On characteristics of two-degree-of-freedom vortex induced vibration of two low-mass circular cylinders in proximity at low Reynolds number

Two-degree-of-freedom vortex induced vibrations (VIVs) of two identical spring-supported circular cylinders in proximity with the mass ratio of 2 and zero damping at Re of 100 are numerically studied. Totally 20 arrangements of cylinders are investigated combining four stagger angles and five normalized center-to-center spacings. Results show that the in-line vibration amplitude is comparable to the transverse one for most arrangements and usually accompanies irregular cylinder trajectories. Extremely slender figure-8 cylinder trajectories usually seen in single-cylinder VIVs exist only for the tandem arrangements. Arranging the trailing cylinder to vibrate near the wake boundary of the leading cylinder enhances the possibility of irregular trajectories and impacts of both cylinders. Impact between cylinders must occur in cases with irregular cylinder trajectories; however, irregular cylinder trajectories could be found in impact-free cases. The stagger angle significantly changes the attribute of the transverse vibration frequency, toward either the single-cylinder VIV frequency or natural structure frequency in still fluid. The major transverse vibration frequency and the natural structure frequency in still fluid are decoupled for all the side-by-side arrangements and some far spaced tandem arrangements and highly correlated for non-tandem and non-side-by-side arrangements. The time-averaged impact frequency increases with decreasing normalized center-to-center spacing for most combinations of stagger angle and reduced velocity. Apart from the side-by-side arrangements, high-frequency impacts occur when the trailing cylinder is initially located in or near the wake zone of the leading cylinder. The mechanism of trailing cylinder chopping the gap-flow vortices plays an important role in determining the near-wake vortex structures for all non-side-by-side arrangements.     

Flow-induced vibration of a circular cylinder subjected to wake interference at low Reynolds number

Two- and three-dimensional numerical simulations of the flow around two circular cylinders in tandem arrangements are performed. The upstream cylinder is fixed and the downstream cylinder is free to oscillate in the transverse direction, in response to the fluid loads. The Reynolds number is kept constant at 150 for the two-dimensional simulations and at 300 for the three-dimensional simulations, and the reduced velocity is varied by changing the structural stiffness. The in-line centre-to-centre distance is varied from 1.5 to 8.0 diameters, and the results are compared to that of a single isolated flexible cylinder with the same structural characteristics, m^?=2.0 and ζ=0.007. The calculations show that significant changes occur in the dynamic behaviour of the cylinders, when comparing the flow around the tandem arrangements to that around an isolated cylinder: for the tandem arrangements, the lock-in boundaries are wider, the maximum displacement amplitudes are greater and the amplitudes of vibration for high reduced velocities, outside the lock-in, are very significant. The main responsible for these changes appears to be the oscillatory flow in the gap between the cylinders.     

Control of vortex shedding behind circular cylinder for flows at low Reynolds numbers

It has been observed by researchers in the past that vortex shedding behind circular cylinders can be altered, and in some cases suppressed, over a limited range of Reynolds numbers by proper placement of a second, much smaller, ‘control’ cylinder in the near wake of the main cylinder. Results are presented for numerical computations of some such situations. A stabilized finite element method is employed to solve the incompressible Navier–Stokes equations in the primitive variables formulation. At low Reynolds numbers, for certain relative positions of the main and control cylinder, the vortex shedding from the main cylinder is completely suppressed. Excellent agreement is observed between the present computations and experimental findings of other researchers. In an effort to explain the mechanism of control of vortex shedding, the streamwise variation of the pressure coefficient close to the shear layer of the main cylinder is compared for various cases, with and without the control cylinder. In the cases where the vortex shedding is suppressed, it is observed that the control cylinder provides a local favorable pressure gradient in the wake region, thereby stabilizing the shear layer locally. Copyright © 2001 John Wiley & Sons, Ltd.     

Effect of blockage on free vibration of a circular cylinder at low Re

The effect of the blockage on vortex‐induced vibrations of a circular cylinder of low non‐dimensional mass (m^*=10) in the laminar flow regime is investigated in detail. A stabilized space–time finite element formulation is utilized to solve the incompressible flow equations in primitive variables form in two dimensions. The transverse response of the cylinder is found to be hysteretic at both ends of synchronization/lock‐in region for 5% blockage. However, for the 1% blockage hysteresis occurs only at the higher Re end of synchronization/lock‐in region. Computations are carried out at other blockages to understand its effect on the hysteretic behavior. The hysteresis loop at the lower Re end of the synchronization decreases with decrease in blockage and is completely eliminated for blockage of 2.5% and less. On the other hand, hysteresis persists for all values of blockage at the higher Re end of synchronization/lock‐in. Although the peak transverse oscillation amplitude is found to be same for all blockage (～0.6D), the peak value of the aerodynamic coefficients vary significantly with blockage. The r.m.s. values show lesser variation with blockage. The effect of streamwise extent of computational domain on hysteretic behavior is also studied. The phase between the lift force and transverse displacement shows a jump of almost 180° at, approximately, the middle of the synchronization region. This jump is not hysteretic and is independent of blockage. Copyright © 2008 John Wiley & Sons, Ltd.     

A three-dimensional simulation of a steady approach flow past a circular cylinder at low Reynolds number

The three-dimensional (3D) unsteady viscous wake of a circular cylinder exposed to a steady approach flow is calculated using a fractional-step finite-difference/spectral-element method. The calculated flow fields at Reynolds numbers of 100 (2D) and 200 (3D) are examined in detail. The flow field at Re = 100 is 2D as expected, while the flow field at Re = 200 has distinct 3D features, with spanwise wavelengths of about 3.75 cylinder diameters. The calculated results produce drag and lift coefficients and Strouhal numbers that agree extremely well with the experimental values. These 3D values at Re = 200 are in better agreement with experimental values than the results of a 2D calculation at Re = 200, which is expected. © 1998 John Wiley & Sons, Ltd.     

Vortex-induced vibration of a cylinder with nonlinear energy sink (NES) at low Reynolds number

Nonlinear Dynamics - Vortex-induced vibration (VIV) is a fluid structure interaction phenomena that can lead to the fatigue failure of high-rise structures. To study the basic principles and method...     

Numerical investigation on vortex-induced vibration of an elastically mounted circular cylinder at low Reynolds number using the fictitious domain method

A direct numerical simulation of two-dimensional (2D) flow past an elastically mounted circular cylinder at low Reynolds number using the fictitious domain method had been undertaken. The cylinder motion was modelled by a two degree-of-freedom mass–spring–damper system. The computing code was verified against a benchmark problem in which flow past a stationary circular cylinder is simulated. Then, analyses of vortex-induced vibration (VIV) responses, drag and lift forces and the phase and vortex structures were carried out. Results show that the cylinder's non-dimensional cross-flow response amplitude reaches its summit of 0.572 in the ‘lock-in’ regime. The ‘2S’, instead of the ‘2P’, vortex shedding mode is dominated in the ‘lower’ branch for this 2D low-Re VIV. A secondary oscillation is observed in the lift force when ‘lock-in’ occurs. It is shown that this secondary component changes the phase, offset the energy input by the primary component and thus reduces the cylinder responses. Effects of the Skop–Griffin parameter on cylinder responses were also investigated.     

Suppression of vortex shedding from a rectangular cylinder at low Reynolds numbers

Small elements of circular, square, triangular and thin-strip cross-sections are used to suppress vortex shedding from a rectangular cylinder of stream-wise to transverse scale ratio L/B=3.0 at Reynolds numbers in the range of Re=V_∞B/ν=75–130, where V_∞ is the on-coming velocity of the stream, and ν is the kinematic viscosity. The relative transverse dimension of the small element b/B is fixed at 0.2. The results of numerical simulation and visualization experiment show that, vortex shedding from both sides of the cylinder can be suppressed and the fluctuating drag and lift of the cylinder can be greatly reduced, if the element is placed in a certain region referred to as the effective zone. Comparisons at a specific Reynolds number indicate that the square element produces the largest size of the effective zone, whereas the triangular element yields the smallest. Results also show that the effective zone for the square element shrinks with increasing Re and disappears at Re>130. Independent of element cross-section shape and Reynolds number, the center of the effective zone is always at X/B=2.5–3.0 and Y/B≈1.0. The mechanism of the suppression is discussed from the view points of velocity profile stability and stress distribution.     

Computation of high Reynolds number flow around a circular cylinder with surface roughness

Incompressible high-Reynolds-number flows around a circular cylinder are analyzed by direct integration of the Navier-Stokes equations using finite-difference method. A generalized coordinate system is used so that a sufficient number of grid points are distributed in the boundary layer and the wake. A numerical scheme which suppresses non-linear instability for calculations of high-Reynolds-number flows is developed. The computation of an impulsively started flow at Re = 1200 is compared with corresponding experimental observations, and excellent agreements are obtained.A series of computations are carried out on the flow around a circular cylinder with surface roughness. The height of the roughness in these computations is 0.5% of the diameter. The range of Reynolds numbers is from 10³ to 10⁵; no turbulence model is employed. Sharp reduction of drag coefficient is observed near Re = 2 × 10⁴, which indicates that the critical Reynolds number is captured in the present computation.     

低雷诺数下弹性圆柱体涡激振动及影响参数分析

利用Fluent软件数值求解不可压缩粘性流体的N-S方程,研究均匀来流Re=200时弹性圆柱体的涡激振动.圆柱体运动简化为质量-弹簧-阻尼系统,将Newmark-β方法代码写入用户自定义函数(UDF)求解运动方程,柱体与流体间的非线性耦合作用通过动网格技术实现.详细分析了涡激力系数、柱体位移特征值和尾流涡结构随频率比的变化关系,获得"相位开关"、"拍"等现象.考虑流向振动对横向振动影响时,圆柱体最大横向振幅为0.65倍直径.当固定频率比,而质量比或折合阻尼增大时,圆柱体流向与横向振动均呈非线性衰减趋势,但增大质量比对流向平均位移的偏离起到更好的控制效果.     

Treadmilling swimmers near a no-slip wall at low Reynolds number

The motion of a circular treadmilling low Reynolds number swimmer near a no-slip wall is studied analytically. First, the exact solution of Jeffrey and Onishi [Q. J. Mech. Appl. Math., 34 (1981)] for a translating and rotating solid cylinder near a no-slip wall is rederived using a novel conformal mapping approach that differs from the original derivation which employed bipolar coordinates. Then it is shown that this solution can be combined with the reciprocal theorem, and the calculus of residues, to produce an explicit non-linear dynamical system for the treadmilling swimmer's velocity and angular velocity. The resulting non-linear dynamical system governing the swimmer motion is used to corroborate the qualitative results obtained by an approximate model of the same swimmer recently presented in Crowdy and Or [Phys. Rev. E., 81 (2010)].     

Analysis of buoyancy-aided convection heat transfer from a horizontal cylinder in a vertical duct at low Reynolds number

This paper reports a numerical study on buoyancy-aided steady convection heat transfer from a horizontal cylinder situated in a vertical adiabatic duct. Numerical results have been generated forH ₁/D=2.5, 4, 8,H/D=8, 16, 24,S/D=2, 4, 6, 20Re60, andRi up to 4. The placing of a horizontal cylinder in a vertical duct of smaller width results in significantly enhanced pure forced convection due to the blockage effect, but degrades appreciably the extent of buoyancy-aided enhancement in the heat transfer rate. Nevertheless, the presence of a vertical duct leads to an overall enhancement of mixed convection heat transfer coefficient relative to that without the confining duct. Moreover, the average Nusselt number is rather insensitive to the variation of either the position of the cylinder in the duct or the duct height in the investigated ranges of these geometric parameters.Dieser Artikel beschreibt eine numerische Studie über auftriebsunterstützte konvektive Wärmeübertragung von einem horizontalen Zylinder der in einem vertikalen adiabaten Kanal positioniert ist. Die numerischen Ergebnisse sind fürH ₁/D=2, 5, 4, 8,H/D=8, 16, 24,S/D=2, 4, 6 sowie 20Re60 undRi bis 4 berechnet worden. Die Anordnung des horizontalen Zylinders in einem schmaleren vertikalen Kanal führt auf Grund des Blockierungs-effektes zu einem deutlichen Anstieg der reinen Zwangskonvektion. Aber sie verschlechtert deutlich den Betrag der auftriebsbedingten Steigerung in der Wärmeübergangsrate. Trotzdem führt die Anwesenheit des vertikalen Kanals insgesamt zu einer Steigerung des Wärmeübergangskoeffizienten bei Mischkonvektion im Vergleich zur Abwesenheit des begrenzenden Kanals. Des weiteren ist die durchschnittliche Nusseltzahl von der Variation der Zylinderposition im Kanal oder der Kanalhöhe abhängig.     

Experimental study of simultaneous measurement of velocity and surface topography: in the wake of a circular cylinder at low Reynolds number

A technique to provide simultaneous measurement on both free surface topography and the velocity vector field of free surface flows is further developed and validated. Testing was performed on the topography measurement by imaging static plastic wave samples over a wide range of amplitudes. Analysis on the accuracy of the topography reconstruction, the sensitivity to noise and the dependence on spatial resolution are presented. The displacement of the free surface is insensitive to noisy input and the sensitivity shows a linear dependence with the sample spacing. Simultaneous measurements of the free surface and associated velocity field in the wake of a circular cylinder are presented for Reynolds numbers between 55 and 100.     

Characteristics of the near wake of a cylinder at low Reynolds numbers

An experimental study has been made of the near wake of two two-dimensional bluff bodies, a circular cylinder and a flat ribbon in the regimes corresponding to the 2-D steady and 2-D periodic wake. Velocity measurements from both hot-wire and laser Doppler anemometry are compared. Detailed measurements of the velocity field in air in the near wake, in isothermal conditions, are presented. The evolutions of the mean longitudinal velocity and the rms transverse velocity fluctuation on the center line can be plotted in a universal form whatever the value of the Reynolds number. These measurements show also that the onset of the instability is related to a critical value of an interaction term characteristic of the strength of the shear layers and the shear layer spacing at the end of the recirculation zone.     

On the origin of wake-induced vibration in two tandem circular cylinders at low Reynolds number

We numerically investigate flow-induced vibrations of circular cylinders arranged in a tandem configuration at low Reynolds number. Results on the coupled force dynamics are presented for an isolated cylinder and a pair of rigid cylinders in a tandem configuration where the downstream cylinder is elastically mounted and free to vibrate transversely. Contrary to turbulent flows at high Reynolds number, low frequency component with respect to shedding frequency is absent in laminar flows. Appearance and disappearance of the vorticity regions due to reverse flow on the aft part of the vibrating cylinder is characterized by a higher harmonic in transverse load, which is nearly three times of the shedding frequency. We next analyze the significance of pressure and viscous forces in the composition of lift and their phase relations with respect to the structural velocity. For both the isolated and tandem vibrating cylinders, the pressure force supplies energy to the moving cylinder, whereas the viscous force dissipates the energy. Close to the excitation frequency ratio of one, the ratio of transverse viscous force to pressure force is found to be maximum. In addition, movement of stagnation point plays a major role on the force dynamics of both configurations. In the case of isolated cylinder, displacement of the stagnation point is nearly in-phase with the velocity. During vortex-body interaction, the phase difference between the transverse pressure force and velocity and the location of stagnation point determines the loads acting on the cylinder. When the transverse pressure force is in-phase with velocity, the stagnation point moves to higher suction region of the cylinder. In the case of the tandem cylinder arrangement, upstream vortex shifts the stagnation point on the downstream cylinder to the low suction region. Thus a larger lift force is observed for the downstream cylinder as compared to the vibrating isolated cylinder. Phase difference between the transverse load and the velocity of the downstream cylinder determines the extent of upstream wake interaction with the downstream cylinder. When the cylinder velocity is in-phase with the transverse pressure load component, interaction of wake vortex with the downstream cylinder is lower compared to other cases considered in this study. We extend our parametric study of tandem cylinders for the longitudinal center-to-center spacing ranging from 4 to 10 diameter.