Conditional sampling and state space reconstruction

This work looks into the existing links between conditional sampling techniques for coherent structure identification and methods for state space reconstruction which come up in the field of nonlinear time series analysis. It is shown that the sampling condition used by the VITA method corresponds to a round hyper-cylinder, having as its axis the main diagonal of an embedding space reconstructed with the delay method. Such a geometrical interpretation allows us to better understand certain typical characteristics of the method and to see bursting events as excursions of the system leaving the high-dimension basic turbulence. Received: 10 October 1997/Accepted: 4 November 1998     

用子波分析修正检测壁湍流猝发的VITA法

应用壁湍流脉动速度信号子波分析的一系列方法对检测壁湍流猝发事件的VITA法进行了修正。其中,用能量最大准则确定VITA法短时间平均周期;以子波变换能量最大尺度脉动速度的短时间平均方差的局部极大值点作为检测函数的中心点,取代了传统VITA法中对短时间周期平均方差选用门限值的方法,避免了VITA法检测结果对门限值的主观经验依赖性,提高了VITA法检测壁湍流猝发事件的客观性和准确性。     

Burst event detection in wall turbulence by WVITA method

Wavelet Variable Interval Time Average (WVITA) is introduced as a method incorporating burst event detection in wall turbulence. Wavelet transform is performed to unfold the longitudinal fluctuating velocity time series measured in the near wall region of a turbulent boundary layer using hot-film anemometer. This unfolding is both in time and in space simultaneously. The splitted kinetic of the longitudinal fluctuating velocity time series among different scales is obtained by integrating the square of wavelet coefficient modulus over temporal space. The time scale that related to burst events in wall turbulence passing through the fixed probe is ascertained by maximum criterion of the kinetic energy evolution across scales. Wavelet transformed localized variance of the fluctuating velocity time series at the maximum kinetic scale is put forward instead of localized short time average variance in Variable Interval Time Average (VITA) scheme. The burst event detection result shows that WVITA scheme can avoid erroneous judgement and solve the grouping problem more effectively which is caused by VITA scheme itself and can not be avoided by adjusting the threshold level or changing the short time average interval. The project supported by the National Natural Science Foundation of China (19732005) and the National Climbing Project of China     

A model for adiabatic supersonic turbulent boundary layers

An asymptotic analysis of the equations describing supersonic turbulent flow over an adiabatic wall is carried out for high Reynolds numbers, Re, and mainstream Mach numbers, M _e=O(1). A general expression for the adiabatic-wall temperature is derived. The asymptotic theory constrains the types of turbulence models that are suitable to represent the effects of viscous dissipation. A simple algebraic turbulence model is proposed and comparisons with measured total enthalpy profile data show good agreement, capturing the overshoot observed in total enthalpy near the boundarylayer edge.This work was supported by NASA Langley Research Center under Grant NAG-1-832 and the Air Force Office of Scientific Research under Grants AFOSR-91-0069 and F49620-93-0130; Dr. Ruban was supported by a grant from United Technologies Corporation.     

用自相关法确定VITA法的门限K

研究了用ＶＩＴＡ条件采样方法壁湍猝发的门限值与壁湍流猝发平均周期之间的关系,根据用壁湍流流向脉动速度自相关函数检测得到的壁湍流猝发平均周期,确定壁,湍猝发ＶＩＴＡ条件采样的门限值Ｋ。     

Some issues of turbulence statistics

The issue of dropping the random forcef _i and the arbitrariness of choosing the basic variable in the variational approach to turbulence closure problem, pointed out recently by the Russian scientists Bazdenkov and Kukharkin, are discussed. According to the mean-square estimation method, the random forcef _i should be dropped in the error expression of the LFP (Langevin-Fokker-Planck) model. However,f _i is not neglected, its effect has been taken into account by the variational approach. In order to optimize the perturbation solution of the Liouville equation, the LFP model requires that the basic variable is as near to Gaussian as possible. Hence, the velocity, instead of the vorticity, should be chosen as the basic variable in the three-dimensional turbulence. Although the LFP model and the zero-order Gaussian term of PDF (probability density function) imply whiteness assumption (zero correlation time off _i ), the higher-order non-Gaussian terms of PDF correspond to the nonwhiteness of turbulence dynamics, the variational approach does calculate the nonwhiteness effect properly. The work is supported by the National Basic Research Program “Non-linear Sciences” and the National Natural Science Foundation of China     

Spanwise propagation of turbulence in a boundary layer

The process of spanwise propagation of turbulence in a laminar boundary layer on a plate is numerically investigated. Three well-known turbulence models are considered. It is shown that the calculated values of the "turbulent wedge" angle are several times less than that observed experimentally. The reason for the deviation of the calculated and experimental data is analyzed. Moscow, Seattle. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 77–84, May–June, 1998. The work was financially supported by the Russian Foundation for Basic Research (project No. 95-01-00251a) and the Moscow Boeing Science-Technology Center.     

A two-scale second-order moment two-phase turbulence model for simulating dense gas-particle flows

A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concepts of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision and through a unified treatment of these two kinds of fluctuations. The proposed model is used to simulate gas-particle flows in a channel and in a downer. Simulation results are in agreement with the experimental results reported in references and are near the results obtained using the single-scale second-order moment two-phase turbulence model superposed with a particle collision model (USM-θ model) in most regions. The project supported by the Special Funds for Major State Basic Research, China (G-1999-0222-08), and the Postdoctoral Science Foundation (2004036239) The English text was polished by Keren Wang     

Turbulent flow in a channel with permeable walls. Direct numerical simulation and results of three-parameter model

Steady turbulent viscous incompressible fluid flow in a plane channel is calculated for the case of uniform blowing and suction through opposite walls. There are no experimental data for flows of this type. The flows were calculated by two methods: a direct numerical simulation method and using a three-parameter turbulence model. Direct numerical simulation was carried out using the same (apart from the boundary conditions) algorithm for numerical solution of the Navier-Stokes equations as that used earlier for calculating flows in pipes and channels with impermeable walls. In the second group of calculations the version of the model published in 1978 was used. The results obtained by the two methods are in good agreement. The difference is within the spread of the experimental data used for determining the parameters of the model. The agreement obtained makes it possible to assert that the turbulence direct numerical simulation algorithm developed can be used for the analysis of flows with quite different boundary conditions, including cases where there are no corresponding experimental data. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 18–26, November–December, 1998. The work was financially supported by the Russian Foundation for Basic Research (project Nos. 96-01-00602 and 96-01-00259).     

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”     

Algorithms for fully automated three-dimensional particle tracking velocimetry

A three-dimensional Particle Tracking Velocimetry (3-D PTV) technique has been developed to provide time-resolved, three-dimensional velocity field measurements throughout a finite volume. This technique offers many advantages for fundamental research in turbulence and applied research in areas such as mixing and combustion. The data acquired in 3-D PTV is a time sequence of stereo images of flow tracer particles suspended in the fluid. In this paper, the implementation of the technique is discussed in detail, as well as the results of an extensive statistical investigation of the performance of the algorithms. The technique has been optimized to allow fully automatic processing of long sequences of image pairs in a computationally efficient manner, hereby providing a viable, practical tool for the study of complex flows.List of symbols x, y, z Particle position - u, v, w Particle velocity This work was supported by a grant from Ford Motor Company, Powertrain Research Department. Their support is gratefully acknowledged.     

Numerical simulation of the effect of void fraction and inlet velocity on two-phase turbulence in bubble-liquid flows

There are contradicted opinions on whether bubbles enhance or reduce the liquid turbulence. In this paper, the effect of void fraction and inlet velocity on the bubble–liquid two-phase turbulence of the multiple bubble–liquid jets in a two-dimensional channel is studied by using the two-phase second-order moment turbulence model. The results confirm the phenomena observed in experiments and reported in references that at a low void fraction and low inlet velocities the bubbles enhance the liquid turbulence, whereas at a high void fraction and high inlet velocities the bubbles reduce the liquid turbulence.The project supported by the China Special Funds for Major State Basic Research (G-1999-0222-08) and the Innovation and Technology Commission of Hong Kong and Aoyagi (H.K.) Ltd, Hong Kong, under the Grant No. UIM/122. The English text was polished by Keren Wang.     

Visualization and analysis of longitudinal vortices at curved walls of 2D laminar and turbulent channel flows

The 3D structure of longitudinal vortices at the curved walls of both laminar and turbulent channel flows are visualized by the hydrogen bubble technique. Together with the conditional sampling of the turbulent characteristics at the wall processed by the VITA method the dynamics of the near-wall structure is discussed. The project is supported by National Natural Science Foundation of China.     

SECOND-ORDER MOMENT MODEL FOR DENSE TWO-PHASE TURBULENT FLOW OF BINGHAM FLUID WITH PARTICLES

The USM-θmodel of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. In this model, phases interaction and the extra term of Bingham fluid yield stress are taken into account. An algorithm for USM-θmodel in dense two-phase flow was proposed, in which the influence of particle volume fraction is accounted for. This model was used to simulate turbulent flow of Bingham fluid single-phase and dense liquid-particle two-phase in pipe. It is shown USM-θmodel has better prediction result than the five-equation model, in which the particle-particle collision is modeled by the particle kinetic theory, while the turbulence of both phase is simulated by the two-equation turbulence model. The USM-θmodel was then used to simulate the dense two-phase turbulent up flow of Bingham fluid with particles. With the increasing of the yield stress, the velocities of Bingham and particle decrease near the pipe centre. Comparing the two-phase flow of Bingham-particle with that of liquid-particle, it is found the source term of yield stress has significant effect on flow.     

固壁温度对壁湍流相干结构的影响

用半导体元件对平板进行加热，用ＶＩＴＡ法和ｍｕ－ｌｅｖｅｌ法两种条件采样技术研究了固壁温度对湍流相干结构的影响，改进了Ｔｉｅｄｅｒｍａｎ等人提出的“归组”方法，并且用“归组”的ＶＩ－ＴＡ法和ｍｕ－ｌｅｖｅｌ法研究了固壁加热对湍流猝发平均周期的影响．实验结果表明，固壁加热使得湍流脉动速度均方根值变大，条件采样检测到的事件数量增多，但猝发周期维持不变     

Numerical modeling of turbulent compound channel flow using the lattice Boltzmann method

The flow of water in a straight compound channel with prismatic cross section is investigated with a relatively new tool, the lattice Boltzmann method. The large eddy simulation model is added in the lattice Boltzmann model for nonlinear shallow water equations (LABSWE^TM) so that the turbulence, caused by lateral exchange of momentum in the shear layer between the main channel and floodplain, can be taken into account and modeled efficiently. To validate the numerical model, a symmetrical compound channel with trapezoidal main channel and flat floodplain is tested. Similar to most natural watercourses, the floodplain has higher roughness values than the main channel. Different relative depths, D_r (the ratio of the depth of flow on the floodplain to that in the main channel), are considered. The Reynolds number is set at 30 000 in the main channel. The lateral distributions of the longitudinal velocity, the boundary shear stress, the Reynolds stress and the apparent shear stress across the channel are obtained after the large eddy simulation is performed. The results of numerical simulations are compared with the available experiment data, which show that the LABSWE^TM is capable of modeling the features of flow turbulence in compound channels and is sufficiently accurate for practical applications in engineering. Copyright © 2008 John Wiley & Sons, Ltd.     

The Damped-Driven 2D Navier–Stokes System on Large Elongated Domains

The Navier–Stokes system with damping, which is motivated by Stommel–Charney model of ocean circulation, is considered in a large elongated periodic rectangular domain with area of the order α⁻¹, as α → 0. We obtain estimates for the dimension of the global attractor that are sharp as both α → 0 and ν → 0, where ν is the viscosity coefficient. This work was supported in part by the US Civilian Research and Development Foundation, grant no. RUM1-2654-MO-05 (A.A.I. and E.S.T.). The work of A.A.I. was supported in part by the Russian Foundation for Fundamental Research, grants no. 06-001-0096 and no. 05-01-429, and by the RAS Programme no. 1 ‘Modern problems of theoretical mathematics’. The work of E.S.T. was supported in part by the NSF, grant no. DMS-0204794, the MAOF Fellowship of the Israeli Council of Higher Education, and by the BSF, grant no. 200423.     

Study on resistance coefficient in compound channels

This paper presents a further study of the Manning and Darcy-Weisbach resistance coefficients, as they play a significant role in assessing the cross-sectional mean velocity, conveyance capacity and determining the lateral distribution of depth mean velocity and local boundary shear stress in compound channels. The relationships between the local, zonal and overall resistance coefficients, and a wide range of geometries and different roughness between the main channel and the flood plain are established by analyzing a vast amount of experimental data from a British Science and Engineering Research Council Flood Channel Facility (SERC-FCF). And the experimental results also show that the overall Darcy-Weisbach resistance coefficient for a compound channel is the function of Reynolds number, but the function relationship is different from that for a single channel. By comparing and analyzing the conventional methods with the experimental data to predict composite roughness in compound channels, it is found that these methods are not suitable for compound channels. Moreover, the reason why the conventional methods can not assess correctly the conveyance capacity of compound channels is also analyzed in this paper.The project supported by the National Natural Science Foundation of China (50279024), the National Key Basic Research and Development Program of China (973 Program) (2003CB415202) and the Specialized Research Fund for the Doctoral Program of Higher Education (20030610039)The English text was polished by Ron Marshall     

KOLMOGOROV BEHAVIOR OF NEAR-WALL TURBULENCE AND ITS APPLICATION IN TURBULENCE MODELING

The near-wall behavior of turbulence is re-examined in a way different from that proposed by Hanjalic and Launder¹ and followers^2,3,4,5. It is shown that at a certain distance from the wall, all energetic large eddies will reduce to Kolmogorov eddies (the smallest eddies in turbulence). All the important wall parameters, such as friction velocity, viscous length scale, and mean strain rate at the wall, are characterised by Kolmogorov microscales. According t o this Kolmogorov behavior of near-wall turbulence, the turbulence quantities, such as turbulent kinetic energy, dissipation rate, etc. at the location where the large eddies become “Kolmogorov” eddies, can be estimated by using both direct numerical simulation (DNS) data and asymptotic analysis of near-wall turbulence. This information will provide useful boundary conditions for the turbulent transport equations. As a n example, the concept is incorporated in the standard κ - εmodel which is then applied t o channel and boundary layer flows. Using appropriate boundary conditions (based on Kolmogorov behaviour of near-wall turbulence), there is no need for any wall-modification to the κ - ε equations (including model constants). Results compare very well with the DNS and experimental data.