On the vortex dynamics in the wake of a finite surface-mounted square cylinder

The shedding process in the near wake of a surface-mounted, square cross-section cylinder of height-to-width aspect ratio 4 at a Reynolds number of 12,000 based on free-stream velocity and the obstacle width was investigated. The boundary layer thickness was 0.18 obstacle heights based on 99% free-stream velocity. The study is performed using planar high frame-rate particle image velocimetry synchronized with pressure measurements and hot-wire anemometry. Spatial cross-correlation, instantaneous phase relationships, and phase-averaged velocity data are reported. Two dominant vortex-shedding regimes are observed. During intervals of high-amplitude pressure fluctuations on the obstacle side faces, alternate formation and shedding of vortices is observed (regime A) similar to the von Kármán process. Regime B is characterized by two co-existing vortices in the obstacle lee throughout the shedding cycle and is observed within low-amplitude pressure fluctuation intervals. Despite the coexisting vortices in the base region, opposite sign vorticity is still shed out-of-phase downstream of this vortex pair giving rise to a staggered arrangement of counter-rotating vortices downstream. While the probability of occurrence of Regime B increases toward the free end, the amplitude modulation remains coherent along the obstacle height. Conditionally phase-averaged reconstructions of the flow field are consistent with the spatial distribution of the phase relationships and their probability density function. Earlier observations are reconciled showing that the symmetric shedding of vortices is a rare occurrence.     

Dynamical mode decomposition of Gurney flap wake flow

The present work uses dynamic mode decomposition (DMD) to analyze wake flow of NACA0015 airfoil with Gurney flap. The physics of DMD is first introduced. Then the PIV-measured wake flow velocity field is decomposed into dynamical modes. The vortex shedding pattern behind the trailing edge and its high-order harmonics have been captured with abundant information such as frequency, wavelength and convection speed. It is observed that high-order dynamic modes convect faster than low-order modes; moreover the wavelength of the dynamic modes scales with the corresponding frequency in power law.     

Uncovering large-scale coherent structures in natural and forced turbulent wakes by combining PIV,POD, and FTLE

Planar velocity data of the unsteady separated flow in the turbulent wake of a circular cylinder obtained by particle image velocimetry (PIV) are analyzed in order to visualize the large-scale coherent structures associated with alternating vortex shedding at a Reynolds number of 2,150. Two different cases are examined: unforced vortex shedding in the natural wake and vortex lock-on incited by forced perturbations superimposed in the inflow velocity. Proper orthogonal decomposition (POD) is employed to reconstruct the low-order wake dynamics from randomly sampled snapshots of the velocity field. The reconstructed flow is subsequently used to determine the evolution of the finite-time Lyapunov exponent (FTLE) fields which identify the Lagrangian coherent structures. The results demonstrate that the combination of methods employed offers a powerful visualization tool to uncover large-scale coherent structures and to exemplify vortex dynamics in natural and forced bluff-body wakes.     

Pressure/velocity coupling induced by a near wall wake

A combined wall pressure/velocity analysis of the wake of a disk located in the vicinity of a flat wall is presented in this paper. One gap ratio only is selected. In this situation, the footprint of the flow unsteadiness on the magnitude of the wall fluctuating pressure is significant while the natural vortex shedding properties of the wake are only slightly altered. Spatio-temporal velocity and pressure/velocity correlations are analyzed. They carry the signature of the large-scale coherence and periodicity associated with vortex shedding and exhibit characteristic phase relations. Advanced statistical analysis techniques are adapted and developed. A conditional phase averaging of the pressure and velocity fields is obtained. The proper orthogonal decomposition of a spatio-temporal pressure data set on the axis of the near wake is shown to be efficient (1) to determine the phase of the spatio-temporal pressure field projected on the two first modes and (2) to distinguish between quiescent random signatures and more energetic phases. Conditional statistics show very clearly that the large-scale structures interact with the flat wall. Finally, a linear stochastic estimation (LSE) of the velocity field is computed from the fluctuating pressure data. We show the superiority of the spatio-temporal LSE over the spatial LSE in predicting the kinetic energy and the coherent spectral properties of the fluctuating velocity field. Moreover, the linear stochastic estimation is very good in predicting the phase-averaged conditional velocity field.     

Aerodynamic flow vectoring of a wake using asymmetric synthetic jet actuation

This paper reports an experimental investigation on the wake of a blunt-based, flat plate subjected to aerodynamic flow vectoring using asymmetric synthetic jet actuation. Wake vectoring was achieved using a synthetic jet placed at the model base 2.5?mm from the upper corner. The wake Reynolds number based on the plate thickness was 7,200. The synthetic jet actuation frequency was selected to be about 75?% the vortex shedding frequency of the natural wake. At this actuation frequency, the synthetic jet delivered a periodic flow with a momentum coefficient, C _??, of up to 62?%. Simultaneous measurements of the streamwise and transverse components of the velocity were performed using particle image velocimetry (PIV) in the near wake. The results suggested that for significant wake vectoring, vortex shedding must be suppressed first. Under the flow conditions cited above, C _?? values in the range of 10?C20?% were required. The wake vectoring angle seemed to asymptote to a constant value of about 30° at downstream distances, x/h, larger than 4 for C _?? values ranging between 24 and 64?%. The phase-averaged vorticity contours and the phase-averaged normal lift force showed that most of the wake vectoring is produced during the suction phase of the actuation, while the blowing phase was mostly responsible for vortex shedding suppression.     

Proper orthogonal decomposition of wall-pressure fluctuations under the constrained wake of a square cylinder

The proper orthogonal decomposition (POD) analysis of the wall-pressure fluctuations below the constrained wake of a two-dimensional square cylinder in proximity to a plane wall was made on two systems, i.e., G/D = 0.25 and 0.5, which corresponds to the wakes with and without suppression of the vortex shedding, respectively. Here, G is the gap distance and D is the width of the square cylinder. Synchronized measurements of wall-pressure fluctuations were made using a microphone array. For the system G/D = 0.5, the first two energetic modes contribute 34.7% and 23.4% to the total fluctuation energy, respectively; however, the fluctuation energy corresponding to the third mode are relatively small and less than 10%. This sharp variation in eigenvalue is due to the presence and dominance of the Karman-like vortex shedding. However, for the system G/D = 0.25, the considerable reduction in the eigenvalues of the first several modes is due to the suppression of the Karman-like vortex shedding. The spatial wavy pattern of the first several energetic eigenmodes was shown to be a good reflection of convective vortices superimposed in the wakes. The spectra of the POD coefficients determined the frequency of the dominant structures. Based on the coherence of the POD coefficients, an effective method of determining the number of POD modes for reconstruction of the low-order wall-pressure field was proposed. Accordingly, the low-order wall-pressure fluctuations in the systems G/D = 0.5 and 0.25 were reconstructed by using the first four and five POD modes, respectively. The coherence and cross-correlation analysis of the reconstructed wall-pressure fluctuations, which excluded the influence of the small-scale structures and background ‘noise’, gave an insight view of the footprints of the dominant flow structures, which otherwise could not be effectively captured by using the original wall-pressure fluctuations.     

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.     

Experimental estimation of a D-shaped cylinder wake using body-mounted sensors

The effectiveness of a small array of body-mounted sensors, for estimation and eventually feedback flow control of a D-shaped cylinder wake is investigated experimentally. The research is aimed at suppressing unsteady loads resulting from the von-Kármán vortex shedding in the wake of bluff-bodies at a Reynolds number range of 100–1,000. A low-dimensional proper orthogonal decomposition (POD) procedure was applied to the stream-wise and cross-stream velocities in the near wake flow field, with steady-state vortex shedding, obtained using particle image velocimetry (PIV). Data were collected in the unforced condition, which served as a baseline, as well as during influence of forcing within the “lock-in” region. The design of sensor number and placement was based on data from a laminar direct numerical simulation of the Navier-Stokes equations. A linear stochastic estimator (LSE) was employed to map the surface-mounted hot-film sensor signals to the temporal coefficients of the reduced order model of the wake flow field in order to provide accurate yet compact estimates of the low-dimensional states. For a three-sensor configuration, results show that the estimation error of the first two cross-stream modes is within 20–40% of the PIV-generated POD time coefficients. Based on previous investigations, this level of error is acceptable for a moderately robust controller required for feedback flow control.     

On vortex shedding behind a circular disk

Abtract  Experiments were performed for individual realizations of the vortex shedding process behind a circular disk at Reynolds numbers of 10³–10⁵, at which periodic vortex shedding prevails in the wake. The phase differences regarding the individual vortex shedding structures detected at multiple circumferential locations in the wake were obtained by analyzing the hot-wire signals with a conditional-sampling scheme. The phase differences of vortex shedding detected at circumferential positions 90° apart show a wide scatter, but the anti-phase character is largely preserved in the individual vortex shedding process as detected at circumferential locations 180° apart. The randomness of phase differences involved in the vortex shedding process is noted to be essential in order to satisfy the axisymmetric property of the global flow. Received: 4 April 19969/Accepted: 29 January 1997     

Dynamics of interaction modes in excited annular jets

Evolution of coherent structures and their interaction dynamics are educed in the near field of an acoustically excited basic annular jet using conditional sampling technique based on a multiple triggering criterion to detect the two dominating modes of structure pattern. Acoustic excitation is applied with an aim to better organize the phase alignment of initial rolling and pairing process in the outer shear layer. Negligible modification of the time-averaged flow field results from the excitation. The educed coherent vorticities show that the two modes of evolution are due to the corresponding two modes of shedding pattern of the wake structures from the centerbody, namely the mode one wake and the mode zero wake. In both modes, the shear-layer mode jet vortex rings in the outer layer are perturbed by the shedding of wake structures in the inner region and interaction involving primary merging of three successive jet vortex rings or their partial circumferential sections is found. This results in the formation of wake-induced structures of the corresponding mode pattern, which possesses concentration of coherent vorticity and fluid circulation over a large spatial extent at 1 < x/D < 2. Secondary interactions, such as vortex tearing, are also observed.     

Resonance in flow past oscillating cylinder under subcritical conditions

Flow around an oscillating cylinder in a subcritical region are numerically studied with a lattice Boltzmann method(LBM). The effects of the Reynolds number,oscillation amplitude and frequency on the vortex wake modes and hydrodynamics forces on the cylinder surface are systematically investigated. Special attention is paid to the phenomenon of resonance induced by the cylinder oscillation. The results demonstrate that vortex shedding can be excited extensively under subcritical conditions, and the response region of vibration frequency broadens with increasing Reynolds number and oscillation amplitude. Two distinct types of vortex shedding regimes are observed. The first type of vortex shedding regime(VSR I) is excited at low frequencies close to the intrinsic frequency of flow, and the second type of vortex shedding regime(VSR II)occurs at high frequencies with the Reynolds number close to the critical value. In the VSR I, a pair of alternately rotating vortices are shed in the wake per oscillation cycle,and lock-in/synchronization occurs, while in the VSR II, two alternately rotating vortices are shed for several oscillation cycles, and the vortex shedding frequency is close to that of a stationary cylinder under the critical condition. The excitation mechanisms of the two types of vortex shedding modes are analyzed separately.     

Experimental investigation of a blunt trailing edge flow field with application to sound generation

The unsteady lift generated by turbulence at the trailing edge of an airfoil is a source of radiated sound. The objective of the present research was to measure the velocity field in the near wake region of an asymmetric beveled trailing edge in order to determine the flow mechanisms responsible for the generation of trailing edge noise. Two component velocity measurements were acquired using particle image velocimetry. The chord Reynolds number was 1.9 × 10⁶. The data show velocity field realizations that were typical of a wake flow containing an asymmetric periodic vortex shedding. A phase average decomposition of the velocity field with respect to this shedding process was utilized to separate the large scale turbulent motions that occurred at the vortex shedding frequency (i.e., those responsible for the production of tonal noise) from the smaller scale turbulent motions, which were interpreted to be responsible for the production of broadband sound. The small scale turbulence was found to be dependent on the phase of the vortex shedding process implying a dependence of the broadband sound generated by the trailing edge on the phase of the vortex shedding process.     

Effect of novel synthetic jet on wake vortex shedding modes of a circular cylinder

A novel actuator signal achieved by changing the ratio of the suction duty cycle to the blowing duty cycle is adopted to enhance the control effect of the synthetic jet for the flow around a circular cylinder. The suction duty cycle factor k defined as the ratio between the time duration of the suction cycle and the blowing cycle and the equivalent momentum coefficient C_μ are introduced as the determining parameters. The synthetic jet is positioned at the rear stagnation point in order to introduce symmetric perturbations upon the flow field. The proper orthogonal decomposition (POD) technique is applied for the analysis of the spanwise vorticity field. Increasing the suction duty cycle factor, the momentum coefficient is enhanced, and thus a stronger and larger scale synthetic jet vortex pair with a higher convection velocity is generated. The synthetic jet vortex pair interacts with the spanwise vorticity shear layers behind both sides of the cylinder, resulting in the variations of the wake vortex shedding modes at Re=950: for k=0.25, C_μ=0.148, vortex synchronization at the subharmonic excitation frequency with antisymmetric shedding mode; for 0.50≤k≤1.00, 0.213≤C_μ≤0.378, vortex synchronization at the excitation frequency with the symmetric or antisymmetric shedding modes; for 2.00≤k≤4.00, 0.850≤C_μ≤2.362, vortex synchronization at the excitation frequency with symmetric shedding mode. Hence, the control effect of the synthetic jet upon the wake vortex of a circular cylinder can be enhanced by increasing the suction duty cycle factor so as to increase the momentum coefficient. This is also validated at a higher Reynolds number Re=1600.     

斑马鱼直线加速游动试验研究

海洋生物低噪音、高速、髙效游动能力是任何人造水下航行器所无法比拟的. 借助时间解析粒子图像测速技术对斑马鱼直线加速游动过程进行精细流场测量, 对其运动学行为特性和动力学机理进行分析. 同时应用双正交分解对涡量场进行模态分解, 获取流场的时间演化和空间分布特征. 从流动机理的角度探究斑马鱼游动过程的流动结构特征及旋涡动态演化特性. 试验结果表明: 流动可视化展现了整体涡流尾迹的结构分布,方便探究运动特性与旋涡尾迹之间的耦合关系. 斑马鱼从运动开始时体干保持着鲹科式的运动规律, 游动时的动能主要由前几次大幅的摆尾过程提供, 后续的摆尾主要调整方向及姿态. 两次不同方向的摆尾动作会形成一对方向相反的旋涡, 并在时序下旋涡逐渐脱落. 同时尾流的涡量变化在一定程度上反映鱼体的游向的变化. 基于双正交分解分解后的时间演化结果验证本次试验在时间上涡量场具有合理的恒定幅度, 空间分布表明低阶空间模态表征斑马鱼游动的主要涡流动结构, 高阶空间模态表征涡流动的细节结构. 研究鱼类游动时的摆尾推进机制与动力学特性能够为高效率的仿鱼类推进装置设计提供一定科学参考.      

单窄条控制件对横向振荡柱体尾流 2P模式 旋涡脱落的改变

横向强迫振荡柱体尾流控制是柱体涡激振动控制的基础,在海洋、土木等工程中具有重要意义. 横向强迫振荡柱体尾流中存在一种锁频旋涡脱落模式,即在一个振荡周期内柱体上、下侧各脱落旋转方向相反的一对涡,称为2P模式. 本文将相对宽度b/D=0.32的窄条控制件置于横向强迫振荡柱体下游,对振幅比A/D=1.25, 无量纲振频f_e D/V_∞=0.22,雷诺数Re=1 200的2P模式旋涡脱落进行干扰,并通过改变控制件位置,研究旋涡的变化规律. 采用二维大涡模拟和实验验证方法进行研究,在控制件位置范围0.8≤X/D≤3.2, 0.4≤Y/D≤3.2内,得到了2P, 2S, P+S和另外6种新发现的旋涡脱落模式,并对各模式旋涡的形成过程作了详细描述. 在控制件位置平面上给出了各旋涡模式的存在区域,画出了旋涡脱落强度的等值线图,并发现在一个相当大的区域内,旋涡脱落强 度可减小一半以上,尾流变窄. 发现柱体大幅振荡引起的横向剪切流在旋涡生成中起关键作用. 探讨了控制件对横向剪切流的影响,分析了控制件在每种旋涡模式形成中的作用机制.      

槽道内涡波流场的POD分析

对槽道内涡波流场的瞬态速度矢量场进行了2DPIV测量实验,将2DPIV测量的矢量场数据进行POD分析,根据POD分解的各阶模态的能量比确定了表征涡波流场主导结构的前15阶模态。结果表明,POD分解的前15阶模态发现槽道内涡波流场是由槽道壁面剪切层诱导的涡列以及伴随的波状主流组成;流场中大尺度的涡旋发展为涡对,对波状主流的脉动频率产生影响;根据涡波流场中的驻点和鞍点,获取了流场的大尺度涡对、平均流场以及Helmholtz涡环等明显特征;最后根据POD分解的前15阶模态对槽道内涡波流场进行重组,重组流场表征了槽道内层流状态下波状主流的形态和涡旋共存的涡波结构以及驻点和鞍点的位置处涡旋的变化等主要特征,有效地剔除了PIV测量流场中的随机信息,保留了PIV测量流场的主导特征。     

Asymmetric vortex shedding flow past an inclined flat plate at high incidence

This paper reports an experimental investigation of the vortex shedding wake behind a long flat plate inclined at a small angle of attack to a main flow stream. Detailed velocity fields are obtained with particle-image velocimetry (PIV) at successive phases in a vortex shedding cycle at three angles of attack, α=20°, 25° and 30°, at a Reynolds number Re≈5,300. Coherent patterns and dynamics of the vortices in the wake are revealed by the phase-averaged PIV vectors and derived turbulent properties. A vortex street pattern comprising a train of leading edge vortices alternating with a train of trailing edge vortices is found in the wake. The trailing edge vortex is shed directly from the sharp trailing edge while there are evidences that the formation and shedding of the leading edge vortex involve a more complicated mechanism. The leading edge vortex seems to be shed into the wake from an axial location near the trailing edge. After shedding, the vortices are convected downstream in the wake with a convection speed roughly equal to 0.8 the free-stream velocity. On reaching the same axial location, the trailing edge vortex, as compared to the leading edge vortex, is found to possess a higher peak vorticity level at its centre and induce more intense fluid circulation and Reynolds stresses production around it. It is found that the results at the three angles of attack can be collapsed into similar trends by using the projected plate width as the characteristic length of the flow.     

Influence of wall proximity on characteristics of wake behind a square cylinder: PIV measurements and POD analysis

Influence of wall proximity on characteristics of the wake behind a two-dimensional square cylinder was experimentally studied in the present work. A low-speed recirculation water channel was established for the experiment; the Reynolds number based on the free-stream velocity and cylinder width (D) was kept at Re_D = 2250. Four cases with different gap width, e.g., G/D = 0.1, 0.2, 0.4 and 0.8, were chosen for comparison. Two experimental techniques, e.g., the standard PIV with high image-density CCD camera and TR-PIV with a high-speed camera were employed in measuring the wake field, enabling a comprehensive view of the time-averaged wake pattern at high spatial resolution and the instantaneous flow field at high temporal resolution, respectively. For the four cases, the difference in spatial characteristics of the wake in the vicinity of the plane wall was analyzed in terms of the time-averaged quantities measured by the standard PIV, e.g., the streamline pattern, the vector field, the streamwise velocity fluctuation intensity and the reverse-flow intermittency. The proper orthogonal decomposition (POD) method was extensively used to decompose the TR-PIV measurements, giving a close-up view of the energetic POD modes buried in the wake. The low-order flow model of the wake at G/D = 0.8 and 0.4 was constructed by using the linear combination of the first two POD modes and the time-mean flow field, which reflected well the vortex shedding process in the sense of the phase-dependent patterns. The intermittent appearance of the weakly separated region near the wall was found at G/D = 0.4. On going from G/D = 0.8 to 0.4, the remarkable variation of the instantaneous wake in the longitudinal direction confirmed that the wall constraint stretches the vortices in the plane of the wall and transfers the energy to the longitudinal component at the expense of the lateral one.