On the study of vortex-induced vibration of a cylinder with helical strakes

While the effect of helical strakes on suppression of Vortex-Induced Vibrations (VIV) has been studied extensively, the mechanism of VIV mitigation using helical strakes is much less well documented in the literature. In the present study, a rigid circular cylinder of diameter d=80 mm attached with three-strand helical strakes of dimensions of 10d in pitch and 0.12d in height was tested in a wind tunnel. It was found that the helical strakes can reduce VIV by about 98%. Unlike the bare cylinder, which experiences lock-in over the reduced velocity in the range of 5-8.5, the straked cylinder does not show any lock-in region. In exploring the mechanism of VIV reduction by helical strakes, measurements in stationary bare and straked cylinder wakes using both a single X-probe at four different Reynolds numbers, i.e. Re=10 240, 20 430, 30 610 and 40 800, and two X-probes with variable separations in the spanwise direction at Re=20 430 were conducted. It was found that vortices shed from the straked cylinder are weakened significantly. The dominate frequency varies by about 30% over the range of x/d=10-40 in the streamwise direction while that differs by about 37.2% of the averaged peak frequency over a length of 3.125d in the spanwise direction. The latter is supported by the phase difference between the velocity signals measured at two locations separated in the spanwise direction. The correlation length of the vortex structures in the bare cylinder wake is much larger than that obtained in the straked cylinder wake. As a result, the straked cylinder wake agrees more closely with isotropy than the bare cylinder wake. Flow visualization on the plane perpendicular to the cylinder axis at Reynolds number of about 300 reveals small-scale vortices in the shear layers of the straked cylinder wake. However, these vortices do not roll up and interact with each other to form the well-organized Karman-type vortices. Flow visualization on the plane parallel to the cylinder axis shows vortex dislocation and swirling flow, which should be responsible for the variations of the peak frequency in the streamwise as well as spanwise directions.     

Experimental investigation of flow-induced vibration on isolated and tandem circular cylinders fitted with strakes

The effect of varying the geometric parameters of helical strakes on vortex-induced vibration (VIV) is investigated in this paper. The degree of oscillation attenuation or even suppression is analysed for isolated circular cylinder cases. How a cylinder fitted with strakes behaves when immersed in the wake of another cylinder in tandem arrangement is also investigated and these results are compared to those with a single straked cylinder. The experimental tests are conducted at a circulating water channel facility and the cylindrical models are mounted on a low-damping air bearing elastic base with one degree-of-freedom, restricted to oscillate in the transverse direction to the channel flow. Three strake pitches (p) and heights (h) are tested: p=5, 10, 15d, and h=0.1, 0.2, 0.25d. The mass ratio is 1.8 for all models. The Reynolds number range is from 1000 to 10 000, and the reduced velocity varies up to 21. The cases with h=0.1d strakes reduce the amplitude response when compared to the isolated plain cylinder, however the oscillation still persists. On the other hand, the cases with h=0.2, 0.25d strakes almost completely suppress VIV. Spanwise vorticity fields, obtained through stereoscopic digital particle image velocimetry (SDPIV), show an alternating vortex wake for the p=10d and h=0.1d straked cylinder. The p=10d and h=0.2d cylinder wake has separated shear layers with constant width and no roll-up close to the body. The strakes do not increase the magnitude of the out-of-plane velocity compared to the isolated plain cylinder. However, they deflect the flow in the out-of-plane direction in a controlled way, which can prevent the vortex shedding correlation along the span. In order to investigate the wake interference effect on the strake efficiency, an experimental arrangement with two cylinders in tandem is employed. The centre-to-centre distance for the tandem arrangement varies from 2 to 6. When the downstream p=10d and h=0.2d cylinder is immersed in the wake of an upstream fixed plain cylinder, it loses its effectiveness compared with the isolated case. Although the oscillations have significant amplitude, they are limited, which is a different behaviour from that of a tandem configuration with two plain cylinders. For this particular case, the amplitude response monotonically increases for all gaps, except one, a trait usually found in galloping-like oscillations. SDPIV results for the tandem arrangements show alternating vortex shedding and oscillatory wake.     

Effects of an asymmetrical confined flow on a rectangular cylinder

The effects of an asymmetric confined flow on a cylinder of rectangular cross-section are investigated and discussed. Experiments are performed in a wind tunnel by placing cylinders of different cross-sections at various elevations from the floor of the test-section. The Reynolds number is varied within the range 6×10³–4×10⁴. Forces exciting the cylinder are measured by built-in dynamometers placed inside the cylinder structure. The flow is characterized by mean and fluctuating local velocity components to define the inflow distribution and the ensuing wake region. The mean dimensionless force coefficients are then calculated and analyzed. The frequency analysis of the force components acting on the cylinder provides the dynamic characterization of the loading and of the wake shedding. The experimental results highlight that the presence of the wall strongly influences the system dynamics also when the cylinder is placed at a relatively large elevation from the wall itself. The cylinder aspect ratio governs effects of the wall condition on the force coefficients and the Strouhal number.     

Fluctuating lift on a circular cylinder: review and new measurements

Apart from providing some new experimental data the paper reviews previous investigations concerning fluctuating lift acting on a stationary circular cylinder in cross-flow. In particular, effects of Reynolds number in the nominal case of an infinitely long and nonconfined cylinder in a smooth oncoming flow are discussed. The Reynolds number range covered is from about Re=47 to 2×10⁵, i.e., from the onset of vortex shedding up to the end of the subcritical regime. At the beginning of the subcritical regime (Re≃0.3×10³) a spanwise correlation length of about 30 cylinder diameters is indicated, the correlation function being based on near-cylinder velocity fluctuations in outer parts of the separated shear layer. In between Reynolds numbers 1.6×10³ and 20×10³, an approximate 10-fold increase in the sectional r.m.s. lift coefficient is indicated. This range contains a fundamental change-over from one flow state to another, starting off at Re≃5×10³ and seemingly fully developed at Re≃8×10³.     

Heat transfer in asymmetric transverse flows over bundles of tubes

Heat transfer was studied on a separate transverse row of tubes with the relative pitch ofs ₁/d=1.5 and a staggered bundle with the relative pitches ofs ₁/d×s ₂/d=1.15×0.98. A test tube in the transverse row was used with a variable displacement from the symmetric position. The tube bundle was placed at different gaps from the shell wall. Experiments were performed in air and water in the range ofRe from 10³ to 6×10⁵. Asymmetric flows over transverse rows are accompanied by augmented heat transfer rates and steady state lift force which becomes higher with the amount of displacement. The presence of the shell wall introduces alterations in the thermal and fluid dynamics over outside tubes in a bundle.     

Numerical Simulation of the Negative Magnus Effect of a Two-Dimensional Spinning Circular Cylinder

Based on the finite volume method, the flow past a spinning circular cylinder at a low subcritical Reynolds number (Re =1 × 10 ⁵), high subcritical Reynolds number (Re =1.3 ×10 ⁵), and critical Reynolds number (Re =1.4 ×10 ⁵) were each simulated using the Navier-Stokes equations and the γ-Re _?? transition model coupled with the SST k?ω turbulence model. The system was solved using an implicit algorithm. The freestream turbulence intensity decay was effectively controlled by the source term method proposed by Spalart and Rumsey. The variations in the Magnus force as a function of the spin ratio, α were obtained for the three Reynolds numbers, and the flow mechanism was analyzed. The results indicate that the asymmetric transitions induced by spin affect the asymmetric separations at the top and bottom surfaces of the circular cylinder, which further affects the pressure distributions at the top and bottom surfaces of the circular cylinder and ultimately result in a negative Magnus force, whose direction is opposite to that of the classical Magnus force. This study is the first to use a numerical simulation method to predict a negative Magnus force acting on a spinning circular cylinder. At the low subcritical Reynolds number, the Magnus force remained positive for all spin ratios. At the high subcritical Reynolds number, the sign of the Magnus force changed twice over the range of the spin ratio. At the critical Reynolds number, the sign of the Magnus force changed only once over the range of the spin ratio. For relatively low spin ratios, the Magnus force significantly differed by Reynolds number; however, this variation diminished as the spin ratio increased.     

Flow-induced oscillation of two circular cylinders in tandem arrangement at low Re

Results are presented for flow-induced vibrations of a pair of equal-sized circular cylinders of low nondimensional mass (m^*=10) in a tandem arrangement. The cylinders are free to oscillate both in streamwise and transverse directions. The Reynolds number, based on the free-stream speed and the diameter of the cylinders, D is 100 and the centre-to-centre distance between the cylinders is 5.5D. The computations are carried out for reduced velocities in the range 2≤U^*≤15. The structural damping is set to zero for enabling maximum amplitudes of oscillation. A stabilized finite element method is utilized to carry out the computations in two dimensions. Even though the response of the upstream cylinder is found to be qualitatively similar to that of an isolated cylinder, the presence of a downstream cylinder is found to have significant effect on the behaviour of the upstream cylinder. The downstream cylinder undergoes very large amplitude of oscillations in both transverse and streamwise directions. The maximum amplitude of transverse response of the downstream cylinder is quite similar to that of a single cylinder at higher Re beyond the laminar regime. Lock-in and hysteresis are observed for both upstream and downstream cylinders. The downstream cylinder undergoes large amplitude oscillations even beyond the lock-in state. The phase between transverse oscillations and lift force suffers a 180 jump for both the cylinders almost in the middle of the synchronization regime. The phase between the transverse response of the two cylinders is also studied. Complex flow patterns are observed in the wake of the freely vibrating cylinders. Based on the phase difference and the flow patterns, the entire flow range is divided into five sub-regions.     

An experimental study of fluctuating lift on a square-section cylinder oscillating transversely in a uniform stream

Experiments on a square-section cylinder fixed and forced to oscillate transversely in a uniform stream were conducted in a water tank. The Reynolds number of the experiments is in the range of 3·10³ to 10⁴, the amplitude to side length ratioA/D is up to 0.7 and the range of reduced velocity is 4.5<V _r <12. This study aims at investigating the lock-in phenomenon, the fluctuating lift and the phase shift between fluctuating lift and displacement of the oscillating cylinder. The problems on the aeroelastic instability relating to present experimental results have been discussed. The flow visualization clearly shows that there are drastic changes of vortex-shedding from cylinder at the resonance point and the upper end of the lock-in range. The results of the flow visualization give better understanding of the physical mechanism of the phase shift. Project supported by National Natural Science Foundation of China     

FLOW-INDUCED VIBRATION OF A CIRCULAR CYLINDER AT LIMITING STRUCTURAL PARAMETERS

Transverse oscillation of a dynamically supported circular cylinder in a flow at Re=100 has been numerically simulated using a high-resolution viscous-vortex method, for a range of dynamical parameters. At the limiting case with zero values of mass, damping and elastic force, the cylinder oscillates sinusoidally at amplitudeA /D=0·47 and frequency fD/U_∞=0·156. For zero damping, the effects of mass and elasticity are combined into a new, “effective” dynamic parameter, which is different from the classic “reduced velocity”. Over a range of this parameter, the response exhibits oscillations at amplitudes up to 0·6 and frequencies between 0·15 and 0·2. From this response function, the classic response in terms of reduced velocity can be obtained for fixed values of the cylinder/fluid ratio m^*. It displays “lock-in” at very high values of m^*.     

Control of mean and fluctuating forces on a circular cylinder at high Reynolds numbers

A narrow strip is used to control mean and fluctuating forces on a circular cylinder at Reynolds numbers from 2.0 × 10⁴ to 1.0 × 10⁵. The axes of the strip and cylinder are parallel. The control parameters are strip width ratio and strip position characterized by angle of attack and distance from the cylinder. Wind tunnel tests show that the vortex shedding from both sides of the cylinder can be suppressed, and mean drag and fluctuating lift on the cylinder can be reduced if the strip is installed in an effective zone downstream of the cylinder. A phenomenon of mono-side vortex shedding is found. The strip-induced local changes of velocity profiles in the near wake of the cylinder are measured, and the relation between base suction and peak value in the power spectrum of fluctuating lift is studied. The control mechanism is then discussed from different points of view. The project supported by the National Natural Science Foundation of China (10172087 and 10472124). The English text was polished by Yunming Chen.     

Mean and fluctuating pressure measurements over a circular cylinder in cross flow using plastic tubing

Not only can mean pressures on a surface over which a fluid flows be accurately measured using a plastic tube which connects the surface tapping points to a remote pressure transducer, but the fluctuating pressures can also, provided that the transfer function, which relates the fluctuating pressures at the opposite ends of the tubing, is known. This technique was used here to measure the mean and fluctuating pressures on the surface of a circular cylinder subject to a cross-flowing airstream in the Reynolds number range from 6.8 × 10⁴ to 9.6 × 10⁴ based on cylinder diameter. Good agreement with published results gave confidence in the technique. Received: 15 April 1998/Accepted: 19 January 2000     

Simulation of the flow past a circular cylinder in the supercritical regime by blending RANS and variational-multiscale LES models

A strategy which blends a variational multiscale large eddy simulation (VMS-LES) model and a RANS model in a hybrid approach is investigated. A smooth blending function, which is based on the value of a blending parameter, is used for switching from VMS-LES to RANS. Different definitions of the blending parameter are investigated. The capabilities of the novel hybrid approach are appraised in the simulation of the flow around a circular cylinder at a Reynolds number 1.4×10⁵, based on the freestream velocity and on the cylinder diameter, in the presence of turbulent boundary-layer due to turbulent inflow conditions. A second study at Reynolds numbers from Re=6.7×10⁵ to 1.25×10⁶ is also presented. The effect of using the VMS-LES approach in the hybrid model is evaluated. Results are compared to those of other RANS, LES and hybrid simulations in the literature and with experimental data     

Interaction between the near wake and the cross-section variation of a circular cylinder in uniform flow

The flow around a circular cylinder with a cross-section variation is experimentally investigated. Particle Image Velocimetry (PIV) is used to scrutinize the interaction of the cylinder’s wall with its near wake. The Reynolds number based on the cylinder’s diameter and freestream velocity is 80 × 10³, corresponding to the upper subcritical flow regime. At a forcing Strouhal number of St _f = 0.02, the maximum vorticity level around the cylinder is reduced by more than 50% as compared to its uncontrolled value. The topology of the bulk flow confined between the primary vortical structure and the cylinder surface is modified resulting in substantial drag reduction.     

LES of incompressible heat and fluid flows past a square cylinder at high Reynolds numbers

This paper presents large eddy simulation (LES) results of incompressible heat and fluid flows around a square cylinder (SC) at zero incident angle at high Reynolds numbers (Re) in the range from 1.25×10⁵ to 3.5×10⁵. LES results are obtained on the basis of swirling strength based sub-grid model, and a higher order upwind scheme developed with respect to the Taylor expansion. It was found that, for the zero incident SC wake flows at a Reynolds number in the range {Re₅ = Re/10⁵ ∈ [1.25, 3.5]}, the Strouhal number equals to 0.1079, completely independent of the Reynolds number; the coefficient of drag is around 1.835 with an uncertainty of about 1.9%, almost non-sensitive to the Re. When Re is beyond 3.0×10⁵, the time-averaged peak value of sub-grid viscosity is over 340, implying that the role of sub-grid model is crucial in some regions where vortex motion is active and vortex interaction is intense. The time–spanwise (t-z) averaged sub-grid viscosity ratio profiles and the profiles of fluctuations of the sub-grid viscosity ratio and velocity components at four locations downstream of the SC are presented. The fields of the t-z averaged sub-grid viscosity ratio, and the instantaneous fields of streamwise and spanwise vorticities are also reported and discussed. The predicted mean Nusselt number is compared with empirical correlations, revealing that swirling strength based LES has its potential in predicting natural and industrial flows.     

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.     

Effect of acoustic resonance on the dynamic lift forces acting on two tandem cylinders in cross-flow

Direct measurements of the dynamic lift force acting on two tandem cylinders in cross-flow are performed in the presence and absence of acoustic resonance. The dynamic lift force is measured because it represents the integrated effect of the unsteady wake and therefore it is directly related to the dipole sound source generated by vortex shedding from the cylinder. Three spacing ratios inside the proximity interference region, L/D=1.75, 2.5 and 3 are considered. During the tests, the first transverse acoustic mode of the duct housing the cylinders is self-excited. In the absence of acoustic resonance, the measured dynamic lift coefficients agree with those reported in the literature. When the acoustic resonance is initiated, a drastic increase in the dynamic lift coefficient is observed, especially for the downstream cylinder. This can be associated with abrupt changes in the phase between the lift forces and the acoustic pressure. The dynamic lift forces on both cylinders are also decomposed into in-phase and out-of-phase components, with respect to the resonant sound pressure. The lift force components for the downstream cylinder are found to be dominant. Moreover, the out-of-phase component of the lift force on the downstream cylinder is found to become negative over two different ranges of flow velocity and to virtually vanish between these two ranges. Acoustic resonance of the first mode is therefore excited over two ranges of flow velocity separated by a non-resonant range near the velocity of frequency coincidence. It is therefore concluded that the occurrence of acoustic resonance is controlled by the out-of-phase lift component of the downstream cylinder, whereas the effect of the in-phase lift component is confined to causing small changes in the acoustic resonance frequency.     

Mixed convection cooling of a heated circular cylinder by laminar upward-directed slot jet impingement

An experimental and numerical study has been carried out to investigate the heat transfer characteristics of a horizontal circular cylinder exposed to a slot jet impingement of air. A square-edged nozzle is mounted parallel with the cylinder axis and jet flow impinges on the bottom of the cylinder. The study is focused on low Reynolds numbers ranging from 120 to 1,210, Grashof numbers up to Gr = 10Re ² and slot-to-cylinder spacing from 2 to 8 of the slot width. The flow field is greatly influenced by the slot exit velocity and the buoyancy force due to density change. A Mach–Zehnder Interferometer is used for measurement of local Nusselt number around the cylinder at 10° interval. It is observed that the average Nusselt number decreases with increasing the jet spacing and increases with rising the Reynolds number. A finite volume method utilizing a curvilinear coordinate transformation is used for numerical modeling. The numerical results show good agreement with the experimental results. The flow and thermal field are seen to be stable and symmetric around the cylinder over the range of parameters studied.     

Volumetric reconstruction of the mean flow around circular cylinders fitted with strakes

The volumetric reconstruction technique presented in this paper employs a two-camera stereoscopic particle image velocimetry (SPIV) system in order to reconstruct the mean flow behind a fixed cylinder fitted with helical strakes, which are commonly used to suppress vortex-induced vibrations (VIV). The technique is based on the measurement of velocity fields at equivalent adjacent planes that results in pseudo volumetric fields. The main advantage over proper volumetric techniques is the avoidance of additional equipment and complexity. The averaged velocity fields behind the straked cylinders and the geometrical periodicity of the three-start configuration are used to further simplify the reconstruction process. Two straked cylindrical models with the same pitch (p = 10d) and two different heights (h = 0.1 and 0.2d) are tested. The reconstructed flow shows that the strakes introduce in the wake flow a well-defined wavelength of one-third of the pitch. Measurements of hydrodynamic forces, fluctuating velocity, vortex formation length, and vortex shedding frequency show the interdependence of the wake parameters. The vortex formation length is increased by the strakes, which is an important effect for the suppression of vortex-induced vibrations. The results presented complement previous investigations concerning the effectiveness of strakes as VIV suppressors and provide a basis of comparison to numerical simulations.     

Phase dynamics of effective drag and lift components in vortex-induced vibration at low mass–damping

In this work, we investigate the dynamics of vortex-induced vibration of an elastically mounted cylinder with very low values of mass and damping. We use two methods to investigate this canonical problem: first we calculate the instantaneous phase between the cylinder motion and the fluid forcing; second we decompose the total hydrodynamic force into drag and lift components that act along and normal to, respectively, the instantaneous effective angle of attack. We focus on the phase dynamics in the large-amplitude–response range, consisting of the initial, upper and lower “branches” of response. The instantaneous phase between the transverse force and displacement shows repeated phase slips separating periods of constant, or continuous-drifting, phase in the second half of the upper branch. The phase between the lift component and displacement shows strong phase locking throughout the large-amplitude range – the average phase varies linearly with the primary frequency – however the modulation of this phase is largest in the second half of the upper branch. These observations suggest that the large-amplitude–response dynamics is driven by two distinct limit cycles – one that is stable over a very small range of reduced velocity at the beginning of the upper branch, and another that consists of the lower branch. The chaotic oscillation between them – the majority of the upper branch – occurs when neither limit cycle is stable. The transition between the upper and lower branches is marked by intermittent switching with epochs of time where different states exist at a constant reduced velocity. These different states are clearly apparent in the phase between the lift and displacement, illustrating the utility of the force decomposition employed. The decomposed force measurements also show that the drag component acts as a damping factor whereas the lift component provides the necessary fluid excitation for free vibration to be sustained.     

Using oscillatory squeezing flow to measure the viscoelastic properties of dental composite resin cements during curing

We have investigated the rheological changes in two particulate-filled dental composite resin cements during the curing process using a Micro-Fourier Rheometer (MFR). In the MFR, the sample was sandwiched between two parallel plates, and pseudorandom small amplitude squeezing was applied by oscillating the upper plate over a range of frequencies. Fourier transforms of the displacement signal and the resulting time dependent force signal enabled the rapid determination of the dynamic properties G′ and G′′ over the frequency range 2π–200π rad/s . This technique permitted us to follow changes in the rheological properties of the resin cements through the setting period. A typical result was that G′ increased from 2×10³ Pa to 2×10⁵ Pa after about 120 s, and that G′′ changed from 4×10³ Pa to 4×10⁴ Pa over the same period at frequency 40π rad/s. We also found that the dental composite resin cements show linear viscoelastic behaviour over a range of strain amplitudes before curing, but the response becomes distinctly non-linear at the later stages of curing for strain amplitudes γ>0.067%.