A swirling jet with vortex breakdown: three-dimensional coherent structures

The paper reports on shape of a three-dimensional coherent structure in a velocity field of a high-swirl turbulent jet with the bubble-type vortex breakdown. A set of the 3D instantenous velocity fields was measured by using the tomographic particle image velocimetry (tomographic PIV) technique and processed by the proper orthogonal decomposition (POD) method. The detected intensive coherent velocity component corresponded to a helical vortex core of the swirling jet and two secondary spiral vortices. The entire coherent structure was rotating around the jet axis in compliance with the direction of the flow swirl. From the 3D data it is concluded that the dynamics of the strsucture can be described by a traveling wave equation: Re[A(y, r)·e ^{i(mθ + ky - ωt)}] with the number of the spiral mode m = +1 for positively defined k and ω.     

对称槽道涡波流场流动特征的POD分析

为深入分析层流状态下对称槽道内涡波流场的流动特性及其变化规律,对流场进行了二维粒子图像测速(2DPIV)测量获取瞬态速度矢量数据,利用本征正交分解(POD)技术进行模态分解以及涡波流场的重构,然后根据重构的流场对对称槽道内涡波流场进行了平均速度剖面、流场脉动强度以及特征点的速度和频谱分布等方面的分析。结果表明:POD的前15阶模态能够表征涡波流场的主导结构,第1,3阶模态主要表现为一对旋向相反的涡对特征,第2阶模态具有涡旋和波状主流的特征;提取了5个涡旋涡核的位置作为流场流动特性的特征点;根据POD重构流场分析发现流向平均速度呈抛物线形状分布,法向平均速度呈对称分布特征;流向脉动强度受壁面的影响较大,法向脉动强度呈现抛物线形状分布;距离中心主流较近的1#,4#,5#特征点的速度脉动程度受主流的脉动强度影响较大,速度的脉动主频0.15 Hz与次频、流场的自然频率0.35 Hz共同影响特征点的速度分布;2#,3#特征点的流向速度呈衰减趋势,法向速度在初期幅度变化较大。     

Large-Scale Coherent Vortex Formation in Two-Dimensional Turbulence

The evolution of a vortex flow excited by an electromagnetic technique in a thin layer of a conducting liquid was studied experimentally. Small-scale vortices, excited at the pumping scale, merge with time due to the nonlinear interaction and produce large-scale structures—the inverse energy cascade is formed. The dependence of the energy spectrum in the developed inverse cascade is well described by the Kraichnan law k^–5/3. At large scales, the inverse cascade is limited by cell sizes, and a large-scale coherent vortex flow is formed, which occupies almost the entire area of the experimental cell. The radial profile of the azimuthal velocity of the coherent vortex immediately after the pumping was switched off has been established for the first time. Inside the vortex core, the azimuthal velocity grows linearly along a radius and reaches a constant value outside the core, which agrees well with the theoretical prediction.     

Experimental investigation of a swirling flow in a cubic container

A flow induced by a rotating disk mounted at the top of a cubic container totally filled with a liquid is studied experimentally. The flow pattern is visualized for Reynolds numbers in the interval 1500–6000, and the velocity variation along the axis of the container, which coincides with the axis of revolution of the disk, is observed by means of Doppler laser anemometry (DLA). As Re grows, the velocity axial component starts fluctuating because of the vortex core precession. The breakdown of the vortex helical structure becomes pronounced at Re>4000 without the formation of the return flow region (vortex breakdown bubble) at the axis. With the Reynolds number and the container height-to-disk radius ratio being the same, the axial flow patterns in standard cylindrical [1] and cubic containers differ radically. In the latter vessel at low Re, the steady flow regime and axisymmetric bubble breakdown of the vortex structure near the axis are absent.     

Self-oscillations in a jet flow and gaseous flame with strong swirl

Investigation results on unsteady flow dynamics in a gaseous jet flame with strong swirl, vortex breakdown, and precession of a vortex core obtained by panoramic optical methods are presented, as well as the results of theoretical analysis of the fastest growing modes of hydrodynamic instability. Characteristics of the most unstable self-oscillating mode in the initial region of the turbulent strongly swirling propane-air jet burning in the atmospheric air in the form of a lifted flame are determined. Analysis of data by principal component analysis and linear stability analysis revealed that evolution of the dominant self-oscillating mode corresponds to quasi-solid rotation with constant angular velocity of the spatial coherent structure consisting of a jet spiral vortex core and two spiral secondary vortices.     

椭圆纳米盘中磁涡旋结构的方位角自旋波模式

本文针对坡莫合金椭圆形盘中的磁涡旋结构, 采用微磁学模拟与傅里叶分析相结合的技术研究了磁涡旋自旋波的本征激发模式. 通过沿样品短轴方向施加一面内方向的脉冲磁场, 观察到一系列方位角自旋波模式. 观察到的自旋波模式具有两重对称性, 可以通过C₂群理论来进行类型的划分. 此外, 自旋波模式的频率随着方位角指标的变化而线性增加. 模拟结果显示样品的平均交换能量密度明显的高于平均静磁能量密度; 局域交换能量密度主要集中在涡核初始位置, 而局域静磁能量密度主要分布在长轴附近. 交换作用对受限于铁磁薄膜椭圆盘中的单个涡旋态的能量要起主导作用, 从而导致方位角自旋波模式频率随着方位角指标的增加而增加.     

飞行器大攻角复杂流动的POD和DMD对比分析

基于非结构/混合网格、耗散自适应2阶混合格式以及脱体涡模拟（detached eddy simulation,DES）方法开展了现代战斗机模型复杂分离流动的数值模拟,并与有限的平均气动力试验数据进行了对比,结果表明计算具有合理性,在此基础上进一步应用本征正交分解（proper orthogonal decomposition,POD）和动力学模态分解（dynamic mode decomposition,DMD）方法对数值模拟流场的非定常特性进行了对比分析.研究表明飞行器背风区流场由一对边条涡的螺旋运动主导,旋涡破裂前在横向空间截面上流场是中性稳定的,同时主涡核的运动是多频耦合的.POD和DMD的对比分析则表明:两者模态配对的方式不同,但主要模态之间具有一定相关性;POD模态中包含多种频率的运动,而且能量较集中于主模态,流场重构效率更高;DMD则将流场的主要特征运动提取为一些单频模态的组合,同时能够给出模态的稳定性.      

Experimental and numerical investigation of the unsteady flow field and tone generation in an isolated centrifugal fan impeller

In spite of a low circumferential Mach number the sound of isolated centrifugal fan impellers is sometimes dominated by distinctive tones at blade passing frequency (BPF) and integer multiples. This paper reports on an experimental and numerical investigation intended to unveil the tone generating mechanism. The sound spectra from three impellers operating at a large range of speed were measured and decomposed into Strouhal and Helmholtz number dependent functions. This led to the preliminary conclusion that the BPF related tones are exclusively flow-induced. Based on hot-wire and blade pressure fluctuation measurements and a subsequent correlation analysis, coherent flow structures different from those associated with the principal azimuthal flow pattern due to the blades were detected. Eventually a numerical three-dimensional unsteady flow simulation revealed an inlet vortex. It takes on a helical form, with the vortex core slowly varying its position with respect to the impeller center. As the blades cut through that quasi-stationary helical vortex they encounter blade force fluctuations, producing the BPF tones. Slow spin of the vortex core and slow variation of vortex strength were identified as the reasons for amplitude modulation of the BPF tone.     

Visualisation and analysis of large-scale vortex structures in three-dimensional turbulent lid-driven cavity flow

In this paper, large eddy simulation (LES) of a three-dimensional turbulent lid-driven cavity (LDC) flow at Re = 10,000 has been performed using the multiple relaxation time lattice Boltzmann method. A Smagorinsky eddy viscosity model was used to represent the sub-grid scale stresses with appropriate wall damping. The prediction for the flow field was first validated by comparing the velocity profiles with previous experimental and LES studies, and then subsequently used to investigate the large-scale three-dimensional vortical structures in the LDC flow. The instantaneous three-dimensional coherent structures inside the cavity were visualised using the second invariant (Q), Δ criterion, λ₂ criterion, swirling strength (λ_ci) and streamwise vorticity. The vortex structures obtained using the different criteria in general agree well with each other. However, a cleaner visualisation of the large vortex structures was achieved with the λ_ci criterion and also when the visualisation is based on the vortex identification criteria expressed in terms of the swirling strength parameters. A major objective of the study was to perform a three-dimensional proper orthogonal decomposition (POD) on the fluctuating velocity fields. The higher energy POD modes efficiently extracted the large-scale vortical structures within the flow which were then visualised with the swirling strength criterion. Reconstruction of the instantaneous fluctuating velocity field using a finite number of POD modes indicated that the large-scale vortex structures did effectively approximate the large-scale motion. However, such a reduced order reconstruction of the flow based on the large-scale vortical structures was clearly not as effective in predicting the small-scale details of the fluctuating velocity field which relate to the turbulent transport.     

Suppression of vortex core precession in a swirling reacting flow

The influence of combustion effect on unsteady vortex structure in the form of precessing vortex core was studied using the non-intrusive method of laser Doppler anemometry and special procedure of extracting the non-axisymmetric mode of flow fluctuations. The studies show that combustion has a significant effect on the parameters of such a core, reducing the amplitude (vortex deviation from the burner center) and increasing precession frequency. At the same time, the acoustic sensors detect almost an order reduction in the level of pressure pulsations generated by the precessing vortex core. Moreover, distributions of tangential velocity fluctuations and cross-correlation analysis show that vortex precession is quite pronounced even under the combustion conditions, bringing a significant coherent component to distributions of velocity fluctuations.     

A steadily rotating plasma disk

A homogeneously rotating plasma disk can be formed in a radially directed Ar-arc discharge at reduced pressure with an externally applied axial magnetic field. The radial pressure distribution is measured, as well as the emitted continuum radiation and the arc voltage. With these experimental values profiles of temperature, radial and azimuthal current density, and flow velocity in the disk are evaluated. Viscosity determines the flow pattern essentially. The effects of magnetic field and rotational motion on the discharge are investigated. The disk exhibits at nonrigid rotation a strong centrifugal force and a minor Coriolis force. A weak double vortex is found to develop in the meridional plane. The electric field in the discharge is altered by the azimuthal plasma flow.     

Experimental investigation on laminar separation control for flow over a two-dimensional bump

The laminar boundary layer separation flow over a two-dimensional bump controlled by synthetic jets is experimentally investigated in a water channel with hydrogen-bubble visualisation and particle image velocimetry (PIV) techniques. The two-dimensional synthetic jet is applied near the separation point. Two Reynolds numbers (Re = 700 and 1120) based on the bump height and free-stream velocity are adopted in this experiment, and seven different excitation frequencies at each Reynolds number are considered, focusing on the separation control as well as the vortex dynamics. The experimental results show that the optimal control can only be achieved within some excitation frequencies at both Reynolds numbers. However, beyond this range, further increasing the excitation frequency leads to an increase in the separation region. The proper orthogonal decomposition (POD) technique and vortex identification by swirling strength (Λ_ci) are applied for the deeper analysis of the separated flow. The reconstructed Λ_ci field by the first four POD modes is used and vortex lock-on phenomenon is observed. It is found that the negative synthetic jet vortex with clockwise rotation draws the separated wake shear layer as it is convected downstream, and then they syncretise together. Thus, the new vortex is induced and shedding downstream periodically.     

Numerical description of axisymmetric blue whirls over liquid-fuel pools

This numerical investigation is focused on determining the structures of blue whirls, recently found to occur in laboratory investigations of fire whirls when the circulation becomes sufficiently large to produce a vortex breakdown that drastically shortens the fire whirl and correspondingly reduces residence times, so that the yellow flames turn blue. The computations address axisymmetric configurations for round pools of liquid fuels flush with and at the center of a larger solid horizontal disc, at the outer edge of which vanes of adjustable angles cause the entrained air to enter with a controllable azimuthal component of velocity. The nondimensionlized conservation equations employed include realistic Lewis numbers with temperature-dependent transport coefficients and a one-step chemical-kinetic approximation that correctly reproduces laminar burning velocities. Buoyancy and radiant energy transport from the flames to the liquid surface are both taken into account, the latter being found to be essential for the blue whirl. Along with the vaporization-equilibrium and energy-conservation boundary conditions at the fuel surface, inflow boundary conditions are provided by a recently developed solution for the boundary-layer flow over the solid disc, while zero-gradient outflow conditions are applied above the whirl. Controlling nondimensional parameters, besides Reynolds, Damköhler, and Froude numbers, are a ratio of radiant to convective energy flux and a ratio of azimuthal to inward radial flow velocity in the boundary layer at the edge of the disc. The computed conditions for the onset of the blue whirl, as well as the computed structure of the whirl itself, bear close resemblance to what was found experimentally.     

Long-lived planetary vortices and their evolution: Conservative intermediate geostrophic model

Large, long-lived vortices, surviving during many turnaround times and far longer than the dispersive linear Rossby wave packets, are abundant in planetary atmospheres and oceans. Nonlinear effects which prevent dispersive decay of intense cyclones and anticyclones and provide their self-propelling propagation are revised here using shallow water equations and their balanced approximations. The main physical mechanism allowing vortical structures to be long-lived in planetary fluid is the quick fluid rotation inside their cores which prevents growth in the amplitude of asymmetric circulation arising due to the beta-effect. Intense vortices of both signs survive essentially longer than the linear Rossby wave packet if their azimuthal velocity is much larger than the Rossby wave speed. However, in the long-time evolution, cyclonic and anticyclonic vortices behave essentially differently that is illustrated by the conservative intermediate geostrophic model. Asymmetric circulation governing vortex propagation is described by the azimuthal mode m=1 for the initial value problem as well as for steadily propagating solutions. Cyclonic vortices move west-poleward decaying gradually due to Rossby wave radiation while anticyclonic ones adjust to non-radiating solitary vortices. Slow weakening of an intense cyclone with decreasing of its size and shrinking of the core is described assuming zero azimuthal velocity outside the core while drifting poleward. The poleward tendency of the cyclone motion relative to the stirring flow corresponds to characteristic trajectories of tropical cyclones in the Earth's atmosphere. The asymmetry in dispersion-nonlinear properties of cyclones and anticyclones is thought to be one of the essential reasons for the observed predominance of anticyclones among long-lived vortices in the atmospheres of the giant planets and also among intrathermoclinic eddies in the ocean.     

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.      

Azimuthal modulational instability of vortices in the nonlinear Schrödinger equation

We study the azimuthal modulational instability of vortices with different topological charges, in the focusing two-dimensional nonlinear Schrödinger (NLS) equation. The method of studying the stability relies on freezing the radial direction in the Lagrangian functional of the NLS in order to form a quasi-one-dimensional azimuthal equation of motion, and then applying a stability analysis in Fourier space of the azimuthal modes. We formulate predictions of growth rates of individual modes and find that vortices are unstable below a critical azimuthal wave number. Steady-state vortex solutions are found by first using a variational approach to obtain an asymptotic analytical ansatz, and then using it as an initial condition to a numerical optimization routine. The stability analysis predictions are corroborated by direct numerical simulations of the NLS. We briefly show how to extend the method to encompass nonlocal nonlinearities that tend to stabilize such solutions.     

Controlled Vortex Breakdown on Modified Delta Wings

This paper studies the effect of perturbation to the breakdown of the leading-edge vortices over delta wings. The passive perturbation in the normal direction is achieved by installing the hemisphere-like bulges on the delta wing along the projection of the vortices. The key purpose of this perturbation is to delay or suppress vortex breakdown over delta wings according to the self-induction mechanism theory. The design of bulge-like surface for delta wings offers a minimization of initial vorticity gradient and an elimination of linearly mutual induction within the vortex core. Three delta wings with swept angles of 60°, 65dg and 70° have been used. Dye flow visualization and force measurement in different water tunnels are performed at the water speed of U=0.10, 0.15, 0.20 and 0.25 m/s. In flow visualization, the results show contributions of bulges as perturbation to leading-edge vortices. The best outcome of perturbing the vortex core occurs in the case of the 65° delta wing. The breakdown positions on the 65° delta wing are delayed in almost the entire range of angles of attack, and that, the results are presented here.     

Large-eddy simulation of impinging jets with embedded azimuthal vortices

We have carried out large-eddy simulations of an impinging jet with embedded azimuthal vortices, a model of the wake of a helicopter hovering in ground effect. The azimuthal vortices are generated by sinusoidal forcing of the velocity at the jet exit. They strengthen while they are advected towards the ground; when they are close to the solid surface, a layer of opposite-sign vorticity is formed at the wall, and lifted up to form a secondary vortex that interacts with the primary one. Regions of reversed flow are caused by the strong, localised, adverse pressure gradient. After this interaction, the primary vortices begin to decay, mostly due to the Reynolds shear stresses, which contribute to the turbulent diffusion of vorticity term in the budget of the phase-averaged azimuthal vorticity. This mechanism is extremely robust, and plays the most important role in the vortex decay even if no turbulence is initially present in the jet, or if the no-slip condition is removed. A three-dimensional instability also plays a role: removing it leads to slower decay. Our results also point out some challenges for turbulence models for the unsteady Reynolds-averaged Navier–Stokes equations.     

Helicity of a toroidal vortex with swirl

Based on the solutions of the Bragg–Hawthorne equation, we discuss the helicity of a thin toroidal vortex in the presence of swirl, orbital motion along the torus directrix. The relation between the helicity and circulations along the small and large linked circumferences (the torus directrix and generatrix) is shown to depend on the azimuthal velocity distribution in the core of the swirling ring vortex. In the case of nonuniform swirl, this relation differs from the well-known Moffat relation, viz., twice the product of such circulations multiplied by the number of linkages. The results can find applications in investigating the vortices in planetary atmospheres and the motions in the vicinity of active galactic nuclei.     

高能重离子碰撞中的横向非对称流

对末态粒子方位角分布的研究可以获得反应中有关横向非对称流的信息.研究了碰撞中侧向流与椭圆流间的方位角关联,给出了一种定量测量反应中椭圆流大小的方法,该方法的计算结果可以有效地消除估计反应平面离散的影响.