壁湍流边界层奇异标度律的实验研究

采用热线风速仪对平板湍流边界层的流向速度进行测量,用速度结构函数研究不同尺度结构标度律的变化规律,结果显示小尺度区的概率密度曲线尾部明显偏离高斯型,说明高幅值间歇性事件占的份额较多;惯性子区的曲线向高斯型靠近,间歇性事件所占份额减少;大尺度结构的曲线趋于高斯型,间歇性事件所占份额最小。在耗散区、惯性子区和较大的尺度结构区存在大小不同的绝对标度指数,越靠近壁面这些区域的标度指数均越偏离p/3而逐渐变小。绝对标度指数与边界层位置有关,在缓冲层各阶标度指数与线性标度律偏差很大,显示较强的奇异性,当过渡到对数层及外区,标度指数逐渐增大,接近均匀各向同性湍流的状态。缓冲层、对数层及外区具有各异的绝对标度指数增长率,与各层的不同湍流结构特征和运动形式有关。     

可解尺度各向同性湍流的标度律

针对大涡模拟, 首先利用 EDQNM 能谱和传输谱理论, 在3种不同的过滤器下分别计算可解尺度各向同性湍流的二阶、三阶结构函数标度律, 并通过速度差扭率验证了可解尺度湍流的 ESS 理论. 研究了该可解尺度湍流标度律及速度差扭率与多个因素的关系, 这些因素包括: 两点距离与过滤尺度的比、大涡模拟雷诺数和过滤器类型. 结果显示, 当两点距离位于过滤尺度量级时或大涡模拟雷诺数较小时, 可解尺度标度律与未过滤流场的标度律相差很大进而必须加以修正, 而且可解尺度流场也不再总是满足 ESS 理论进而对应的速度差扭率也需要修正. 然后通过3个例子介绍了这些结果在大涡模拟亚格子模型中的应用.      

壁面湍流标度律的PIV实验研究

利用高分辨率、高帧率PIV系统对湍流边界层内的自相似标度律在不同的壁面距离的具体表达形式进行了实验研究。在动量损失雷诺数（Reθ=2167）下测量平板湍流边界层内的二维瞬时速度场。应用小波分析和传统统计学方法,在垂直于平板的平面内,对不同法向位置的自相似的标度律的具体形式及其随尺度的变化情况进行考察,并与已知的She-leveque（简称SL）标度律进行比较分析。结果表明,越接近壁面,结构函数的概率密度曲线尾部越宽,表现出逐渐增强的间歇性;并且随着壁面距离的减小,ESS标度律曲线与SL标度律曲线之间的差别也就越大,而新形式标度律曲线则与SL标度律曲线的差别逐渐减小。在提取的结构尺度一样时,结构函数的标度指数随法向位置的不同变化不大,但是随着提取结构尺度的增加,两种形式的标度律适用的尺度范围也在逐渐增大。     

壁面加热边界条件对湍流扩展的自相似性的影响

用热线风速仪测量了风洞中壁面加热和不加热平板湍流边界层不同法向位置的瞬时流向速度的时间序列,研究了壁面加热的边界条件对流向速度增量的p阶结构函数的扩展的自相似性和层次结构模型的影响。实验结果表明,壁面加热的边界条件对流向速度增量的结构函数扩展的自相似标度律的相对标度指数δ（p,3）和层次结构模型中间歇参数β、最奇异指数γ的影响明显存在。     

自由端射流多尺度湍涡结构标度律的实验研究

利用后向接收式激光多普勒测速仪（ＬＤＶ）对自由湍射流进行了测量,我们对采集到的充分发展的湍流信号先求其１－８阶的结构函数及其标度指数,结果验证了Ｋｏｌｍｏｇｏｒｏｖ提出的标度律理论。然后用子波变换将自由湍流脉动速度分解为多尺度湍流结构,研究每一个尺度湍涡速度的结构函数的标度律及其与湍涡速度的自相关函数的关系。     

自由湍射流边界层标度律的实验测量

用IFA300热线风速仪以低于最小低湍流时间尺度的高分辨率，精细测量了圆自由射流中同一流向断面内不同径向位置的流向速度分量，研究了不同径向位置的非均匀、非各向同性对充分发展湍流速度结构函数自相似标度律及其层次结构模型的影响。     

可压缩各向同性衰减湍流直接数值模拟研究

采用五阶有限差分WENO格式直接模拟了高初始湍流Mach数的可压缩均匀各向同性湍流,主要分析了湍流的统计特性 和压缩性的影响,包括能谱特征、激波串、耗散率、标度律等. 研究表明,湍动能主要来自于速度场螺旋分量的贡献;各向同性湍流的小尺度脉动对压缩性更为敏感,并且压缩性的增强加快了湍流大 尺度脉动向小尺度脉动的湍动能输运;随着湍流Mach数的升高,胀量(压缩)耗散率所占比率也显著增长. 标度律分析表明,强可压缩湍流的横向速度结构函数仍然具有扩展自相似性;当阶数较高(p ≥ 5)时,纵向速度结构函数的扩展自相似性则不再成立. 对于压缩性较弱的湍流,与不可压缩湍流一致,横向湍流脉动的间歇性要强于纵向湍流脉动;而对于强可压缩湍流,纵向湍流脉动的 间歇性要强于横向湍流脉动.     

）IRECT NUMERICAL SIMULATION OF DECAYING COMPRESSIBLE ISOTROPIC TURBULENCE

采用五阶有限差分WENO格式直接模拟了高初始湍流Mach数的可压缩均匀各向同性湍流,主要分析了湍流的统计特性和压缩性的影响,包括能谱特征、激波串、耗散率、标度律等.研究表明,湍动能主要来自于速度场螺旋分量的贡献;各向同性湍流的小尺度脉动对压缩性更为敏感,并且压缩性的增强加快了湍流大尺度脉动向小尺度脉动的湍动能输运;随着湍流Mach数的升高,胀量（压缩）耗散率所占比率也显著增长.标度律分析表明,强可压缩湍流的横向速度结构函数仍然具有扩展自相似性;当阶数较高（p≥5）时,纵向速度结构函数的扩展自相似性则不再成立.对于压缩性较弱的湍流,与不可压缩湍流一致,横向湍流脉动的间歇性要强于纵向湍流脉动;而对于强可压缩湍流,纵向湍流脉动的间歇性要强于横向湍流脉动.     

自由湍射流多尺度湍涡结构标度律的实验研究

利用后向接收式激光多普勒测速仪（ＬＤＶ）对自由湍射流进行了测量,我们对采集到的充分发展的湍流信号先求其１－ ８阶的结构函数及其标度指数,结果验证了Ｋｏｌｍ ｏｇｏｒｏｖ提出的标度律理论． 然后用子波变换将自由湍流脉动速度分解为多尺度湍涡结构, 研究每一个尺度湍涡速度的结构函数的标度律及其与湍涡速度的自相关函数的关系．     

壁湍流扩展的自相似标度律的实验研究

对风洞中零压力梯度平板湍流边界层进行了实验研究，用热线风速仪测量了不同法向位置的脉动速度，研究了湍流边界层不同法向位置速度结构函数的扩展的自相似标度律。     

A multifractal model for linking Lagrangian and Eulerian velocity structure functions

A multifractal model is developed to connect the Lagrangian multifractal dimensions with their Eulerian counterparts. We propose that the characteristic time scale of a Lagrangian quantity should be the Lagrangian time scale, and it should not be the Eulerian time scale which was widely used in previous studies on Lagrangian statistics. Using the present model, we can obtain the scaling exponents of Lagrangian velocity structure functions from the existing data or models of scaling exponents of Eulerian velocity structure functions. This model is validated by comparing its prediction with the results of experiments, direct numerical simulations, and the previous theoretical models. The comparison shows that the proposed model can better predict the scaling exponents of Lagrangian velocity structure functions, especially for orders larger than 6.     

Modal interactions and energy transfers in isotropic turbulence as predicted by local energy transfer theory

Energy transfer processes in decaying, three-dimensional, isotropic turbulence are investigated using numerical results from local energy transfer (LET) theory. The study covers a wide range of evolved, microscale Reynolds numbers (5 < R_λ < 250). It is found that the energy transfer is mainly local (between scales of similar size), but there are also some signs of nonlocal transfer at higher Reynolds number. The nature of the underlying triad-wavenumber interactions, on the other hand, seems to depend on both the Reynolds number and the wavenumber range of interest. In the energy containing and dissipation ranges, both local (all three scales of the triad interaction are of comparable size) and nonlocal (one scale is much larger than the remaining two) interactions are important, with the latter becoming more dominant as the Reynolds number increases. But our nonlocal interactions tend to be less severe than those observed by Domaradzki and Rogallo. More significantly, in the inertial range of high Reynolds number flows, the LET theory predicts dominance of local and near-local interactions. While this is contrary to the result from eddy damped quasi-normal Markovian theory that the important triad interactions are mainly nonlocal, it is closer to the Kolmogorov picture of turbulence. Another interesting result is that, despite their inherent differences, the LET theory and the full simulation of Ohkitani and Kida predict inertial-range values for the energy transfer locality function in fairly good agreement, not only with each other, but also with the analytical closure theory result for infinite Reynolds number, stationary turbulence by Kraichnan. The calculated values reveal that the contributions to the net energy transfer are predominantly from near-local interactions (scale ratios ≈ 4), which is indicative of cancellation of large numbers of highly nonlocal interactions.     

On the nature of multitude scalings in decaying isotropic turbulence

We report multitude scaling laws for isotropic fully developed decaying turbulence through group theoretic method employing on the spectral equations both for modelling and without any modelling of nonlinear energy transfer. For modelling, besides the existence of classical power law scalings, an exponential decay of turbulent energy in time is obtained subject to exponentially decaying integral length scale at infinite Reynolds number limit. For the transfer without modelling, at finite Reynolds number, in addition to general power law decay of turbulence intensity with integral length scale growing as a square root of time, an exponential decay of energy in time is explored when integral length scale remains constant. Both the power and exponential decaying laws of energy agree to the theoretical results of George (1992), George and Wang (2009) and experimental results of fractal grid generated turbulence by Hurst and Vassilicos (2007). At infinite Reynolds number limit, a general power law scaling is obtained from which all classical scaling laws are recovered. Further, in this limit, turbulence exhibits a general exponential decaying law of energy with exponential decaying integral length scale depending on two scaling group parameters. The role of symmetry group parameters on turbulence dynamics is discussed in this study.     

Extended self-similar scaling law of multi-scale eddy structure in wall turbulence

ＩｎｔｒｏｄｕｃｔｉｏｎＭｕｃｈｗｏｒｋｈａｓｂｅｅｎｄｅｖｏｔｅｄｉｎｔｈｅｌａｓｔｆｅｗｄｅｃａｄｅｓｔｏｔｈｅｍｅａｓｕｒｅｍｅｎｔａｎｄｍｏｄｅｌｉｎｇｏｆｔｈｅｓｃａｌｉｎｇｌａｗｏｆｓｔｒｕｃｔｕｒｅｆｕｎｃｔｉｏｎｏｆｔｕｒｂｕｌｅｎｔｆｌｏｗｓ.Ｔｈｅｓｏ＿ｃａｌｌｅｄ“ｖｅｌｏｃｉｔｙｓｔｒｕｃｔｕｒｅｆｕｎｃｔｉｏｎｏｆｏｒｄｅｒｎ”ｆｏｒｔｕｒｂｕｌｅｎｔｆｌｏｗｓｉｓｄｅｆｉｎｅｄａｓ〈ΔＶ(ｒ) ｎ〉 ,ｗｈｅｒｅΔＶ(ｒ) =Ｖ(ｘ ｒ) -Ｖ(ｘ)ｉｓｔｈｅｖｅｌｏｃｉｔｙｃｏｍｐ…     

Direct Numerical Simulation of Self-Similar Turbulent Boundary Layers in Adverse Pressure Gradients

Direct numerical simulations of the Navier–Stokes equations have been carried out with the objective of studying turbulent boundary layers in adverse pressure gradients. The boundary layer flows concerned are of the equilibrium type which makes the analysis simpler and the results can be compared with earlier experiments and simulations. This type of turbulent boundary layers also permits an analysis of the equation of motion to predict separation. The linear analysis based on the assumption of asymptotically high Reynolds number gives results that are not applicable to finite Reynolds number flows. A different non-linear approach is presented to obtain a useful relation between the freestream variation and other mean flow parameters. Comparison of turbulent statistics from the zero pressure gradient case and two adverse pressure gradient cases shows the development of an outer peak in the turbulent energy in agreement with experiment. The turbulent flows have also been investigated using a differential Reynolds stress model. Profiles for velocity and turbulence quantities obtained from the direct numerical simulations were used as initial data. The initial transients in the model predictions vanished rapidly. The model predictions are compared with the direct simulations and low Reynolds number effects are investigated.     

二维槽道湍流的标度律分析

对不同Reynolds数的二维不可压槽道湍流（即二维槽道流动的扰动饱和态）进行了标度律分析.指出二维槽道湍流中存在明显的标度律及扩展自相似性;分析了标度指数随着流动Reynolds数的变化,指出随着Reynolds数的增长,标度指数的奇异性并没有减小的趋势;由此推测充分发展的二维槽道湍流的标度指数也是奇异的、将所得计算值和余振苏等人的SL标度律预测值相比较,认为余等人的SL标度律公式能很好描述二维湍流.     

Turbulence modelling of the flow past a pitching NACA0012 airfoil at and Reynolds numbers

This paper provides a study of the NACA0012 dynamic stall at Reynolds numbers 10⁵ and 10⁶ by means of two- and three-dimensional numerical simulations. The turbulence effect on the dynamic stall is studied by statistical modelling. The results are compared with experiments concerning each test case. Standard URANS turbulence modelling have shown a quite dissipative character that attenuates the instabilities and the vortex structures related to the dynamic stall. The URANS approach Organised Eddy Simulation (OES) has shown an improved behaviour at the high Reynolds number range. Emphasis is given to the physical analysis of the three-dimensional dynamic stall structure, for which there exist few numerical results in the literature, as far as the Reynolds number range is concerned. This study has shown that the downstroke phases of the pitching motion are subjected to strong three-dimensional turbulence effects along the span, whereas the flow is practically two-dimensional during the upstroke motion.     

Optimized group velocity control scheme and DNS of decaying compressible turbulence of relative high turbulent Mach number

To overcome the difficulty in the DNS of compressible turbulence at high turbulent Mach number, a new difference scheme called GVC8 is developed. We have succeeded in the direct numerical simulation of decaying compressible turbulence up to turbulent Mach number 0.95. The statistical quantities thus obtained at lower turbulent Mach number agree well with those from previous authors with the same initial conditions, but they are limited to simulate at lower turbulent Mach numbers due to the so‐called start‐up problem. The energy spectrum and coherent structure of compressible turbulent flow are analysed. The scaling law of compressible turbulence is studied. The computed results indicate that the extended self‐similarity holds in decaying compressible turbulence despite the occurrence of shocklets, and compressibility has little effects on relative scaling exponents when turbulent Mach number is not very high. Copyright © 2005 John Wiley & Sons, Ltd.     

Vortices for computing: the engines of turbulence simulation

Vortices have been described as the “sinews of turbulence”. They are also, increasingly, the computational engines driving numerical simulations of turbulence. In this paper, I review some recent advances in vortex-based numerical methods for simulating high Reynolds number turbulent flows. I focus on coherent vortex simulation, where nonlinear wavelet filtering is used to identify and track the few high energy multiscale vortices that dominate the flow dynamics. This filtering drastically reduces the computational complexity for high Reynolds number simulations, e.g. by a factor of 1000 for fluid–structure interaction calculations (Kevlahan and Vasilyevvon in SIAM J Sci Comput 26(6):1894–1915, 2005). It also has the advantage of decomposing the flow into two physically important components: coherent vortices and background noise. In addition to its computational efficiency, this decomposition provides a way of directly estimating how space and space–time intermittency scales with Reynolds number, Re ^α . Comparing α to its non-intermittent values gives a realistic Reynolds number upper bound for adaptive direct numerical simulation of turbulent flows. This direct measure of intermittency also guides the development of new mathematical theories for the structure of high Reynolds number turbulence.