混沌动力学方法在等离子体尾迹流场研究中的应用

用混沌动力学方法对多道扫描静电探针的离子饱和电流信号进行分析,研究了等离子体尾迹流场.通过对相关维、Renyi熵和最大Lyapunov指数的分析,得到了近尾流场的分层结构.利用最大Lyapunov指数,观测到了在x>10D以后的远尾流场与自由流场相似.结合探针信号的自相关函数,研究流场湍流结构,发现近尾可能存在大涡拟序结构,而在远尾则没有湍流.观察到了流场具有一定的间歇特征,认为这种间歇性与湍流有关.结果还表明,混沌动力学的分析方法对信号中非周期成分十分敏感,在研究等离子体尾迹流场这一类非线性系统时,它具有明显的优越性 关键词： 混沌动力学 尾迹 等离子体湍流 静电探针     

How does flow in a pipe become turbulent?

The transition to turbulence in pipe flow does not follow the scenario familiar from Rayleigh-Benard or Taylor-Couette flow since the laminar profile is stable against infinitesimal perturbations for all Reynolds numbers. Moreover, even when the flow speed is high enough and the perturbation sufficiently strong such that turbulent flow is established, it can return to the laminar state without any indication of the imminent decay. In this parameter range, the lifetimes of perturbations show a sensitive dependence on initial conditions and an exponential distribution. The turbulence seems to be supported by threedimensional travelling waves which appear transiently in the flow field. The boundary between laminar and turbulent dynamics is formed by the stable manifold of an invariant chaotic state. We also discuss the relation between observations in short, periodically continued domains, and the dynamics in fully extended puffs.     

Spontaneous edge <Emphasis Type="Italic">E</Emphasis> × <Emphasis Type="Italic">B</Emphasis> sheared flow development studies in the TJ-II stellarator

The influence of plasma density and edge gradients in the development of perpendicular sheared flow has been investigated in the plasma edge region of the TJ-II stellarator. It has been experimentally observed that the generation of spontaneous perpendicular sheared flow (i.e. the naturally occurring shear layer) requires a minimum plasma density or gradient. It has been found that there is a coupling between the onset of sheared flow development and an increase in the level of plasma edge turbulence; once sheared flow is fully developed the level of fluctuations and turbulent transport slightly decreases whereas edge gradients and plasma density increase. The resulting shearing rate is close to the one required to trigger a transition to improved confinement regimes with reduction of edge turbulence, showing that spontaneous sheared flows and fluctuations keep themselves near marginal stability. Presented at the Workshop “Electric Fields, Structures and Relaxation in Edge Plasmas”, Tarragona, Spain, July 3–4, 2005.     

Noise due to turbulent flow past a trailing edge

A theoretical method [I] for calculating far field noise from an airfoil in an incident turbulent flow is extended to apply to the case of noise produced by turbulent flow past a trailing edge, and some minor points of the theory in reference [1] are clarified. For the trailing edge noise, the convecting surface pressure spectrum upstream of the trailing edge is taken to be the appropriate input. The noise is regarded as generated almost totally by the induced surface dipoles near the trailing edge and thus equal, but anticorrelated, noise is radiated into the regions above and below the airfoil wake, respectively. The basic assumption of the analysis, from which these concepts of appropriate input and dominance of dipole sources follow, is that the turbulence remains stationary in the statistical sense as it moves past the trailing edge. The results show that such trailing edge noise often is quite small, compared say to that produced by typical oncoming turbulence levels of one percent, but that it might be appreciable for an airfoil with a flow separation, or for a blown flap.     

MHD from a Microscopic Concept and Onset of Turbulence in Hartmann Flow

We derive higher order magneto-hydrodynamic （MHD） equations from a microscopic picture using pro-jection and perturbation formalism. In an application to Hartmann flow we find velocity profiles flattening towards the center at the onset of turbulence in hydrodynamic limit. Comparison with the system under the effect of a uniform magnetic field yields difference in the onset of turbulence consistent with observations, showing that the presence of magnetic field inhibits onset of instability or turbulence. The laminar-turbulent transition is demonstrated in a phase transition plot of the development in time of the relative average velocities vs. Reynolds number showing a sharp increase of the relative average velocity at the transition point as determined by the critical Reynolds number.     

Self-regulation of E x B flow shear via plasma turbulence

The momentum balance has been applied to the ExB flow in the edge region of a reversed field pinch (RFP) configuration. All terms, including those involving fluctuations, have been measured in stationary condition in the edge region of the Extrap-T2R RFP experiment. It is found that the component of the Reynolds stress driven by electrostatic fluctuations is the term playing the major role in driving the shear of the ExB flow to a value marginal for turbulent suppression, so that the results are in favor of a turbulence self-regulating mechanism underlying the momentum balance at the edge. Balancing the sheared flow driving and damping terms, the plasma viscosity is found anomalous and consistent with the diffusivity due to electrostatic turbulence.     

Magnetic reconnection in toroidal eta(i) mode turbulence

Based on three-dimensional simulations of the Braginskii equations we show that for typical plasma-edge parameters the saturation of electromagnetic toroidal eta(i) mode turbulence is controlled by the self-generation and subsequent annihilation of radial magnetic field perturbations. This should be contrasted with the electrostatic limit, where the growth of the linear eta(i) mode is terminated by the onset of sheared flow modes driven by the radial plasma streams. The impact of the saturation amplitude on the transport level is substantial and is not in accord with simple mixing length arguments, suggesting that electromagnetic effects should generally be included in simulations of eta(i) mode turbulence.     

Formation of zones of an inverse energy cascade in an axisymmetric jet

The results of investigation into the mechanism of formation of an inverse turbulence energy cascade in an axially symmetric submerged jet based on numerical modeling by the large eddy simulation. The flow structure is calculated using two models of subgrid turbulence in a broad range of Reynolds numbers with the imposed external harmonic low-amplitude perturbation and swirling. Calculations showed that upon imposing swirling, the effect of formation of the inverse cascade is suppressed, while upon imposing the external low-amplitude harmonic perturbations corresponding to the frequency of highest perceptivity, it is enhanced. We can assume that the regions with the inverse turbulence energy flow are formed there where the dynamics of large quasi-2D structures is determined by the mechanisms of combining eddies and involvement processes, while the tension mechanism of vortex tubes is suppressed. It is shown that the balance of these mechanisms can be controlled by means of imposition of low-amplitude harmonic perturbations.     

Edge of chaos in a parallel shear flow

We study the transition between laminar and turbulent states in a Galerkin representation of a parallel shear flow, where a stable laminar flow and a transient turbulent flow state coexist. The regions of initial conditions where the lifetimes show strong fluctuations and a sensitive dependence on initial conditions are separated from the ones with a smooth variation of lifetimes by an object in phase space which we call the "edge of chaos." We describe techniques to identify and follow the edge, and our results indicate that the edge is a surface. For low Reynolds numbers we find that the surface coincides with the stable manifold of a periodic orbit, whereas at higher Reynolds numbers it is the stable set of a higher-dimensional chaotic object.     

近失速状态轴流压气机转子内尖区三维流动结构

用激光测速系统测量了低速大尺寸单级压气机近失速状态转子内尖区三维流场。结果表明泄漏流在转子进口开始产生,泄漏涡约在１０％弦长最强,并迅速向压力面和低叶高方向移动,沿程造成高紊流和高阻滞。叶尖吸力面附面层发生分离,迫使角区低能物质和旋涡在下游逐渐向通道中部移动,造成转子出口尖部通道中部大面积流动阻塞和紊流脉动。角区旋涡及泄漏涡影响区域紊流强度较高,其中径向分量最高,远大于轴向和切向分量。前缘马蹄涡压力面分支存在于转子进口叶尖压力面角区,并迅速向低叶高和通道中部移动,约在２０％弦长和泄漏涡交汇。     

Impact of turbulence on flame brush development of acoustically excited rod-stabilized flames

Coherent structures, such as those arising from hydrodynamic instabilities or excited by thermoacoustic oscillations, can significantly impact flame structure and, consequently, the nature of heat release. The focus of this work is to study how coherent oscillations of varying amplitudes can impact the growth of the flame brush in a bluff-body stabilized flame and how this impact is influenced by the free stream turbulence intensity of the flow approaching the bluff body. We do this by providing external acoustic excitation at the natural frequency of vortex shedding to simulate a highly-coupled thermoacoustic instability, and we vary the in-flow turbulence intensity using perforated plates upstream of the flame. We use high-speed stereoscopic particle image velocimetry to obtain the three-component velocity field and we use the Mie-scattering images to quantify the behavior of the flame edge. Our results show that in the low-turbulence conditions, presence of high-amplitude acoustic excitation can cause the flame brush to exhibit a step-function growth, indicating that the presence of strong vortical structures close to the flame can suppress flame brush growth. This impact is strongly dependent on the in-flow turbulence intensity and the flame brush development in conditions with higher levels of in-flow turbulence are minimally impacted by increasing amplitudes of acoustic excitation. These findings suggest that the sensitivity of the flow and flame to high-amplitude coherent oscillations is a strong function of the in-flow turbulence intensity.     

Maintenance and suppression of chaos by weak harmonic perturbations: a unified view

General results concerning maintenance or enhancement of chaos are presented for dissipative systems subjected to two harmonic perturbations (one chaos inducing and the other chaos enhancing). The connection with previous results on chaos suppression is also discussed in a general setting. It is demonstrated that, in general, a second harmonic perturbation can reliably play an enhancer or inhibitor role by solely adjusting its initial phase. Numerical results indicate that general theoretical findings concerning periodic chaos-inducing perturbations also work for aperiodic chaos-inducing perturbations, and in arrays of identical chaotic coupled oscillators.     

May chaos always be suppressed by parametric perturbations?

The problem of chaos suppression by parametric perturbations is considered. Despite the widespread opinion that chaotic behavior may be stabilized by perturbations of any system parameter, we construct a counterexample showing that this is not necessarily the case. In general, chaos suppression means that parametric perturbations should be applied within a set of parameters at which the system has a positive maximal Lyapunov exponent. Analyzing the known Duffing-Holmes model by a Melnikov method, we showed that chaotic dynamics cannot be suppressed by harmonic perturbations of a certain parameter, independently from the other parameter values. Thus, to stabilize the behavior of chaotic systems, the perturbation and parameters should be carefully chosen.     

The displacement-thickness theory of trailing edge noise

The problem of estimating the sound generated by turbulent boundary layer flow over the edge of a rigid half-plane is re-examined. A theory is proposed which is strictly valid at low Strouhal numbers based on boundary layer width, wherein the flow inhomogeneities are specified in terms of the fluctuations in the boundary layer displacement thickness. This enables account to be taken of changes in the properties of the turbulence as it translates past the edge, which are shown to result in the appearance of an acoustic dipole whose axis is aligned with the mean flow, and which supplements the radiation field predicted by conventional methods [1,2]. Detailed comparison is made with acoustic and surface pressures which are calculated according to the evanescent wave theory of edge noise [3–5].     

Temperature and disorder chaos in three-dimensional Ising spin glasses

We study the effects of small temperature as well as disorder perturbations on the equilibrium state of three-dimensional Ising spin glasses via an alternate scaling ansatz. By using Monte Carlo simulations, we show that temperature and disorder perturbations yield chaotic changes in the equilibrium state and that temperature chaos is considerably harder to observe than disorder chaos.     

Specific features of excitations of “flow”-type self-oscillations in a two-component active medium of a fast-flow gas laser

The mechanism of “flow”-type self-oscillations in a two-component active medium of a flow laser with an unstable resonator is studied. It is shown that this mechanism is associated with the excitation of edge self-oscillatory in-phase perturbations of the medium components. These flow perturbations with low damping reach the optical axis of the resonator and result in an instability.     

Symbolic regression modeling of noise generation at porous airfoils

Based on data sets from previous experimental studies, the tool of symbolic regression is applied to find empirical models that describe the noise generation at porous airfoils. Both the self noise from the interaction of a turbulent boundary layer with the trailing edge of an porous airfoil and the noise generated at the leading edge due to turbulent inflow are considered. Following a dimensional analysis, models are built for trailing edge noise and leading edge noise in terms of four and six dimensionless quantities, respectively. Models of different accuracy and complexity are proposed and discussed. For the trailing edge noise case, a general dependency of the sound power on the fifth power of the flow velocity was found and the frequency spectrum is controlled by the flow resistivity of the porous material. Leading edge noise power is proportional to the square of the turbulence intensity and shows a dependency on the fifth to sixth power of the flow velocity, while the spectrum is governed by the flow resistivity and the integral length scale of the incoming turbulence.     

Parallel Correlation Studies of Fluctuations and the Impact of Perturbations in the Magnetic Configuration

The plasma turbulence in the boundary of fusion relevant experiments is known to have a quasi two‐dimensional nature: the scale lengths perpendicular to the magnetic field are in the order of mm to cm, but parallel to the magnetic field, the correlation lengths are in the order of several meters. Recent parallel correlation studies with Langmuir probes at the JET tokamak over very long connection lengths (23 m and 66 m probe tip separation along the magnetic field) showed a correlation of less than 50%, in contrast to the finding of 80–90% correlation in other devices at measurements with smaller probe tip separations. However, it was not clear if this is a genuine physical property of the electrostatic turbulence in the scrape‐off layer or whether perturbations in the magnetic configuration had caused an additional decorrelation by a time‐dependent misalignment of the two probe tips along the connecting field line. In this contribution we analyze the effect of such perturbations in the magnetic configuration on the parallel correlation measurements in a simple model and compare the results with those of the measurements at JET.     

Quasiparticle approach to the modulational instability of drift waves coupling to zonal flows

The interaction between broadband drift mode turbulence and zonal flows has been studied through the wave-kinetic approach. Simulations have been conducted in which a particle-in-cell representation is used for the quasiparticles, while a fluid model is employed for the plasma. The interactions have been studied in a plasma edge configuration which has applications in both tokamak physics and magnetopause boundary layer studies. Simulation results show the development of a zonal flow through the modulational instability of the drift wave distribution, as well as the existence of solitary zonal flow structures about an ion gyroradius wide, drifting towards steeper relative density gradients.     

考虑来流角变化影响的叶栅稳健性优化设计

进、出口边界流动扰动是叶轮机械中一种典型的不确定性因素,对叶片气动性能产生重要影响。开展考虑边界流动扰动影响的叶片稳健性气动优化设计(RADO)研究,对提高叶片的平均气动性能及气动稳健性具有重要意义。首先介绍叶片RADO的基本原理、实现方法及关键问题。之后开展基于自适应非嵌入式多项式混沌模型的某型跨音速涡轮叶栅来流角不确定性研究,对叶栅总压损失进行量化。最后开展叶片气动外形的RADO研究,通过与确定性气动优化设计的对比揭示RADO在提高优化叶片气动稳健性方面的优越性。