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].     

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。     

Creating homogeneous and isotropic turbulence without a mean flow

A novel method of creating homogeneous and isotropic turbulence with small mean flow has been developed. Eight synthetic jet actuators on the corners of a cubic chamber can create energetic turbulence with root-mean-square (rms) velocities as large as 0.87 m/s, corresponding to a Taylor microscale Reynolds number, Re , of 218. Stationary turbulence results show that the turbulence was isotropic, with the rms velocity ratio equal to 1.03, and also homogeneous within the region of interest. Natural decaying turbulence measurements confirmed the power-law decay of the turbulent kinetic energy, with the decay exponent n equal to 1.86 for an initial Re of 224.     

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.     

Decaying turbulence in a passive mean scalar gradient

We consider the generation of passive scalar fluctuations by decaying isotropic turbulence in the presence of a uniform mean scalar gradient. At high Reynolds numbers, two distinct similarity states may be established depending on the form of the energy spectrum at low wavenumber magnitude (k). In the first similarity state characterized by a low wavenumber magnitude energy spectrum proportional tok ², the mean-square scalar fluctuation grows liket ^4/5, while in the second similarity state characterized by a spectrum proportional tok ⁴, the mean-square scalar fluctuation grows approximately liket ^4/7. These two high Reynolds number asymptotic similarity states have been subsequently confirmed by large-eddy numerical simulations. As a consequence of the decreasing flow Reynolds number as the turbulence decays, these similarity states do not continue indefinitely. At very long times, a final period of decay of the turbulence occurs, and in this final period, the mean-square scalar fluctuation in the first state continues to grow liket ^1/2, while that in the second state ultimately decays liket ^–1/2.     

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.     

Performance of a probe for measuring turbulent energy and temperature dissipation rates

A probe consisting of four X-wires (a total of eight hot wires operated in constant temperature mode) and two pairs of parallel cold wires (operated in constant current mode) is in principle capable of providing simultaneous data for the instantaneous energy and temperature dissipation rates. To evaluate the performance of this probe, measurements have been made in decaying turbulence downstream of a grid/screen combination. The directly measured mean values of the energy and temperature dissipation rates are compared with those obtained from the streamwise decay rates of the mean turbulent energy and temperature variance. The probe also yields all three fluctuating vorticity components; after applying spatial resolution corrections, their spectra are in close agreement with isotropic calculations over nearly all wavenumbers. Both the vorticity variance and the mean energy dissipation rate exhibit the same power-law decay rate. Transport equations for the mean energy and temperature dissipation rates are satisfied to within ᆞ%.     

Dynamic coefficient evaluation for an algebraic subgrid stress model

Static model coefficients for an algebraic subgrid stress (SGS) model are determined using a dynamic approach, based on results from simulations of isotropic decaying turbulence. The study was motivated by the discrepancies in energy transfer predictions using the previously documented coefficients (Bhushan and Warsi, Int. J. Numer. Meth. Fluids 2005; 49 : 489–519). The discrepancies are identified to be due to inconsistent filter functions used in the analytic estimates and the simulations. The study emphasizes that SGS model development should use filter functions compatible with those inherent in CFD application solvers. The dynamic approach predicts consistent model and transfer coefficients for different grid resolutions and is judged to be a reliable basis for model coefficient adjustments. The predicted Leonard's stress coefficient and associated energy transfer coefficients agree very well with the analytic estimates using a Gaussian/cutoff combination filter. This suggests that the modeling of Leonard's stress term using a truncated Taylor series expansion is robust and may not benefit significantly from dynamic modeling. Validation simulations were performed for turbulent channel flow at Re_τ = 180 and 590. The dynamic approach was found to be reliable only for the lower log‐layer of the Re_τ = 590 case, where the scale invariance condition was satisfied. Nonetheless, in this narrow range, the model and transfer coefficients compare well with the isotropic case. The static coefficient algebraic model with new adjusted coefficients shows improved predictions compared with the previous coefficients, for both isotropic decaying turbulence and channel flow cases. Copyright © 2013 John Wiley & Sons, Ltd.     

Hybrid URANS/LES Turbulence Simulation of Vortex Shedding Behind a Triangular Flameholder

In this study a detached eddy simulation (DES) model, which belongs to the group of hybrid URANS/LES turbulence models, is used for the simulation of vortex shedding behind a triangular obstacle. In the near wall region or in regions where the grid resolution is not sufficiently fine to resolve smaller structures, the two-equation RANS shear-stress transport (SST) model is used. In the other regions with higher grid resolution a LES model, which uses a transport equation for the turbulent subgrid energy, is applied. The DES model is first investigated for two standard test cases, namely decaying homogeneous isotropic turbulence and the backward facing step, respectively. For the decaying homogeneous isotropic turbulence test case the evolution of the energy spectra in wavenumber space for different times are studied for both the DES and a Smagorinsky type LES model. Different grid resolutions are analyzed with a special emphasis on the modeling constant connecting the filter length scale to the grid size. The results are compared to experimental data. The backward facing step test case is used to study the model behavior for a case with a transition region between a RANS modeling approach close to the wall and LES based modeling in the intense shear flow region. The final application is the simulation of the vortex shedding behind a triangular obstacle. First, the influence of the inlet condition formulation is studied in detail as they can have a significant influence especially for LES based models. Detailed comparisons between simulation and experiment for the flow structure past the obstacle and statistical quantities such as the shedding frequency are shown. Finally the additional temporal and spatial information provided by the DES model is used to show the predicted anisotropy of turbulence.     

Velocity fidelity of flow tracer particles

Recent developments concerning the unsteady dynamic forces on a spherical particle at finite Reynolds number are reviewed for solid particles and clean micro-bubble. A particle frequency :response function and an energy transfer function are derived for a solid particle or a contaminated micro-bubble in gas or liquid flow. A simple, unified method for estimating the cut-off frequency, or cut-off size, of a solid particle or a contaminated bubble is developed. Particle motion in isotropic turbulence is examined. Responses of the tracer particle to integral length scale structure, to turbulence energy, and to Taylor micro-scale structure are discussed in terms of the particle turbulence diffusivity, the particle turbulence intensity, and the ensemble average of the second invariant of fluid turbulence deformation tensor evaluated on the particle trajectory.The author is grateful to R. J. Adrian and C. Kent for their encouragement and support in writing this paper. This work is supported by the Engineering Research Center (ERC) for Particle Science and Technology at the University of Florida, the National Science Foundation (EEC-9402989), and industrial partners of ERC.     

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     

A novel tethered-sphere add-on to enhance grid turbulence

The new turbulence generator consists of a standard uniform grid with tethered spheres attached to its nodes and is capable of producing approximately twice the turbulence energy per unit pressure drop coefficient C _p than the same bare grid without the spheres. At the same time, the Reynolds number Re_λ based on the Taylor microscale is also amplified by a factor of roughly 2, and the turbulence anisotropy is reduced to a constant level of 10% at all downstream distances without further flow conditioning after the grid. The new grid’s simple design makes it suitable for a variety of fluid-flow facilities, in particular smaller water tunnels. Its performance in comparison with the plain grid is documented by measurements of the streamwise decay of turbulence energy and velocity spectra in the Re_λ range of 50–100.     

Comparison of turbulence length scales assessed with three measurement systems in increasingly complex turbulent flows

This paper proposes to compare turbulence length scales measured with three different experimental systems commonly used in aerodynamic measurements, namely hot wire anemometer, Laser Doppler Velocimetry and Particle Image Velocimetry, using turn-key systems from Dantec and TSI, and for three different turbulent flows: a homogeneous and isotropic turbulent flow, a homogeneous shear flow and the wake of a porous disc.This study will show that Taylor macro scale assessment is not clearly dependent on the experimental system used, except for nonconstant shear, where the measurement volume size seems to be a critical parameter. On the other hand, Taylor micro-scale is highly dependent on the space or time resolution of the correlation and on the presence of random measurement noise. Among the three systems, only the hot wire anemometer seems to provide the right requirements to properly assess the Taylor micro-scale.     

Direct numerical simulation of modulation of isotropic turbulence by poly‐dispersed particles

A direct numerical simulation technique based on two‐way coupling is presented to study a particle‐laden, decaying isotropic turbulent flow. Physical characteristics of turbulence modulation because of the mono‐dispersed (i.e., particles with single Stokes number) and poly‐dispersed particles (i.e., particles with more than one Stokes number) were investigated. A scale dependent effective viscosity that summarizes the aspects of the interaction between the velocity field and particles is defined in the study. Particles of Stokes number (St) 3.2,6.4 and 12.8 were used in performing the simulations. Poly‐dispersed particles were acquired by mixing particles of two different Stokes numbers at a time. As a whole, decay of turbulence because of the poly‐dispersed particles is observed to be larger than that of the decay of turbulence because of the mono‐dispersed particles. Simulations of poly‐dispersed particle indicate nonlinear characteristics in the modification of the temporal evolution of turbulence energy and dissipation. The scale dependent effective viscosity, which correlates with the energy spectrum plot, indicates that the decay of turbulence is mostly observed at the intermediate scales of turbulence. The effective viscosity for the simulations of the poly‐dispersed particles was calculated to be higher than that of the simulations of the mono‐dispersed particles. Copyright © 2011 John Wiley & Sons, Ltd.     

A finite volume approach to large eddy simulation of compressible,homogeneous, isotropic,decaying turbulence

Large eddy simulation of compressible, homogeneous, isotropic, decaying turbulence in a rectangular box is performed using finite volume techniques. An analysis of the energy spectra obtained from the simulations shows that an agreement with the Kolmogorov law for the inertial range is found only when an appropriate spatial discretization method is used. This agreement is obtained both for a low (0·05) and a moderate (0·6) Mach number when Smagorinsky's subgrid model is employed.     

Resolution-optimised nonlinear scheme for secondary derivatives

A 5-point-stencil optimised nonlinear scheme with spectral-like resolution within the whole wave number range for secondary derivatives is devised. The proposed scheme can compensate for the dissipation deficiency of traditional linear schemes and suppress the spurious energy accumulation that occurs at high wave numbers, both of which are frequently encountered in large eddy simulation. The new scheme is composed of a linear fourth-order central scheme term and an artificial viscosity term. These two terms are connected by a nonlinear weight. The proposed nonlinear weight is designed based on Fourier analysis, rather than Taylor analysis, to guarantee a spectral-like resolution. Moreover, the accuracy is not affected by the optimisation, and the new scheme reaches fourth-order accuracy. The new scheme is tested numerically using the one-dimensional diffusion problem, one-dimensional steady viscous Burger’s shock, two-dimensional vortex decaying, three-dimensional isotropic decaying turbulence and fully developed turbulent channel flow. All the tests confirm that the new scheme has spectral-like resolution and can improve the accuracy of the energy spectrum, dissipation rate and high-order statistics of turbulent flows.     

Assessment of Five SGS Models for Low-Rem MHD Turbulence

Assessment of three regularization-based and two eddy-viscosity-based subgrid-scale (SGS) turbulence models for large eddy simulations (LES) are carried out in the context of magnetohydrodynamic (MHD) decaying homogeneous turbulence (DHT) with a Taylor scale Reynolds number (Re_λ) of 120 and a MHD transition-to-turbulence Taylor-Green vortex (TGV) problems with a Reynolds number of 3000, through direct comparisons to direct numerical simulations (DNS). Simulations are conducted using the low-magnetic Reynolds number approximation (Re_m<<1). LES predictions using the regularization-based Leray- α,LANS- α, and Clark- α SGS models, along with the eddy viscosity-based non-dynamic Smagorinsky and the dynamic Smagorinsky models are compared to in-house DNS for DHT and previous results for TGV. With regard to the regularization models, this work represents their first application to MHD turbulence. Analyses of turbulent kinetic energy decay rates, energy spectra, and vorticity fields made between the varying magnetic field cases demonstrated that the regularization models performed poorly compared to the eddy-viscosity models for all MHD cases, but the comparisons improved with increase in magnitude of magnetic field, due to a decrease in the population of SGS eddies within the flow field.     

均匀各向同性湍流的频率波数能量谱

对均匀各向同性湍流的频率波数能量谱进行了初步研究，得出均匀各向同性湍流中能量随时间、空间尺度分布的解析表达式，并运用直接数值模拟的方法对理论预测进行验证．数值结果很好地支持了理论预测：横扫速度是决定频率波数能量谱的特征量．     

Corrections for underresolved scalar measurements in turbulent flows using a DNS database

We estimate the effect of finite spatial resolution of a probe for scalar measurements, using a database from direct numerical simulations (DNS). These are for homogeneous isotropic turbulence in temporal decay, Schmidt number unity, and low Taylor-microscale Reynolds number (≃27–42). The probe could be a cold wire for measuring temperature in a turbulent flow. Correction factors for the scalar variance, scalar dissipation rate, and mixed velocity-scalar derivative skewness are estimated, for a sensor length up to 15 times the Batchelor length scale. It is shown that the lack of resolution yields the largest attenuation on the dissipation rate, followed by the scalar variance. On the contrary, the mixed skewness, which is affected the least, is overestimated. Further, it is shown that if one estimates the mixed skewness via the scalar variance dynamical equation and neglects the term involving the time derivative of the scalar energy spectrum, large errors in the correction factor of the mixed skewness are introduced. Finally, it is found that correction factors obtained assuming Kraichnan scalar model spectrum and following Wyngaard (in Phys Fluids 14:2052–2054, 1971) approach are close to those from the DNS.     

Dynamic Model for LES Without Test Filtering: Quantifying the Accuracy of Taylor Series Approximations

The dynamic model for large-eddy simulation (LES) of turbulent flows requires test filtering the resolved velocity fields in order to determine model coefficients. However, test filtering is costly to perform in LES of complex geometry flows, especially on unstructured grids. The objective of this work is to develop and test an approximate but less costly dynamic procedure which does not require test filtering. The proposed method is based on Taylor series expansions of the resolved velocity fields. Accuracy is governed by the derivative schemes used in the calculation and the number of terms considered in the approximation to the test filtering operator. The expansion is developed up to fourth order, and results are tested a priori based on direct numerical simulation data of forced isotropic turbulence in the context of the dynamic Smagorinsky model. The tests compare the dynamic Smagorinsky coefficient obtained from filtering with those obtained from application of the Taylor series expansion. They show that the expansion up to second order provides a reasonable approximation to the true dynamic coefficient (with errors on the order of about 5% for c _s ²), but that including higher-order terms does not necessarily lead to improvements in the results due to inherent limitations in accurately evaluating high-order derivatives. A posteriori tests using the Taylor series approximation in LES of forced isotropic turbulence and channel flow confirm that the Taylor series approximation yields accurate results for the dynamic coefficient. Moreover, the simulations are stable and yield accurate resolved velocity statistics. Received 20 February 2001 and accepted 24 July 2001