maneuvering force production.