A stability condition for turbulence model: From EMMS model to EMMS-based turbulence model

The closure problem of turbulence is still a challenging issue in turbulence modeling. In this work, a stability condition is used to close turbulence. Specifically, we regard single-phase flow as a mixture of turbulent and non-turbulent fluids, separating the structure of turbulence. Subsequently, according to the picture of the turbulent eddy cascade, the energy contained in turbulent flow is decomposed into different parts and then quantified. A turbulence stability condition, similar to the principle of the energy-minimization multi-scale (EMMS) model for gas–solid systems, is formulated to close the dynamic constraint equations of turbulence, allowing the inhomogeneous structural parameters of turbulence to be optimized. We name this model as the “EMMS-based turbulence model”, and use it to construct the corresponding turbulent viscosity coefficient. To validate the EMMS-based turbulence model, it is used to simulate two classical benchmark problems, lid-driven cavity flow and turbulent flow with forced convection in an empty room. The numerical results show that the EMMS-based turbulence model improves the accuracy of turbulence modeling due to it considers the principle of compromise in competition between viscosity and inertia.     

A stability condition for turbulence model： From EMMS model to EMMS-based turbulence model

The closure problem of turbulence is still a challenging issue in turbulence modeling. In this work, a stability condition is used to close turbulence. Specifically, we regard single-phase flow as a mixture of turbulent and non-turbulent fluids, separating the structure of turbulence. Subsequently, according to the picture of the turbulent eddy cascade, the energy contained in turbulent flow is decomposed into different parts and then quantified. A turbulence stability condition, similar to the principle of the energy-minimization multi-scale （EMMS） model for gas-solid systems, is formulated to close the dynamic constraint equa- tions of turbulence, allowing the inhomogeneous structural parameters of turbulence to be optimized. We name this model as the ＂EMMS-based turbulence model＂, and use it to construct the corresponding turbulent viscosity coefficient. To validate the EMMS-based turbulence model, it is used to simulate two classical benchmark problems, lid-driven cavity flow and turbulent flow with forced convection in an empty room, The numerical results show that the EMMS-hased turbulence model improves the accuracy of turbulence modeling due to it considers the principle of compromise in competition between viscosity and inertia.     

Constant Reynolds number turbulence downstream of an orificed perforated plate

Quasi-isotropic turbulence was experimentally produced in a wind tunnel via an orificed, perforated plate (OPP) at 10.5 m/s. The OPP consists of a lattice arrangement of 38.1 mm holes occupying 57% of the plate area. The OPP turbulence was found to be homogeneous over the cross section normal to the mean flow with Gaussian-like turbulence fluctuation. The isotropy of the turbulence field as portrayed by the streamwise/lateral turbulence intensity ratio was found to be approximately 1.1. The OPP turbulence is essentially self-preserving wherein the Taylor microscale Reynolds number remains nearly constant and the lateral velocity correlations collapse into a single curve.     

Modern turbulence and new challenges

The paper briefly reviews the progress in turbulence research in the 20th century and a number of issues are addressed based on achievements. The modern theroy of Navier-Stokes equation provides the theoretical basis for the development of turbulence research. The significance and bottle neck of DNS and the physical experiment in exploring turbulent flows are analyzed. The active manipulation of turbulence is directly guided by the knowledge of large-scale coherent structures. The existing problems in the large-eddy simulation are also pointed out. Scalar turbulence, which behaves quite different from fluid turbulence in many aspects, has drawn much attention in recent years. Besides the analysis of the difficulties in turbulence research, a number of examples are also presented to show how to use modern theory, computer and high technology to explore the nature of turbulence. The project supported by the National Natural Science Foundation of China (NSFC) (19572041 and 19732005)     

Numerical investigation of the flow and heat behaviours of an impinging jet

The flow and temperature fields of a turbulent impinging jet are rather complex. In order to accurately describe the flow and heat-transfer process, two important factors that must be taken into account are the turbulence model and the wall function. Several turbulence models, including κ–? turbulence models, κ–ω turbulence models, low-Re turbulence models, the κ–κ_l–ω turbulence model, the Transition SST turbulence model, the V2F turbulence model and the RSM turbulence model, are examined and compared to experimental data. Furthermore, for the near wall region, various wall functions are presented for comparison and they include the standard wall function, the scale wall function, the non-equilibrium wall function and the enhanced wall function. The distribution features of velocity, turbulent kinetic energy and Nusselt number are determined in order to provide a reliable reference for the multiphase impinging jet in the future.     

磁流体湍流及数值模拟研究综述

自从20世纪90年代初,AJAX计划的提出掀起了磁流体技术的研究热潮.本文总结了国内外关于磁流体湍流研究的成果,包括两方面:磁流体湍流的特点和数值模型.相比于普通湍流,磁流体湍流表现出电磁诱导的各向异性、线性焦耳耗散、湍流重层流化等特性,本文同时对磁流体湍流的结构和脉动抑制现象进行了描述:数值模型研究从雷诺平均方程和大涡模拟两方面作了介绍.当前研究集中在不可压缩磁流体湍流,距离能够应用于航空航天问题还有很长的路要走.     

Numerical simulation on compressible turbulence by spectral method

The numerical and physical issues of simulations on compressible turbulence are reviewed in the present paper. An outline of the global spectral methods and the progress of recent local spectral methods are illustrated. Several typical subjects in this field are studied, including homogeneous isotropic turbulence, autoignition in premixed turbulence, interaction between flames and turbulence, and shock wave in turbulence. The results of the numerical simulations are discussed, enabling us to discover and to understand the physical phenomena which have not been solved by experiments.     

Turbulence Intensity and Length Scale Effects on Premixed Turbulent Flame Propagation

The effects of varying turbulence intensity and turbulence length scale on premixed turbulent flame propagation are investigated using Direct Numerical Simulation (DNS). The DNS dataset contains the results of a set of turbulent flame simulations based on separate and systematic changes in either turbulence intensity or turbulence integral length scale while keeping all other parameters constant. All flames considered are in the thin reaction zones regime. Several aspects of flame behaviour are analysed and compared, either by varying the turbulence intensity at constant integral length scale, or by varying the integral length scale at constant turbulence intensity. The turbulent flame speed is found to increase with increasing turbulence intensity and also with increasing integral length scale. Changes in the turbulent flame speed are generally accounted for by changes in the flame surface area, but some deviation is observed at high values of turbulence intensity. The probability density functions (pdfs) of tangential strain rate and mean flame curvature are found to broaden with increasing turbulence intensity and also with decreasing integral length scale. The response of the correlation between tangential strain rate and mean flame curvature is also investigated. The statistics of displacement speed and its components are analysed, and the findings indicate that changes in response to decreasing integral length scale are broadly similar to those observed for increasing turbulence intensity, although there are some interesting differences. These findings serve to improve current understanding of the role of turbulence length scales in flame propagation.

     

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.     

Non-equilibrium turbulent phenomena in the ?ow over a backward-facing ramp

Non-equilibrium turbulence phenomena have raised great interests in recent years. Significant efforts have been devoted to non-equilibrium turbulence properties in canonical flows, e.g., grid turbulence, turbulent wakes, and homogeneous isotropic turbulence(HIT). The non-equilibrium turbulence in non-canonical flows, however, has rarely been studied due to the complexity of the flows. In the present contribution, a directnumerical simulation(DNS) database of a turbulent flow is analyzed over a backwardfacing ramp, the flow near the boundary is demonstrated, and the non-equilibrium turbulent properties of the flow in the wake of the ramp are presented by using the characteristic parameters such as the dissipation coefficient C and the skewness of longitudinal velocity gradient Sk, but with opposite underlying turbulent energy transfer properties. The equation of Lagrangian velocity gradient correlation is examined, and the results show that non-equilibrium turbulence is the result of phase de-coherence phenomena, which is not taken into account in the modeling of non-equilibrium turbulence. These findings are expected to inspire deeper investigation of different non-equilibrium turbulence phenomena in different flow conditions and the improvement of turbulence modeling.     

Experimental study of 3D turbulence by solving an inverse problem

The problem of the investigation of 3D turbulence from the projected data is studied here. It is shown that statistical information about turbulence can be recovered in such situations through a solution of an inverse problem. Unlike earlier papers, the adopted model of the turbulence envisages the turbulence characteristics to vary inside the 3D volume. Analytical solutions expressing turbulence characteristics (correlation functions, spectra) in terms of experimental data are found for this realistic model.     

On the effects of free-stream turbulence on axisymmetric disc wakes

Wind tunnel experiments have been used to study the effects of free-stream turbulence on the axisymmetric wake behind a disc. The disc and its wake were introduced to various turbulent streams having various levels of turbulence intensity and length scale. It was found that the presence of free-stream turbulence enhances the body??s drag and hence wake momentum deficit, if it is of sufficient strength, changes the far wake??s decay rate and prevents the appearance of self-similarity. The external turbulence causes a significant transformation in the wake??s turbulence structure. This gradually evolves towards the character of the free-stream turbulence itself and thus is characterised by much weaker turbulence (cross-stream) transport processes and a consequent dominance of shear stress production, which acts to maintain the shear stress and mean velocity profiles.     

Turbulence generation by electric body forces

The effect of an electric body force on vorticity production and turbulence generation in a gas is investigated by examination of the governing electrohydrodynamic equations. The theoretical concepts are illustrated by hot-film anemometer measurements of the electrically induced turbulence in a large scale electrostatic precipitator. The results indicate dramatic increases in turbulence and diffusivity due to the corona discharge and suggest that turbulence control in this application requires a modification in electrode geometry.This paper was presented at the Ninth symposium on turbulence, University of Missouri-Rolla, October 1–3, 1984     

关于植被中湍流的研究

本文从实验和模式理论两个方面介绍了近年来在植被湍流研究方面的进展.实验研究表明,植被内湍流是高度间歇性的,大尺度涡在湍流输运中起主导作用.植物枝、干、叶打碎了大尺度涡,产生的迹湍流中的小尺度涡更容易耗散成热。因此,植被内能量不按一般的能量级串理论预示的方式进行,而要发生所谓“短路”现象,使得功率谱曲线的斜率在惯性区比-2/3律更负.现有的高阶封闭模式虽然取得了很大成功,但在模拟湍流强度上高估了其大小,还需根据实验加以改进.      

Evaluation of bubble-induced turbulence using direct numerical simulation

The presented research evaluates the interaction between a single bubble and homogeneous turbulent flow using direct numerical simulation (DNS) approach. The homogeneous single-phase turbulence is numerically generated by passing a uniform flow through grid planes. The turbulence decay rate is compared with experiment-based correlation. The single phase turbulence is then used as an inflow boundary condition for a set of single bubble studies. By estimating the turbulent field around the fully resolved bubble, the effects of bubble deformability, turbulent intensity and relative velocity on the bubble-induced turbulence are investigated. The existence of bubble creates new vortices in the wake region and the enhancement of turbulence is observed in the region behind the bubble. The results show that the magnitude of the turbulence enhancement would increase as the bubble encounters larger liquid turbulent intensity or higher relative velocity. Set of bubble Weber numbers from 0.34 to 3.39 are used to investigate the effect of bubble deformability. The more deformable bubble is the higher the increase in the magnitude of the turbulence enhancement behind the bubble. This research provides systematic insight on the bubble-induced turbulence (BIT) mechanism and is important for multiphase computational fluid dynamics (M-CFD) closure model development.     

THE EXAMINATION OF TURBULENCE MODELING WITH LES DATABASE

ＴＨＥＥＸＡＭＩＮＡＴＩＯＮＯＦＴＵＲＢＵＬＥＮＣＥＭＯＤＥＬＩＮＧＷＩＴＨＬＥＳＤＡＴＡＢＡＳＥＳｕＭｉｎｇ－ｄｅ（苏铭德）（ＱｉｎｇｈｕａＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ）Ｒ．Ｆｒｉｅｄｒｉｃｈ（ＬｅｈｒｓｉｒｈｌｆｕｒＦｌｕｉｄｓｍｅｃｈａ...     

INTERNAL LEE WAVES AND TURBULENCE MIXING OVER AN ISOLATED SEAMOUNT: RESULTS FROM TURBULENCE ENERGY MODELS

A three-dimensional, primitive equation, baroclinic numerical model incorporating a range of turbulence energy submodels is used to study the generation of internal lee waves over an isolated seamount. Attention is given to the turbulence mixing enhanced by the internal lee waves. The results show that regions of strong turbulence energy appear over the lee side of the seamount associated with the production of the lee waves. The computed vertical eddy viscosity and diffusivity using turbulence models can be as large as 1 m²s⁻¹. A comparison of the magnitude and spatial distribution of the internal lee waves does not reveal any major differences in results computed using different turbulence energy models or mixing determined from a Richards on number formulation. However, the magnitude of the vertical mixing is sensitive to the form of turbulence energy submodel. Also, a study of the relevant importance of the various terms in the turbulence energy equation shows that the term representing the advection of turbulence needs to be retained in order to accurately reproduce the mixing produced by the internal lee waves. Calculations using a range of seamount profiles show that the magnitude of near-bed turbulence is sensitive to the shape of the seamount. The magnitude and spatial distribution of the lee waves and associated flow field are affected by the parametrization of horizontal diffusion, with significant differences between the use of Laplacian and biharmonic forms of horizontal diffusion. The application of biharmonic horizontal diffusion is recommended.     

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.      

Structure of turbulent pipe flow

The problem of turbulent flow in a straight circular pipe is solved. We consider a system consisting of the equation of motion, the equation for the turbulence energy, the expression relating the turbulence coefficient with the turbulence scale, and the integral formula for determining the turbulence scale. A numerical solution is presented for this closed system of equations for turbulent flow. The results of calculations are compared with experimental data.     

在我国开展工程湍流研究的设想

本文包括三部分:１）提出开展工程湍流研究的背景;２）工程湍流研究的特征和内容;３）开展工程湍流研究的设想,其中包括:ａ）湍流理论的概念鉴别和在工程中的应用,ｂ）湍流模式理论的应用和完善,ｃ）湍流测量和ｄ）湍流控制．