Transition phenomena in the wake of an inclined square cylinder

The division of flow regimes in a square cylinder wake at various angles of attack (α) is studied. This study provides evidence of the existence of modes A and B instabilities in the wake of an inclined square cylinder. The critical Reynolds numbers for the inception of these instability modes were identified through the determination of discontinuities in the Strouhal number versus Reynolds number curves. The spectra and time traces of wake streamwise velocity were observed to display three distinct patterns in different flow regimes. Streamwise vortices with different wavelengths at various Reynolds numbers were visualized. A PIV technique was employed to quantitatively measure the parameters of wake vortices. The wavelengths of the streamwise vortices in the modes A and B regimes were measured by using the auto-correlation method. From the present investigation, the square cylinder wake at various angles of attack undergoes a similar transition path to that of a circular cylinder, although various quantitative parameters measured which include the critical Reynolds numbers, spanwise wavelength of secondary vortices, and the circulation and vorticity of wake vortices all show an α dependence.     

Dynamics of vortical structures in cylinder/wall interaction with moderate gap ratio

The interaction between the wake of a transverse circular cylinder and the underlying flat-plate boundary layer with a moderate gap ratio G/D=1.0 is investigated using both hydrogen-bubble-based and PIV-based visualization techniques. The spanwise rollers in the cylinder wake are found to be capable of inducing secondary vortices in the near-wall region. The mutual induction from the counter-clockwise rollers, which are closer to the wall, plays a primary role, so that these secondary vortices present linear lift-up motion at first. Their subsequent evolution dominantly determines the characteristics of the wake/boundary-layer interaction. Two different vortex interaction scenarios are observed: the secondary vortices can be either entrained into the rollers or pushed down towards the wall. This leads to a rapid three-dimensional destabilization process, through which streamwise vortices are generated. And it is suggested that these streamwise vortices are the dominant structures to promote the following boundary layer transition.     

Intrinsic relationship of vorticity between modes A and B in the wake of a bluff body

The intrinsic physical relationship of vorticity between modes A and B in the three-dimensional wake transition is investigated.Direct numerical simulations for the flow past a square-section cylinder are carried out at Reynolds numbers of 180 and 250,associated with modes A and B,respectively.Based on the analysis of spacial distributions of vorticity in the near wake,characteristics of the vertical vorticity in modes A and B are identified.Moreover,the relationship of three vorticity components with specific signs is summarized into two sign laws,as intrinsic physical relationships between two instability modes.By the theory of vortex-induced vortex,such two sign laws confirm that there are two and only two kinds of vortex-shedding patterns in the near wake,just corresponding to modes A and B.In brief,along the free stream direction,mode A can be described by the parallel shedding vertical vortices with the same sign,while mode B is described by the parallel shedding streamwise vortices with the same sign.Finally,it is found out that the|-type vortex is a basic kind of vortex structure in both modes A and B.     

Mode competition in streamwise-only vortex induced vibrations

Time-resolved Particle-Image Velocimetry (PIV) has been used to study mode competition and transient behaviour in the wake of a cylinder experiencing Vortex-Induced Vibrations (VIV) in the streamwise direction. The cylinder response regime contained two branches, occurring above and below the onset of synchronisation between the wake and the cylinder motion (lock-in). During the first branch, the wake exhibited both the S-I mode (in which two vortices are shed simultaneously per vibration cycle) and the alternate A-II mode (similar to the well known von Kármán vortex street). An extended PIV data set acquired in this region revealed mode switching between the S-I and A-II modes. A criterion based on Proper-Orthogonal Decomposition was developed to identify which mode was dominant as a function of time. The A-II mode was found to be dominant for over 90% of the instantaneous fields examined, while the S-I mode appeared to be more unstable.Symmetrically shed vortices were found to rearrange downstream into an alternate structure in which the wake was no longer synchronised to the cylinder motion. The dominant frequency of transverse velocity fluctuations was measured throughout the wake in order to study the effects of this breakdown in more detail. For the majority of the wake, the fluctuations occurred at the Strouhal frequency, while in a region in the near wake the fluctuations occurred at the frequency of the cylinder motion. It is thought that during the first response branch vortices are formed at the cylinder response frequency, but tend to quickly rearrange downstream into an alternate structure which is no longer synchronised to the cylinder motion. As a result, the fluctuating drag will be synchronised to the structural motion, and is capable of providing positive energy transfer in the apparent absence of lock-in. Finally, the spatial dependence of the frequency of velocity fluctuations throughout the wake is used to explain some of the conflicting results in the literature regarding streamwise VIV, and the implications for the general study of VIV are discussed.     

On vortex shedding from low aspect ratio dual step cylinders

A dual-step cylinder is comprised of two cylinders of different diameters. A large diameter cylinder (D) with low aspect ratio (L/D) is attached to the mid-span of a small diameter cylinder (d). The present study investigates the effect of Reynolds number (Re_D) and L/D on dual step cylinder wake development for D/d=2, 0.2≤L/D≤3, and two Reynolds numbers, Re_D=1050 and 2100. Experiments have been performed in a water flume facility utilizing flow visualization, Laser Doppler Velocimetry (LDV), and Particle Image Velocimetry (PIV). The results show that vortex shedding occurs from both the large and small diameter cylinders for 1≤L/D≤3 at Re_D=2100 and 2≤L/D≤3 at Re_D=1050. At these conditions, large cylinder vortices predominantly form vortex loops in the wake and small cylinder vortices form half-loop vortex connections. At lower aspect ratios, vortex shedding from the large cylinder ceases, with the dominant frequency in the large cylinder wake attributed to the passage of vortex filaments connecting small cylinder vortices. At these lower aspect ratios, the presence of the large cylinder induces periodic vortex dislocations. Increasing L/D increases the frequency of occurrence of vortex dislocations and decreases the dominant frequency in the large cylinder wake. The identified changes in wake topology are related to substantial variations in the location of boundary layer separation on the large cylinder, and, consequently, changes in the size of the vortex formation region. The results also show that the Reynolds number has a substantial effect on wake vortex shedding frequency, which is more profound than that expected for a uniform cylinder.     

Wall proximity effects on the effectiveness of upstream control rod

Two dimensional flow over a circular cylinder with an upstream control rod of same diameter is simulated in unbound condition and in wall bounded conditions. The cylinders are placed at various heights from the wall and the inter-distance between cylinders is also varied. The control rod is subjected to different rotation rates. It is found that, in unbound condition, rotating the control rod decreases the critical pitch length (S/D_cr) and increases the drag and Strouhal number of the main cylinder. In presence of plane wall, the shielding provided by the separated shear layers from the control rod in cavity regime is deteriorated due to deflection of shear layers which results in higher drag and large fluctuation of lift coefficient. However, in wake impingement regime, the binary vortices from the control rod are weakened due to diffusion of vorticity and hence, the main cylinder experiences a lower drag and small lift fluctuations than that of unbound condition. The critical height of vortex suppression (H/D_cr) is higher in cavity regime than that of wake impingement regime due to the single extended-bluff body like configuration. The rotation of control rod energizes the wall boundary layer and increases the critical height of vortex suppression. Increasing the rotational rate of control rod decreases the drag force and reduces the amplitude of lift fluctuation. Analysis of the wall shear stress distribution reveals that it suffers a sudden drop at moderate height where the normal Karman vortex shedding changes to irregular shedding consisting of single row of negative vortices. Modal structures obtained from dynamic mode decomposition (DMD) reveal that the flow structures behind the main cylinder are suppressed due to wall and the flow is dominated by the wake of control rod.     

TR-PIV measurement of the wake behind a grooved cylinder at low Reynolds number

A comparative study of the wakes behind cylinders with grooved and smooth surfaces was performed with a view to understand the wake characteristics associated with the adult Saguaro cacti. A low-speed recirculation water channel was established for the experiment; the Reynolds number, based on the free-stream velocity and cylinder diameter (D), was kept at Re_D=1500. State-of-the-art time-resolved particle image velocimetry (TR-PIV) was employed to measure a total of 20 480 realizations of the wake field at a frame rate of 250 Hz, enabling a comprehensive view of the time- and phase-averaged wake pattern. In comparison to the wake behind the smooth cylinder, the length of the recirculation zone behind the grooved cylinder was extended by nearly 18.2%, yet the longitudinal velocity fluctuation intensity was considerably weakened. A global view of the peaked spectrum of the longitudinal velocity component revealed that the intermediate region for the grooved cylinder, which approximately corresponds to the transition region where the shear layer vortices interact, merge and shed before the formation of the Karman-like vortex street, was much wider than that for the smooth one. The unsteady events near St=0.3-0.4 were detected in the intermediate region behind the grooved cylinder, but no such events were found in the smooth cylinder system. Although the formation of the Karman-like vortex street was delayed by about 0.6D downstream for the grooved cylinder, no prominent difference in the vortex street region was found in the far wake for both cylinders. The Proper Orthogonal Decomposition (POD) method was used extensively to decompose the vector and swirling strength fields, which gave a close-up view of the vortices in the near wake. The first two POD modes of the swirling strength clarified the spatio-temporal characteristics of the shear layer vortices behind the grooved cylinder. The small-scale vortices superimposed on the shear layers behind the grooved cylinder were found to be generated and convected downstream in the same phase, which would significantly reduce the fluctuating force on the cylinder surface.     

Effect of velocity ratio on the streamwise vortex structures in the wake of a stack

The time-averaged velocity and streamwise vorticity fields within the wake of a stack were investigated in a low-speed wind tunnel using a seven-hole pressure probe. The experiments were conducted at a Reynolds number, based on the stack external diameter, of Re_D=2.3×10⁴. The stack, of aspect ratio AR=9, was mounted normal to a ground plane and was partially immersed in a flat-plate turbulent boundary layer, where the ratio of the boundary layer thickness to the stack height was δ/H≈0.5. The jet-to-cross-flow velocity ratio was varied from R=0 to 3, which covered the downwash, crosswind-dominated and jet-dominated flow regimes. In the downwash and crosswind-dominated flow regimes, two pairs of counter-rotating streamwise vortex structures were identified within the stack wake. The tip vortex pair located close to the free end of the stack, and the base vortex pair located close to the ground plane within the flat-plate boundary layer, were similar to those found in the wake of a finite circular cylinder, and were associated with the upwash and downwash flow fields within the stack wake, respectively. In the jet-dominated flow regime, a third pair of streamwise vortex structures was observed, referred to as the jet-wake vortex pair, which occurred within the jet-wake region above the free end of the stack. The jet-wake vortex pair had the same orientation as the base vortex pair and was associated with the jet rise. The peak vorticity and strength of the streamwise vortex structures were functions of the jet-to-cross-flow velocity ratio. For the tip vortex structures, their peak vorticity and strength reduced as the jet-to-cross-flow velocity ratio increased.     

Three-dimensional evolution of vortices and early features of coherent structure in the turbulent wake behind a 2-D circular cylinder

3-D evolution of Kármán vortex filaments and vortex filaments in braid regions in the turbulent wake of a 2-D circular cylinder is investigated numerically based on inviscid vortex dynamics by analyzing the response of the initially 2-D spanwise vortex filaments to periodic spanwise disturbance of varying magnitude, wavelength and initial phase angles. Our results reveal a kind of 3-D vortex system in the wake which consists of large scale horseshoe-shaped vortices and small scale γ-shaped vortex filaments as well as vortex loops. The mechanism and the dynamic process about the generation of streamwise vortical structure and the 3-D coherent structure are reported. currently published in the Chinese Edition of Acta Mechanica Sinica, Vol.25, No.3, 1993 The project supported by National Natural Science Foundation of China and the National Basic Research Project “Nonlinear Science”     

Global aerodynamic instability of twin cylinders in cross flow

This paper comprises an in-depth physical discussion of the flow-induced vibration of two circular cylinders in view of the time-mean lift force on stationary cylinders and interaction mechanisms. The gap-spacing ratio T/D is varied from 0.1 to 5 and the attack angle α from 0° to 180° where T is the gap width between the cylinders and D is the diameter of a cylinder. Mechanisms of interaction between two cylinders are discussed based on time-mean lift, fluctuating lift, flow structures and flow-induced responses. The whole regime is classified into seven interaction regimes, i.e., no interaction regime; boundary layer and cylinder interaction regime; shear-layer/wake and cylinder interaction regime; shear-layer and shear-layer interaction regime; vortex and cylinder interaction regime; vortex and shear-layer interaction regime; and vortex and vortex interaction regime. Though a single non-interfering circular cylinder does not correspond to a galloping following quasi-steady galloping theory, two circular cylinders experience violent galloping vibration due to shear-layer/wake and cylinder interaction as well as boundary layer and cylinder interaction. A larger magnitude of fluctuating lift communicates to a larger amplitude vortex excitation.     

Thermal characteristics of the wake shear layers from a slightly heated circular cylinder

In this paper, we investigate the thermal characteristics of wake shear layers generated by a slightly heated circular cylinder. Measurements of the fluctuating temperature were made in the region x/d = 0.6 to x/d = 3 (where x is the downstream distance from the cylinder axis and d is the cylinder diameter) using a single cold-wire probe. The Reynolds number Re was varied in the range 2,600–8,600. For Re = 5,500, simultaneous measurements were made with a rake of 16 cold wires, aligned in the direction of the mean shear, at x/d = 2 and 3. The results indicate that the passive temperature can be an effective marker of various instabilities of the wake shear layers, including the Kelvin–Helmholtz (KH) instability. The temperature data have confirmed the approximate Re ^m dependence of the KH instability frequency (f _KH) with different values of m over different ranges of Re, as reported previously in the literature. However, it is found that this power-law dependence is not exact, and a third-order polynomial dependence appears to fit the data well over the full range of Re. Importantly, it is found that the wake shear-layer instabilities can be grouped into three categories: (1) one with frequencies much smaller than the Bénard–Kármán-vortex shedding frequency, (2) one associated with the vortex shedding and (3) one related to the KH instability. The low-frequency shear-layer instabilities from both sides of the cylinder are in-phase, in contrast to the anti-phase high-frequency KH instabilities. Finally, the observed streamwise decrease in the mean KH frequency provides strong support for the occurrence of vortex pairing in wake shear layers from a circular cylinder, thus implying that both the wake shear layer and a mixing layer develop in similar fashion.     

Numerical study on evolution of subharmonic varicose low-speed streaks in turbulent channel flow

The evolution of two spanwise-aligned low-speed streaks in a wall turbulent flow, triggered by the instability of the subharmonic varicose (SV) mode, is studied by a direct numerical simulation (DNS) method in a small spatial-periodic channel. The results show that the SV low-speed streaks are self-sustained at the early stage, and then transform into subharmonic sinuous (SS) low-speed streaks. Initially, the streamwise vortex sheets are formed by shearing, and then evolve into zigzag vortex sheets due to the mutual induction. As the intensification of the SV low-speed streaks becomes prominent, the tilted streamwise vortex tubes and the V-like streamwise vortex tubes can be formed simultaneously by increasing \( + \frac{{\partial u}}{{\partial x}}\). When the SV low-speed streaks break down, new zigzag streamwise vortices will be generated, thus giving birth to the next sustaining cycle of the SV low-speed streaks. When the second breakdown happens, new secondary V-like streamwise vortices instead of zigzag streamwise vortices will be generated. Because of the sweep motion of the fluid induced by the secondary V-like streamwise vortices, each decayed low-speed streak can be divided into two parts, and each part combines with the part of another streak, finally leading to the formation of SS low-speed streaks.     

Wake modes of a cylinder undergoing free streamwise vortex-induced vibrations

Simultaneous measurements of the response of a circular cylinder experiencing vortex-induced vibrations (VIVs) in the streamwise direction and the resulting wake field were performed for a range of reduced velocities using time-resolved Particle-Image Velocimetry in the Reynolds number range 450–3700. The dominant vortex shedding mode was identified using phase-averaged vorticity fields. The cylinder response amplitude was characterised by two response branches, separated by a low amplitude region at resonance, as has been previously reported in the literature. During the first response branch the wake exhibited not only the symmetric S-I mode, but also the alternate A-II mode at slightly higher reduced velocities. For both modes, the vortices were observed to be shed at the cylinder response frequency, but rearranged downstream into a more stable structure in which the velocity fluctuations were no longer synchronised to the cylinder motion. A special case of the A-II mode, referred to as the SA mode, was found to dominate in the second response branch and the low amplitude region, while the far wake and the cylinder motion were synchronised (lock-in). A change in the timing of the vortex shedding with respect to the cylinder motion was observed between the low amplitude region and the second response branch. This is likely to correspond to a change in the fluid forcing and levels of excitation, and may explain the variation in the cylinder amplitude observed in this region. Lock-in and the second response branch were found to coincide with a contraction of the wake and an increase in strength of the shed vortices. This work reveals the inherent differences between the extensively studied case of transverse-only VIV and the streamwise-only case, which is crucial if the wealth of information available on transverse VIV is to be extended to the more practical two degree-of-freedom case.     

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.     

An experimental investigation of flow past a dual step cylinder

Flow development in the wake of a dual step cylinder has been investigated experimentally using Laser Doppler Velocimetry and flow visualization. The dual step cylinder model is comprised of a large diameter cylinder (D) mounted at the mid-span of a small diameter cylinder (d). The experiments have been performed for a Reynolds number (Re _D ) of 1,050, a diameter ratio (D/d) of 2, and a range of large cylinder aspect ratios (L/D). The results show that the flow development is highly dependent on L/D. The following four distinct flow regimes can be identified based on vortex dynamics in the wake of the large cylinder: (1) for L/D ≥ 15, three vortex shedding cells form in the wake of the large cylinder, one central cell bounded by two cells of lower frequency, (2) for 8 < L/D ≤ 14, a single vortex shedding cell forms in the wake of the large cylinder, (3) for 2 < L/D ≤ 6, vortex shedding from the large cylinder is highly three-dimensional. When spanwise vortices are shed, they deform substantially and attain a hairpin shape in the near wake, (4) for 0.2 ≤ L/D ≤ 1, the large cylinder induces vortex dislocations between small cylinder vortices. The results show that for Regimes I to III, on the average, the frequency of vortex shedding in the large cylinder wake decreases with L/D, which is accompanied by a decrease in coherence of the shed vortices. In Regime IV, small cylinder vortices connect across the large cylinder wake, but these connections are interrupted by vortex dislocations. With decreasing L/D, the frequency of dislocations decreases and the dominant frequency in the large cylinder wake increases toward the small cylinder shedding frequency.     

Large Eddy Simulation of Compressible Subsonic Turbulent Jet Starting From a Smooth Contraction Nozzle

Compressible subsonic turbulent starting jet with a relatively large Reynolds number of significant practical importance is investigated using large eddy simulation (LES), starting from a smooth contraction nozzle. The computational domain of truncated conical shape is determined through the comparison of the time-averaged numerical solution with the particle imaging velocimetry measurements for the steady jet. It is shown that the starting jet consists of a leading vortex ring followed by a quasi-steady jet, and the instantaneous velocity field exhibits contraction and expansion zones, corresponding to the high pressure (HP) and low pressure (LP) regions formed by the convecting vortex rings, and are related to the Kelvin-Helmholtz instability. The thin boundary layer inside the smooth contraction nozzle evolves into a shear layer at the nozzle exit and develops with the downstream penetration of the jet. Using λ ₂ criterion, the formation and evolution of the vortical structures are temporally visualized, illustrating distortion of vortex rings into lobed shapes prior to break-down. Rib-shape streamwise vortex filaments exist in the braid region between a pair of consecutive vortex rings due to secondary instabilities. Finally, formation and dynamics of hairpin vortices in the shear layer is identified.     

圆柱尾迹涡的三维演化及结构特征

应用无粘涡丝运动学理论和局部诱导近似(LIA)方法,以Lagrange观点跟踪涡丝在背景流场中运动,用数值方法研究了中等Re数(≈10~3)下圆柱分离尾迹中Kármán涡和涡辫区涡丝的三维演化的机制和动力学过程,及其结构特征。背景流场考虑为尾迹时间平均速度流场和Kármán涡街流场。初始展向小扰动为指数形式和谐波形式。结果指出:Kármán涡和涡辫区中的涡丝具有展向不稳定性,形成流向涡量。在尾迹的初期输运过程中,表现出有序的大、小尺度涡结构。并进一步分析了其产生的机理。     

Helical-mode excitation of lifted flames using piezoelectric actuators

 Experiments of helical excitation using piezoelectric actuators on jet flows and lifted flames are performed to enhance the understanding of the effects of vortical structures of various instability modes on the stabilization mechanism of the lifted flame. In addition to the common ring and braid structures, five or seven azimuthal fingers (or lobes) can be identified in the transverse image of the jet near field. Excitation with various helical modes enhances the azimuthal structures and entrainment in the near field. When helically excited with the asymmetric m=1 mode, one of the fingers is enhanced and may evolve into a strong streamwise vortex. The streamwise vortices generated in the braid region between the adjacent ring vortices may enhance fuel-air mixing due to additional azimuthal entrainment upstream of a lifted flame when helically excited with the m=1 mode. Therefore, the streamwise vortex serves as an additional path of high probability of premixed flammable layer for the upstream propagation of the lifted flame so that the flame base on one side of the lifted flame may extend farther upstream and the flame base is inclined. In addition to the inclined flame base, multiple-legs phenomenon is also observed in the flame base, which is strongly associated with fingers of the helical modes of the jet flow. Received: 21 August 1997/Accepted: 24 January 1999     

Numerical simulation of three-dimensional instability of flow past a short cylinder

The plane-parallel flow past an infinitely long circular cylinder becomes three-dimensional starting with Reynolds numbers Re ≈ 190. The corresponding instability mode is called mode A. When Re ≈ 260, vortex structures with a smaller cross scale are formed in the wake as a result of a secondary three-dimensional instability (mode B). The transition to three-dimensionality for a short cylinder bounded by planes is considered. The length of the cylinder is chosen to eliminate the unstable perturbations of mode A. Two instability modes similar to modes A and B modified under the effect of the bounding lateral planes are found. The problems of three-dimensional flow are numerically solved using the Navier-Stokes equations.     

Strouhal numbers,forces and flow structures around two tandem cylinders of different diameters

This paper presents a detailed investigation of Strouhal numbers, forces and flow structures in the wake of two tandem cylinders of different diameters. While the downstream cylinder diameter, D, was fixed at 25 mm, the upstream cylinder diameter, d, was varied from 0.24D to D. The spacing between the cylinders was 5.5d, at which vortices were shed from both cylinders. Two distinct vortex frequencies were detected behind the downstream cylinder for the first time for two tandem cylinders of the same diameter. The two vortex frequencies remained for d/D=1.0–0.4. One was the same as detected in the gap of the cylinders, and the other was of relatively low frequency and was ascribed to vortex shedding from the downstream cylinder. While the former, if normalized, declined progressively from 0.196 to 0.173, the latter increased from 0.12 to 0.203 with decreasing d/D from 1 to 0.24. The flow structure around the two cylinders is examined in the context of the observed Strouhal numbers. The time-averaged drag on the downstream cylinder also climbed with decreasing d/D, though the fluctuating forces dropped because vortices impinging upon the downstream cylinder decreased in scale with decreasing d/D.