Correction of wandering smoothing effects on static measurements of a wing-tip vortex

Wandering is a typical feature of wing-tip vortices and it consists in random fluctuations of the vortex core. Consequently, vortices measured by static measuring techniques appear to be more diffuse than in reality, so that a correction method is needed. In the present paper statistical simulations of the wandering of a Lamb-Oseen vortex are first performed by representing the vortex core locations through bi-variate normal probability density functions. It is found that wandering amplitudes smaller than 60% of the core radius are well predicted by using the ratio between the RMS value of the mean cross-velocity and its slope measured at the mean vortex center. Furthermore, the principal axes of wandering can be accurately evaluated from the opposite of the cross-correlation coefficient between the spanwise and the normal velocities measured at the mean vortex center. The correction of the wandering smoothing effects is then carried out through four different algorithms that perform the deconvolution of the mean velocity field with the probability density function that represents the wandering. The corrections performed are very accurate for the simulations with wandering amplitudes smaller than 60% of the core radius, whereas errors become larger with increasing wandering amplitudes. Subsequently, the whole procedure to evaluate wandering and to correct the mean velocity field is applied to static measurements, carried out with a fast-response five-hole pressure probe, of a tip vortex generated from a NACA 0012 half-wing model. It is found that the wandering is predominantly in the upward-outboard to downward-inboard direction. Furthermore, the wandering amplitude grows with increasing streamwise distance from the wing, whereas it decreases with increasing angle of attack and free-stream velocity.     

Effect of tip vortex aperiodicity on measurement uncertainty

Vortex aperiodicity introduces random uncertainty in the measured vortex center location. Unless corrected, this may lead to systematic uncertainty in the vortex properties derived from the measured velocity field. For example, the vortex core size derived from averaged or mean flow field appears larger because of aperiodicity. Several methodologies for aperiodicity correction have been developed over the past two decades to alleviate this systematic uncertainty. However, these do not always reduce the accompanying random uncertainty. The current work shows that the analysis methods used to derive the vortex properties from the measured velocity field play an important role in the resultant random uncertainty in these properties; perhaps, even more important role than the aperiodicity correction methodology itself. It is hypothesized that a class of methods called global methods, which use a large extent of measured data, yield a smaller measurement uncertainty compared to local methods. This hypothesis is verified using a newly proposed global method based on a planar least-squares fit. The general applicability of the method is demonstrated using previous particle image velocimetry measurements of rotor tip vortices. The results clearly demonstrate a reduced random uncertainty in the vortex core properties, even in the presence of secondary vortical structures. Furthermore, the results are independent of the choice of aperiodicity correction methodology.     

三曝光三相关PIV技术研究

对不等间隔三次曝光单幅记录的PIV粒子图像,本文提出一和中三相关位移诊断方法,三相关函数有两个次大峰,且不对称地人布在最大峰两侧,本方法可同时获得位移值及判别位移方向,可有效解决位移方向二义性问题,对线性涡流模拟粒子图像,应用本方法进行粒子位移诊断,结果证实了本方法对含涡复杂流动速度方向判别的有效性。     

Vorticity in plane parallel, axially symmetrical or spherical flows of viscous fluid

For viscous (barotropic or incompressible) fluids it is shown that, if the vorticity and the viscous force are orthogonal, vortex lines are convected by a vector field which fits with the velocity field when viscosity vanishes (extension of Helmholtz theorem); it is also found that energy remains constant along the field lines of this vector field (extension of Bernoulli theorem).If, moreover, vorticity and velocity are orthogonal too, the magnitude of the vorticity then behaves as the density of a fluid which flows along streamsheets according to this very same vector field. These properties are mainly encountered for plane parallel flows, axially symmetrical flows, spherical flows, but also for some other miscellaneous flow geometries such as unidirectional or radial flows. The set of the former three flows can even be characterized by these properties; that enhances this set of important flow geometries, avails a general view on vorticity behavior, and explains the great simplicity of vorticity equations in these cases. Numerous examples and comments are given for illustrating.     

非对称槽道中涡旋波的特性研究

利用PIV流场显示技术，对振荡流体在非对称槽道中涡旋波的产生、发展和消失的规律进 行了实验研究和分析，测得了涡旋波流场的速度矢量图，阐明了涡旋波流场周期性变化的特 点. 结合涡动力学方程，深入分析并揭示了做周期性运动的流体能在槽道中产生波的特性这 一规律，从中发现：流体周期变化的非定常性和不对称的槽道结构是形成涡旋波流动的主要 因素. 本文对涡旋波流场中各个旋涡的速度分布和涡量进行了测量和计算，分析了涡旋波 强化传质的机理，并研究了Re数对涡旋波流动的影响     

用拉格朗日相关结构研究圆盘启动过程的流体输运

利用粒子成像测速(PIV)技术,得到了圆盘启动涡环流场的速度分布和涡量分布.圆盘启动涡环流场的有限时间李雅普诺夫指数场(Finit-time Lyapunov exponents,FTLE)以及拉格朗日相关结构(Lagrangian coherent structures,LCS)被计算出来.基于圆盘启动涡环流场的有限时间李雅普诺夫指数场以及拉格朗日相关结构,通过跟踪流体质点,对圆盘启动涡环流场的输运情况进行了分析.在圆盘启动涡环形成过程中,流体发现被圆盘和相互排斥的拉格朗日相关结构分成三部分.剪切流窗口(vorticity-flux window)被发现,涡量流通过剪切流窗口进入涡核.涡环的非定常边界被确定,它由相互排斥的拉格朗日相关结构背风面、圆盘以及剪切流窗口组成.     

非定常流动的快速拉格朗日涡方法数值模拟

采用快速拉格朗日涡方法数值模拟有复杂旋涡运动的非定常流动. 利用离散涡元模拟旋涡的产生、聚集和输送过程. 拉格朗日描述法用来计算离散涡元的移动,而移动速度则利用广义毕奥-萨伐尔公式结合快速多极子展开法计算,修正的涡半径扩散模型用来模拟离散涡元的黏性扩散. 突然起动圆柱和大攻角下突然起动翼型的非定常有涡流动的数值模拟,及其与试验结果的对比验证了方法的有效性. 另外,大攻角下突然起动翼型的计算结果给出了翼型起动后吸力面旋涡的产生、发展,周期性非定常流动的形成,以及尾流旋涡结构等一些重要的流动特征.[关键词] 非定常流有涡流动快速涡方法      

Topology of the vorticity field in three-dimensional shear layers and wakes

An experimental and numerical study of the three-dimensional transition of plane wakes and shear layers behind a flat plate is presented. Flow visualization techniques are used to monitor the response of laminar flows at moderate Reynolds numbers (≈100) to perturbations periodically distributed along the span. In this way, the formation and evolution of streamwise vortex tubes and their interaction with the spanwise vortices are analyzed. The flow was studied numerically by means of three-dimensional inviscid vortex dynamics. Assuming periodicity in the spanwise and the streamwise direction, we discretize the vorticity field into two layers of vortex filaments with finite core diameter. Comparison between experiment and visualization indicates that important features of the three-dimensional evolution can be reproduced by inviscid vortex dynamics. Vortex stretching in the strain field of the spanwise rollers appears to be the primary mechanism for the three-dimensional transition in this type of flows.     

Direct Numerical Simulation of a Recirculating, Swirling Flow

A direct numerical simulation (DNS) of a recirculating, swirling flow is performed at a Reynolds number of 5000. Detailed one and two point statistics are presented in this paper. Flow visualization and frequency analysis are used to identify a precessing vortex core and to characterize its position, extent and influence on the flow field. The results are compared with laser Doppler velocimetry (LDV) measurements as well as large eddy simulation (LES) data reported in the literature. The present work constitutes a first step in setting up a DNS data base for complex flows.     

Measurements of the orthogonal blade–vortex interaction using a particle image velocimetry technique

This paper describes the results of application of a particle image velocimetry (PIV) technique to an orthogonal blade–vortex interaction experiment. To help resolve the problem of vortex meander during the tests, two PIV systems were used, which produced two velocity vector maps closely separated in time. During the PIV analysis an image-based vector validation scheme was used, which was shown to reduce significantly the number of wild vectors reaching the vector map. Preliminary results from the tests showed that, close to the blade, a significant radial outflow was superimposed on the vortex flow field. The radial flow is thought to be due to the dispersion of the vortex axial core flow during vortex cutting, which distorts the vortex flow field and enlarges the vortex. Further away from the blade, no significant radial flow was detected and the vortex remained undisturbed. Received: 26 April 1999/Accepted: 9 November 1999     

基于速度梯度张量特征值的陷窝内旋涡分析

作为一种新型的涡流发生器,陷窝具有流动阻力小、综合传热性能高的特点,是现代高性能涡轮叶片内部冷却新技术. 旋涡的定量分析是陷窝强化传热优化设计的重要依据. 针对在不同陷窝模型下的旋涡结构、分离方式和背景压力变化引起的旋涡强度无法定量分析的问题,本文提出采用涡核速度和 涡核速度梯度张量特征值来定量分析旋涡的方法. 通过采用涡核处局部坐标系表示的速度矢量和速度梯度张量,得到了涡核的轴 向速度、径向速度、旋转角速度、轴向加速度和径向加速度,并在此基础上简化出了用最大轴向速度、最大轴向加速度和最大旋 转角速度综合表示的旋涡强度的定量分析方法. 用该方法分析了不同深宽比陷窝诱导的旋涡结构,随着深宽比的增大,最大轴向 速度、最大轴向加速度和最大旋转角速度均呈现明显的增大趋势,旋涡强度增大. 研究表明此方法具有数据处理简单、通用性强、 不受分离方式限制、不受背景压力影响的特点,且提取到的数据具有明确的物理意义,适用于各类旋涡定量分析.      

Granular vortices: Identification,characterization and conditions for the localization of deformation

We relate the micromechanics of vortex evolution to that of force chain buckling and, on this basis, formulate the conditions for strain localization in a continuum model of dense granular media. Using the traditional bifurcation analysis of shear bands, we show that kinematic vortex fields are in fact solutions to the boundary value problem satisfying null boundary conditions. To establish an empirical basis for our study, we first develop a method to identify the location of the core and boundary of each vortex from a given displacement field in two dimensions. We then employ this method to characterize the residual deformation field (i.e., the deviation of particle motions from the continuum deformation) in a physical experiment and a discrete element simulation of dense granular samples submitted to biaxial compression. Vortices in the failure regime are essentially confined to the shear band. Primary vortices, the clear majority, rotate in the same direction as the shear band; secondary vortices, the so-called wakes, rotate in the opposite direction. Primary vortices align in spatial succession along the central axis of the band; wakes form next to the band boundaries, in between and beside two adjacent primary vortices. Force chain buckling, the governing mechanism for shear bands, is responsible for vortex formation in the failure regime. Vortex dynamics are consistent with stick-slip dynamics. From quiescent conditions of jamming or stick, vortical motions arise from force chain buckling and associated relative particle rotations and sliding; these in turn precipitate intermittent periods of unjamming or slip, evident in the attendant drops in stress ratio and bursts in both kinetic energy and local nonaffine deformation. A kinematic vortex field inside shear bands is proposed that is consistent with the equations of continuum mechanics and the underlying instability of force chain buckling: such a field is periodic with a repeating unit cell comprising a primary vortex at the center of the band, with two trailing wakes close next to the band boundaries.     

Three-dimensional reconstruction of cardiac flows based on multi-planar velocity fields

Measurement of the three-dimensional flow field inside the cardiac chambers has proven to be a challenging task. This is mainly due to the fact that generalized full-volume velocimetry techniques cannot be easily implemented to the heart chambers. In addition, the rapid pace of the events in the heart does not allow for accurate real-time flow measurements in 3D using imaging modalities such as magnetic resonance imaging, which neglects the transient variations of the flow due to averaging of the flow over multiple heartbeats. In order to overcome these current limitations, we introduce a multi-planar velocity reconstruction approach that can characterize 3D incompressible flows based on the reconstruction of 2D velocity fields. Here, two-dimensional, two-component velocity fields acquired on multiple perpendicular planes are reconstructed into a 3D velocity field through Kriging interpolation and by imposing the incompressibility constraint. Subsequently, the scattered experimental data are projected into a divergence-free vector field space using a fractional step approach. We validate the method in exemplary 3D flows, including the Hill’s spherical vortex and a numerically simulated flow downstream of a 3D orifice. During the process of validation, different signal-to-noise ratios are introduced to the flow field, and the method’s performance is assessed accordingly. The results show that as the signal-to-noise ratio decreases, the corrected velocity field significantly improves. The method is also applied to the experimental flow inside a mock model of the heart’s right ventricle. Taking advantage of the periodicity of the flow, multiple 2D velocity fields in multiple perpendicular planes at different locations of the mock model are measured while being phase-locked for the 3D reconstruction. The results suggest the metamorphosis of the original transvalvular vortex, which forms downstream of the inlet valve during the early filling phase of the right ventricular model, into a streamline single-leg vortex extending toward the outlet.     

Simulation on motion of particles in vortex merging process

In a two-phase flow, the vortex merging influences both the flow evolution and the particle motion. With the blobs-splitting-and-merging scheme, the vortex merging is calculated by a corrected core spreading vortex method （CCSVM）. The particle motion in the vortex merging process is calculated according to the particle kinetic model. The results indicate that the particle traces are spiral lines with the same rotation direction as the spinning vortex. The center of the particle group is in agreement with that of the merged vortex. The merging time is determined by the circulation and the initial ratio of the vortex radius and the vortex center distance. Under a certain initial condition, a stretched particle trail is generated, which is determined by the viscosity, the relative position between the particles and the vortex, and the asymmetrical circulation of the two merging vortices.     

Construction of three-dimensional images of flow structure via particle tracking techniques

Construction of three-dimensional images of flow structure, based on the quantitative velocity field, is assessed for cases where experimental data are obtained using particle tracking technique. The experimental data are in the form of contiguous planes of particle images. These contiguous data planes are assumed to correspond to successive spatial realizations in steady flow, or to phase-referenced realizations in an unsteady flow.Given the particle images on contiguous planes, the in-plane velocity fields are determined. Then, the out-of-plane velocity field is obtained using a spectral interpolation method. Application of this method allows, in principle, construction of the three-dimensional vorticity field and the streamline patterns.A critical assessment is made of the uncertainties arising from the in-plane interpolation of the velocity field obtained from particle tracking and the evaluation of the out-of-plane velocity component. The consequences of such uncertainties on the reconstructed vorticity distributions and streamline patterns are addressed for two basic types of vortex flows: a columnar vortex, for which the streamlines are not closed and are spatially periodic in the streamwise direction; and for a spherical (Hill's) vortex exhibiting closed streamline patterns, and no spatial periodicity.     

Stereo particle image velocimetry applied to a vortex pipe flow

Stereo particle image velocimetry (PIV) has been employed to study a vortex generated via tangential injection of water in a 2.25 inch (57 mm) diameter pipe for Reynolds numbers ranging from 1,118 to 63,367. Methods of decreasing pipe-induced optical distortion and the PIV calibration technique are addressed. The mean velocity field analyses have shown spatial similarity and revealed four distinct flow regions starting from the central axis of rotation to the pipe wall in the vortex flows. Turbulence statistical data and vortex core location data suggest that velocity fluctuations are due to the axis of the in-line vortex distorting in the shape of a spiral.     

A HYBRID VORTEX METHOD FOR FLOWS OVER A BLUFF BODY

A hybrid vortex method was developed to simulate the two-dimensional viscous incompressible flows over a bluff body numerically. It is based on a combination of the diffusion–vortex method and the vortex-in-cell method by dividing the flow field into two regions. In the region near the body surface the diffusion–vortex method is used to solve the Navier–Stokes equations, while the vortex-in-cell method is used in the exterior domain. Comparison with results obtained by the finite difference method, other vortex methods and experiments shows that the present method is well adapted to calculate two-dimensional external flows at high Reynolds number. It is capable of calculating not only the global characteristics of the separated flow but also the evolution of the fine structure of the flow field with time precisely. The influence of the grid system and region decomposition on the results will also be discussed. © by 1997 John Wiley & Sons, Ltd.     

Spherical Vortex Structures with a Core and a Shell

In this paper we construct and investigate the vortex structure consisting of a spherical vortex (vortex core) inside a spherical vortex layer (shell). A partial case of this structure is a spherical vortex with uniformly helical motion of the fluid within the core and the shell. The strengths of the helical flows in the core and the shell are generally different. The case of identical strengths is analyzed in detail. The streamline pattern is presented. The vortex velocity limit at which the vortex does not collapse is found. This proves to be less by a factor 1.7 than the analogous quantity for a vortex without a shell and 4 times lower than the maximum velocity of the Hill vortex.