正弦波沟槽对湍流边界层相干结构影响的TR-PIV实验研究

利用高时间分辨率粒子图像测速(time-resolved particle image velocimetry, TR-PIV)技术,在不同雷诺数下对光滑壁面和二维顺流向、三维正弦波(two/three dimensional, 2D/3D)沟槽壁面湍流边界层流场进行了实验测量,从不同沟槽对湍流边界层相干结构影响的角度分析了其减阻的机理.对比不同壁面的各阶统计量结果发现:沟槽降低了壁面摩擦阻力,存在减阻效果,正弦波沟槽的减阻率增大.运用相关函数、λ_(ci)检测准则等方法提取了不同壁面湍流边界层发卡涡和低速条带等典型相干结构的空间拓扑形态,结果表明:两种沟槽壁面的相干结构在流向和法向上的空间尺度均有不同程度的减小,且相干结构与主流之间的倾角趋于更小,流体在法向上的运动及结构的抬升受到明显抑制,发卡涡诱导喷射和扫掠的能力降低,从而影响了湍流中能量与动量的输运过程及湍流的自维持机制,且相比于2D沟槽, 3D正弦波沟槽作用效果更为明显.在同一雷诺数下,随着距离壁面法向位置的增加,不同壁面湍流边界层低速条带的展向间距都变宽;但同一法向位置处2D/3D沟槽壁面湍流边界层低速条带的间距与光滑壁面的相比更宽,沟槽的存在有效抑制了低速条带在展向上的运动,使得低速条带更稳定.     

Convection and correlation of coherent structure in turbulent boundary layer using tomographic particle image velocimetry

The present experimental work focuses on a new model for space–time correlation and the scale-dependencies of convection velocity and sweep velocity in turbulent boundary layer over a flat wall. A turbulent boundary layer flow at Reθ= 2460 is measured by tomographic particle image velocimetry(tomographic PIV). It is demonstrated that arch, cane,and hairpin vortices are dominant in the logarithmic layer. Hairpins and hairpin packets are responsible for the elongated low-momentum zones observed in the instantaneous flow field. The conditionally-averaged coherent structures systemically illustrate the key roles of hairpin vortice in the turbulence dynamic events, such as ejection and sweep events and energy transport. The space–time correlations of instantaneous streamwise fluctuation velocity are calculated and confirm the new elliptic model for the space–time correlation instead of Taylor hypothesis. The convection velocities derived from the space–time correlation and conditionally-averaged method both suggest the scaling with the local mean velocity in the logarithmic layer. Convection velocity result based on Fourier decomposition(FD) shows stronger scale- dependency in the spanwise direction than in streamwise direction. Compared with FD, the proper orthogonal decomposition(POD) has a distinct distribution of convection velocity for the large- and small-scales which are separated in light of their contributions of turbulent kinetic energy.     

Spatial hot-wire visualization of the Λ-structure transformation into the turbulent spot on the smooth flat plate surface and riblet effect on this process

Abstract  

Evolution of the Λ-vortex and its transformation into the turbulent spot in a flat plate boundary layer are investigated experimentally. Extensive measurements visualizing the Λ-structure transformation into the turbulent spot on the smooth and ribbed surfaces of the flat plate are presented. The flow behavior in the course of spatial evolution of the Λ-structure and turbulent spot is discussed. Specific features of the downstream evolution of Λ-structure and turbulent spot on the smooth and ribbed surfaces are demonstrated, such as suppression by riblets of the Λ-vortex transformation into the turbulent spot, appearance of the coherent structures of Λ-vortex within ensemble-averaged turbulent spot, and oblique waves generation both by the Λ-vortex and turbulent spot.     

沟槽壁面减阻机理实验研究

利用IFA300型热线风速仪,测量了光滑壁面和沟槽减阻壁面湍流边界层内的瞬时速度,利用自行设计的阻力天平仪测量了壁面摩擦力。得到了边界层无量纲速度分布和平均湍动能分布。对测得的脉动速度信号,利用离散正交小波变换按时间和尺度分解,得到各尺度分量的湍动能,并且发现其分布在湍流惯性区具有极大值。分析表明,当沟槽有减阻效果时,边界层内的平均湍动能减小,湍流惯性区各分量的湍动能极大值亦减小。     

湍流边界层对数律区相干结构的Tomo-TRPIV实验研究

应用层析高时间分辨率粒子图像测速技术（tomographic time-resolved particle image velocimetry，Tomo-TRPIV），测量了Re_θ=2 460的平板湍流边界层三维3分量瞬时速度场的时间序列.提出湍流空间多尺度局部平均速度结构函数的概念，应用流向脉动速度沿流向的空间多尺度局部平均速度结构函数的正负过零点法，从瞬时脉动速度场中检测相干结构的喷射和扫掠事件，对检测到的喷射和扫掠事件的瞬态局部速度场、速度梯度场、涡量场、速度变形率场进行空间相位对齐叠加平均，获得喷射和扫掠事件的局部速度场、速度梯度场、涡量场、速度变形率场的典型特征.研究发现，相干结构喷射和扫掠时，速度梯度、速度变形率、涡量均表现为空间反对称分布的4极子结构.特别是流向涡量是沿流向、法向、展向均为反对称分布的法向多层4极子结构，表明法向各层相干结构是紧密联系，互相关联的.这种法向多层的4极子反对称结构导致强烈的动量、质量和能量交换，维持了相干结构的演化和发展过程.      

Identification of lagrangian coherent structures in the turbulent boundary layer

Using Finite-Time Lyapunov Exponents (FTLE) method, Lagrangian coherent structures (LCSs) in a fully developed flat-plate turbulent boundary layer are successfully identified from a two-dimensional (2D) velocity field obtained by time-resolved 2D PIV measurement. The typical LCSs in the turbulent boundary layer are hairpin-like structures, which are characterized as legs of quasi-streamwise vortices extending deep into the near wall region with an inclination angle θ to the wall, and heads of the transverse vortex tube located in the outer region. Statistical analysis on the characteristic shape of typical LCS reveals that the probability density distribution of θ accords well with t-distribution in the near wall region, but presents a bimodal distribution with two peaks in the outer region, corresponding to the hairpin head and the hairpin neck, respectively. Spatial correlation analysis of FTLE field is implemented to get the ensemble-averaged inclination angle θ _R of typical LCS. θ _R first increases and then decreases along the wall-normal direction, similar to that of the mean value of θ. Moreover, the most probable value of θ saturates at y ⁺=100 with the maximum value of about 24°, suggesting that the most likely position where hairpins transit from the neck to the head is located around y ⁺=100. The ensemble- averaged convection velocity U _c of typical LCS is finally calculated from temporal-spatial correlation analysis of FTLE field. It is found that the wall-normal profile of the convection velocity U _c(y) accords well with the local mean velocity profile U(y) beyond the buffer layer, evidencing that the downstream convection of hairpins determines the transportation properties of the turbulent boundary layer in the log-region and beyond. Supported by the National Natural Science Foundation of China (Grant Nos. 10425207 and 10832001)     

扰流板作用下湍流/非湍流界面特性

在零压梯度平板湍流边界层流动中安装垂直流向高度为h的扰流板,诱导流场产生横向涡,研究横向涡影响下湍流/非湍流界面特性沿流向的发展。结果表明,在本实验条件下,整个流动经历了从湍流边界层到流动分离和再附,再向湍流边界层恢复的过程。在扰流板下游约18h距离后,扰流板尾迹的影响逐渐衰退,壁面剪切对湍流强度的贡献开始逐渐恢复,在扰流板下游约55h距离后,湍流边界层再次充分发展。与此同时,由于扰流板后流场流动结构拟序性的增强,湍流/非湍流界面的分形维度受扰流板影响而减小,表明脱落涡有使界面多尺度特性、三维性减弱的趋势。此外,界面高度的概率密度分布受扰流板影响呈现显著的右偏,主要与扰流板增强喷射运动强度,使得界面更容易抬升相关。流动结构及界面特性受扰流板影响后的流向演化有同步变化的模式,扰流板对界面特性影响主要集中于（-5~18）h的流向范围。      

Lagrangian analysis of the formation and mass transport of compressible vortex rings generated by a shock tube

In order to understand the mass transport and the dynamic genesis associated with a compressible vortex formation,a dynamic analysis of compressible vortex rings (CVRs) generated by shock tubes by using the framework of Lagrangiancoherent structures (LCSs) and finite-time Lyapunov exponents field (FTLE) is performed. Numerical calculation is performed to simulate the evolution of CVRs generated by shock tubes with 70 mm, 100 mm, and 165 mm of the driver sectionat the circumstances of pressure ratio = 3. The formation of CVRs is studied according to FTLE fields. The mass transportduring the formation is obviously seen by the material manifold reveled by FTLE fields. A non-universal formation numberfor the three CVRs is obtained. Then the elliptic LCSs is implemented on three CVRs. Fluid particles separated by ellipticLCSs and ridges of FTLE are traced back to t = 0 to identify the fluid that eventually forms the CVRs. The elliptic LCSsencompass around 60% fluid material of the advected bulk but contain the majority of the circulation of the ring. The otherparts of the ring carrying almost zero circulation advect along with the ring. Combining the ridges of FTLE and the ellipticLCS, the whole CVR can be divided into three distinct dynamic parts: vortex part, entrainment part, and advected part. Inaddition, a criterion based on the vortex part formation is suggested to identify the formation number of CVRs.     

Lagrangian coherent structures and the smallest finite-time Lyapunov exponent

We point out that local minimizing curves, or troughs, of the smallest finite-time Lyapunov exponent (FTLE) field computed over a time interval [t(0), t] and graphed over trajectory positions at time t mark attracting Lagrangian coherent structures (LCSs) at t. For two-dimensional area-preserving flows, we conclude that computing the largest forward-time FTLE field by itself is sufficient for locating both repelling LCSs at t(0) and attracting LCSs at t. We illustrate our results on analytic examples, as well as on a two-dimensional experimental velocity field measured near a swimming jellyfish.     

A synthesis approach for reproducing the response of aircraft panels to a turbulent boundary layer excitation

Random wall-pressure fluctuations due to the turbulent boundary layer (TBL) are a feature of the air flow over an aircraft fuselage under cruise conditions, creating undesirable effects such as cabin noise annoyance. In order to test potential solutions to reduce the TBL-induced noise, a cost-efficient alternative to in-flight or wind-tunnel measurements involves the laboratory simulation of the response of aircraft sidewalls to high-speed subsonic TBL excitation. Previously published work has shown that TBL simulation using a near-field array of loudspeakers is only feasible in the low frequency range due to the rapid decay of the spanwise correlation length with frequency. This paper demonstrates through theoretical criteria how the wavenumber filtering capabilities of the radiating panel reduces the number of sources required, thus dramatically enlarging the frequency range over which the response of the TBL-excited panel is accurately reproduced. Experimental synthesis of the panel response to high-speed TBL excitation is found to be feasible over the hydrodynamic coincidence frequency range using a reduced set of near-field loudspeakers driven by optimal signals. Effective methodologies are proposed for an accurate reproduction of the TBL-induced sound power radiated by the panel into a free-field and when coupled to a cavity.     

基于流动显示的压缩拐角流动结构定量研究

在Ma = 3.0的超声速风洞中, 采用NPLS技术对上游边界层为层流的25° 压缩拐角进行了流动显示实验, 获得了压缩拐角的精细流动结构, 边界层、剪切层和激波等结构清晰可见. 基于流动显示数据, 采用间歇性、空间相关性和分形分析对流动结构进行了定量研究, 计算了边界层和分离区的间歇因子分布, 获取了边界层中拟序结构和结构角的大小, 给出了边界层分形维数的分布, 并与Ringuette和Bookey等的实验结果进行比较, 阐述了压缩拐角流动结构的定量特征.     

An objective-adaptive refinement criterion based on modified ridge extraction method for finite-time Lyapunov exponent (FTLE) calculation

Journal of Visualization - Visualizing finite-time Lyapunov exponent (FTLE) efficiently and accurately has long been a research objective in identifying the coherent structures of turbulence or...     

Imaging of supersonic flow over a double elliptic surface

The coherent structures of flow over a double elliptic surface are experimentally investigated in a supersonic lownoise wind tunnel at Mach number 3 using nano-tracer planar laser scattering(NPLS)and particle image velocimetry(PIV)techniques.High spatiotemporal resolution images and velocity fields of both laminar and turbulent inflows over the test model are captured.Based on the time-correlation images,the spatial and temporal evolutionary characteristics of the coherent structures are investigated.The flow structures in the NPLS images are in good agreement with the velocity fluctuation fields by PIV.From statistically significant ensembles,spatial correlation analysis of both cases is performed to quantify the mean size and the orientation of coherent structures.The results indicate that the mean structure is elliptical in shape and the structural angles in the separated region of laminar inflow are slightly smaller than that of turbulent inflow.Moreover,the structural angles of both cases increase with their distance away from the wall.     

Three-dimensional turbulent flow over cube-obstacles

In order to investigate the influence of surface roughness on turbulent flow and examine the wall-similarity hypothesis of Townsend, three-dimensional numerical study of turbulent channel flow over smooth and cube-rough walls with different roughness height has been carried out by using large eddy simulation(LES) coupled with immersed boundary method(IBM). The effects of surface roughness array on mean and fluctuating velocity profiles, Reynolds shear stress, and typical coherent structures such as quasi-streamwise vortices(QSV) in turbulent channel flow are obtained. The significant influences on turbulent fluctuations and structures are observed in roughness sub-layer(five times of roughness height).However, no dramatic modification of the log-law of the mean flow velocity and turbulence fluctuations can be found by surface cube roughness in the outer layer. Therefore, the results support the wall-similarity hypothesis. Moreover, the von Karman constant decreases with the increase of roughness height in the present simulation results. Besides, the larger size of QSV and more intense ejections are induced by the roughness elements, which is crucial for heat and mass transfer enhancement.     

湍流边界层拟序结构的大涡模拟研究

采用动力亚格子模型,利用大涡模拟方法模拟了雷诺数为13000的充分发展槽道湍流流动。从瞬时速度和脉动 速度场、脉动速度相关、均方根脉动涡量分布、以及瞬时涡量场等多个方面,对湍流边界层流动的拟序结构进行了分析, 包括近壁区小尺度湍流结构和瞬态过程,如条纹结构、喷射和扫掠过程、以及近壁旋涡结构等。     

有限时间Lyapunov指数的高精度计算新方法

针对目前有限时间Lyapunov指数(FTLE)计算方法准确度不高和无法获得边界值的问题,基于对偶数理论提出了一种新的高精度计算方法.首先描述了基于有限空间差分方法计算FTLE的缺点和问题:其次介绍了基于对偶数理论的高精度导数计算方法及其显著优点,并将动力系统的柯西一格林形变张量计算问题转化为对偶数空间中非线性微分方程数值求解问题;最后对单摆和非线性Duffing振子两个典型物理动力系统进行了数值实验.结果表明:基于对偶数理论的新方法能有效、方便和高精度地计算出有限时间Lyapunov指数场,并成功识别出所包含的拉格朗日相关结构.     

Turbulent plane wall jets over smooth and rough surfaces

Large-eddy simulations were carried out to study the effects of surface roughness on a plane wall-jet using the Lagrangian dynamic eddy-viscosity subgrid-scale model, at Re = 7500 (based on the jet bulk velocity and height). Results over both smooth and rough surfaces were validated by experimental data at the same Reynolds number. As the jet is injected into the still environment, large-scale rollers are generated in the shear layer between the high-momentum fluid of the jet and the surrounding and are convected downstream with the flow. To understand the extent to which the outer-layer structures modify the flow in the inner layer and the extent to which the effect of roughness spreads away from the wall, both instantaneous and mean flow fields were investigated. The results revealed that, for the Reynolds number and roughness height considered in this study, the effect of roughness is mostly confined to the near-wall region of the wall jet. There is no structural difference between the outer layer of the wall jet over the smooth and rough surfaces. Roughness does not affect the size of the outer-layer structures or the scaling of the profiles of Reynolds stresses in the outer layer. However, in the inner layer, roughness redistributes stresses from streamwise to wall-normal and spanwise directions toward isotropy. Contours of joint probability-density function of the streamwise and wall-normal velocity fluctuations at the bottom of the logarithmic region match those of the turbulent boundary layer at the same height; while the traces of the outer-layer structure were detected at the top of the logarithmic region, indicating that they do not affect the flow very close to the wall, but still modify a major portion of the inner layer. This modification must be taken into consideration when the inner layer of a wall jet is compared with the conventional turbulent boundary layer.     

Scattering from a rough layer of a random medium

This paper deals with scattering from a random-medium layer with rough boundaries. The fluctuations of the surface heights and medium permittivity are assumed to be small and smooth. All random quantities are assumed to be stationary and independent of each other. After the introduction of approximate boundary conditions, the system of partial differential equations is transformed into an integral equation where the fluctuations of the problem are represented as a zero-mean random operator. Employing smoothing, integral equations for the coherent fields are obtained. Use of the Helmholtz operator leads to solution for the coherent propagation constant while the boundary operators lead to coherent Fresnel coefficients. The characteristics of the results are illustrated by considering several examples.     

Experimental investigation of supersonic flow over elliptic surface

The coherent structures of flow over a compression elliptic surface are experimentally investigated in a supersonic low-noise wind tunnel at Mach Number 3 using nano-tracer planar laser scattering (NPLS) and particle image velocimetry (PIV) techniques. High spacial resolution images and the average velocity profiles of both laminar inflow and turbulent inflow over the testing model were captured. From statistically significant ensembles, spatial correlation analysis of both cases is performed to quantify the mean size and orientation of large structures. The results indicate that the mean structure is elliptical in shape and structure angles in separated region of laminar inflow are slightly smaller than that of turbulent inflow. Moreover, the structure angle of both cases increases with its distance away from from the wall. POD analysis of velocity and vorticity fields is performed for both cases. The energy portion of the first mode for the velocity data is much larger than that for the vorticity field. For vorticity decompositions, the contribution from the first mode for the laminar inflow is slightly larger than that for the turbulent inflow and the cumulative contributions for laminar inflow converges slightly faster than that for turbulent inflow     

Effects of single synthetic jet on turbulent boundary layer

The turbulent boundary layer (TBL) is actively controlled by the synthetic jet generated from a circular hole. According to the datasets of velocity fields acquired by a time-resolved particle image velocimetry (TR-PIV) system, the average drag reduction rate of 6.2% in the downstream direction of the hole is obtained with control. The results of phase averaging show that the synthetic jet generates one vortex pair each period and the consequent vortex evolves into hairpin vortex in the environment with free-stream, while the reverse vortex decays rapidly. From the statistical average, it can be found that a low-speed streak is generated downstream. Induced by the two vortex legs, the fluid under them converges to the middle. The drag reduction effect produced by the synthetic jet is local, and it reaches a maximum value at x⁺=400, where the drag reduction rate reaches about 12.2%. After the extraction of coherent structure from the spatial two-point correlation analysis, it can be seen that the synthetic jet suppresses the streamwise scale and wall-normal scale of the large scale coherent structure, and slightly weakens the spanwise motion to achieve the effect of drag reduction.