二维衰减湍流的速度加速度结构函数

湍流场中二阶速度加速度结构函数 (velocity-acceleration structure function, VASF) 被认为与尺度间能量或者拟涡能的传递相关,其正负表明传递的方向. 三维湍流中,能量从大尺度向 小尺度传递,VASF 为负. 在二维湍流中,能量反向传递到大尺度,拟涡能正向传递到小尺度,因此理论上 VASF 无论在反向能量级串区还是在正向拟 涡能级串区均为正. 然而,相对于三维湍流中 VASF 的充分研究,二维湍流中 VASF 的正负性迄今尚无实验或数值模拟数据验证. 本文通过三维二维湍流中普适的公式推导,指出在空间非均匀湍流场中,VASF 除了尺度间传递,还受到非均匀项的影响. 一种常见的空间非均匀湍流场是在实验研究中常用的风洞或水洞中,湍流发生装置 (如栅格) 后的湍流. 该流场中,湍流强度随下游位置增大而逐渐衰减,这种衰减则带来空间上的非均匀性. 本文在基于竖直流动皂膜的二维衰减湍流场中,利用拉格朗日粒子追踪法测得在拟涡能级串区的 VASF,并分析各部分的影响. 结果表明,虽然尺度间传递项为正值,但由于衰减带来的非均匀项为负值,使得 VASF 的值为负,使之失去了表征拟涡能传递方向的意义. 因此,在类似风洞、水洞、水槽等衰减流场中对 VASF 的讨论不应忽略非均匀项. 最后对与 VASF 密切相关的弥散过程进行分析,发现后期弥散过程变慢是由于负的 VASF 导致.      

Direct simulation of two‐dimensional turbulent flow over a surface‐mounted obstacle

Two‐dimensional turbulent flow over a surface‐mounted obstacle is studied as a numerical experiment that takes place in a wind tunnel. The transient Navier–Stokes equations are solved directly with Galerkin finite elements. The Reynolds number defined with respect to the height of the wind tunnel is 12 518. Instantaneous streamline patterns are shown that give a complete picture of the flow phenomena. Energy and enstrophy spectra yield the dual cascade of two‐dimensional turbulence and the ?1 power law decay of enstrophy. Mean values of velocities and root mean square fluctuations are compared with the available experimental results. Other statistical characteristics of turbulence such as Eulerian autocorrelation coefficients, longitudinal and lateral coefficients are also computed. Finally, oscillation diagrams of computed velocity fluctuations yield the chaotic behaviour of turbulence. Copyright © 2007 John Wiley & Sons, Ltd.     

粉尘等容燃烧容器内扬尘系统诱导湍流特性的实验研究

采用热线风速仪与系统平均法测定和研究了三种圆柱形封闭容器内的扬尘诱导湍流衰减特性,并与球形爆炸容器内已测定的扬尘诱导湍流衰减特性进行了比较。探讨了扬尘装置、容器体积、形状对扬尘诱导湍流瞬态特性的影响。实验结果显示,在粉尘等容燃烧容器内扬尘诱导湍流强度随时间的衰减特性具有一定相似性,它们均呈负指数关系。     

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.     

Effects of the Similarity Model in Finite-Difference LES of Isotropic Turbulence Using a Lagrangian Dynamic Mixed Model

A Lagrangian dynamic formulation of the mixed similarity subgrid (SGS) model for large-eddy simulation (LES) of turbulence is proposed. In this model, averaging is performed over fluid trajectories, which makes the model applicable to complex flows without directions of statistical homogeneity. An alternative version based on a Taylor series expansion (nonlinear mixed model) is also examined. The Lagrangian models are implemented in a finite difference code and tested in forced and decaying isotropic turbulence. As comparison, the dynamic Smagorinsky model and volume-averaged formulations of the mixed models are also tested. Good results are obtained, except in the case of low-resolution LES (32³) of decaying turbulence, where the similarity coefficient becomes negative due to the fact that the test-filter scale exceeds the integral scale of turbulence. At a higher resolution (64³), the dynamic similarity coefficient is positive and good agreement is found between predicted and measured kinetic energy evolution. Compared to the eddy viscosity term, the similarity or the nonlinear terms contribute significantly to both SGS dissipation of kinetic energy and SGS force. In order to dynamically test the accuracy of the modeling, the error incurred in satisfying the Germano identity is evaluated. It is found that the dynamic Smagorinksy model generates a very large error, only 3% lower than the worst-case scenario without model. Addition of the similarity or nonlinear term decreases the error by up to about 50%, confirming that it represents a more realistic parameterization than the Smagorinsky model alone.     

Verification of a model to predict the influence of particle inertia and gravity on a decaying turbulent particle-laden flow

In an earlier publication some of the authors presented a theoretical model for the calculation of the influence of particle inertia and gravity on the turbulence in a stationary particle-laden flow. In the present publication the model is extended for application to a decaying suspension. Also a comparison is given between predictions made with the model and experimental data (own data and data reported in the literature) on a decaying turbulent flow with particles in a water tunnel or in a wind tunnel. For most of the experiments a prediction with reasonable accuracy and an interpretation is possible by means of the model.     

涡度拟能传输惯性区二维湍流标量场方差谱

本文应用非平衡统计力学封闭方法,给出涡度拟能传输惯性区二维湍流标量场方差谱的完整表达式,数值计算该表达式中的比例系数B。由于传输过程的非局部性,B依赖于表征波数变化范围的局部化因子,不再是普适常数。     

Numerical methods for the solution of the turbulence energy equations in shelf seas

This paper investigates the accuracy of numerical finite difference methods for solving the turbulence kinetic energy equations in thermally stratified shelf seas with wind and tidal mixing. Alternative discretisation methods are presented for both the source terms and the diffusion term in the turbulence kinetic energy equation. It is shown that techniques not widely used in this field maintain greater accuracy at low spatial and temporal resolution than is obtained with commonly used ones, with no added computational cost. Therefore, these techniques are valuable for use in three‐dimensional models. Copyright © 1999 John Wiley & Sons, Ltd.     

大气边界层流场的模拟与大气边界层风洞

动态风荷载测试数据的可靠性依赖于大气边界层流场的正确模拟。本文根据作者在ＦＤ－４大气边界层风洞中,进行大气边界层流场调试时,就如何准确模拟自然风的四个参数方面所积累经验的总结。     

Inlet grid-generated turbulence for large-eddy simulations

A new technique of generating turbulence in large-eddy simulations (LES) has been investigated and results compared with previous studies for validation. The proposed gridInlet technique uses a grid pattern on the inlet boundary patch to produce grid-generated turbulence as used in wind tunnel experiments. This allows the turbulence integral length scale to be controlled by changing the grid size, while the turbulence intensity is controlled by changing the inlet distance. The objective of this paper is to investigate domain and mesh requirements to implement the gridInlet technique. This technique is most suited to studies on the influence of high-intensity isotropic turbulence on objects, particularly if comparisons are to be made to experimental data obtained with grid-generated turbulence.     

Decaying homogeneous turbulence under strong density stratification at low-Prandtl number

The characteristics of decaying homogeneous turbulence under strong density stratification have been studied using direct numerical simulations. While our previous study dealt with rotating stratified turbulence, here we investigate the detailed flow structure of stratified turbulence without rotation especially at low-Prandtl number. By assuming a low-Prandtl-number fluid, e.g. liquid sodium: Pr ≈ 0.01, gallium: Pr ≈ 0.025, internal gravity waves are markedly attenuated due to the large thermal conductivity, and turbulence soon reaches a two-component state, where vertical energy, coupled with potential energy, significantly decays, and becomes negligible as observed experimentally (Praud et al. in J Fluid Mech 522:1–33, 2005). In the horizontal plane, there appear large-scale vortices with vertical vorticity, and those with the same sign of vorticity increase their horizontal length scale by merging with each other. In the vertical plane, highly sheared regions represented by horizontal vorticity also tend to horizontally increase their length scale and become layered structures by the combined effects of vortex coalescence and energy cascade into higher vertical wavenumbers.      

Systematic tuning of dispersion models for simulation of evaporating sprays

In this study, via an Eulerian–Lagrangian framework, the performance of two recent dispersion models, i.e. a first-order autoregressive process and the PDF model, is compared. The appropriate relations for the turbulence scales and the drift correction term are suggested and the tuned values for the constants of the models are proposed in a systematic approach by starting with the simplest case, i.e. particle-laden stationary isotropic turbulence and adding more complexities in the subsequent cases, including the homogeneous anisotropic shear flow, decaying grid turbulence, and inhomogeneous gas–solid spray. Also, the isotropic relation for the effect of inertia in the Lagrangian turbulence time scale seen by particles is extended to the anisotropic case while it remains consistent in the isotropic limit. Finally, the performance of the tuned models is evaluated for the simulation of an evaporating spray. It is observed that, the tuned constants for the evaporating spray are close to the ones obtained for the homogeneous shear flow.     

Direct Numerical Simulation of Statistically Stationary One- and Two-Phase Turbulent Combustion: A Turbulent Injection Procedure

A new turbulent injection procedure dedicated to fully compressible direct numerical simulation (DNS) or large eddy simulation (LES) solvers is proposed. To avoid the appearance of spurious acoustic waves, this method is based on an accurate tracking of the turbulent structures crossing the boundary at the inlet of the domain. A finite difference DNS solver has been coupled with a spectral simulation in which a statistically stationary homogeneous turbulence evolves to provide fluctuating boundary conditions.A new turbulence forcing method, dedicated to spectral solvers, has been developed as well to control the major properties of the injected flow (turbulent kinetic energy, dissipation rate and integral length scale). One-dimensional Navier–Stokes characteristic boundary conditions extended to non-stationary flows are coupled with the injection procedure to evaluate is potential in four various configurations: spatially decaying turbulence, dispersion of vaporizing sprays, propagation of one- and two-phase V-shape turbulent flames.     

Un opérateur de diffusion spatialement sélectif pour le transport d'un traceur passif ou actif par un écoulement de grande échelle

In a fluid flow, fields are measurable up to a cut-off scale at which they are regularized. We show that, for a smooth velocity field, this regularization adds to the advection equation a diffusive term proportional to the strain tensor. We study in two dimensions its effect on the dynamics of velocity and vorticity, and on the conservation of quadratic invariants. Vorticity and energy are still conserved, while enstrophy and tracer variance are dissipated depending on the flow topology. These properties (conservation, dissipation, spatial selectivity) suggest the use of this selective strain–diffusion operator for numerical simulations of inhomogeneous flows in the quasi-two-dimensional approximation.     

从光闪烁频谱反演大气湍流谱:原理与数值模拟

建立了一种数值算法,从光波在湍流大气中传播的闪烁时间频谱的高频特征反演大气光学湍流谱.此算法具有两点优越性:（1）反演出的湍流谱直接表征大气折射率的起伏而非大气温度场的起伏;（2）可以获得高空间波数、大部分位于耗散区的湍流谱,而用其它方法不易获得此区域的湍流谱.对Hill湍流谱以及一种复杂的湍流谱进行了大量数值模拟来检验此种算法,结果表明:如果知道大气风速与湍流内尺度就可以相当有效地获得湍流谱.     

网格湍流微结构的实验研究

本文试验研究了网格湍流从前期到后期整个连续衰变过程即湍能和Taylor微尺度随时间的变化规律,以及高阶速度相关系数的变化规律,试验结果是在一个低湍流度、低速风洞内,用TSI热线风速仪测得的,而拟均匀各向同性湍流是用在风洞试验段入口处加网格产生的,本文的试验结果与文献[1]提出的涡旋结构理论的计算结果做了比较,发现理论计算的和曲线与本文实测值非常吻合,本文的实测结果与Townsendt早年的试验以及Beanett七十年代末的试验也做了比较。结果表明,这些试验结果彼此也很一致,因而,所有这些试验结果与理论计算值都相互获得了验证。     

体育场环状悬挑屋盖脉动风压数值模拟

本文提出了预测悬挑屋盖上脉动风压的实用方法,用数值模拟中稳态计算得到的平均压力、平均速度和湍动能的分布计算大跨屋盖的脉动风压。以昆山体育场为例,通过数值模拟的平均压力系数、湍动能分布及脉动风压与风洞实验结果的比较,验证了用数值模拟方法预测环状悬挑屋盖脉动风压的有效性,并建议了需选用的合适湍流模型和参考点的风速。     

The experimental results of micro-structure in grid-produced turbulence

The variation of main turbulent quantities in an isotropic turbulent flow, such as the decay of turbulent energy and the variation of Taylor microscale of turbulence with time are obtained, by employing a hot-wire anemometer and a nearly isotropic turbulent flow which is produced by a gridscreen located at the entrance of the test section in a low-level turbulence and low-speed wind tunnel in Peking University. The experimental results of the decay of turbulent energy and the variation of Taylor microscale of turbulence with time at the whole period from initial to final stage, normalized in an non-dimensional form, are consistent quite well with the computational results by the theory of the statistical vorticity structure^[1]. The experimental results presented in this paper also agree with Townsend's results obtained in earlier years^[2] as well as with Bennett's in the seventy's^[3].