Characteristics of large-scale and superstructure motions in a turbulent boundary layer overlying complex roughness

The structural attributes of turbulent flow over a complex roughness topography are explored using high-frame-rate stereo particle-image velocimetry measurements in the wall-normal–spanwise plane. The roughness under consideration was replicated from a turbine blade damaged by deposition of foreign materials and contains a broad range of topographical scales arranged in a highly irregular manner. Previous results from Barros and Christensen [Observations of turbulent secondary flows in a rough-wall boundary layer. J Fluid Mech. 2014;748] revealed strong spanwise heterogeneity in the flow attributed to the formation of roughness-induced turbulent secondary flows identified by spanwise-alternating low- and high-momentum flow pathways (HMP & LMP, respectively) in the mean flow marked by enhanced Reynolds stresses and turbulent kinetic energy. Frequency spectra of streamwise velocity at fixed wall-normal location presented herein also display strong dependence on spanwise position. In particular, the roughness promotes enhanced energy content of the large-scale and smaller-scale motions (as opposed to very-large-scale ones). Depending on spanwise position, pre-multiplied spectra highlight significant modification of the energy content of the very large-scale motions (superstructures) due to roughness compared to smooth-wall flow. Of note, a shift in both TKE and RSS content to shorter streamwise scales at an LMP was noted, while less of an impact was found coincident with an HMP.     

Influence of uniform momentum zones on frictional drag within the turbulent boundary layer

Based on a set of experimental databases of turbulent boundary layers obtained from particle image velocimetry in the streamwise-wall-normal plane at friction-velocity-based Reynolds number Reτ=612,the influence of uniform momentum zones(UMZs)on the skin-friction drag is investigated.The skin-friction drag is measured by the single-pixel ensemble correlation method.The results show that the velocity fields with the number of UMZs larger than the mean value have a relatively low skin-friction drag,while the velocity fields with the number of UMZs less than the mean value have a relatively high skin-friction drag.By analyzing the statistical characteristics of UMZs,the dynamic correlation between the UMZs and skin-friction drag is explored.The velocity fields with a low number of UMZs present a sweep event.These sweep motions intensify the small-scale Reynolds shear stress in the near-wall region by modulation effects.The enhancement of small-scale Reynolds shear stress is the direct reason for the high skin-friction drag.Increasing the proportion of velocity fields with high UMZs amount may be a direction to reduce the skin-friction drag within the TBL.     

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.     

Wind-tunnel simulation of thick turbulent boundary layer

An experimental study aimed at revealing the possibility of simulation, in a subsonic wind tunnel, of enhanced Reynolds numbers Re^** via modeling a thick flat-plate boundary layer possessing the properties of a Clauser-equilibrium shear flow is reported. We show that turbulators prepared in the form of variable-height cylinders of height h and diameter d = 3 mm and installed in two rows along the normal to the streamlined wall offer rather an efficient means for modification of turbulent boundary layer in solving the problem. In the majority of cases, mean and fluctuating characteristics of the boundary layer exhibit values typical of naturally developing turbulent boundary layers at a distance of 530 cylinder diameters. The profiles of mean velocity with artificially enhanced boundary-layer thickness can be well approximated, in the law-of-the-wall variables, with the well-known distribution of velocities for canonical boundary layer.     

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.     

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.     

Analytical model of the time developing turbulent boundary layer

An analytical model for the time-developing turbulent boundary layer (TD TBL) over a flat plate is presented. The model provides explicit formulae for the temporal behavior of the wall-shear stress and both the temporal and spatial distributions of the mean streamwise velocity, the turbulence kinetic energy and Reynolds shear stress. The resulting profiles are in good agreement with the DNS results of spatially-developing turbulent boundary layers at momentum thickness Reynolds numbers equal to 1430 and 2900 [5–7]. Our analytical model is, to the best of our knowledge, the first of its kind for TD TBL. The text was submitted by the authors in English.     

Nonlinear instability research of longitudinal structure generated by roughness in unswept wing boundary layer

The results of experimental study of a nonlinear varicose instability of the streaky structure generated by roughness element in unswept-wing boundary layer are presented. Features of the varicose breakdown of longitudinal steady streaky structure such as modulation of structure in transverse and streamwise directions by secondary disturbance, occurrence of the new streaky structures and A-structures downstream are shown. Spatio-temporal pictures of the hot-wire visualization of flow during spatial evolution of the streaky structures under influence of secondary high-frequency disturbance are discussed. Features of the adverse pressure gradient influence upon processes of the nonlinear varicose instability evolution and flow structure are revealed. Essential influence of the adverse pressure gradient on evolution of disturbances in shown. Comparison of varicose instability of the streaky structures generated in two different ways (the roughness element as in the given work, and continuous air blowing as in the earlier published work) is the carried out. The work supported by the Ministry of Education and Science of the Russian Federation (Grant No. RNP. 2.1.2.3370) and by the Russian Foundation for Basic Research (Grant No. 05-01-00034).     

Evolution of turbulent kinetic energy in a perturbed turbulent boundary layer

The paper considers the evolution of turbulent kinetic energy in a turbulent boundary layer perturbed by suction. The results show that the boundary layer equilibrium is altered in a non-linear manner due to suppression of the structures near the wall. The behavior, however, suggests that the wavelength of alteration of the equilibrium of the layer is unaffected by a change in Reynolds number and suction rate.     

A turbulent data analysis in the Antarctic boundary layer

Summary Data collected by the Institute of Atmospheric Physics of CNR (Italy) during the 1991 Italian Antarctic expedition are used for the development of Earth-air-sea interaction studies. In this paper wind and temperature data obtained by a digitized ultrasonic anemometer-thermometer describe the temporal, statistical and spectral turbulence behaviour in the surface atmospheric boundary layer at different wind conditions and in morphologically different sites. The vertical momentum and thermal fluxes, evaluated through the direct method, are found to be strictly dependent on the local stability condition recorded during the measurements. The examination of the velocities and temperature probability density functions confirms the Lumley and Panofsky hypothesis on the influence of both velocity components on temperature fluctuations. A multichannel spectral analysis confirms the obtained results for the low-frequency range. The authors of this paper have agreed to not receive the proofs for correction.     

Roughness sub-layer investigation of a turbulent boundary layer

Particle image velocimetry (PIV) measurements at relatively low Reynolds numbers in a turbulent boundary layer over a three-dimensional roughened surface, consisting of pyramidal rows, have been presented. Measurements have been taken in a streamwise wall-normal plane intercepting the apex of a row of pyramids and the diagonal of the square base. The results shown in this paper point out the non-homogeneity of the flow in the roughness sub-layer. The different flow behaviour along the ascendant and the descendent part of the pyramids and in the region between two consecutive pyramids has been visualised. Low values of the streamwise component of the mean velocity and high values of the streamwise and wall-normal component of the Reynolds normal stresses, turbulent kinetic energy and Reynolds shear stresses are present in the downstream part of the pyramids, near their base. The mean representation of the flow shows swirling patterns in correspondence of the top of the pyramids. It is suggested that this representation is produced mainly by vortical structures travelling along the wall, retarded and intensified when interacting with the flow around the roughness element and by swirling patterns originating from the interaction of the incoming flow with the pyramids. In order to understand the origin of the high turbulence activity observed downstream the pyramids, near their base, a conditional analysis based on the quadrant method has been performed. It has been shown that sweep events are the major contributor to the very high values of the Reynolds shear stresses observed in this region and are due to the combination of the vortical flow at the top of the pyramid and a large scale (with respect to the roughness element) inflow motion.     

Phase-relationships between scales in the perturbed turbulent boundary layer

The phase-relationship between large-scale motions and small-scale fluctuations in a non-equilibrium turbulent boundary layer was investigated. A zero-pressure-gradient flat plate turbulent boundary layer was perturbed by a short array of two-dimensional roughness elements, both statically, and under dynamic actuation. Within the compound, dynamic perturbation, the forcing generated a synthetic very-large-scale motion (VLSM) within the flow. The flow was decomposed by phase-locking the flow measurements to the roughness forcing, and the phase-relationship between the synthetic VLSM and remaining fluctuating scales was explored by correlation techniques. The general relationship between large- and small-scale motions in the perturbed flow, without phase-locking, was also examined. The synthetic large scale cohered with smaller scales in the flow via a phase-relationship that is similar to that of natural large scales in an unperturbed flow, but with a much stronger organizing effect. Cospectral techniques were employed to describe the physical implications of the perturbation on the relative orientation of large- and small-scale structures in the flow. The correlation and cospectral techniques provide tools for designing more efficient control strategies that can indirectly control small-scale motions via the large scales.     

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)     

湍流边界层压力起伏频谱特性研究

本工作对水中回转体TBL(湍流边界展)压力起伏频谱特性进行了分析研究.将TBL压力起伏谱分频率高于迁移频率f₀和低于f₀的两个频段描述,给出与实验用模型相应的f₀计算关系;由实验结果的分析得到TBL转捩区和发展区压力起伏频谱与频率、速度间的关系。     

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.     

The evolution of synthesised vortices in turbulent boundary layer

Particle image velocimetry technique has been used to investigate the evolution of synthesised vortical structures in the turbulent boundary layer. Synthetic jet actuator is implemented on the flat plate surface to synthesise various vortical structures by operating the actuator at varying operating parameters. The vortices are issued into the boundary layer and their evolution and subsequent interaction with the relatively less energetic near wall fluid is studied. The investigation is based on the quantitative measurements that are made both on the central and parallel lateral planes. Finally, the enhancement of the wall shear stress resulted in by the passing vortices is measured to evaluate the effectiveness of the actuator towards flow separation control.     

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.