Analyzing the fluctuating pressures acting on a circular cylinder using stochastic decomposition

Fluctuating wind pressures acting on bluff bodies are influenced by approaching turbulence and signature (body-induced) turbulence. For a circular cylinder, the signature turbulence is closely related to the formation of Karman vortex shedding. In this paper, proper orthogonal decomposition (POD) and spectral proper transformation techniques (SPT) are applied to the pressure fluctuations acting on a circular cylinder. The physical relationships between the decomposed modes and vortex shedding are discussed to identify the dominant aerodynamic behavior (lift or drag) and to evaluate its contribution to overall behavior. The effect of Reynolds number (Re) is also addressed. It is found that the application of POD and SPT can separate the along-wind and across-wind effects on the cylinder model in both subcritical and supercritical regimes. In contrast to POD, the SPT mode is formulated in the frequency domain, and the dynamic coherent structures can be defined in terms of amplitude and phase angle, which allows detection of the advection features of vortex shedding. In addition, it is observed that the energy contribution of the shedding induced lift force increases with Re and gradually becomes a dominant aerodynamic force at Reynolds numbers in the supercritical regime.     

Response of the Sphere Wake to Freestream Fluctuations

Direct numerical simulations have been used to investigate the response of the wake of a sphere to freestream fluctuations. This study has been motivated by the need to understand particle-induced turbulence enhancement in particulate flows. A sequence of simulations of flow past a sphere have been carried out where the frequency and amplitude of the freestream fluctuations and the flow Reynolds number has been varied systematically. It has been suggested that turbulence enhancement is primarily caused by vortex shedding from particles (Gore and Crowe, 1989; Hetsroni, 1989). Our simulations of the forced wake indicate that turbulence enhancement may be attributed to natural vortex shedding only when the freestream fluctuation level is low and the Reynolds number is greater than about 300. In addition to natural vortex shedding, the current simulations also suggest another mechanism for turbulence enhancement. It is found that in the presence of freestream fluctuations, the wake behaves like an oscillator and returns large amounts of kinetic energy to the surrounding fluid at resonance. This mechanism is not associated with natural vortex shedding and is therefore capable of enhancing freestream turbulence even at Reynolds numbers less than 300. Simulations also indicate that when the turbulence intensity of the carrier fluid is high, this resonance mechanism might be solely responsible for turbulence enhancement. Finally, our simulations also suggest a possible explanation for the correlation between turbulence enhancement and the ratio of the particle size to the size of energy containing eddies of turbulence found by Gore and Crowe (1989). Received 5 October 1999 and accepted 14 October 1999     

外部激励Stuart-Landau模型的数值研究

将非线性常微分方程组周期解的求解看作一个边值问题 ,运用Newton迭代构造求解这组方程的数值方法。利用上述方法求得了激励Stuart Landau方程的周期解 ,研究了圆柱振动对圆柱后Karman涡街的抑制现象 ,和振动的频率锁定现象 ,证明了激励Stuart Landau方程描写钝体尾迹动力系统的有效性     

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.     

VORTEX SHEDDING OF BLUFF BODIES: A REVIEW

In this paper the various types of vortex generation and the related response characteristics of bluff bodies are described. The vortices are, in general, generated by a certain stimulation, leading to one- or two-shear layer instability; the related unsteady forces could excite flexible structures such as tall towers, tall buildings and long-span bridges. Karman vortex shedding is well known as the alternate shedding vortex behind bluff bodies, but the one-shear layer instability related vortices and symmetrical vortex shedding should also be taken into account as additional mechanisms for the evaluation of structural safety, because they result in structural response at comparatively low wind speeds. In this paper, the symmetrical vortex shedding, which is enhanced by the longitudinally fluctuating flow for 2-D rectangular cylinders with a 0.5 side ratio, and one-shear layer related vortices, which are generated on the side surfaces of flat 2-D rectangular cylinders and many bridge girder box sections by the stimulation of body motion or applied sound, are introduced. Furthermore, as a peculiar 3-D vortex, the “axial vortex”, which is formed in near wake of inclined cables and then over restricted velocity ranges, is also discussed.     

Feedback control of vortex shedding from two tandem cylinders

The effect of feedback control on vortex shedding from two tandem cylinders in cross-flow is investigated experimentally. The objective is to reduce the downstream cylinder response to vortex shedding and turbulence excitations. Feedback control is applied to a resonant case, where the frequency of vortex shedding coincides with the resonance frequency of the downstream cylinder, and to a nonresonant case, in which the shedding frequency is about 30% higher than the downstream cylinder resonance frequency. A “synthetic jet” issuing through a narrow slit on the upstream cylinder is employed to impart the control effect to the flow. The effect of open-loop control, using pure tones and white noise to activate the synthetic jet, is also examined. It is demonstrated that feedback control can significantly reduce the downstream cylinder response to both vortex shedding and turbulence excitations. For example, the cylinder response is reduced by up to 70% in the resonant case and 75% in the nonresonant case. Open-loop control also can reduce the cylinder response, but is less effective than feedback control. The frequency of vortex shedding is found to increase substantially when white noise is applied. This increase in the shedding frequency is higher than the largest frequency shift that could be produced by open-loop tone excitation.     

Effect of span length and temperature on the 3-D confined flow around a vortex promoter

This article presents a numerical study on the influence of span length and wall temperature on the 3-D flow pattern around a square section vortex promoter located inside a micro-channel in the low Reynolds number regime. The first objective of the work is to quantify the critical Reynolds number that defines the onset of vortex shedding and to identify the different regimes that appear as a function of the channel aspect ratio (span to height ratio). We found that the critical Reynolds number for the onset of the Karman street regime increases as the aspect ratio decreases. In particular, for the aspect ratio of 1/2 the critical Reynolds number is nearly six times the critical Reynolds number of the 2-D problem. An intermediate oscillating regime between the steady and the Karman street solutions was also found to exist within a rather wide range of Reynolds numbers for small channel aspect ratios. The second objective was to investigate the influence of the vortex promoter wall temperature on both vortex shedding and flow pattern. This has practical engineering implications because the working fluid considered in the article is water that has a viscosity that depends significantly on temperature and promotes a strong coupling between the momentum and energy equations that influences the system behaviour. Results indicate that high surface temperature on the prism promotes the onset of the Karman street, suggesting design guidelines for micro-channel based heat sinks that make use of vortex promoters.     

Effect of span length and temperature on the 3-D confined flow around a vortex promoter

This article presents a numerical study on the influence of span length and wall temperature on the 3-D flow pattern around a square section vortex promoter located inside a micro-channel in the low Reynolds number regime. The first objective of the work is to quantify the critical Reynolds number that defines the onset of vortex shedding and to identify the different regimes that appear as a function of the channel aspect ratio (span to height ratio). We found that the critical Reynolds number for the onset of the Karman street regime increases as the aspect ratio decreases. In particular, for the aspect ratio of 1/2 the critical Reynolds number is nearly six times the critical Reynolds number of the 2-D problem. An intermediate oscillating regime between the steady and the Karman street solutions was also found to exist within a rather wide range of Reynolds numbers for small channel aspect ratios. The second objective was to investigate the influence of the vortex promoter wall temperature on both vortex shedding and flow pattern. This has practical engineering implications because the working fluid considered in the article is water that has a viscosity that depends significantly on temperature and promotes a strong coupling between the momentum and energy equations that influences the system behaviour. Results indicate that high surface temperature on the prism promotes the onset of the Karman street, suggesting design guidelines for micro-channel based heat sinks that make use of vortex promoters.     

An upwind finite element scheme for high-Reynolds-number flows

A new upwind finite element scheme for the incompressible Navier-Stokes equations at high Reynolds number is presented. The idea of the upwind technique is based on the choice of upwind and downwind points. This scheme can approximate the convection term to third-order accuracy when these points are located at suitable positions. From the practical viewpoint of computation, the algorithm of the pressure Poisson equation procedure is adopted in the framework of the finite element method. Numerical results of flow problems in a cavity and past a circular cylinder show excellent dependence of the solutions on the Reynolds number. The influence of rounding errors causing Karman vortex shedding is also discussed in the latter problem.     

Application of the SAS turbulence model to predict the unsteady flow field behaviour in a forward centrifugal fan

In the current study, the unsteady flow in a centrifugal fan is carried out using Computational Fluid Dynamics calculation based on the Scale Adaptive Simulation (SAS) approach to model the turbulence phenomenon. The SAS concept is based on the introduction of the von Karman length scale into the turbulence scale equation. The information provided by the von Karman length scale allows SAS models to dynamically adjust to resolved structures in an Unsteady Reynolds-Averaged Navier–Stokes (URANS) simulation, which results in a Large Eddy Simulation-like behaviour in unsteady regions of the flow field. At the same time, the model provides standard RANS capabilities in stable flow regions. The introduction of the von Karman length scale is based on the reformulation of Rottas's equation for the integral length scale. To validate the numerical results, the overall performances of the fan and the wall pressure fluctuations computed upon the volute casing surface are compared with the unsteady measured data.     

Space potential particles to enhance the stability of projection-based particle methods

Particle methods have been seldom verified by a Karman vortex simulation, which is commonly performed as a typical benchmark in computational fluid dynamics. This is mainly due to a difficulty in suppression of occurrence of unphysical voids manifested usually in a strong vortex on account of definition of free surface by the Lagrangian tracking framework with inconsistency in volume conservation. This paper presents a simple and effective scheme as a free-surface boundary condition of projection-based particle methods, namely the MPS (moving particle semi-implicit) and Incompressible SPH (ISPH) methods to handle the free surface with consistency in volume conservation. The new scheme is introduced into the Poisson pressure equation (PPE) with consideration of a potential in void space as space potential particle (SPP), to reproduce physical motions of particles around free surface through a particle–void interaction. The enhancing effect of the newly proposed SPP scheme is shown by simulating a few numerical tests, including a whirling water flow, a two-phase surfacing flow, and a set of Karman vortex simulations.     

水平液─固流中颗粒抑制湍流的行为和条件

用激光多普勒分相测量方法，考察了水平含颗粒水流的主流区，亚毫米颗粒对水流湍流有抑制行为，湍流削弱程度与颗粒浓度、流动发展长度、水流雷诺数等因素有关．按照不出现尾涡脱落和至少能响应一部分大尺度涡的运动这两个基本条件，分析了湍流抑制与有关参量的依赖性．结果表明，流动尺度和颗粒尺寸之比，对于颗粒消耗而不增生湍流起着最主要的作用．在一定的水流雷诺数下，只要这一比值很大，亚毫米颗粒就会表现出对湍流的抑制作用     

圆柱绕流流场结构的大涡模拟研究

为进一步揭示绕流现象的形成机理,本文分别对处于层流稳态区、尾流过渡区、剪切层转换区Re分别为26、200、1.4×105的三种典型流态下的单圆柱绕流进行了二维数值模拟研究。Re为26时应用层流模型直接求解N-S方程,而Re分别为200、1.4×105时使用大涡模拟的方法进行计算。数值模拟很好地再现了稳定的涡旋结构、周期性交替脱落的卡门涡街结构、不规则的涡旋结构,在此基础上分析了尾流结构的基本特征及其压强分布规律、平均的流场特性、积分参数(如升力系数、阻力系数、斯特劳哈尔等),并与有关研究成果进行了对比。研究发现,采用不同流动介质时流场特性有所差异,空气为介质时的计算结果更符合实验的成果,而水为介质时计算结果偏差较大,这主要是由尾流涡旋产生的不合理负压造成的。     

Mean and fluctuating components of drag and lift forces on an isolated finite-sized particle in turbulence

We perform fully resolved direct numerical simulations of an isolated particle subjected to free-stream turbulence in order to investigate the effect of turbulence on the drag and lift forces at the level of a single particle, following Bagchi and Balachandar’s work (Bagchi and Balachandar in Phys Fluids 15:3496–3513, 2003). The particle Reynolds numbers based on the mean relative particle velocity and the particle diameter are Re?=?100, 250 and 350, which covers three different regimes of wake evolution in a uniform flow: steady axisymmetric wake, steady planar symmetric wake, and unsteady planar symmetric vortex shedding. At each particle Reynolds number, the turbulent intensity is 5–10% of the mean relative particle velocity, and the corresponding diameter of the particle is comparable to or larger than the Kolmogorov scale. The simulation results show that standard drag values determined from uniform flow simulations can accurately predict the drag force if the turbulence intensity is sufficiently weak (5% or less compared to the mean relative velocity). However, it is shown that for finite-sized particles, flow non-uniformity, which is usually neglected in the case of the small particles, can play an important role in determining the forces as the relative turbulence intensity becomes large. The influence of flow non-uniformity on drag force could be qualitatively similar to the Faxen correction. In addition, finite-sized particles at sufficient Reynolds number are inherently subjected to stochastic forces arising from their self-induced vortex shedding in addition to lift force arising from the local ambient flow properties (vorticity and strain rate). The effect of rotational and strain rate of the ambient turbulence seen by the particle on the lift force is explored based on the conditional averaging using the generalized representation of the quasi-steady force proposed by Bagchi and Balachandar (J Fluid Mech 481:105–148, 2003). From the present study, it is shown that at Re?=?100, the lift force is mainly influenced by the surrounding turbulence, but at Re = 250 and 350, the lift force is affected by the wake structure as well as the surrounding turbulence. Thus, for a finite-sized particle of sufficient Reynolds number supporting self-induced vortex shedding, the lift force will not be completely correlated with the ambient flow. Therefore, it appears that in order to reliably predict the motion of a finite-sized particle in turbulence, it is important to incorporate both a deterministic component and a stochastic component in the force model. The best deterministic contribution is given by the conditional average. The influence of ambient turbulence at the scale of the particle, which are not accounted for in the deterministic contribution, can be considered in stochastic manner. In the modeling of lift force, additional stochastic contribution arising from self-induced vortex shedding must also be included.     

Experimental study on the confined 3D laminar flow past a square prism with a high blockage ratio

An experimental PIV study is presented that addresses the confined 3D laminar flow behaviour past a square prism. The Reynolds number (Re), based on prism cross-section height varies between 100 and 256. The channel aspect ratio is 1/1 and the blockage ratio is 1/2.5. This geometry is representative of a passive method to enhance mixing in otherwise highly ordered laminar channel flow. It is found that the lateral walls exert a strong effect on the flow behaviour with two main consequences: (a) the onset of vortex shedding is delayed to a Re in the vicinity of 170, as opposed to the unconfined case where the critical Re is reported to be between 50 and 60 and (b) transition from the steady closed recirculation bubble regime to the vortex shedding regime is not abrupt. In particular, there is a range of Re for which the closed recirculation bubble pulsates with increasing amplitude prior to the onset of the Karman street regime. The experimental results are supported by numerical computations, and the relation of the results with the practical design of engineering systems is also discussed.     

水平液─固流中颗粒抑制湍流的行为和条件

用激光多普勒分相测量方法，考察了水平含颗粒水流的主流区，亚毫米颗粒对水流湍流有抑制行为，湍流削弱程度与颗粒浓度、流动发展长度、水流雷诺数等因素有关．按照不出现尾涡脱落和至少能响应一部分大尺度涡的运动这两个基本条件，分析了湍流抑制与有关参量的依赖性．结果表明，流动尺度和颗粒尺寸之比，对于颗粒消耗而不增生湍流起着最主要的作用．在一定的水流雷诺数下，只要这一比值很大，亚毫米颗粒就会表现出对湍流的抑制作用     

锅炉省煤器和空气预热器振动可靠性分析的研究

提出了锅炉尾部受热面的振动可靠性分析方法。该方法把卡门漩涡频率和声学驻波频率处理为随机变量，使用概率设计法确定锅炉省煤器和管式空气预热器避开声振动的可靠度。文中给出了管式空气预热器振动可靠性分析的实例。     

Vortex dynamics mechanisms of separated boundary layer in a highly loaded low pressure turbine cascade

This paper investigates the vortex dynamics in the suction-side boundary layer on an aero-engine low pressure turbine blade at two different Reynolds numbers at which short and long laminar separation bubbles occur. Different vortical patterns are observed and investigated through large eddy simulation (LES). The results show that at the higher Reynolds number, streamwise streaks exist upstream of separation line. These streaks initiate spanwise undulation in the form of vortex tubes, which roll-up and shed from the shear layer due to the Kelvin–Helmholtz instability. The vortex tubes alternately pair together and eventually distort and break down to small-scale turbulence structures near the mean reattachment location and convect into a fully turbulent boundary layer. At the lower Reynolds number, streamwise streaks are strong and the separated flow is unable to reattach to the blade surface immediately after transition to turbulence. Therefore, bursting of short bubbles into long bubbles can occur, and vortex tubes have larger diameters and cover a part of the blade span. In this case vortex pairing does not occur and vortex shedding process is promoted mainly by flapping phenomenon. Moreover, the results of dynamic mode decomposition (DMD) analysis show a breathing motion as a source of unsteadiness in the separation location, which is accompanied by the flapping phenomenon.     

Roughness and turbulence intensity effects on the induced flow oscillation of a single cylinder

The effects of the surface roughness and the turbulence intensity on the dynamic characteristics of the flow induced oscillations of an elastically supported single circular cylinder in a cross flow in the vortex shedding and fluid elastic regions were experimentally investigated. The results of these experiments indicate that, for the vortex shedding region, increasing the surface roughness results in a reduction of the amplitude of oscillation, while in the fluid elastic region, increasing the surface roughness tends to enhance the oscillations. A similar trend for the dynamic response of the cylinder in the vortex shedding region was also observed when the free stream turbulence intensity was varied, while in the fluid elastic region variations in the free stream turbulence intensity were observed to have no drastic effect on the dynamic response of the cylinder.