Effects of inclined impermeable bed on the turbulent characteristics of the flow using particle image velocimetry

In this study, the turbulent characteristics of the flow in an open channel with horizontal and inclined impermeable beds were studied experimentally using two-dimensional particle image velocimetry (PIV). The experiments were conducted in a channel of 6.5 m in length, 7.5 cm in width and 25 cm in height. The slope of the channel was S = 0 for the horizontal impermeable bed and for S = ?0.002, S = ?0.004 and S = ?0.006 for the inclined impermeable bed. Hydraulic characteristics such as distributions of velocities, turbulent intensities and Reynolds stress are investigated at a fine resolution using the PIV. Velocity is measured above the horizontal and inclined impermeable bed for the same different heights (h = 5, 7, 9, 11 and 13 cm) and for the same different discharges (Q = 0.735, 0.845 and 0.970 lt/s). Results show that the channel slope influences significantly near the impermeable bed but not near the free surface the variation of turbulent characteristics of the flow and also the alteration of the channel slope from ?0.002 to ?0.006 doesn't influence the variation of turbulent characteristics of the flow, which are the longitudinal turbulent intensity u′U_*, the vertical turbulent intensity v′/U_* and the turbulent kinetic energy. The channel slope doesn't influence the Reynolds stress.     

Dynamic model of coherent structure in the wall region of a turbulent boundary layer

Based on the theoretical model for a single coherent structure in the wall region of a turbulent boundary layer, we studied the interaction of two coherent structures by direct numerical simulation in order to explain the mechanism for the formation of low-speed streaks.     

Brownian motion and correlation in particle image velocimetry

In particle image velocimetry applications involving either low velocities or small seed particles, Brownian motion can be significant. This paper addresses the effects of Brownian motion. First, general equations describing cross-correlation particle image velocimetry are derived that include Brownian motion. When light-sheet illumination particle image velocimetry (PIV) is used Brownian motion diminishes the signal strength. A parameter describing this effect is introduced, and a weighting function describing the contribution to the measured velocity as a function of position is derived. The latter is unaffected by Brownian motion. Microscopic PIV Brownian motion also diminishes the signal strength. The weighting function for microscopic PIV is found to depend on Brownian motion, thus affecting an important experimental parameter, the depth of correlation. For both light-sheet illumination and microscopic PIV, a major consequence of Brownian motion is the spreading of the correlation signal peak. Because the magnitude of the spreading is dependent on temperature, PIV can, in principle, be used to simultaneously measure velocity and temperature. The location of the signal peak provides the velocity data, while the spreading of the peak yields temperature.     

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)     

激光散斑测速和粒子像测速技术中的频谱模板方法

文中提出了用流场的一次曝光像的强度谱作为模板提取杨氏条纹，以获取尖锐的自相关分布的方法，并给出了该方法用于激光散斑测速和粒子像测速技术的计算机模拟结果以及粒子像测速的应用例子。     

Effect of wall temperature on hypersonic turbulent boundary layer

Turbulent boundary layers at Mach 4.9 with the ratio of wall temperature to recovery temperature from 0.5 to 1.5 are investigated by means of direct numerical simulation. Various fundamental properties relevant to the influence of wall temperature on Morkovin’s scaling, standard and modified strong Reynolds analogies, and coherent vortical structures have been studied. It is identified that the scaling relations proposed for cool and adiabatic wall conditions, such as Morkovin’s scaling and the modified strong Reynolds analogy, are also applicable for hot wall condition. Moreover, the relation between the density and temperature fluctuations under the second-order approximation is derived and verified to provide a reliable prediction. Based on the analysis of coherent vortical structures, it is found that the orientation of vortex core can be quantitatively determined by means of the vector with its direction and modulus using the local strain direction and the imaginary part of the eigenvalue of velocity gradient tensor, respectively. As the increase of wall temperature, the spanwise distance between the two legs of hairpin vortex increases, and the mean swirling strength and the angle of vortical structure with respect to the wall plane also increase in the inner layer. The statistical properties relevant to vortical structures are nearly insensitive to the wall temperature in the outer layer.     

Interaction between strain and vorticity in compressible turbulent boundary layer

The interaction of strain and vorticity in compressible turbulent boundary layers at Mach number 2.0 and 4.9 is studied by direct numerical simulation(DNS)of the compressible Navier-Stokes equations.Some fundamental characteristics have been studied for both the enstrophy producing and destroying regions.It is found that large enstrophy production is associated with high dissipation and high enstrophy,while large enstrophy destruction with moderate ones.The enstrophy production and destruction are also correlated with the dissipation production and destruction.Moreover,the enstrophy producing region has a distinct tendency to be‘sheet-like’structures and the enstrophy destroying region tends to be‘tube-like’in the inner layer.Correspondingly,the tendency to be‘sheet-like’or‘tube-like’structures is no longer obvious in the outer layer.Further,the alignment between the vorticity vector and the strain-rate eigenvector is analyzed in the flow topologies.It is noticed that the enstrophy production rate depends mainly on the alignment between the vorticity vector and the intermediate eigenvector in the inner layer,and the enstrophy production(destruction)mainly on the alignment between the vorticity vector and the extensive(compressive)eigenvector in the outer layer.     

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.     

Analysis of the turbulent boundary layer in the vicinity of a self-excited cylindrical Helmholtz resonator

This study investigates the changes in the structure of a turbulent boundary layer downstream of a flow-excited Helmholtz resonator. To this end, a fully developed turbulent boundary layer over a resonator mounted flush with a flat plate was simulated by implementing a large eddy simulation (LES). To assist in understanding the effect of the resonator on the flow structure, a sensitivity study was undertaken by changing the main geometrical parameters of the resonator. The results demonstrated that when the boundary layer thickness equals the orifice length, the cross-stream component of velocity fluctuations penetrates the boundary layer, resulting in a reduction of the turbulence intensity by up to 12%. Therefore, it is concluded that a Helmholtz resonator has the potential to reduce the instabilities within the boundary layer. These investigations also assist in identifying the optimal parameters to delay turbulence events within the grazing flow using Helmholtz resonators.     

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.     

Temporal evolution of optical path difference of a supersonic turbulent boundary layer

The density distribution of a supersonic turbulent boundary layer is measured with the nanoparticle-based planar laser scattering technique, and the temporal evolution of its optical path difference (OPD) in a short time interval is characterized by proper orthogonal decomposition (POD). Based on the advantage of POD in capturing the energy of a signal, a temporal evolution model is suggested for the POD coefficients of OPD. In this model, the first few coefficients vary linearly with time, and the others are modeled by Gaussian statistics. As an application, this method is used to compute the short-exposure optical transfer function.     

机体表面湍流边界层噪声特性及预测方法研究

湍流边界层噪声是飞机巡航过程中的主要外部噪声源,对舱内噪声水平的影响尤为重要。因此,对飞机机体表面湍流边界层噪声的研究具有重要意义。本文通过试验获得了某型民机巡航过程中的湍流边界层噪声,试飞工况为3500ft/0.78、3500ft/0.7、2500ft/0.67、1500ft/0.66。对实测数据进行分析,发现湍流边界层噪声与动压、边界层厚度等参数有关。同时,利用计算流体力学的方法得到了飞机机体表面的压力分布,并分析了压力梯度对湍流边界层噪声的影响。最后,基于工程预测方法对湍流边界层噪声进行了预测,对于不存在逆压梯度的区域,预测结果与试验结果吻合较好,仅部分频段存在一定偏差。通过对模型的参数进行优化,改善了预测结果。     

Predetermined control of turbulent boundary layer with a piezoelectric oscillator

With a piezoelectric(PZT) oscillator, the predetermined controls of the turbulent boundary layer(TBL) are effective in reducing the drag force. The stream-wise velocities in the TBL are accurately measured downstream of the oscillator driven by an adjustable power source. The mean velocity profiles in the inner and outer scales are reported and the skin friction stresses with different voltage parameters are compared. Reduction of integral spatial scales in the inner region below y+of 30 suggests that the oscillator at work breaks up the near-wall stream-wise vortices responsible for high skin friction. For the TBL at Reθof 2183, the controls with a frequency of 160 Hz are superior among our experiments and a relative drag reduction rate of 26.83% is exciting. Wavelet analyses provide a reason why the controls with this special frequency perform best.     

Temporal evolution of the optical path difference of a supersonic turbulent boundary layer

The density distribution of a supersonic turbulent boundary layer is measured with the nanoparticle-based planar laser scattering technique, and the temporal evolution of its optical path difference (OPD) in a short time interval is characterized by proper orthogonal decomposition (POD). Based on the advantage of POD in capturing the energy of a signal, a temporal evolution model is suggested for the POD coefficients of the OPD. In this model, the first few coefficients vary linearly with time, and the others are modeled by Gaussian statistics. As an application, this method is used to compute the shortexposure optical transfer function.     

Investigation of scaling laws in a turbulent boundary layer flow with adverse pressure gradient using PIV

We present an experimental investigation and data analysis of a turbulent boundary layer flow at a significant adverse pressure gradient at Reynolds number up to Re_θ = 10, 000. We combine large-scale particle image velocimetry (PIV) with microscopic PIV for measuring the near wall region including the viscous sublayer. We investigate scaling laws for the mean velocity and for the total shear stress in the inner part of the boundary layer. In the inner part the mean velocity can be fitted by a log-law. In the outer part of the inner layer the log-law ceases to be valid. Instead, a modified log-law provides a good fit, which is given in terms of the pressure gradient parameter and a parameter for the mean inertial effects. Finally we describe and assess a simple quantitative model for the total shear stress distribution which is local in wall-normal direction without streamwise history effects.     

湍流边界层中下扫流与“反发卡涡”

用氢气泡法观测湍流边界层的下扫流和有关的流动结构.实验中发现一种新型涡结构，它的特征与典型的发卡涡正好相反.发卡涡的头部指向下游，而它的头部指向上游； 发卡涡的两腿之间，由于涡的诱导产生上升流，而它则在其两腿之间，由于涡的诱导产生下扫流. 关键词： 湍流边界层 流动显示 流动结构 发卡涡     

Constrained large-eddy simulation of supersonic turbulent boundary layer over a compression ramp

A supersonic turbulent boundary layer over a compression ramp is numerically investigated using the constrained large-eddy simulation (CLES) method. The compression corner is characterised by a deflection angle of 24°. The free-stream Mach number is Ma_∞ = 2.9, and the Reynolds number based on the momentum thickness of inlet boundary layer is Re_θ = 2300. The mean and statistical quantities, such as mean velocity, wall pressure and Reynolds stresses, are thoroughly analysed and compared with those from traditional large-eddy simulation (LES), experimental measurement and direct numerical simulation (DNS). It turns out that CLES can predict the friction coefficient, wall-pressure distribution, size of separation bubble, Reynolds stresses, etc. more accurately than traditional LES, and the results are in reasonable agreement with the experimental and/or DNS data. Also discussed are the effects of specific parameterisations of the Reynolds constraint and interfacial positions separating the constrained and unconstrained regions on the performance of the CLES method.     

Experimental investigation on drag reduction in a turbulent boundary layer with a submerged synthetic jet

This work investigates the active control of a fully developed turbulent boundary layer by a submerged synthetic jet actuator.The impacts of the control are explored by measuring the streamwise velocities using particle image velocimetry,and reduction of the skin-friction drag is observed in a certain range downstream of the orifice.The coherent structure is defined and extracted using a spatial two-point correlation function,and it is found that the synthetic jet can efficiently reduce the streamwise scale of the coherent structure.Proper orthogonal decomposition analysis reveals that large-scale turbulent kinetic energy is significantly attenuated with the introduction of a synthetic jet.The conditional averaging results show that the induction effect of the prograde vortex on the low-speed fluid in a large-scale fluctuation velocity field is deadened,thereby suppressing the bursting process near the wall.