竖直平板间自然对流大尺度相干结构的POD分析

POD方法是研究湍流相干结构的有效手段．将该方法应用于竖直平板间自然对流的问题,考虑到流场的热耦合性,采取了速度场与温度场相关联的POD分析．研究表明,该流场具有显著的结构性,流场中的主要含能流动形态为大尺度螺旋涡与纵向涡结构．用POD分析方法,得到广义“能量”在各模态问的分布,发现其分布有比较明显的收敛性．通过POD方法重构流场,可以用较少的模态捕捉到该流场的主要信息．     

PIV速度场坏矢量的本征正交分解处理技术

介绍了一种针对粒子图像测速(PIV)基于本征正交分解(POD)的速度场后处理技术.该技术改变了现在后处理技术将速度场坏矢量识别和修正分开实现的局面,通过迭代方法有效地实现了速度场坏点统一的识别和修复算法.算法利用POD分解的低阶模态信息重构出可以用于坏矢量识别的参考速度场,利用该参考速度场对全流场进行坏点识别并完成修正.通过对一套光滑的PIV速度场数据引入高斯分布的随机误差,测试验证了该POD方法的优越性.在坏矢量识别方面新方法较归一化中值检验有更高的正确性,能识别大面积出现的坏矢量区域.在坏矢量修补的插值算法中,新方法的计算效率又高于传统Gappy POD方法,且计算精度优于常见的矢量场内插数学方法.特别是在数据缺失的大连通区域,该方法对物理流场有很好的预测效果.     

基于动力学模态分解法的绕水翼非定常空化流场演化分析

空化是船舶和水下航行体推进器中经常发生的一种特殊流动现象,它具有强烈的非定常性,空化的发生往往会影响推进器的水动力性能和效率. 为探究绕水翼非定常空化流场结构,本文基于 Schnerr-Sauer 空化模型和 SST $k$-$\omega $ 湍流模型,开展绕二维水翼非定常空化流动数值预报与流场结构分析. 通过将数值预报的空泡形态演变和压力数据与试验结果对比,验证了建立的数值方法的有效性. 并基于动力学模态分解方法对空化流场的速度场进行模态分解,分析了各个模态的流场特征. 结果表明,第一阶模态对应频率为 0,代表平均流场;第二阶模态对应频率约为空泡脱落频率,揭示了空泡在水翼前缘周期性地生长与脱落,第三阶模态对应频率约为第二阶模态的 2 倍,揭示了两个大尺度旋涡在水翼后方存在融合行为. 第四阶模态对应频率约为第二阶模态的 3 倍,具有更高的频率,表征流场中存在一些小尺度旋涡的融合行为. 最后对不同空化数下的空化流场进行了模态分解分析,发现脱落空泡的旋涡结构随着空化数的减小而增大,第二阶模态频率随着空化数的减小而减小.      

ANALYSIS OF UNSTEADY CAVITATION FLOW OVER HYDROFOIL BASED ON DYNAMIC MODE DECOMPOSITION$^{\bf 1)}$

空化是船舶和水下航行体推进器中经常发生的一种特殊流动现象,它具有强烈的非定常性,空化的发生往往会影响推进器的水动力性能和效率. 为探究绕水翼非定常空化流场结构,本文基于 Schnerr-Sauer 空化模型和 SST $k$-$\omega $ 湍流模型,开展绕二维水翼非定常空化流动数值预报与流场结构分析. 通过将数值预报的空泡形态演变和压力数据与试验结果对比,验证了建立的数值方法的有效性. 并基于动力学模态分解方法对空化流场的速度场进行模态分解,分析了各个模态的流场特征. 结果表明,第一阶模态对应频率为 0,代表平均流场;第二阶模态对应频率约为空泡脱落频率,揭示了空泡在水翼前缘周期性地生长与脱落,第三阶模态对应频率约为第二阶模态的 2 倍,揭示了两个大尺度旋涡在水翼后方存在融合行为. 第四阶模态对应频率约为第二阶模态的 3 倍,具有更高的频率,表征流场中存在一些小尺度旋涡的融合行为. 最后对不同空化数下的空化流场进行了模态分解分析,发现脱落空泡的旋涡结构随着空化数的减小而增大,第二阶模态频率随着空化数的减小而减小.     

基于l2范数的EMD滤波方法在光纤陀螺信号中的应用

光纤陀螺的随机漂移限制了惯性导航系统的精度,如何减小它是一项非常艰巨的任务.结合经验模态分解(EMD)和信号与模态之间的概率密度函数,提出了一种新型的依赖Hurst指数的信号滤波方法.当H＜0.5时,利用l2范数选择出相关模态,累加并形成的部分重构方法来对光纤陀螺的信号进行滤波;当H≥0.5时,间隔阈值的经验模态(EMD-IT)被引入对相关模态进行滤波,之后按照部分重构的方法对光纤陀螺的信号进行滤波;称为混合的EMD-pdf和EMD-IT.与其它的滤波方法进行对比,如基于相关函数的EMD部分重构(EMD-cor),基于概率密度函数的EMD部分重构(EMD-pdf),仿真信号和实际数据结果表明,该混合模型的优越性,有效减小了光纤陀螺的随机误差.     

槽道内涡波流场的POD分析

对槽道内涡波流场的瞬态速度矢量场进行了2DPIV测量实验,将2DPIV测量的矢量场数据进行POD分析,根据POD分解的各阶模态的能量比确定了表征涡波流场主导结构的前15阶模态。结果表明,POD分解的前15阶模态发现槽道内涡波流场是由槽道壁面剪切层诱导的涡列以及伴随的波状主流组成;流场中大尺度的涡旋发展为涡对,对波状主流的脉动频率产生影响;根据涡波流场中的驻点和鞍点,获取了流场的大尺度涡对、平均流场以及Helmholtz涡环等明显特征;最后根据POD分解的前15阶模态对槽道内涡波流场进行重组,重组流场表征了槽道内层流状态下波状主流的形态和涡旋共存的涡波结构以及驻点和鞍点的位置处涡旋的变化等主要特征,有效地剔除了PIV测量流场中的随机信息,保留了PIV测量流场的主导特征。     

稳态条件下气溶胶粒子在口腔模型中的沉淀率

以实际人体解剖学数据为基础,利用流体力学软件构建了口腔模型。由于口腔形状不规则,流场中会有湍流产生,所以本文选用的是k-ω方程。在此基础上,假设吸入空气流量为一个常量,改变吸入气体、气溶胶粒子的物理参数,以调整St数的变化,模拟不同情况下气溶胶粒子运动情况。由模拟结果可知:气溶胶粒子在口腔中的沉淀率受粒子半径、密度、及流速的影响,并随这些量的增加而增加;沉淀率可以视作St数的函数,并随St数的增加而增加;气溶胶粒子在口腔中的沉淀分布受模型几何形状和湍流的影响,在喉部附近沉淀较为明显;粒子在口腔中将沿怎样的轨迹运动则取决于粒子在入口处的初始位置。     

一种基于增量径向基函数插值的流场重构方法

由于流场参数重构中, 用于重构的基网格单元的物理参数波动量相对于均值较小, 径向基函数（RBF） 直接插值方法重构会产生较大的数值振荡, 论文提出了一种增量RBF 插值方法, 并用于有限体积的流场重构步, 明显改善了插值格式的收敛性和稳定性. 算例首先通过简单的一维模型说明该方法的有效性, 当目标函数波动量相对于均值为小量时, 增量RBF 插值能够抑制数值振荡; 进一步通过二维亚音速、跨音速定常无黏算例、静止圆柱绕流非定常算例以及超音速前台阶算例来说明该方法在典型流场数值求解中的通用性和有效性. 研究表明增量RBF 重构方法可陡峭地捕捉激波间断, 可有效改善流场求解的收敛性和稳定性, 数值耗散小, 计算效率高.      

基于希尔伯特-黄变换的去噪法在外测数据处理中的应用

针对靶场测量设备种类多,外测数据中存在各种不确定因素的误差,且难以用统一的误差模型来描述,提出了一种基于希尔伯特-黄变换的滤波去噪方法。通过经验模式分解将外测数据自适应地分解成一组内蕴模态函数(IMF),然后对内蕴模态函数进行希尔伯特频谱分析,采用基于自适应阈值的消噪方法对模态函数进行消噪,最后对消噪后的模态函数重构,得到去噪后的外测数据。数据结果分析证明,该方法最大限度地抑制了测量数据中的噪声,特别是对于外测数据中的瞬时强噪声干扰剔除效果非常有效,在高精度的外测数据处理中具有较好的实用性。     

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采用谱单元方法推导带阻尼梁的传递函数矩阵. 采用一维连续梁的解析解作为动力形状函 数. 与有限元法相比,谱单元方法的自由度和单元数目小且计算精度高. 传递函数表示为梁 的几何和物理参数的超越隐函数,不同于用模态参数表示的传统传递函数. 提出了采用遗传 算法的结构物理参数识别方法. 以变截面悬臂梁为数值算例,显示该方法的有效性.     

Flow temporal reconstruction from non time-resolved data part II: practical implementation,methodology validation,and applications

This paper proposes a method to sort experimental snapshots of a periodic flow using information from the first three POD coefficients. Even in presence of turbulence, phase-average flow fields are reconstructed with this novel technique. The main objective is to identify and track traveling coherent structures in these pseudo periodic flows. This provides a tool for shedding light on flow dynamics and allows for dynamical contents comparison, instead of using mean statistics or traditional point-based correlation techniques. To evaluate the performance of the technique, apart from a laminar test on the relative strength of the POD modes, four additional tests have been performed. In the first of these tests, time-resolved PIV measurements of a turbulent flow with an externally forced main frequency allows to compare real phase-locked average data with reconstructed phase obtained using the technique proposed in the paper. The reconstruction technique is then applied to a set of non-forced, non time-resolved Stereo PIV measurements in an atmospheric burner, under combustion conditions. Besides checking that the reconstruction on different planes matches, there is no indication of the magnitude of the error for the proposed technique. In order to obtain some data regarding this aspect, two additional tests are performed on simulated non-externally forced laminar flows with the addition of a digital filter resembling turbulence (Klein et al. in J Comput Phys 186:652–665, 2003). With this information, the limitation of the technique applicability to periodic flows including turbulence or secondary frequency features is further discussed on the basis of the relative strength of the Proper Orthogonal Decomposition (POD) modes. The discussion offered indicates coherence between the reconstructed results and those obtained in the simulations. In addition, it allows defining a threshold parameter that indicates when the proposed technique is suitable or not. For those researchers interested on the background and possible generalizations of the technique, part I of this work (Legrand et al. in Exp Fluid (submitted in 2010) 2011) offers the mathematic fundamentals of the general space–time reconstruction technique using POD coefficients. Noteworthy, the involved computational time is relatively small: all the reconstructions have been performed in the order of minutes.     

Flow temporal reconstruction from non-time-resolved data part I: mathematic fundamentals

At least two circumstances point to the need of postprocessing techniques to recover lost time information from non-time-resolved data: the increasing interest in identifying and tracking coherent structures in flows of industrial interest and the high data throughput of global measuring techniques, such as PIV, for the validation of computational fluid dynamics (CFD) codes. This paper offers the mathematic fundamentals of a space--time reconstruction technique from non-time-resolved, statistically independent data. An algorithm has been developed to identify and track traveling coherent structures in periodic flows. Phase-averaged flow fields are reconstructed with a correlation-based method, which uses information from the Proper Orthogonal Decomposition (POD). The theoretical background shows that the snapshot POD coefficients can be used to recover flow phase information. Once this information is recovered, the real snapshots are used to reconstruct the flow history and characteristics, avoiding neither the use of POD modes nor any associated artifact. The proposed time reconstruction algorithm is in agreement with the experimental evidence given by the practical implementation proposed in the second part of this work (Legrand et al. in Exp Fluids, 2011), using the coefficients corresponding to the first three POD modes. It also agrees with the results on similar issues by other authors (Ben Chiekh et al. in 9 Congrès Francophone de Vélocimétrie Laser, Bruxelles, Belgium, 2004; Van Oudheusden et al. in Exp Fluids 39-1:86?C98, 2005; Meyer et al. in 7th International Symposium on Particle Image Velocimetry, Rome, Italy, 2007a; in J Fluid Mech 583:199?C227, 2007b; Perrin et al. in Exp Fluids 43-2:341?C355, 2007). Computer time to perform the reconstruction is relatively short, of the order of minutes with current PC technology.     

Reduced-order models for control of fluids using the eigensystem realization algorithm

As sensors and flow control actuators become smaller, cheaper, and more pervasive, the use of feedback control to manipulate the details of fluid flows becomes increasingly attractive. One of the challenges is to develop mathematical models that describe the fluid physics relevant to the task at hand, while neglecting irrelevant details of the flow in order to remain computationally tractable. A number of techniques are presently used to develop such reduced-order models, such as proper orthogonal decomposition (POD), and approximate snapshot-based balanced truncation, also known as balanced POD. Each method has its strengths and weaknesses: for instance, POD models can behave unpredictably and perform poorly, but they can be computed directly from experimental data; approximate balanced truncation often produces vastly superior models to POD, but requires data from adjoint simulations, and thus cannot be applied to experimental data. In this article, we show that using the Eigensystem Realization Algorithm (ERA) (Juang and Pappa, J Guid Control Dyn 8(5):620?C627, 1985) one can theoretically obtain exactly the same reduced-order models as by balanced POD. Moreover, the models can be obtained directly from experimental data, without the use of adjoint information. The algorithm can also substantially improve computational efficiency when forming reduced-order models from simulation data. If adjoint information is available, then balanced POD has some advantages over ERA: for instance, it produces modes that are useful for multiple purposes, and the method has been generalized to unstable systems. We also present a modified ERA procedure that produces modes without adjoint information, but for this procedure, the resulting models are not balanced, and do not perform as well in examples. We present a detailed comparison of the methods, and illustrate them on an example of the flow past an inclined flat plate at a low Reynolds number.     

A study of the energetic turbulence structures during stall delay

This study revealed the three-dimensional instantaneous topologies of the large-scale turbulence structures in the separated flow on the suction surface of wind turbine’s blade during stall delay. These structures are the major contributors to the first two POD (proper orthogonal decomposition) modes. The two kinds of instantaneous flow structures as major contributors to the first POD mode are: (1) extended regions of downwash flow with an upstream upward flow beside it and a compact vortex pair closer to the blade’s leading edge; (2) a large-scale clockwise vortex with strong induced flows. The two kinds of flow structures contributing significantly to the second POD mode are: (1) large counter-rotating vortices inducing strong upward velocities and a series of small vortices; (2) strong downwash flow coming from the leading-edge shear layer with a large and strong vortex on the left side and small vortices upstream. The statistical impacts of these large-scale and energetic structures on the turbulence have also been studied. It was observed that when these turbulence structures were removed from the flow, the peak values of some statistics were significantly reduced.     

Turbulence Filter and POD Analysis for Velocity Fields in Lifted CH4-Air Diffusion Flames

The turbulence filter and the proper orthogonal decomposition (POD)methods are applied to PIV measurements of lifted CH₄-air diffusionflames at three different Reynolds numbers. Properties such as vorticityand strain rate distributions of the decomposed fields are analyzed inorder to assess the physical behavior. The turbulence filter can userelatively less data than the POD method while still providingsignificant insight about the flow field. The energy activation ratesshow the first modes (mean flow) account for 85% of the total energy.Reconstruction of the POD modes reveals that the combination of modesyields a complex fluctuating behavior. The averaged Reynolds stress ofthe mean flow removed parts shows interesting correlation with the meanflow vorticity and strain rate distributions. Selected turbulentproperties are calculated and discussed.     

同心旋转圆柱间粘弹性流的非线性动力学模型

基于小间隙假设,将速度场和应力场有杉Ｆｏｕｒｉｅｒ展开式截断近似,推导了同心旋转圆柱间Ｏｌｄｒｏｙｄ－Ｂ型流体的六维动力系统,探讨了高分子添加对滑动轴承间油膜稳定性的影响。结果表明,少量的高分子添加剂具有推迟流体层流失稳的作用。     

Proper orthogonal decomposition analysis of coherent motions in a turbulent annular jet

A three-dimensional incompressible annular jet is simulated by the large eddy simulation(LES) method at a Reynolds number Re = 8 500. The time-averaged velocity field shows an asymmetric wake behind the central bluff-body although the flow geometry is symmetric. The proper orthogonal decomposition(POD) analysis of the velocity fluctuation vectors is conducted to study the flow dynamics of the wake flow.The distribution of turbulent kinetic energy across the three-dimensional POD modes shows that the first four eigenmodes each capture more than 1% of the turbulent kinetic energy, and hence their impact on the wake dynamics is studied. The results demonstrate that the asymmetric mean flow in the near-field of the annular jet is related to the first two POD modes which correspond to a radial shift of the stagnation point. The modes 3 and 4 involve the stretching or squeezing effects of the recirculation region in the radial direction. In addition, the spatial structure of these four POD eigenmodes also shows the counter-rotating vortices in the streamwise direction downstream of the flow reversal region.     

Proper orthogonal decomposition of the flow in geometries containing a narrow gap

Geometries containing a narrow gap are characterized by strong quasi-periodical flow oscillations in the narrow gap region. The above mentioned phenomena are of inherently unstable nature and, even if no conclusive theoretical study on the subject has been published, the evidence shown to this point suggests that the oscillations are connected to interactions between eddy structures of turbulent flows on opposite sides of the gap. These coherent structures travel in the direction of homogeneous turbulence, in a fashion that strongly recalls a vortex street. Analogous behaviours have been observed for arrays of arbitrarily shaped channels, within certain range of the geometric parameters. A modelling for these phenomena is at least problematic to achieve since they are turbulence driven. This work aims to address the use of Proper Orthogonal Decomposition (POD) to reduce the Navier–Stokes equations to a set of ordinary differential equations and better understand the dynamics underlying these oscillations. Both experimental and numerical data are used to carry out the POD.     

Turbulent time-events in channel with rough walls

This brief communication quantifies the time-events that contribute to the dynamics of wall-bounded flows with rough walls. Lumley’s Proper Orthogonal Decomposition (POD) methodology has been used to extract the energetic modes of the flow. We have used the concept of entropy, a representation of lack of organization in the flow, to represent the extent of spread of turbulent kinetic energy to higher modes. The rough-wall dynamics is dominated by fast activity (short time period) propagating modes and slow activity (long time period) roll modes. A single dominant timescale has been captured for all the propagating modes in flows over smooth walls; multiple dominant timescales representing various vortex shedding events are captured for rough walls. Variable-interval time averaging technique has been used to obtain the bursting frequency. The bursting frequency of rough-wall turbulence is higher compared to smooth-wall turbulence, suggesting that roughness enhances turbulence production activity. Another insightful observation for rough walls revealed by our study is that the vortex shedding frequency of roughness elements is much higher compared to the bursting frequency of rough-wall turbulence. POD provides a straightforward method to extract the natural frequency of shed vortices due to roughness, an important dynamical activity in rough-wall turbulent boundary layers.