Flow-Induced Vibrations Of A Cylinder With Two Degrees Of Freedom Near Rigid Plane Boundary

Based on similarity analyses, the flow-induced vibrations of a near-wall cylinder with 2 degrees of freedom are investigated experimentally by employing a hydroelastic apparatus in conjunction with a flume. The cylinder's vibration amplitude, vibration frequency and vortex shedding frequency were measured and analyzed. The effects of gap-to-diameter ratio (e,ID) upon the vibration responses are further investigated. The experimental results indicate that, when the reduced velocity (Vr) is small (e.g. Vr = 1.2 similar to 2.6), only streamwise vibration occurs, and its frequency is quite close to its natural frequency in still water. When increasing Vr (e.g. Vr > 3.4), both streamwise and transverse vibrations of the near-wall cylinder may occur. In the examined range of gap-to-diameter ratio (0.42 < e(0)/D < 2.68), 2 vibration stages (in terms of Vr) of streamwise vibrations usually exist: First Streamwise Vibration (FSV) and Second Streamwise Vibration (SSV). In the SSV stage, the vortex shedding frequency may either undergo a jump to that of the streamwise vibration, or stay consistent with that of the transverse vibration. The amplitudes of transverse vibration are usually much larger than those of streamwise vibration for the same value of e(0)/D. The maximum amplitudes of both streamwise and transverse vibration get larger with the increase of e(0)/D (0.42 < e(0)/D < 2.68).

An Approximate Method For Calculation Of Fluid Force And Response Of A Circular Cylinder At Lock-In

In this paper, equations calculating lift force of a rigid circular cyclinder at lock-in uniform flow are deduced in detail. Besides, equations calculating the lift force on a long flexible circular cyclinder at lock-in are deduced based on mode analysis of a multi-degree freedom system. The simplified forms of these equations are also given. Furthermore, an approximate method to predict the forces and response of rigid circular cyclinders and long flexible circular cyclinders at lock-in is introduced in the case of low mass-damping ratio. A method to eliminate one deficiency of these equations is introduced. Comparison with experimental results show the effectiveness of this approximate method.

Experimental Investigation Of Influence Of Interfacial Tension On Convection Of Two-Layer Immiscible Liquid

Benard-Marangoni convections of two-layer fluids heated from the bottom are investigated experimentally with a particle imagine velocimetry. The flows are visualized from the side, and various velocity fields near the onset of convection, such as three-layer vortex convective patterns, are observed when the depth ratio varies in a wide range. A new classification of the convective patterns is proposed with more detail than in previous studies. The analysis of the results indicates that the interface tension greatly influences the motion intensities of the bottom and top layers. The dimensionless wave number increases with the Bond number when the motion in the top layer is not more intense than that in the bottom layer, which agrees with the theoretical prediction.

A Note On The Numerical Simulations Of Flow Past A Wavy Square-Section Cylinder

The flow past a square-section cylinder with a geometric disturbance is investigated by numerical simulations. The extra terms, due to the introduction of mapping transformation simulating the effect of disturbance into the transformed Navier-Stokes equations, are correctly derived, and the incorrect ones in the previous literature are pointed out and analyzed. Furthermore, the relationship between the vorticity, especially on the cylinder surface, and the disturbance is derived and explained theoretically. The computations are performed at two Reynolds numbers of 100 and 180 and three amplitudes of waviness of 0.006, 0.025 and 0.167 with another aim to explore the effects of different Reynolds numbers and disturbance on the vortex dynamics in the wake and forces on the body. Numerical results have shown that, at the mild waviness of 0.025, the Karman vortex shedding is suppressed completely for Re = 100, while the forced vortex dislocation is appeared in the near wake at the Reynolds number of 180. The drag reduction is up to 21.6% at Re = 100 and 25.7% at Re = 180 for the high waviness of 0.167 compared with the non-wavy cylinder. The lift and the Strouhal number varied with different Reynolds numbers and the wave steepness are also obtained.

VISUALIZATION RESULTS OF AXISYMMETRICAL WAKE FLOW WITH/WITHOUT ACOUSTIC EXCITATION

Visualization results demonstrate the evolution of Kelvin-Helmholtz unstable waves into vortex pairing in a separated shear layer of a blunf circular. The results with acoustic excitation are quite different from that without acoustic excitation, and the phenomenon with excitation in a separated shear layer follows the rule of Devil s staircase, which always occurs in a non-linear dynamical system of two coupling vibrators.

On separated shear layer of blunt circular cylinder

Separated shear layer of blunt circular cylinder has been experimentally investigated for the Reynolds numbers (based on the diameter) ranging from 2.8 x 10(3) to 1.0 x 10(5), with emphasis on evolution of separated shear layer, its structure and distribution of Reynolds shear stress and turbulence kinetic energy. The results demonstrate that laminar separated shear layer experiences 2 similar to 3 times vortex merging before it reattaches, and turbulence separated shear layer takes 5 similar to 6 times vortex merging. In addition, relationship between dimensionless initial frequencies of K-H instability and Reynolds numbers is identified, and reasons for the decay of turbulence kinetic energy and Reynolds shear stress in reattachment region are discussed.

MILU-CG method and the numerical study on the flow around a rotating circular cylinder

A hybrid finite difference method and vortex method (HDV), which is based on domain decomposition and proposed by the authors (1992), is improved by using a modified incomplete LU decomposition conjugate gradient method (MILU-CG), and a high order implicit difference algorithm. The flow around a rotating circular cylinder at Reynolds number R-e = 1000, 200 and the angular to rectilinear speed ratio alpha is an element of (0.5, 3.25) is studied numerically. The long-time full developed features about the variations of the vortex patterns in the wake, and drag, lift forces on the cylinder are given. The calculated streamline contours agreed well with the experimental visualized flow pictures. The existence of critical states and the vortex patterns at the states are given for the first time. The maximum lift to drag force ratio can be obtained nearby the critical states.

Numerical exploration of new features on three-dimensional transition of a cylinder wake

The three-dimensional transition of the wake flow behind a circular cylinder is studied in detail by direct numerical simulations using 3D incompressible N-S equations for Reynolds number ranging from 200 to 300. New features and vortex dynamics of the 3D transition of the wake are found and investigated. At Re = 200, the flow pattern is characterized by mode A instability. However, the spanwise characteristic length of the cylinder determines the transition features. Particularly for the specific spanwise characteristic length linear stable mode may dominate the wake in place of mode A and determine the spanwise phase difference of the primary vortices shedding. At Re = 250 and 300 it is found that the streamwise vortices evolve into a new type of mode - "dual vortex pair mode" downstream. The streamwise vortex structures switch among mode A, mode B and dual vortex pair mode from near wake to downstream wake. At Re = 250, an independent low frequency f(m) in addition to the vortex shedding frequency f(s) is identified. Frequency coupling between f(m) and f(s) occurs. These result in the irregularity of the temporal signals and become a key feature in the transition of the wake. Based on the formation analysis of the streamwise vorticity in the vicinity of cylinder, it is suggested that mode A is caused by the emergence of the spanwise velocity due to three dimensionality of the incoming flow past the cylinder. Energy distribution on various wave numbers and the frequency variation in the wake are also described.

Numerical simulation of Richtmyer-Meshkov instability

The compressible Navier-Stokes equations discretized with a fourth order accurate compact finite difference scheme with group velocity control are used to simulate the Richtmyer-Meshkov (R-M) instability problem produced by cylindrical shock-cylindrical material interface with shock Mach number Ms = 1.2 and density ratio 1:20 (interior density/outer density). Effect of shock refraction, reflection, interaction of the reflected shock with the material interface, and effect of initial perturbation modes on R-M instability are investigated numerically. It is noted that the shock refraction is a main physical mechanism of the initial phase changing of the material surface. The multiple interactions of the reflected shock from the origin with the interface and the R-M instability near the material interface are the reason for formation of the spike-bubble structures. Different viscosities lead to different spike-bubble structure characteristics. The vortex pairing phenomenon is found in the initial double mode simulation. The mode interaction is the main factor of small structures production near the interface.

Variation of added mass and its application to the calculation of amplitude response for a circular cylinder

In the present study, analyzed are the variation of added mass for a circular cylinder in the lock-in ( synchronization) range of vortex-induced vibration (VIV) and the relationship between added mass and natural frequency. A theoretical minimum value of the added mass coefficient for a circular cylinder at lock-in is given. Developed are semi-empirical formulas for the added mass of a circular cylinder at lock-in as a function of flow speed and mass ratio. A comparison between experiments and numerical simulations shows that the semi-empirical formulas describing the variation of the added mass for a circular cylinder at lock-in are better than the ideal added mass. In addition, computation models such as the wake oscillator model using the present formulas can predict the amplitude response of a circular cylinder at lock-in more accurately than those using the ideal added mass.

Attractor crisis and bursting in a fluid flow with two no-slip directions

Characteristic burtsing behavior is observed in a driven, two-dimensional viscous flow, confined to a square domain and subject to no-slip boundaries. Passing a critical parameter value, an existing chaotic attractor undergoes a crisis, after which the flow initially enters a transient bursting regime. Bursting is caused by ejections from and return to a limited subdomain of the phase space, whereas the precrisis chaotic set forms the asymptotic attractor of the flow. For increasing values of the control parameter the length of the bursting regime increases progressively. Passing another critical parameter value, a second crisis leads to the appearance of a secondary type of bursting, of very large dynamical range. Within the bursting regime the flow then switches in irregular intervals from the primary to the secondary type of bursting. Peak enstrophy levels for both types of bursting are associated to the collapse of a primary vortex into a quadrupolar state.

On the topological bifurcation of flows around a rotating circular cylinder

Flow fields around a rotating circular cylinder in a uniform stream are computed using a low dimensional Galerkin method. Results show that the formation of a Fopple vortex pair behind a stationary circular cylinder is caused by the structural instability in the vicinity of the saddle located at the rear of the cylinder. For rotating cylinder a bifurcation diagram with the consideration of two parameters, Reynolds number Re and rotation parameter a, is built by a kinematic analysis of the steady flow fields.

Transition waves and nonlinear interactions in the near wake of a circular cylinder

Transition waves and interactions between two kinds of instability-vortex shedding and transition wave in the near wake of a circular cylinder in the Reynolds number range 3 000-10 000 are studied by a domain decomposition hybrid numerical method. Based on high resolution power spectral analyses for velocity new results on the Reynolds-number dependence of the transition wave frequency, i.e. f(t)/f(s) similar to Re-0.87 are obtained. The new predictions are in good agreement with the experimental results of Wei and Smith but different from Braza's prediction and some early experimental results f(t)/f(s) similar to Re-0.5 given by Bloor et nl. The multi-interactions between two kinds of vortex are clearly visualized numerically. The strong nonlinear interactions between the two independent frequencies (f(t), f(s)) leading to spectra broadening to form the coupling mf(s) +/- nf(t) are predicted and analyzed numerically, and the characteristics of the transition are described. Longitudinal variations of the transition wave and its coupling are reported. Detailed mechanism of the flow transition in the near wake before occurrence of the three-dimensional evolution is provided.

Numerical study of bifurcation solutions of spherical Taylor-Couette flow

The steady bifurcation flows in a spherical gap (gap ratio sigma=0.18) with rotating inner and stationary outer spheres are simulated numerically for Re(c1)less than or equal to Re less than or equal to 1 500 by solving steady axisymmetric incompressible Navier-Stokes equations using a finite difference method. The simulation shows that there exist two steady stable flows with 1 or 2 vortices per hemisphere for 775 less than or equal to Re less than or equal to 1 220 and three steady stable flows with 0, 1, or 2 vortices for 1 220depends mainly on the acceleratio n, but that of one-vortex flow also depends on the perturbation breaking the equatorial symmetry. The mechanism of development of a saddle point in the meridional plane at higher Re number and its role in the formation of two-vortex flow are analyzed.

Compact finite difference - Fourier spectral method for three-dimensional incompressible Navier-Stokes equations

A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported.