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.     

Turbulence modeling for the axially rotating pipe from the viewpoint of analytical closures

A single-point model eddy viscosity model of rotation effects on the turbulent flow in an axially rotating pipe is developed based on two-point closure theories. Rotation is known to impede energy transfer in turbulence; this fact is reflected in the present model through a reduced eddy viscosity, leading to laminarization of the mean velocity profile and return to a laminar friction law in the rapid rotation limit. This model is compared with other proposals including linear redistribution effects through the rapid pressure-strain correlation, Richardson number modification of the eddy viscosity in a model of non-rotating turbulence, and the reduction of turbulence through the suppression of near-wall production mechanisms. PACS 47.27.Eq, 47.32.-y     

湍流基础问题研究进展:能量传递,相互作用尺度,各向同性衰减的自保持性

为了更深入地了解湍流的物理过程,本文综述了各向同性湍流的基础问题．在评述了Ｋｏｌｍｏｇｏｒｏｖ能谱及能量级串过程后,深入讨论了Ｋｏｌｍｏｇｏｒｏｖ局部各向同性假设．接着综述了涉及能量传递的以及包括三元组相互作用的各向同性湍流相互作用尺度的详细物理过程．还讨论了惯性区、自相似性以及小尺度对大尺度各向异性的响应和末期衰减过程．之后为了举例说明这些论点,详细讨论了根据各向同性湍流直接模拟及大涡模拟得到的结果（包括对亚格子模型的讨论）.最后,综述了各向同性湍流的自保持性,并展望了今后的研究方向．文末列出了１５５篇参考文献     

High resolution DNS of shear-convective turbulence and its implications to second-order parameterizations

Shear-convective turbulence is studied using a high resolution 3D direct numerical simulation (DNS). Flow configuration consisting of a modeled jet capping a thermally unstable layer is simulated and the results are compared with the reference situation where only the convective layer is present. Quasi-equilibrium turbulent datasets, in which the turbulent energy budgets are nearly balanced, are obtained. A mechanical barrier is identified near the jet centerline in the shear-convective case. Intense and elongated vorticity regions are created in a narrow layer above the barrier in a way similar to the shear-sheltering effect. Vertical profiles of turbulence statistics and budgets are presented. We have unambiguously identified layers of counter-gradient momentum and heat fluxes which occur near regions of penetrative convection. Using quasi-equilibrium DNS datasets, we evaluate the performance of some popular second-order closure models of turbulence. The models satisfactorily predict the triple moments and dissipation, except in the counter-gradient region. The models, however, fail to predict the pressure correlation terms. Dedicated to Professor Charles SpezialePACS 92, 47.27     

On the evolution of decaying isotropic turbulence

A direct numerical simulation is performed on 256³ grids for decaying isotropic turbulence. The total kinematic energy, Taylor micro-scale, Taylor micro-scale Reynolds number and the velocity derivative skewness are calculated. The snapshots of energy spectra and energy transfer spectra are plotted. These measurements verify the DIA predictions: decaying isotropic turbulence has the energy propagation and occupies the final decay periods. The skewness remains to some level with small variation even in the final decay period.     

Gas turbulence modulation in the pneumatic conveying of massive particles in vertical tubes

The present work is concerned with the interaction between large particles and gas phase turbulence. Gas turbulence modulation in these systems is considered to be dominated by a generation mechanism which arises due to the presence of wakes behind particles. Following a recent proposal, a closure for gas turbulence modulation accounting for the effect of wakes is employed within the context of a mathematical model for particle-laden, turbulent flows. The model accounts for particle particle and particle-wall interactions associated with larger particles based on concepts from gas kinetic theory. It is shown that due to the significant flattening of the mean gas velocity profile with the addition of particles, and the corresponding decrease in turbulent energy production, a generation mechanism must be present in order to produce gas velocity fluctuation predictions which are consistent with the experimental measurements, even in the case where the experimental results indicate a net suppression of gas phase turbulence in the presence of particles.     

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.     

On pre-dissipative ‘bumps' and a Reynolds-number-dependent spectral parameterization of turbulence

Considerable experimental, numerical and theoretical evidence has accumulated during the last two decades for the presence of a maximum above the right end of the inertial plateau in compensated high-Reynolds-number turbulence spectra k^+5/3E(k). This energy pileup, due to the reduced nonlocal triadic interactions near the viscous cut-off, complies with Kolmogorov's 1941 theory but hampers experimental interpretation about its intermittency corrections. It has been included in a semi-empirical Reynolds-number-dependent complete (i.e. from the largest to the smallest scales) spectral model of isotropic turbulence. This simple parameterization is shown to represent satisfactorily well experimental data over a large variety of situations.     

激波和湍流相互作用的数值模拟

本文综述了关于激波和湍流相互作用数值模拟的近期研究进展, 主要包括激波和均匀各向同性湍流、激波和湍流边界层、激波和射流以及激波和尾迹的相互作用. 激波和湍流相互作用特性受到诸多因素的影响,如激波的强度、位置、形状和流动边界以及来流的湍流状态和可压缩性等. 激波和湍流的相互作用会引起流场结构、激波特性和湍流统计特性的显著变化. 最后简要讨论了激波和湍流相互作用数值研究需要关注的一些问题.      

Numerical simulation of expansion/compression effect on shock induced turbulent flow

The interaction of homogeneous and isotropic turbulence with a shock wave is observed by solving the Reynolds-averaged Navier–Stokes equations with the k–? turbulence model. All turbulent fluctuations are measured at the period of expansion in the turbulent field and during compression by the reflected shock on turbulent field, and it is observed that the longitudinal turbulent velocity fluctuation is enhanced more at the period of expansion due to incident shock wave movement far from the turbulent field. The amplification of the turbulent kinetic energy (TKE) level in the shock/turbulence interaction depends on the shock wave strength and the longitudinal velocity difference across the shock wave. On decreasing the longitudinal velocity difference across the shock, the turbulent kinetic energy (TKE) level is less amplified. The TKE level is amplified by the factor of 1.5–1.8 in the shock/turbulence interaction where the dissipation rate of TKE decreases in all cases of shock/turbulence interaction. After the shock/turbulence interaction, the turbulent dissipative-length scale is amplified slightly and the amplification of the length scales decreases when increasing the shock strength. To cite this article: M.A. Jinnah, K. Takayama, C. R. Mecanique 333 (2005).     

An analysis of subgrid-resolved scale interactions with use of results from direct numerical simulations

Subgrid nonlinear interaction and energy transfer are analyzed using direct numerical simulations of isotropic turbulence. Influences of cutoff wave number at different ranges of scale on the energetics and dynamics have been investigated. It is observed that subgrid-subgrid interaction dominates the turbulent dynamics when cut-off wave number locates in the energy-containing range while resolved-subgrid interaction dominates if it is in the dissipation range. By decomposing the subgrid energy transfer and nonlinear interaction into ‘forward’ and ‘backward’ groups according to the sign of triadic interaction, we find that individually each group has very large contribution, but the net of them is much smaller, implying that tremendous cancellation happens between these two groups.     

A two-scale second-moment turbulence closure based on weighted spectrum integration

A two-scale second-moment turbulence closure has been derived based on the weighted integration of the dynamic equation for the covariance spectrum. The goal is to close the Reynolds stress equations with two additional scalar equations that provide separately the scales of the spectral energy transfer and of the turbulence energy dissipation rate. Such a model should provide better prediction of nonequilibrium turbulent flows. The derivation consists of analytical integration of the wave-number-weighted covariance spectrum using a model of the spectral equations with an assumed simple representation of the shape of the energy spectrum. The resulting closure consists of a set of three tensorial equations, one for the Reynolds stress and two for length scale tensors, the latter representing the energy containing- and dissipative eddies respectively. The trace of the two tensor-scale equations leads to a set of two scalar scale parameters. In the equilibrium limit, the model reduces to the standard second-moment single-scale closure. The approach makes it also possible to derive the scale equations in a more systematic manner as compared with the common single-scale and other multi-scale models. The performance of the model in capturing the scale dynamics is illustrated by predictions of several generic homogeneous and inhomogeneous unsteady flows, demonstrating the expected response of the two scale equations. PACS 03.50.De, 04.20-q, 42.65-k     

From single-scale turbulence models to multiple-scale and subgrid-scale models by Fourier transform

A theoretical method based on mathematical physics formalism that allows transposition of turbulence modeling methods from URANS (unsteady Reynolds averaged Navier–Stokes) models, to multiple-scale models and large eddy simulations (LES) is presented. The method is based on the spectral Fourier transform of the dynamic equation of the two-point fluctuating velocity correlations with an extension to the case of non-homogenous turbulence. The resulting equation describes the evolution of the spectral velocity correlation tensor in wave vector space. Then, we show that the full wave number integration of the spectral equation allows one to recover usual one-point statistical closure whereas the partial integration based on spectrum splitting gives rise to partial integrated transport models (PITM). This latter approach, depending on the type of spectral partitioning used, can yield either a statistical multiple-scale model or subfilter transport models used in LES or hybrid methods, providing some appropriate approximations are made. Closure hypotheses underlying these models are then discussed by reference to physical considerations with emphasis on identification of tensorial fluxes that represent turbulent energy transfer or dissipation. Some experiments such as the homogeneous axisymmetric contraction, the decay of isotropic turbulence, the pulsed turbulent channel flow and a wall injection induced flow are then considered as typical possible applications for illustrating the potentials of these models.      

Skewness factor of turbulent velocity derivative

Using nonequilibrium statistical mechanics closure method, it is shown that the skewness factor of the velocity derivative of isotropic turbulence approaches a constant −0.515 when the Reynolds number is very high, which is in agreement with the DNS (direct numerical simulation) result of Vincent and Meneguzzi (1991). The project supported by the National Basic Research Program “Non-linear Science”     

基于湍流类比的金属橡胶吸声特性定量分析

金属橡胶材料从表到里都具有大量互相贯通且混乱的孔隙, 经分析认为, 这种混乱性及一定的周期性与湍流中的不规则性和准周期性极其相似. 由于金属橡胶材料内部芯材结构的不规则性, 即便此时的雷诺数很小, 波在金属橡胶中的传播仍是以湍流流动为主. 因此, 引入Kolmogorov的关于湍流的局部各向同性概念, 同时对Kolmogorov关于湍流局部各向同性的两个假设进行类比. 从湍流物理模型出发, 借鉴了湍流的统计处理方法, 对金属橡胶材料的吸声特性进行定量分析, 得到金属橡胶材料的能量耗散率与其结构参数之间的表达式. 研究结果表明, 湍流统计方法的引入, 为基于金属橡胶材料的减振器、阻尼器、消声器等的优化设计提供了可靠的理论依据, 也为超轻金属多孔材料的工程应用提供了一种有效的定量分析方法.      

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.     

Two-phase turbulence models for simulating dense gas-particle flows

The two-fluid model is widely adopted in simulations of dense gas-particle flows in engineering facili- ties. Present two-phase turbulence models for two-fluid modeling are isotropic. However, turbulence in actual gas-particle flows is not isotropic. Moreover, in these models the two-phase velocity correlation is closed using dimensional analysis, leading to discrepancies between the numerical results, theoretical analysis and experiments. To rectify this problem, some two-phase turbulence models were proposed by the authors and are applied to simulate dense gas-particle flows in downers, risers, and horizontal channels; Experimental results validate the simulation results. Among these models the USM-O and the two-scale USM models are shown to give a better account of both anisotropic particle turbulence and particle-particle collision using the transport equation model for the two-phase velocity correlation.     

Energy dynamics in a turbulent channel flow using the Karhunen‐Loéve approach

The dynamical equations for the energy in a turbulent channel flow have been developed by using the Karhunen‐Loéve modes to represent the velocity field. The energy balance equations show that all the energy in the flow originates from the applied pressure gradient acting on the mean flow. Energy redistribution occurs through triad interactions, which is basic to understanding the dynamics. Each triad interaction determines the rate of energy transport between source and sink modes via a catalyst mode. The importance of the proposed method stems from the fact that it can be used to determine both the rate of energy transport between modes as well as the direction of energy flow. The effectiveness of the method in determining the mechanisms by which the turbulence sustains itself is demonstrated by performing a detailed analysis of triad interactions occurring during a turbulent burst in a minimal channel flow. The impact on flow modification is discussed. Copyright © 2002 John Wiley & Sons, Ltd.     

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].