Reynolds number effects on a turbulent boundary layer with separation,reattachment, and recovery

The present paper addresses experimental studies of Reynolds number effects on a turbulent boundary layer with separation, reattachment, and recovery. A momentum thickness Reynolds number varies from 1,100 to 20,100 with a wind tunnel enclosed in a pressure vessel by varying the air density and wind tunnel speed. A custom-built, high-resolution laser Doppler anemometer provides fully resolved turbulence measurements over the full Reynolds number range. The experiments show that the mean flow is at most a very weak function of Reynolds number while turbulence quantities strongly depend on Reynolds number. Roller vortices are generated in the separated shear layer caused by the Kelvin–Helmholtz instability. Empirical Reynolds number scalings for the mean velocity and Reynolds stresses are proposed for the upstream boundary layer, the separated region, and the recovery region. The inflectional instability plays a critical role in the scaling in the separated region. The near-wall flow recovers quickly downstream of reattachment even if the outer layer is far from an equilibrium state. As a result, a stress equilibrium layer where a flat-plate boundary layer scaling is valid develops in the recovery region and grows outward moving downstream.     

A three-velocity-component laser-Doppler velocimeter for measurements inside the linear compressor cascade

A 24′′ (610 mm) access laser-Doppler velocimeter (LDV) system was developed to make simultaneous three-velocity-component measurements in a low speed linear cascade wind tunnel with moving wall simulation. The probe has a 610 mm access length and achieves a measurement spatial resolution of 100 μm by using off-axis optical heads. With the relatively large access length, the LDV probe allows for measurements from the side of a wind tunnel instead of through the tunnel floor, while the high spatial resolution allows for quality near-wall measurements. The probe has been tested in a zero-pressure gradient 2D turbulent boundary layer and the test results agree well with the experimental data measured with different LDV systems and hot-wire anemometery for the boundary layer flows. The energy spectral density was estimated using a slot correlation, and Von Kármán’s model for the energy-spectrum function was used to analyze the measured spectral data to estimate the turbulent kinetic energy dissipation rate, which compares favorably with the measured production values in the log-layer region of the turbulent boundary layer. Measurements are presented for the moving endwall boundary layer at the inlet of the linear compressor cascade facility to validate the capability of this LDV for tip leakage flow measurements. These results indicate that the moving endwall reduces velocity gradients in the near-wall region and results in less production of Reynolds stresses and turbulent kinetic energy compared to the stationary endwall case.     

An experimental investigation of unsteady turbulent-wake/boundary-layer interaction

An experimental investigation of unsteady-wake/boundary-layer interaction, similar to that occurring in turbomachinery, has been conducted in a specially modified wind tunnel. Unsteadiness in a turbomachine is periodic in nature, due to the relative motion of rotor and stator blades, resulting in travelling-wave disturbances that affect the blade boundary layers. In the experimental rig, travelling-wave disturbances were generated by a moving airfoil apparatus installed upstream of a flat plate to provide a two-dimensional model of a turbomachine stage. The boundary layer on the flat plate was tripped near the leading edge to generate a turbulent flow prior to interaction with the wakes, and measurements of velocity throughout the boundary layer were taken with a hot-wire probe. The Reynolds number, based on distance along the plate, ranged from 0.144×10⁵ to 1.44×10⁵, and all data were reduced through a process of ensemble averaging. Due to the nonlinear interactions with the boundary layer, the travelling discrete frequency wakes were found to decrease the shape factor of the velocity profile and to increase the level of turbulent fluctuations. Unlike the phase advance found with stationary-wave external disturbances, velocity profiles subject to the travelling wake fluctuations exhibited increasingly negative phase shifts from the free-stream towards the wall.     

Propagation of wall pressure perturbations in a large aspect ratio shallow cavity

Wall pressure fluctuations generated by turbulent boundary layers over a shallow cavity are studied experimentally in a low-speed wind tunnel facility. The scope of the present work is to characterize the propagation of the pressure perturbations at the wall by means of pressure cross-correlations and cross-spectra measured through a microphone pair translated along the cavity floor. It is found that the mechanism characterizing the pressure propagation close to the backward facing step and in the middle of the cavity is similar to what is commonly observed in equilibrium boundary layer being the convection velocity smaller than the external mean velocity. On the other hand, in the close vicinity of the forward-step, the hydrodynamic contribution of the pressure fluctuations is accompanied by a relevant acoustic effect characterized by a convection velocity close to the speed of sound. Furthermore, in the regions close to the two steps, the spectral decay of the coherence function, even though of exponential type, is faster than that obtained in the quasi-equilibrium region.     

Statistical laws of the pressure fluctuations in a hypersonic turbulent boundary layer

The results of measuring the pressure fluctuations on the wall of the nozzle of a hypersonic wind tunnel beneath a developed turbulent boundary layer are presented for the Mach number M_∞ = 7.5. On the basis of a statistical analysis, it is shown that the action of the turbulent flow is dynamically similar to the propagation of a random sequence of wave packets with continuously distributed temporal and spatial scales. Low-frequency disturbances are associated with large-scale structures of long duration that propagate at a mean-statistical velocity similar in value to the outer flow velocity. The continuous generation of weakly-correlated small-scale disturbances ensuring the maintenance and development of turbulence occurs chiefly in the inner region of the boundary layer. Spectral estimates of the power generated by the turbulent flow in the wall region of the boundary layer are presented.     

一类平衡大气边界层边界条件研究

基于标准k-ε湍流模型,首先利用湍流粘度方程和剪切应力在整个边界层内恒定的假设,推导出一类耗散率表达式,并根据常用的湍动能入口剖面方程以及平均风速剖面方程,计算获得相应的耗散率方程;然后在输运方程中添加自定义源项,通过已经确定的平均速度方程、湍动能方程、耗散率方程计算得到相应输运方程的自定义源项表达式,并进行空风洞数值模拟,从而得到了一类满足平衡大气边界层的来流边界条件．通过将这种边界条件与由湍流平衡条件得到的边界条件进行比较,表明本方法获得的边界条件更适用．并且,本方法无需考虑修正壁面函数和修正湍流模型常数,因而计算更为简单,可为平衡大气边界层的研究提供一种新的思路．     

A new calibration and data reduction method for turbulence measurement by multihotwire probes

A new calibration technique has been developed for the simultaneous measurement of the instantaneous velocity components in a three dimensional turbulent flow field by miniature pyramidoidal four-wire probes. The method was tested in the boundary layer of a wind tunnel by comparison measurements with X-wire probes. The results are very satisfactory and in good agreement with other experiments known from the literature.     

Stereo particle image velocimetry of nonequilibrium turbulence relaxation in a supersonic boundary layer

Measurements using stereo particle image velocimetry are presented for a developing turbulent boundary layer in a wind tunnel with a Mach 2.75 free stream. As the boundary layer exits from the tunnel nozzle and moves through the wave-free test section, small initial departures from equilibrium turbulence relax, and the boundary layer develops toward the equilibrium zero-pressure-gradient form. This relaxation process is quantified by comparison of first and second order mean, fluctuation, and gradient statistics to classical inner and outer layer scalings. Simultaneous measurement of all three instantaneous velocity components enables direct assessment of the complete turbulence anisotropy tensor. Profiles of the turbulence Mach number show that, despite the M = 2.75 free stream, the incompressibility relation among spatial gradients in the velocity fluctuations applies. This result is used in constructing various estimates of the measured-dissipation rate, comparisons among which show only remarkably small differences over most of the boundary layer. The resulting measured-dissipation profiles, together with measured profiles of the turbulence kinetic energy and mean-flow gradients, enable an assessment of how the turbulence anisotropy relaxes toward its equilibrium zero-pressure-gradient state. The results suggest that the relaxation of the initially disturbed turbulence anisotropy profile toward its equilibrium zero-pressure-gradient form begins near the upper edge of the boundary layer and propagates downward through the defect layer.     

Spalding公式在脊状表面湍壁摩擦力测量中的应用

在低速风洞中来流速度一定的情况下使用IFA300恒温热线风速仪测量了光滑表面和两种不同尺寸的脊状表面湍流边界层平均速度分布剖面,并验证了试验段湍流发展的充分性;通过应用Spalding壁面公式使用最小二乘法精准拟合了实验测量的边界层内层速度分布曲线,得到了湍流边界层壁面摩擦速度并进一步求得湍流壁面摩擦应力,较准确地计算出脊状表面的虚拟原点位置,并通过与对数律公式拟合结果比较分析,证实了该方法更加准确有效. 最后分别计算了3种实验模型的湍流边界层动量损失厚度. 通过对比脊状表面与光滑表面动量损失厚度和壁面摩擦应力,反映了动量损失厚度的大小与壁面摩擦应力的大小具有一致性,充分证实了脊状表面在湍流中具有一定的减阻效果.      

用平均速度剖面法测量壁湍流摩擦阻力

用IFA300恒温热线风速仪精细测量风洞中不同雷诺数流动条件下的平板湍流边界层近壁区域对数律平均速度剖面．利用平板湍流边界层近壁区域的对数律平均速度剖面与壁面摩擦速度、流体黏性系数等内尺度物理量的关系和壁面摩擦速度与壁面摩擦切应力的关系,在准确测量平板湍流边界层近壁区域对数律平均速度剖面的基础上,测量平板湍流边界层的壁面摩擦阻力．实现了平板湍流边界层壁面摩擦阻力的无干扰或微小干扰测量．该种方法操作简便,不需要在流场中安装测力天平、传感器等复杂的测量装置,不需要对湍流边界层的壁面进行破坏,不会影响湍流边界层壁面附近区域原有的流场条件,是一种切实可行的测量平板湍流边界层壁面摩擦阻力的简便方法．     

Multi-scale coherent structures in turbulent boundary layer detected by locally averaged velocity structure functions

Introduction Inearlyperiodofstudyofturbulentflow,itwasdeemedrandomanddisorderedmotionsof fluidparticles,sothecharacteristicsofturbulencewerestudiedbystatisticsaveragemethod. Kolmogorov[1]analyzedtherelativemotionoffluidparticlesinfullydeveloped(Reynolds numbertrendstoinfinity)isotropicandhomogeneousturbulentflow,onbasisofrandomfield theory,andpresentedtheconceptofstructurefunctions,whichdescribedtherelativevelocityof twofluidparticlesindistanceofl,toresearchthelawbetweenthemulti_orderstatistic…     

Mean and turbulence measurements in the boundary layer and wake of a symmetric aerofoil

Detailed measurements of two-dimensional profiles of static pressure, mean velocity, turbulence intensity and Reynolds shear stress were carried out with conventional pressure probes and hot wire probes at preselected streamwise stations in the boundary layer and wake of a 12.5% thick, 600 mm chord two-dimensional symmetric aerofoil mounted at zero incidence in a low speed wind tunnel. The chord Reynolds number was one million and the wake measurements extended up to three chord lengths (or nearly 660 trailing edge momentum thicknesses) downstream of the trailing edge. The data indicate rapid interaction of the wall layers immediately behind the trailing edge, leading to significant changes in the flow parameters close to the trailing edge. The relaxation of the wake is preceded by initial ‘overshoot’ in the streamwise profiles of mean-flow parameters and peak values of turbulence components. Further growth of the wake towards similarity/equilibrium is discussed.     

Effects of velocity fluctuations on heat transfer enhancement

The three-dimensional velocity fluctuation effects on heat transfer enhancement were experimentally investigated using a wind tunnel system and cylinders placed upstream of the test section in the wind tunnel. The cylinders with different diameters were used as turbulators to generate vortical flow motions with three-dimensional velocity fluctuations. A heated plate, part of the tunnel wall, was placed far downstream of the cylinders such that it was subjected mainly to flows with velocity fluctuations but with negligible steady vortical motions. These studies included three-component velocity measurements to characterize the near-wall and cross-section velocity fields and to obtain the turbulent kinetic energy. The temperatures were measured by thermocouples on the heated plate to obtain the convection heat transfer coefficients and the Nusselt numbers. Results indicate that the heat transfer was enhanced by the velocity fluctuations, which is attributed to the modification of boundary layer velocity profiles without the modification of boundary layer thickness. The resulting normalized Nusselt number was approximately a parabolic function of a dimensionless parameter, the product of Reynolds number and normalized turbulent kinetic energy.     

湍流边界层相干结构剩余脉动雷诺应力项的实验测量

用IFA300恒温热线风速仪和X形二分量热线探针以采样间隔小于湍流耗散时间尺度的分辨率精细测量了风洞中平板湍流边界层不同法向位置的瞬时流向、法向速度分量的时间序列信号。用条件采样和相位平均技术提取了相干结构猝发过程中相干结构剩余脉动雷诺应力和随机脉动对相干结构贡献的雷诺应力的条件相位平均波形。基于理论上对湍流相干结构动量方程中随机脉动对相干结构贡献的雷诺应力和相干结构剩余脉动雷诺应力项的分析,对两种雷诺应力项进行了对比研究。研究发现,相干结构剩余脉动雷诺应力项在数值上具有和随机脉动对相干结构贡献的雷诺应力相同的数量级,表明在相干结构动力学模型方程中,相干结构剩余脉动雷诺应力项并不像以前估计的那样可以忽略不计。     

Structures of Density Fluctuations at a Low-Mach-Number Turbulent Boundary Layer by DNS

We performed a direct numerical simulation of a low-Mach-number turbulent boundary layer using fundamental equations of compressible flow to investigate the relation between vortex structures and the density distribution. A fully developed turbulent boundary layer of compressible flow was reproduced in the simulation. From the turbulence statistics and instantaneous structures of the density fluctuation, we identified different features in the three regions of a near-wall field, far field and flow field outside the turbulent boundary layer. Structures of the density fluctuation could correspond to sound sources in a turbulent boundary layer. We then observed fine-scale structures of the density fluctuation that were strongly related to turbulent vortices in the vicinity of the wall. In addition, there were large-scale density structures in the upper boundary layer. The large-scale structures seem to correlate with the fine-scale structures close to the wall, with there being a non-steady larger-scale density fluctuation profile in the outer region of the boundary layer.     

EXPERIMENTAL STUDY OF MEASUREMENT FOR DISSIPATION RATE SCALING EXPONENT IN HEATED WALL TURBULENCE

Experimental investigations have been devoted to the study of scaling law of coarse-grained dissipation rate structure function for velocity and temperature fluctuation of non-isotropic and inhomogeneous turbulent flows at moderate Reynolds number. Much attention has been paid to the case of turbulent boundary layer, which is typically the non-istropic and inhomogeneous trubulence because of the dynamically important existence of organized coherent structure burst process in the near wall region . Longitudinal velocity and temperature have been measured at different vertical positions in turbulent boundary layer over a heated and unheated flat plate in a wind tunnel using hot wire anemometer. The influence of non-isotropy and inhomogeneity and heating the wall on the scaling law of the dissipation rate structure function is studied because of the existence of organized coherent structure burst process in the near wall region . The scaling law of coarse-grained dissipation rate structure function is foun     

Meander of a fin trailing vortex and the origin of its turbulence

The low-frequency meander of a trailing vortex shed from a tapered fin installed on a wind tunnel wall has been studied using stereoscopic particle image velocimetry in the near-wake at Mach 0.8. Distributions of the instantaneous vortex position reveal that the meander amplitude increases with downstream distance and decreases with vortex strength, indicating meander is induced external to the vortex. Trends with downstream distance suggest meander begins on the fin surface, prior to vortex shedding. Mean vortex properties are unaltered when considered in the meandering reference frame, apparently because turbulent fluctuations in the vortex shape and strength dominate positional variations. Conversely, a large peak of artificial turbulent kinetic energy is found centered in the vortex core, which almost entirely disappears when corrected for meander, though some turbulence remains near the core radius. Turbulence originating at the wind tunnel wall was shown to contribute to vortex meander by energizing the incoming boundary layer using low-profile vortex generators and observing a substantial increase in the meander amplitude, while greater turbulent kinetic energy penetrates the vortex core. An explanatory mechanism has been hypothesized, in which the vortex initially forms at the apex of the swept leading edge of the fin where it is exposed to turbulent fluctuations within the wind tunnel wall boundary layer, introducing an instability into the incipient vortex core.     

The Effect of Wall Normal Actuation on a Turbulent Boundary Layer

In this work, a series of direct numerical simulations are conducted to study the effect of wall normal spanwise homogeneous wall actuation on a turbulent boundary layer. The moving boundary is represented by a boundary data immersion technique. A parametric study was performed, varying the actuator length, the wall normal actuation amplitude and the actuation frequency. It was found that localized actuation, relying only on wall motion instead of requiring a plenum in the case of synthetic jets, generated a net momentum flux jet affecting the flow not only in the immediate vicinity of the actuator but also for a significant distance downstream. The cases with an actuator velocity of \( u^{+}_{act}=?20.1 \) showed a particularly pronounced effect on the boundary layer and resulted in a recirculation region.     

Measurements of a supersonic turbulent boundary layer by focusing schlieren deflectometry

 Some novel, non-intrusive, high-frequency, localized optical measurements of turbulence in compressible flows are described. The technique is based upon focusing schlieren optics coupled with high-speed quantitative measurement of light intensity fluctuations in the schlieren image. Measurements of density gradient fluctuations confined to a thin slice of the flowfield are thus obtained. The new instrument was used to investigate the structure of a two-dimensional, adiabatic, wind tunnel wall boundary layer at a Mach number of 3. The measurements were compared to data obtained using hot-wire anemometry and good agreement was found between the two. Distributions of broadband convection velocity of large-scale structures through the boundary later were also measured. In marked contrast to earlier results, it is shown here that the convection velocity is essentially identical to the local mean velocity. Further, results obtained using the VITA conditional sampling technique shed new light on the turbulent boundary layer structure. Overall, the data presented herein serve to validate the new measurement technique. Received: 12 February 1997/Accepted: 31 January 1998     

明渠湍流边界层中颗粒的运动与分布

利用直接数值模拟、点球浸入边界法和颗粒离散元法相结合的方法, 模拟了颗粒在明渠湍流边界层中的运动, 并对颗粒的瞬时位置进行了Voronoi 分析, 定量研究了颗粒在湍流边界层中的运动和分布规律. 研究发现:颗粒的输运对湍流的统计特征有影响, 其运动与近壁区湍流拟序结构密切相关, 在"喷发"结构作用下被带离壁面, 在"扫掠" 结构和自身重力作用下回到壁面; 在湍流边界层中, 颗粒倾向于聚集在低流速带, 呈条带状分布;颗粒在大部分时间处于"簇"状态, 偶尔跳跃到"空" 状态, 但能够很快回到邻近低速区域.