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.     

Surface roughness effects on the turbulence statistics in a low Reynolds number channel flow

A high-resolution particle image velocimetry was used to characterize a low Reynolds number turbulent flow in a channel. Experiments were conducted over a sand grain-coated surface of large relative roughness, and the results were compared with measurements over a smooth surface. The roughness perturbation significantly modified the outer layer. Even though the streamwise Reynolds stress shows less sensitivity in the outer layer to the boundary condition, significant enhancements were observed in the wall-normal Reynolds stress and the Reynolds shear stress. These modifications were considered as footprints of the larger-scale eddies transporting intense wall-normal motions away from the rough wall. A quadrant decomposition shows that strong and more frequent ejections are responsible for the larger values of the mean Reynolds shear stress over the rough wall. The results also indicate that spanwise vortex cores with mean vorticity of the same sign as the mean shear are the dominant smaller-scale vortical structures over the smooth and rough walls. A linear stochastic estimation-based analysis shows that the average larger-scale structure associated with these vortices is a shear layer that strongly connects the outer layer flow to the near-wall flow. A proper orthogonal decomposition of the flow suggests that the large-scale eddy is more energetic for the rough wall, and contributes more significantly to the resolved turbulent kinetic energy and the Reynolds shear stress than the smooth wall.     

平板湍流边界层瞬时摩擦阻力的光学测量和统计分析

采用近壁粒子图像测速（particle image velocimetry,PIV）技术实现了中低Reynolds数光滑平板湍流边界层瞬时摩擦阻力的测量.发展了单行互相关算法和迭代拟合技术估算瞬时摩擦阻力,其法向空间分辨率可达到2~4 pixel.作为对比,同时分析了相似Reynolds数范围的直接数值模拟数据.统计结果表明:摩擦阻力的脉动强度随Reynolds数升高呈现对数增长趋势,证实了外区大/超大尺度结构对壁面的影响.谱分析结果表明近壁区的低速条带结构主导着摩擦阻力的多尺度脉动特性,外区大/超大尺度结构对摩擦阻力的印迹作用较小,其主要通过调制作用实现对摩擦阻力的影响,这一结论可以从瞬时摩擦阻力的偏度以及概率密度函数曲线具有Reynolds数不变性得到进一步证实.      

超声速湍流边界层湍流统计与湍流结构分析

可压缩边界层转捩问题与湍流问题一直是制约高超声速飞行器发展的关键基础问题,也是近年来流体力学领域研究的热点问题.采用直接数值模拟方法,获得了空间发展的Ma=2.25超声速湍流边界层流场,通过对湍流边界层的发展状态进行评估,得出有效的Reynolds数Reθ 范围约为2600～4600.对壁面摩阻系数开展了分解,获得了各...     

LES of spatially developing turbulent boundary layer over a concave surface

We revisit the problem of a spatially developing turbulent boundary layer over a concave surface. Unlike previous investigations, we simulate the combined effects of streamline curvature as well as curvature-induced pressure gradients on the turbulence. Our focus is on investigating the response of the turbulent boundary layer to the sudden onset of curvature and the destabilising influence of concave surface in the presence of pressure gradients. This is of interest for evaluating the turbulence closure models. At the beginning of the curve, the momentum thickness Reynolds number is 1520 and the ratio of the boundary layer thickness to the radius of curvature is δ₀/R = 0.055. The radial profiles of the mean velocity and turbulence statistics at different locations along the concave surface are presented. Our recently proposed curvature-corrected Reynolds Averaged Navier-Stokes (RANS) model is assessed in an a posteriori sense and the improvements obtained over the base model are reported. From the large Eddy simulation (LES) results, it was found that the maximum influence of concave curvature is on the wall-normal component of the Reynolds stress. The budgets of wall-normal Reynolds stress also confirmed this observation. At the onset of curvature, the effect of adverse pressure gradient is found to be predominant. This decreases the skin friction levels below that in the flat section.     

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.     

低速压气机叶栅附面层分离的实验研究

本文利用表面热膜对某高负荷压气机叶片吸力面附面层的分离过程进行了实验研究,捕捉到了边界层分离点的位置及其随攻角的变化情况,给出了利用表面热膜测量的准壁面剪切应力米预判分离先兆和分离点位置的判据.同时,分析了 Re数对附面层分离特性的影响.结果表明:准壁面剪切应力及其均方根极小值对应的位置点是进入分离泡内的第一个测量点;在所有测量的工况条件下,表面热膜都捕捉到了吸力面附面层的长分离泡,并能准确捕捉到攻角所引起的分离点位置变化;低Re数下,Re数对附面层分离影响较小.     

Characterisation of backflow events over a wing section

Rare backflow (negative wall-shear stress) events have recently been found and quantified in the near-wall region of canonical wall-bounded turbulent flows. Although their existence and correlation with large-scale events have been established beyond numerical and measurement technique uncertainties, their occurrence at numerically high Reynolds numbers is still rare (less than 1 per thousand and 1 per million at the wall and beyond the viscous sublayer, respectively). To better quantify these rare events, the turbulent boundary layer developing over the suction side of a wing section, experiencing an increasing adverse pressure gradient (APG) without separation along its chord c, is considered in the present work. We find that the backflow level of 0.06% documented in turbulent channels and zero-pressure-gradient (ZPG) turbulent boundary layers is already exceeded on the suction side for x/c > 0.3, at friction Reynolds numbers three times lower, while close to the trailing edge the backflow level reaches 30%. Conditional analysis of extreme events indicates that for increasing Clauser pressure-gradient parameters (reaching β ? 35), the flow reaches a state in which the extreme events are more likely aligned with or against the freestream, and that the otherwise strong spanwise component of the wall-shear stress reduces towards the vicinity of the trailing edge. Backflow events subjected to moderate up to strong APG conditions (0.6 < β < 4.1) exhibit an average width of Δz⁺ ? 20, and an average lifetime of Δt⁺ ? 2. This directly connects with the findings by Lenaers et al., and implies that there is a connection between high-Re ZPG and strong APG conditions.     

横向粗糙元壁面槽道湍流的大涡模拟研究

采用大涡模拟和浸没边界法相结合对不同高度和不同间距横向粗糙元壁面槽道湍流进行了模拟,得到了光滑壁面和粗糙壁面湍流的流向平均速度分布,雷诺剪切应力,脉动速度均方根和近壁区拟序结构。结果发现横向粗糙元降低了流向平均速度,增大了流动阻力,粗糙壁面湍流的雷诺剪切应力大于光滑壁面。粗糙元降低了流向脉动速度,增强了展向和法向脉动速度。粗糙元高度越高,对湍流流动影响越大,而粗糙元间距对湍流统计特性的影响不大。粗糙壁面仍然存在着和光滑壁面类似的条带结构。     

Visualization study on vortex structure over an airfoil using planar laser induced fluorescence

Abstract

The research discussed the application of planar laser-induced fluorescence technique for visualizing the flow over an airfoil at different Reynolds numbers and angles of attack. The proposed arrangement allows visualizing the development process of the flow field structure around the airfoil. The focus of the study is the influence of the angles of attack and the Reynolds number on the separation boundary layer, which causes the wake vortex or separation bubble. Compared with the traditional visualization technology, the technology of planar laser-induced fluorescence has better time resolution (50?ns) and followability (Reynolds number?=?219,500). In order to achieve high-speed flow field visualization, planar laser-induced fluorescence provides a reliable means of measurement to solve the related engineering problems.     

A diagnostic study of turbulence features in wind tunnel flow over simple topographic shapes

Summary The turbulence features observed in wind tunnel experiments of flow over isolated simple-shaped two-dimensional hills and valleys are analysed in the light of transport equations of Reynolds stresses in the streamline coordinate system. The analysis has shown that near the surface the streamwise pressure gradient is the driving parameter for all the stresses. At higher levels, the effects of streamline curvature and streamwise pressure gradient act differently on the source terms of stresses, showing that the shear stress is the most sensitive to streamline curvature, whereas the streamwise stress is the most sensitive to streamwise pressure gradient. Although two of the considered topographies are specular images, the turbulence response is not so, since it depends on the sequence of curvatures to which it is subjected. The information and analysis presented will constitute a valuable resource to those seeking an understanding of atmospheric boundary layer development over complex terrain. It will also provide a support for the development and validation of more rigorous turbulence models.     

Vortex pattern of the turbulent flow around a single cube on a flat surface and its heat transfer at different attack angles

Experimental results on convective heat transfer from a single cube on a flat surface are presented for different attack angles to the incident flow and Reynolds numbers. The character of vortex formation and the effect of flow structure on heat transfer at detached flow around a cube were studied by visualization. Local heat transfer and heat transfer averaged over the separate faces and the whole lateral surface of the cube were studied. Contribution of separate cube faces to total heat transfer depending on the attack angle was estimated. Data obtained were compared with those published in literature. The reasons for observed differences caused by the effect of many factors: boundary layer thickness, turbulence level of the incident flow, channel constraint, etc., are analysed.     

空间发展平板混和层流动的大涡模拟-3D与2D模拟的比较

本文利用大涡模拟方法研究了空间发展平板混合层流动,分别在三维模型和二维模型下,比较了大尺度结构涡的演化过程,以及流向速度、流向脉动速度、横向脉动速度和Reynolds应力的统计时均结果,并与实验结果对照,指出3D模拟无论在物理真实性还是预报结果准确性方面都要明显优于2D模拟。     

基于温敏漆技术的圆锥高超声速大攻角绕流背风面流动结构实验研究

高超声速流动中, 大攻角下圆锥背风面边界层会存在流动分离与再附、边界层转捩等多种流动现象, 进而对圆锥表面温度分布产生显著的影响。为了对这一复杂流动规律及其对表面温升分布的影响进行讨论, 研究基于温敏漆技术, 得到了在Mach数为6的低湍流度来流条件下, 攻角为10°的圆锥背风面温升分布结果。通过对不同位置、不同方位角处温升分布曲线的分析, 对大攻角下圆锥背风面边界层流动发展过程及不同发展阶段的流动特征进行了讨论。同时, 通过对来流总压的调节, 得到了不同Reynolds数下的圆锥背风面温升分布结果, 总结了Reynolds数对流动的影响规律。研究发现, 高超声速大攻角圆锥背风面边界层流动发展过程中会依次出现层流分离、定常横流涡影响、转捩以及湍流分离与再附等流动特征, 而在不同的Reynolds数下, 各个流动特征产生影响的范围不同, 随着Reynolds数的降低, 层流范围和定常横流涡影响范围均有所增加, 而从观察到横流影响到转捩开始发生的范围基本相同。      

New expressions for the surface roughness length and displacement height in the atmospheric boundary layer

An alternative model for the prediction of surface roughness length is developed. In the model a new factor is introduced to compensate for the effects of wake diffusion and interactions between the wake and roughness obstacles. The experiments are carried out by the use of the hot wire anemometry in the simulated atmospheric boundary layer in a wind tunnel. Based on the experimental data, a new expression for the zero-plane displacement height is proposed for the square arrays of roughness elements, which highlights the influence of free-stream speed on the roughness length. It appears that the displacement height increases with the wind speed while the surface roughness length decreases with Reynolds number increasing. It is shown that the calculation results based on the new expressions are in reasonable agreement with the experimental data.     

黏弹性流体泡状流混合层流动的PIV实验研究

本文对注入气泡的黏弹性流体气液两相泡状流混合层流动进行实验研究,含气率为0.5%。与纯水气液两相流相似,气泡的注入也会削弱黏弹性流体中的涡结构,影响大涡的卷起。雷诺应力与涡量的分布规律类似,其峰值集中在混合层中心区域。注入气泡使混合层中心区域内的雷诺应力增大,峰值区域范围减小,添加聚合物的混合层中的雷诺应力峰值增大得更多。对涡量而言,注入气泡使峰值产生非常明显的减小,黏弹性流体的涡量所受的影响比纯水的要小。     

Noise of a turbulent boundary layer flow over smooth and rough plates at low mach numbers

The spectral levels of the quadrupole noise generated by a boundary layer flow over a smooth surface are calculated. Explicit dependences of the noise levels on the Reynolds number are obtained for the low-frequency and high-frequency ranges. It is shown that the logarithmic zone of the velocity profile is responsible for the region of the quadrupole noise spectrum with a hyperbolic dependence on frequency. A method of calculating the dipole noise of a boundary layer flow over a rough surface is developed. The method is based on the use of the combined probability density for the turbulent velocity fluctuations and the random dimensions of protuberances of the rough surface. The two constants involved in this theory are determined from a special experiment. It is shown that the surface roughness noticeably increases the radiation levels of a boundary layer flow in a certain frequency range.     

Mean momentum balance analysis of rough-wall turbulent boundary layers

Mean momentum balances (MMB) are carried out for zero pressure gradient rough-wall turbulent boundary layer flows. The balance characterizes the mean dynamical mechanisms and reveals dominant terms in the governing equation, which constitutes a necessary step in the derivation of scaling behaviors. The Reynolds stress profiles in rough-wall boundary layers are, however, quite scattered and the uncertainty in the data poses challenges for educing the MMB. The present study employs a method that invokes theoretical constraints to more reliably reveal Reynolds stress gradient behaviors in the presence of data scatter.Properties of the rough-wall mean momentum balances are compared to those of the smooth-wall case. Important qualitative features of the layer structure that exists for the smooth-wall are shown to also exist for rough-wall boundary layers. Specifically, the present analysis reveals the existence of a stress gradient balance layer, and thus the importance of the viscous force term well above the roughness crests. The smooth-wall Reynolds stress peak position scales in proportion with the geometric mean of inner-outer characteristic lengths. Roughness, however, imposes new dynamical length scales and evidence is provided to indicate that the scale separations between the inner length, roughness length, peak Reynolds stress length and outer length are important. The failure of the rough-wall Reynolds stress profiles to merge under smooth-wall meso-scalings clearly reveals the additional richness of the problem.Although more data are required to gain a complete characterization, the present results provide evidence that the combined roughness-Reynolds number problem exhibits significantly greater complexity than captured by the prevalent scheme for characterizing and classifying roughness regimes.     

Heat Transfer in an Upper Convected Maxwell Fluid with Fluid Particle Suspension

An analysis is carried out to study the magnetohydrodynamic (MHD) flow and heat transfer characteristics of an electrically conducting dusty non-Newtonian fluid, namely, the upper convected Maxwell (UCM) fluid over a stretching sheet. The stretching velocity and the temperature at the surface are assumed to vary linearly with the distance from the origin. Using a similarity transformation, the governing nonlinear partial differential equations of the model problem are transformed into coupled non-linear ordinary differential equations and the equations are solved numerically by a second order finite difference implicit method known as the Keller-box method. Comparisons with the available results in the literature are presented as a special case. The effects of the physical parameters on the fluid velocity, the velocity of the dust particle, the density of the dust particle, the fluid temperature, the dust-phase temperature, the skin friction, and the wall-temperature gradient are presented through tables and graphs. It is observed that, Maxwell fluid reduces the wall-shear stress. Also, the fluid particle interaction reduces the fluid temperature in the boundary layer. Furthermore, the results obtained for the flow and heat transfer characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid flow phenomena, especially the dusty UCM fluid flow phenomena.     

Flow characteristics of an offset jet over a surface mounted square rib

A three-dimensional offset jet flow over a surface mounted square rib was investigated using particle image velocimetry at Reynolds number of 7600. The square rib was mounted at three different locations downstream of the nozzle exit. Contour and profile plots in the symmetry plane were used to investigate the effect of the rib on the mean flow distribution and turbulence statistics. Changing the rib location enhanced the mixing and entrainment characteristics of the jet thereby leading to larger wall-normal spread rates. The quadrant analysis revealed a significant contribution of all events towards the Reynolds shear stress. The joint probability density function analysis showed that the structures within the outer shear layer of the jet differed from those of boundary layers. Results from the two-point correlation analysis indicated that the introduction of a surface mounted rib modified the flow structures within the developing region. However, there was no significant structural difference between the flow with mounted rib and the no rib case within the self-similar region. The proper orthogonal decomposition was used to examine how changes in rib location modified the dynamics of the energetic modes towards the turbulent kinetic energy and Reynolds shear stress within the developing and self-similar regions.