A reduced-order deterministic model describing an intermittency route to combustion instability

Recently, there has been a growing interest in understanding and characterising intermittent burst oscillations that presage the onset of combustion instability. We construct a deterministic model to capture this intermittency route to instability in a bluff-body stabilised combustor by coupling the equations governing vortex shedding and the acoustic wave propagation in a confinement. A feedback mechanism is developed wherein the sound generated due to unsteady combustion affects the vortex shedding. This feedback leads to a variation in the time of impingement of the vortices with the bluff body causing the system to exhibit chaos, intermittency, and limit cycle oscillations. Experimental validation of the model is provided using various precursor measures that quantify the observed intermittent states.     

Vortex shedding process investigation downstream a surface-mounted block

The laminar flow around a surface-mounted block is investigated by visualizations and PIV measurements. Flow topology and, especially, the vortex shedding dynamics are emphasized. The existence of two vortex shedding processes is highlighted by particles visualizations and instantaneous velocity fields analyses. On one hand, a dominant swirling mechanism with vortex matching process and a symmetrical topology sets up and, on the other hand, a non periodical evolution with a dissymmetric topology exist. In order to inquire about those processes, double velocity correlation functions are calculated and from those new data the space and time evolutions of the vortices are detailed.     

Interaction of induced sound with flow past a square leading edged plate in a duct

The interaction of resonant sounds with the flow past a thick, blunt, flat plate in a rigid walled square duct has been examined. Sound pressure levels of up to 146 dB (re 20 μPa) have been recorded. It has been established that the resonant sound can initially be excited at a harmonic of the normal vortex shedding frequency. In some cases, the sound “feeds back” on the vortex shedding process causing a step change in the shedding frequency, increasing the Strouhal number for the plate by up to twice the normal value. This excited vortex shedding and associated resonances can be suppressed by locating the plate at incidence to the air flow direction. Complex duct modes can be generated by the vortex shedding resulting in different regions of the plate shedding at different Strouhal numbers.     

Review of sound induced by vortex shedding from cylinders

Sound induced by periodic vortex shedding from cylinders has been studied more-or-less continuously since the first quantitative study by Strouhal in 1878. Measurements have shown that vortex shedding is a dipole source of sound. Theoretical models for aeroacoustic sound in a free space, mostly inspired by Lighthill's work, have been developed which can replicate the measurements once the vortex shedding force, coherence, and periodicity are experimentally measured. Vortex shedding from tubes in heat exchanger tube bundles can reach damaging intensities because the acoustic mode is bound by the lower speed of sound within the tube bank itself. However, the amplitude and occurrence of the resonance can only be approximately predicted at present.     

前缘弯掠子午加速叶轮尾缘脱落涡的研究

本文采用DPIV实验研究方法,在不同转速工况下,对开式前缘弯掠子午加速风扇转子叶尖涡在叶轮尾缘的脱落流动现象进行了测量.结果表明:在不同转速下,转子尾缘处均存在明显的叶尖涡流动现象.该叶尖脱落涡流动现象具有相似性,随着转速的增大,叶尖涡区和吸力面之间的径向速度差增大,叶尖涡强度随转速增加而增强.随着转速的增大,叶尖涡和主流相互作用加剧,涡量负值增大,叶尖涡影响区域也逐渐扩大.径向速度梯度同样随转速增大而增大的结果,增强了叶尖涡对尾迹区作用的影响.最后,本文通过CFD对该开式风扇叶尖涡流动现象进行模拟,其结果给出了相似的叶尖涡在转子尾缘脱落流动现象,为前缘弯掠开式子午加速风扇在户室中央空调室外机上的应用和风机系统的优化设计及其降噪研究提供了重要的内流数据.     

Vortex dynamics of a trapezoidal bluff body placed inside a circular pipe

The influence of Reynolds number and blockage ratio on the vortex dynamics of a trapezoidal bluff body placed inside a circular pipe is studied experimentally and numerically. Low aspect ratio, high blockage ratio, curved end conditions (junction of pipe and bluff body), axisymmetric upstream flow with shear and turbulence are some of the intrinsic features of this class of bluff body flows which have been scarcely addressed in the literature. A large range (200:200,000) of Reynolds number (Re_D) is covered in this study, encompassing all the three pipe flow regimes (laminar, transition and turbulent). Four different flow regimes are defined based on the distinct features of Strouhal number (St)–Re_D relation: steady, laminar irregular, transition and turbulent. The wake in the steady regime is stationary with no oscillations in the shear layer. The laminar regime is termed as irregular owing to irregular vortex shedding. The vortex shedding in this regime is observed to be symmetric. The emergence of separation bubble downstream of the bluff body on either side is another interesting feature of this regime, which is further observed to be symmetric. Two pairs of mean streamwise vortices are noticed in the near-wake regime, which are termed as reverse dipole-type wake topology. Beyond the irregular laminar regime, the Strouhal number falls gradually and vortex shedding becomes more periodic. This regime is named transition and occurs close to the Reynolds number at which transition to turbulence takes place in a fully developed pipe. The turbulent regime is characterised by a nearly constant Strouhal number. Typical Karman-type vortex shedding is noticed in this regime. The convection velocity, wake width formation length and irrecoverable pressure loss are quantified to highlight the influence of blockage ratio. These results will be useful to develop basic understanding of vortex dynamics of confined bluff body flow for several practical applications.     

Energy constraints in vortex-excited vibrations

Excitation or damping of flow-induced vibrations depends upon the magnitude and the phase relationship between the fluid dynamic force and the oscillatory motion of the body. These have been measured for two aerofoil shapes in mechanically controlled heaving motion in a water channel. At the same time, measurements have been made of the strength and spacing of the associated vortex trails. To help interpret the significance of these measurements, an analysis based upon energy conservation has been performed. When taken together with the classical momentum equation, this yields a relationship giving the energy available for vibration work in terms of three dimensionless vortex trail parameters. Comparing this analysis with the experimental data leads to a qualitative discussion of the significance of the vortex formation mechanism in controlling the excitation or damping of that class of vibrations which is affected by vortex shedding.     

The excitation of acoustic resonances by vortex shedding

A single acoustic resonance, excited by vortex shedding from the trailing edge of a flat plate, has been studied in detail. The resonance was generated in the working section of a low-speed wind tunnel and the scale was large enough for accurate measurements to be made. The trailing edge was designed so that it could be made to oscillate slightly to simulate the correlating effect of the resonance on the vortex shedding.     

Effects of mean flow convection,quadrupole sources and vortex shedding on airfoil overall sound pressure level

This paper presents a further analysis of results of airfoil self-noise prediction obtained in the previous work using large eddy simulation and acoustic analogy. The physical mechanisms responsible for airfoil noise generation in the aerodynamic flows analyzed are a combination of turbulent and laminar boundary layers, as well as vortex shedding (VS) originated due to trailing edge bluntness. The primary interest here consists of evaluating the effects of mean flow convection, quadrupole sources and vortex shedding tonal noise on the overall sound pressure level (OASPL) of a NACA0012 airfoil at low and moderate freestream Mach numbers. The overall sound pressure level is the measured quantity which eventually would be the main concern in terms of noise generation for aircraft and wind energy companies, and regulating agencies. The Reynolds number based on the airfoil chord is fixed at _Rec=408,000${\mathit{Re}}_c=408,000$ for all flow configurations studied. The results demonstrate that, for moderate Mach numbers, mean flow effects and quadrupole sources considerably increase OASPL and, therefore, should be taken into account in the acoustic prediction. For a low Mach number flow with vortex shedding, it is observed that OASPL is higher when laminar boundary layer separation is the VS driving mechanism compared to trailing edge bluntness.     

A study on drag reduction of a rotationally oscillating circular cylinder at low Reynolds number

The flow field around a rotationally oscillating circular cylinder in a uniform flow is studied by using a particle image velocimetry to understand the mechanism of drag reduction and the corresponding suppression of vortex shedding in the cylinder wake at low Reynolds number. Experiments are conducted on the flow around the circular cylinder under rotational oscillation at forcing Strouhal number 1, rotational amplitude 2 and Reynolds number 2,000. It is found from the flow measurement by PIV that the width of the wake is narrowed and the velocity fluctuations are reduced by the rotational oscillation of the cylinder, which results in the drag reduction rate of 30%. The mechanism of drag reduction is studied by phase-averaged PIV measurement, which indicates the formation of periodic small-scale vortices from both sides of the cylinder. It is found from the cross-correlation measurement between the velocity fluctuations that the large-scale structure of vortex shedding is almost removed in the cylinder wake, when the small-scale vortices are generated at the unstable frequency of shear layer by the influence of rotational oscillation.     

基于POD方法开缝圆柱绕流流场的研究

利用粒子成像测速技术（particle image velocimetry,PIV）,在水槽中探究缝隙对圆柱流场结构的影响,应用频谱分析和本征正交分解（proper orthogonal decomposition,POD）方法,研究了开缝圆柱流场相干结构.实验Reynolds数范围内,缝隙的"吹吸"作用从根本上改变了圆柱绕流近区尾流结构,前6阶模态形态是流场中最主要的相干结构.第1,2阶模态形态控制着圆柱绕流流场涡街相继脱落过程,1或2阶模态系数为尾迹涡的固有频率;第3,4阶模态形态控制着脱落旋涡沿流向方向能量运输;第5,6阶模态形态中的同向涡旋结构作用于旋涡缓慢脱离柱体这一过程,并对旋涡能量起着衰减作用.      

Structure-based interpretation of the Strouhal-Reynolds number relationship

The wake in the flow past a circular cylinder has posed a long-standing challenge to scientists since the late 19th century. Many aspects of this seemingly simple phenomenon remain unexplained. Of particular interest is the relationship between the dimensionless vortex shedding frequency (the Strouhal number St) and the ratio of inertial to viscous forces in the fluid (the Reynolds number Re). We propose a new St-Re relation based on the observations of the structure of a vortex street in flowing soap films. The measurements suggest a simple two-parameter form St=1/(A+B/Re) that describes laminar vortex shedding remarkably well for bulk fluids as well as for two-dimensional flowing soap films.     

Acoustic diffraction by a half-plane with discontinuous boundary conditions

A theoretical investigation of the wake pattern downstream of airfoils under predominantly laminar flow conditions and the resultant noise generation is presented. Under these conditions the wake is dominated by a Karman vortex street. A method is developed to theoretically predict the vortex shedding frequency by relating the wake pattern to the airfoil boundary layer parameters through the momentum equation. The generated noise is found to be dominated by a pure tone at the vortex shedding frequency. The results obtained with the present approach were found to agree quite well with experimental results obtained by other investigators.     

On whistling of pipes with a corrugated segment: Experiment and theory

Corrugated pipes are commonly used because of their local rigidity combined with global flexibility. The flow through such a pipe can induce strong whistling tones, which is an environmental nuisance and can be a threat to the mechanical integrity of the system. This paper considers the use of a composite pipe: a shorter corrugated pipe segment embedded between smooth pipe segments. Such a pipe retains some flexibility, while the acoustical damping in the smooth pipe reduces whistling tones. Whistling is the result of coherent vortex shedding at the cavities in the wall. This vortex shedding is synchronized by longitudinal acoustic waves traveling along the pipe. The acoustic waves trigger the vortex shedding, which reinforces the acoustic field for a critical range of the Strouhal number values. A linear theory for plane wave propagation and the sound production is proposed, which allows a prediction of the Mach number at the threshold of whistling in such pipes. A semi-empirical approach is chosen to determine the sound source in this model. This source corresponds to a fluctuating force acting on the fluid as a consequence of the vortex shedding. The functional form of the Strouhal number dependency of the dimensionless sound source amplitude is based on numerical simulations. The magnitude of the source and the Strouhal number range in which it can drive whistling are determined by matching the model to results for a specific corrugated pipe segment length. This semi-empirical source model is then applied to composite pipes with different corrugated segment lengths. In addition, the effect of inlet acoustical convective losses due to flow separation is considered. The Mach number at the threshold of whistling is predicted within a factor 2.     

Experimental characterization of onset of acoustic instability in a nonpremixed half-dump combustor

This paper reports work on a nonpremixed half-dump combustor, in which methane is injected at the backward-facing step, and mixes and burns with the air flowing past the step in the unsteady recirculation zone. The flow and geometric parameters are widely varied, to gradually change from conditions of low-amplitude noise to excitation of high-amplitude discrete tones. The purpose of the work is to focus on the transition from the former condition to the latter, and to mark the onset of instability. Dimensionless groups such as the Helmholtz and Strouhal numbers are formed based on the observed dominant frequencies, whose variation with the air flow Reynolds number is used to identify the oscillations as those due to the natural acoustic modes or the vortex shedding process. High-speed chemiluminescence imaging reveals shedding of vortical structures in the flame zone. With variation in the conditions, flow-acoustic lock-on and transition from one vortex shedding mode to another is marked by nonlinearity in the corresponding amplitude variations. Such conditions are identified as the onset of instability in terms of the ratio of the flow time scale to the acoustic time scale and mapped against the operating fuel-air equivalence ratio of the combustor.     

圆柱近尾迹湍流涡结构的直接数值模拟

本文运用谱元方法对圆柱尾流进行直接数值模拟。通过对中等Re数（1000）时的圆柱近尾迹湍流涡结构的演变系统细致的研究,经过长时间流动计算,用速度矢量及相应涡结构示意图显示主涡,二次涡结构的相互作用,显示整个尾迹涡结构在一个周期内的演变过程,获得了在实验中难以清楚观察到的近壁流动特征。本文得到圆柱近壁处二次涡形成有两种不同的机理,并总结出涡的合并所需要的条件。     

Visualization study on suppression of vortex shedding from a cylinder

A narrow strip has been introduced as a control element to suppress vortex shedding from a cylinder. The strip is set parallel to the cylinder axis, and the key parameter of control in this study is the strip position, which is determined by the angle of attack of the strip and the distance between the strip and the cylinder axis. A circular cylinder and a square cylinder were tested respectively. Flow visualization and hot-wire measurement were performed in a low turbulence wind tunnel in the range of Reynolds numberRe=4.0×10³≈2.0×10⁴. Test results show that, vortex shedding from both sides of the cylinder can be effectively suppressed if the strip is located in a certain zone in the wake. The effective zones in circular cylinder wakes at different Reynolds numbers have been found out, and the mechanism of the suppression has been discussed.     

基于VLES模型的振动圆柱数值模拟

本文将一种VLES(Very Large Eddy Simulation)模型引入到动网格数值计算中,并验证了VLES模型用于模拟类似振动圆柱绕流的动边界问题的有效性.数值求解了不同振幅和频率下非稳态振动圆柱绕流问题.研究表明:随着振幅和激励频率的增加,绕圆柱流动涡脱离形式从2S模式转换到2P0模式,再到P+S模式.在...     

Experiments on effective source locations and velocity dependence of the broad band noise from a rotating rod

Effective acoustic source positions (observed from the far field) have been located for the broad band noise from a cylindrical rod rotated about its mid-point by measuring the cross spectral density function of two microphone signals on the axis of rotation. Local source position Strouhal numbers could thereby be calculated. On the basis of acoustic power measurements it was demonstrated that the noise may be normalized on a rod tip Strouhal number basis, and that the velocity exponent is nearly constant when plotted against this parameter. The results indicate that vortex shedding like that for stationary cylinders in a cross flow (occurring along the outer $\text{1}\text{3}$ of the rod for a rotational speed of 1000 rpm) is responsible for the high levels of broad band noise in a major peak region. Sources influenced by harmonics of the rod passing frequency were found for frequencies lower than the vortex shedding ones. At higher frequencies broad band noise was found to be emitted from the rod tip area.     

Vortex shedding and vorticity fluxes in the wake of cylinders within a random array

This work investigates the impact of the background turbulence generated by randomly placed cylinders on the vortex shedding regime and the mechanisms associated to vorticity fluxes. The goals are achieved by exploring velocity databases acquired with a two-dimensional particle image velocimetry system in two types of turbulent flow experiments: flow around a single infinite cylinder and flow within random array of infinite cylinders. Formation lengths, power spectral density functions and vortex distributions are employed to discuss the vortex shedding regime. The effects of background turbulence and vorticity cancellation, due to opposite sign vorticity, on the vorticity fluxes are discussed. The results show that the background turbulence reduces the formation length and consequently increase the shedding frequency. The stronger decay of longitudinal vorticity flux in denser arrays is not accompanied by an increase of the lateral flux of vorticity. Furthermore, it was concluded that the decay of longitudinal vorticity flux is mainly caused by the vorticity cancellation due to the vorticity of opposite sign of close downstream cylinders.