Lagrangian Time-Scales in Homogeneous Non-Gaussian Turbulence

Lagrangian time-scales in homogeneous non-Gaussian turbulence were studied using a one-dimensional Lagrangian Stochastic Model. The existence of two time-scales τ _L and T _L , one typical of the inertial subrange and the other which is an integral property, is outlined. Variations of the ratio T _L /τ _L in the plane skewness-flatness (S, F) are shown and a connection with the statistical constraint F ≥S ² + 1 is evidenced. The Lagrangian autocorrelation function ρ(t) of particle velocity was computed for some values of (S, F). It is shown that for small times, say t < T _L , the influence of non-Gaussianity is negligible and ρ(t) presents the same behaviour as in the Gaussian case regardless of variations in (S, F).As the time increases, departures from Gaussianity are observed and autocorrelation turns out to be always larger than in the Gaussiancase. This is supported by some considerations in terms of information entropy, which is shown to decrease with increasing departures from Gaussianity. Spectral analysis of Lagrangian velocity shows that non-Gaussianity is relevant only to large scales of the stochastic process and that the expected inertial subrange decay ω⁻² is attained by spectra of all simulations, except for one case in which the model probability density function is bimodal, due to the vicinity to the statistical limit. This revised version was published online in July 2006 with corrections to the Cover Date.     

Renormalization Group Model of Large-Scale Turbulence in Porous Media

Renormalization group methods are used to develop a macroscopic (large-scale) turbulence model for incompressible flow in porous media. The model accounts for the large-distance and large-time behavior of velocity correlations generated by the momentum equation for a randomly stirred, incompressible flow. Utilizing the renormalization procedure, the transport equations for the large-scale modes and expressions for effective transport coefficients are obtained. Expressions for renormalized turbulent viscosity, which accounts for the ultraviolet subrange of the turbulent kinetic energy spectrum, are also obtained.     

From Two-Point Closures of Isotropic Turbulence to LES of Shear Flows

We first recall the EDQNM two-point closure approach of three-dimensional isotropic turbulence. It allows in particular prediction of the infrared kinetic-energy dynamics (with ak ₄ backscatter) and the associated time-decay law of kinetic-energy, useful in particular for one-point closure modelling. Afterwards, we show how the spectral eddy viscosity concept may be used for large-eddy simulations: we introduce the plateau-peak model and the spectral-dynamic models. They are applied to decaying isotropic turbulence, and allow recovery of the EDQNM infrared energy dynamics. Anew infrared k ₂ law for the pressure spectrum, predicted by the closure, is also well verified. Assuming that subgrid scales are not too far from isotropy, the spectral-dynamic model is applied to the channel flow at h ₊= 390, with statistics in very good agreement with DNS, while reducing considerably the computational time. We study with the aid of DNS and LES the case of the channel rotating about an axis of spanwise direction. The calculations allow to recover the universal linear behaviour of the mean velocity profile, with a local Rossby number equal to −1. We present also LES (using the Grenoble Filtered Structure-Function Model), of a turbulent boundary layer passing over a cavity. Finally, we make some remarks on the future of LES for industrial applications. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

各向同性湍流内颗粒碰撞率的直接模拟研究

对 Re_{\lambda } 约为51均匀各向同性湍流内 St_{k}(=\tau_{p}/\tau_{k}) 为 0 ~10.0 的 有限惯性颗粒的碰撞行为进行了直接数值模拟，以研究湍流对有限惯性 颗粒碰撞的影响. 结果表明，具有一定惯性颗粒的湍流碰撞率完全不同于零惯性的轻颗粒 (St_{k}=0) 和可忽略湍流作用的重颗粒 (St{k} \to \infty) , 其变化趋势极其复杂： 在Stk为 0~1.0 之间，颗粒的碰撞率随 St 的增加而近乎线性地剧烈增长，在 Stk≈1.0 3.0(对应的StE=τp/Te≈0.5)附近，颗粒碰撞率出现两个峰值，在Stk>3.0以后，颗粒的碰撞率随惯性增 大而逐渐趋向于重颗粒极限；在峰值处，有限惯性颗粒的平均碰撞率的峰值较轻颗粒增强了 30倍左右. 为进一步分析湍流作用下颗粒碰撞率的影响因素，分别使用可能发生碰撞 的颗粒对的径向分布函数和径向相对速度来量化颗粒的局部富集效应和湍流掺混效应，表明 St_{k} \approx 1.0 时局部富集效应最为强烈，使得颗粒的碰撞率出现第1个峰值； 湍流掺混效应则随着颗粒Stk的增大而渐近增大；局部富集和湍流掺混联合作用的结果， 使得颗粒碰撞率在 St_{k} \approx 3.0 附近出现另一个峰值.     

Numerical Simulation of Isotropic Turbulence Dynamics

The Karman-Howarth closed equation is used to describe the behavior of homogeneous isotropic turbulence. A numerical solution is obtained by the collocation-grid and finite-difference methods using moving grids. The predicted results are compared with experimental data on the decay of fully developed and weak turbulence. The numerical realization of the Loitsiansky-MilHonshtchikov asymptotic solution has been made.     

Particle Clustering in Isotropic Turbulent Flow

A kinetic statistical model for describing the dispersion and clustering of heavy particles in homogeneous isotropic turbulence is presented. The model developed is used for calculating the relative velocities and the radial distribution function of a pair of particles in a steady suspension. The results obtained are compared with the known data obtained by direct numerical simulation.     

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。     

Mixing in Isotropic Turbulence with Scalar Injection and Applications to Subgrid Modeling

A new technique for injecting scalar fluctuations in a DNS of isotropic turbulence is presented. It is used to study statistically steady states associated with different levels of mixing. The results are analysed in terms of spectra and PDF, and they are used as a database to investigate the effect of the filtering operation that is performed in LES. It is shown that the PDF of the scalar is substantially affected by the filtering operation. It is also shown that the Cook and Riley [1] subgrid model allows reconstruction of a PDF which is in fairly good agreement with the unfiltered DNS results. The consequences of estimating the scalar subgrid variance by scale similarity assumptions are investigated. It is found that the results are improved by a local determination of the model constant. This revised version was published online in July 2006 with corrections to the Cover Date.     

Reynolds Number Dependence of Energy Spectra in the Overlap Region of Isotropic Turbulence

A Near-Asymptotics analysis of the turbulence energy spectrum is presented that accounts for the effects of finite Reynolds number recently reported by Mydlarski and Warhaft [21]. From dimensional and physical considerations (following Kolmogorov and von Karman), proper scalings are defined for both low and high wavenumbers, but with functions describing the entire range of the spectrum. The scaling for low wavenumbers uses the kinetic energy and the integral scale, L, based on the integral of the correlation function. The fact that the two scaled profiles describe the entire spectrum for finite values of Reynolds number, but reduce to different profiles in the limit, is used to determine their functional forms in the “overlap” region that both retain in the limit. The spectra in the overlap follow a power law, E(k) =Ck _{−5/3 + μ}, where μ and C are Reynolds number dependent. In the limit of infinite Reynolds number, μ → 0 and C → constant, so the Kolmogorov/Obukhov theory is recovered in the limit. Explicit expressions for μ and the other parameters are obtained, and these are compared to the Mydlarski/Warhaft data. To get a better estimate of the exponent from the experimental data, existing models for low and high wavenumbers are modified to account for the Reynolds number dependence. They are then used to build a spectral model covering all the range of wavenumbers at every Reynolds number. Experimental data from grid-generated turbulence are examined and found to be in good agreement with the theory and the model. Finally, from the theory and data, an explicit form for the Reynolds number dependence of φ = ɛL/u ₃ is obtained. This revised version was published online in July 2006 with corrections to the Cover Date.     

初期Taylor弥散实验观察

本文利用激波管所能产生的瞬时定常流场,观察了一种具有间断初始密度分布的物质在这个流场中 Taylor 弥散过程.实验中所测量的物质,是空气中的 CO_2成份;测量手段是红外光谱吸收法;所观察到的过程发生在无量纲时间<0.07的范围内.实验数据与理论结果的比较表明:湍流 Taylor 弥散在初始阶段具有一定的对称性质.     

复合型紊流润滑理论模式的研究

对复合型紊流润滑理论模式和国际上通用的几种紊流润滑理论模式进行比较研究,针对纯Ｃｏｕｅｔｔｅ流动和兼有压力梯度与剪切运动的复杂流动２种流场,用各种紊流润滑模式进行计算分析,并与不同雷诺数下时均速度的现有试验数据对比,研究表明：与其它紊流模式比较,复合型紊流润滑模式能准确分析不同工况的流场,与试验数据最为吻合;在低雷诺数下,复合型紊流模式由于理论基础的坚实性,仍能很好地适用,当用于既有高雷诺数又有低     

两空泡运动特性研究

本文应用边界方法研究了两个相邻空泡的运动特性,得到了空泡的演化规律,以及空泡溃灭时的射流速度与溃灭时间的变化趋势,对于两个空泡之间的距离和半径比的影响进行了讨论。计算结果表明：不同大小的空泡在一起时则小泡会先溃灭,且人泡的存在时间与两泡的半径比成正比;大泡对小泡来说其作用相当于－固壁面,小泡会形成－指向大泡的溃灭射流。相同大小的空泡在一起溃灭时,会同时形成指向中间的射 流,与单空泡在固壁面附近的溃     

A New Low-Reynolds-Number One-Equation Model of Turbulence

In this study, we propose a new Low-Reynolds-Number (LRN)one-equation model, which is derived from an LRN two-equation(k-ε) model. The derivation of the transport equation, in principle, is based on the assumption that the turbulent structure parameter remains constant. However, the relation for the turbulent structure parameter a ₁(=|− |/k) is modified to account for near-wall turbulence. As a result, the present one-equation model contains a term which takes the near-wall limiting behavior explicitly into account. Thus, the present model provides the correct wall-limiting behavior of turbulence in the vicinity of the wall and can be applied to the analysis of heat transfer. The validity of the present model is tested in channel flows, boundary layer flows with and without pressure gradient, plane wall jet, and flow with separation and reattachment. The calculated results showed good agreement with the direct numerical simulation (DNS) and experimental data. This revised version was published online in July 2006 with corrections to the Cover Date.     

Dispersion and clustering of bidisperse particles in isotropic turbulence

A statistical kinetic model describing the dispersion and clustering of particles with different inertia in homogeneous turbulence is presented. The model developed is used for calculating the relative velocity, the radial distribution function, and the particle collision kernel in a stationary bidisperse suspension. The results obtained are compared with the data of a direct numerical simulation.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 94–107. Original Russian Text Copyright © 2005 by Alipchenkov and Zaichik.     

Modeling the Dynamics of Ensemble-Averaged Linear Disturbances in Homogeneous Shear Flow

In order to expand the predictive capability of single-point turbulence closure models to account for the early-stage transition regime, a methodology for the formulation and calibration of model equations for the ensemble-averaged disturbance kinetic energy and energy dissipation rate is presented. The calibration is based on homogeneous shear flow where disturbances can be described by rapid distortion theory (RDT). The relationship between RDT and linear stability theory is exploited in order to obtain a closed set of modeled equations. The linear disturbance equations are solved directly so that the numerical simulation yields a database from which the closure coefficients in the ensemble-averaged disturbance equations can be determined. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Stress State of a Transversely Isotropic Ferromagnetic with a Parabolic Crack in a Homogeneous Magnetic Field

The magnetoelastic problem for a transversely isotropic ferromagnetic body with a parabolic crack in the plane of isotropy is solved explicitly. The body is in an external magnetic field, which is perpendicular to the plane of isotropy. The field induces elastic strains and a magnetic field in the body. The characteristics of the stress–strain distribution and induced magnetic field are determined; and their singularities in the neighborhood of the crack are analyzed. Formulas for the stress intensity factors of the mechanical and magnetic fields near the crack tip are presented     

The Peculiar Dynamics of Cavitation Bubbles

Details from cavitation bubble dynamics are reported: jet formation, counterjet formation, shock wave radiation and light emission. Multiple shock wave radiation from single bubble collapse with jet formation could be time resolved by high speed photography with 20 million frames per second. An explanation of counterjet formation is given. Pictures of the light emission (sonoluminescence) in acoustic cavitation are presented.