Simulation of a Viscous Flow Around an Oscillating Cylinder at Low Keulegan-Carpenter Numbers

A finite difference simulation method for a viscous flow around a circular cylinder sinusoidally oscillating at low Keulegan-Carpenter numbers is presented. Navier-Stokes equations in finite difference form are solved on a moving grid system, based on a time dependent coordinate transformation. Evolution with time of the flow structures induced by a circular cylinder performing sinusoidal oscillations in a fluid at rest, by means of stream lines, pressure contours and vortex shedding is studied in detail at Keulegan-Carpenter numbers, Kc = 9.4 and 14. The time dependent drag and lift are also explained.     

Unsteady Flow of an Oscillating Porous Disk and a Fluid at Infinity

An exact analytic solution of the unsteady Navier–Stokes equations is obtained for the flow caused by the non-coaxial rotations of a porous disk and a fluid at infinity. The porous disk is executing oscillations in its own plane with superimposed injection or suction. An increasing or decreasing velocity amplitude of the oscillating porous disk is also discussed. Further, it is shown that a combination of suction/injection and decreasing/increasing velocity amplitude is possible as well. In addition, the flow due to porous oscillating disk and a fluid at infinity rotating about an axis parallel to the z-axis is attempted as a second problem. Sommario. Si studia il flusso non stazionario prodotto dall'oscillazione di un disco poroso in un fluido e si fornisce una soluzione analitica delle equazioni di Navier–Stokes. Si discute l'effetto di una suzione/iniezione e di una variazione sull'ampiezza della velocità' di oscillazione. Infine si studia il flusso dovuto alle oscillazioni non coassiali di un disco poroso e di un fluido all'infinito.     

Numerical Study of the Flow Behind a Rotary Oscillating Circular Cylinder

A numerical study is performed of flow behind a rotationally oscillating circular cylinder in a uniform flow by solving the two-dimensional incompressible Navier-Stokes equations. The flow behavior in lock-on regime and the timing of vortex formation from the oscillating cylinder are studied. When the frequency of excitation of the cylinder is in the vicinity of the natural vortex formation frequency, a lock-on vortex formation regime appears. As the excitation frequency being increased relative to the natural frequency the initially formed vorticity concentration switches to the opposite side of the cylinder. The effects of oscillating frequency and amplitude on the vortex structures formed in the near wake of the cylinder are also investigated. Based on the present calculated results, some complicated vortex patterns are identified and are consistent with the previous experimental visualizations.     

振荡流中圆柱受力测量研究

本文叙述了测量振荡流中圆柱受力大小和性质的方法和步骤。给出了测量结果,并首次给出这种力的频谱特性。     

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.     

Forces Exerted on a Body in an Unsteady Vortex Separation Flow of an Ideal Incompressible Fluid

A formula relating the forces exerted on a three-dimensional body to the motion of a vortex and source system simulating that body is derived for an unsteady vortex separation flow of an ideal incompressible fluid. The shape of the body can vary with time. In the case of steady-state homogeneous flow past an airfoil the formula obtained coincides with the Joukovski formula.     

On the Arnold Stability of a Solid in a Plane Steady Flow of an Ideal Incompressible Fluid

We study the stability of a rigid body in a steady rotational flow of an inviscid incompressible fluid. We consider the two-dimensional problem: a body is an infinite cylinder with arbitrary cross section moving perpendicularly to its axis, a flow is two-dimensional, i.e., it does not depend on the coordinate along the axis of a cylinder; both body and fluid are in a two-dimensional bounded domain with an arbitrary smooth boundary. Arnold's method is exploited to obtain sufficient conditions for linear stability of an equilibrium of a body in a steady rotational flow. We first establish a new energy-type variational principle which is a natural generalization of the well-known Arnold's result (1965a, 1966) to the system “body + fluid.” Then, by Arnold's technique, a general sufficient condition for linear stability is obtained. Received 21 February 1997 and accepted 23 June 1997     

Transport Phenomenon in a Third-Grade Fluid Over an Oscillating Surface

The heat and mass transfer effects on the flow of a conducting third-grade fluid over an oscillating vertical porous plate with chemical reactions are considered. Highly nonlinear governing equations of the third-grade fluid are solved analytically by using a multi-parameter perturbation technique and compared with the numerical results obtained by the parallel shooting method. The fluid flow velocity, temperature, and concentration are analyzed as functions of the Hartmann number, suction parameter, Prandtl and Schmidt numbers, and chemical reaction parameter.     

Simple Oscillating Fluid Flow Transducer (Wiggle-wand Flapper)

Experimental Techniques -     

Motion of a Pulsating Rigid Body in an Oscillating Viscous Fluid

The motion of a rigid sphere in a viscous fluid due to specified pulsations of the sphere and specified oscillations of the fluid away from the sphere is considered.     

Linear Longwave Instability of a Single Class of Steady-State Jet Flows of an Ideal Fluid in the Field of a Self-Electric Current

A necessary and sufficient condition of linear stability of a certain two-parameter class of cylindrical steady-state shear jet MHD flows of an inviscid incompressible ideally-conducting fluid with a free boundary is obtained by the direct Lyapunov method. The magnetic field is induced by a direct current flowing along the jet so that the field linearly depends on the radius. The stability with respect to small axisymmetric longwave perturbations is considered. The perturbations conserve leave the ratio of the distance between a fluid particle and the jet axis to the azimuthal vorticity component unchanged in each fluid particle. Two-sided exponential estimates of the perturbation growth are derived in the case of violation of the stability condition obtained.     

Similarities of Patterns in Fluid and Granulated Flow Inside a Horizontally Rotating Cylinder

The formation of flow patterns in liquid and granulated media is studied experimentally. Many phenomena such as segregation of particles different in dimensions, surface properties, and density are observed only in granulated media. However, there exist many effects typical of flows in both liquid and granulated media in a horizontal circular cylinder rotating about its axis. Eight classes of the following similar patterns in fluids and granulated mixtures were studied experimentally: vortex-like patterns, deformation of the trailing and leading edges of a layer, shark-teeth patterns, fish-like patterns, formation of rotating layers, ring-like patterns, and cellular patterns     

Linear Instability Criteria for Ideal Fluid Flows Subject to Two Subclasses of Perturbations

We examine the linear stability of both 2D and 3D steady state solutions to Euler’s equation subject to two classes of high frequency perturbations: those that preserve the topology of vortex lines and those that do not. Lower bounds for the essential spectral radius of the linear evolution operator are given for both types of perturbations.     

Instability of a Cantilever with a Propeller in an Incident Flow

A physical explanation is given to the mechanism of back coupling of the perturbed motion of a propeller in its plane of rotation and the force in the same plane. This unusual feedback may cause a mechanical system with a propeller to self-excite in the plane of possible oscillations of its axis upon propeller reversal. Instability occurs easier at the resonance of the system when the resultant moment of external forces lags in phase behind the angle of attack by approximately 5/4.     

Instability of an Unbounded Elastic Plate in a Gas Flow

The stability of an unbounded plane elastic plate in gas moving on one side of the plate and at rest on the other is analyzed. The gases are inviscid and in general different. The plate is under tension and has flexural stiffness. It is shown that the system is always unstable to plane sinusoidal perturbations with wave vector parallel to the velocity. As limiting cases, a tangential discontinuity between the two gases and unilateral flow past a plate with constant pressure on the opposite side are considered. In these cases, the conditions of stability to plane perturbations are non-trivial and are investigated below.     

Criteria for the Separation of Unsteady Ideal Fluid Flow past a Smooth Airfoil

Criteria for the separation of unsteady flow past a closed smooth airfoil are studied using the ideal fluid model and the Brillouin-Villat criterion. The necessary separation conditions are formulated. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 74–81, January– February, 2006.     

纳米柱绕流的分子动力学模拟分析

采用分子动力学方法,对不同雷诺数的纳米柱绕流问题进行模拟.统计及对比结果表明,在微观尺度下的纳米圆柱绕流的流场与宏观的圆柱绕流类似,但又具有自己的特点.雷诺数为16.2时,圆柱后会持续的周期性产生漩涡并脱落,类似宏观现象中的卡门涡街;而雷诺数为5.4时的圆柱后面没有出现漩涡.流场中圆柱表面存在速度滑移,说明无滑移不是产生漩涡的必要条件.圆柱前后会分别形成高压区和低压区,压强差的大小与来流速度有关.流场中存在顺压强梯度和逆压强梯度,顺压强梯度使圆柱上下两边区域流速超过来流速度,而逆压强梯度则会减小流速甚至使流场中出现回流.流场中密度最小处分布在圆柱右上和右下附近而不是圆柱的正后方.     

Global Nonlinear Stability for Steady Ideal Fluid Flow in Bounded Planar Domains

We prove stability of steady flows of an ideal fluid in a bounded, simply connected, planar region, that are strict maximisers or minimisers of kinetic energy on an isovortical surface. The proof uses conservation of energy and transport of vorticity for solutions of the vorticity equation with initial data in L^p for p>4/3. A related stability theorem using conservation of angular momentum in a circular domain is also proved.     

床面固体颗粒圆柱绕流的试验现象观察

本文介绍了床面固体颗粒随水流绕过圆柱体时，将在圆柱周围的床面上形成一个无粒子运动区的试验现象。水槽试验结果表明，当固体颗粒的粒径减小时，无粒子区的范围将增大；无粒子区的范围随圆柱直径的增大而增大；水流条件的变化直接影响着床面固体颗粒的运动情况，同无粒子区的形成、消失及范围大小有密切的关系。根据试验资料，结合量纲分析，建立了无粒子区的无量纲经验关系式     

Instability of a Tangential Discontinuity in an Axisymmetric Flow with a Stagnation Point

The linear problem of the stability of a plane tangential discontinuity occurring at the interface of two counter-streaming inviscid incompressible axisymmetric flows and including a stagnation point is considered. Using the integral Hankel transform, the problem was reduced to the solution of a single elliptic differential equation governing the discontinuity shape. An analysis of this equation by the normal-mode technique leads to a dispersion relation from which there follows the instability of the discontinuity. A similar problem for the plane-symmetric case has previously been studied by the author.