一种改进的均匀各向同性湍流初始化方法

秦泽聪; 方乐

doi:10.6052/0459-1879-16-180

一种改进的均匀各向同性湍流初始化方法

doi: 10.6052/0459-1879-16-180

秦泽聪^1,2,
方乐^1, ,

1.
北京航空航天大学中法工程师学院, 北京 100191
2. 法国里昂中央理工大学流体与声学实验室, 里昂 69130, 法国

基金项目: 国家自然科学基金资助项目（11202013，11302012，51420105008）.

详细信息

通讯作者:
方乐,副教授,主要研究方向:流体力学.E-mail:le.fang@zoho.com

中图分类号: O357.1
计量
- 文章访问数: 1437
- HTML全文浏览量: 124
- PDF下载量: 718
- 被引次数: 0
出版历程
- 收稿日期: 2016-07-01
- 修回日期: 2016-09-04
- 刊出日期: 2016-11-18

AN IMPROVED METHOD FOR INITIALIZING HOMOGENEOUS ISOTROPIC TURBULENT FLOWS

Qin Zecong^1,2,
Fang Le^{1
, ,}

1.
Sino-French Engineer School, Beihang University, Beijing 100191, China
2. LMFA, CNRS, Ecole Centrale de Lyon-Université de Lyon, Ecully 69130, France

摘要

摘要: 均匀各向同性湍流是一种最简单的湍流理想状态，也是湍流基础理论研究的最重要对象之一.为了用数值方法产生均匀各向同性湍流场，一般采用Rogallo提出的方法在谱空间生成初始场，然后再转换到物理空间.研究表明，由该方法生成的初始湍流场在3个棱向上呈各向异性，在结构函数和速度概率密度分布上均有体现.尽管在初始场样本很多时，这种各向异性可以在平均意义上消除，但作为数值模拟采用的单个流场则波动较大，不利于在实际计算中作为单个初始场生成各向同性湍流.在此基础上提出一种改进的Rogallo初始化方法，称为模量平均法，将Rogallo方法在3个轴向分别进行，并进行模量平均，最后采用能谱进行模量控制.这种方法可以一方面保持初始场能谱，另一方面减小单个流场的各向异性波动，以产生各向同性程度更佳的单个初始场.在统计意义上，新方法可以分别将结构函数和速度概率密度的相对标准差减小约10%.
- 均匀各向同性湍流 /
- Rogallo初始化方法 /
- 结构函数 /
- 概率密度分布
Abstract: Homogeneous isotropic turbulence (HIT) is one of the simplest ideal turbulence states, and is also one of the most important subjects in basic turbulence theory researches. HIT fields are usually initialized in the spectrum space via the method proposed by Rogallo, and then transformed in physical space. The current paper points out that initial fields thus generated are anisotropic in axis directions of their computational domain, which can be reflected in structure functions and in possibility density distribution of velocity components. Even though such anisotropy will disappear after an average operation of a large number of initial field samples, the anisotropy fluctuation between samples is considerately big, which is not favorable for the establishment of an HIT. Basing on this existing methodology, we then proposed an improved Rogallo method, named the modulus-averaging method, which firstly conducts the Rogallo method in all the 3 axis directions, then carries out a modulus-averaging operation, and finally control the modulus via a given spectrum function. This method can keep the initial filed spectrum and, reduce the anisotropy fluctuation of each single field to generate "more isotropic" initial fields. Statistically, this new method can lower the relative standard deviations of structure functions and velocity possibility density distribution by about 10%.
- homogeneous isotropic turbulence /
- rogallo initialization method /
- structure function /
- possibility density distribution

HTML全文

参考文献(30)

1 张兆顺,崔桂香,许春晓. 湍流大涡数值模拟的理论与应用. 北京:清华大学出版社,2008(Zhang Zhaoshun, Cui Guixiang, Xu Chunxiao. Theory and Application of Large Eddy Numerical Simulation. Beijing:Tsinghua University Press, 2008(in Chinese))

2 Pope SB. Turbulent Flows. New York:Cambridge University Press, 2000

3 李瑞霞,柳朝晖,贺铸等. 各向同性湍流内颗粒碰撞率的直接模拟研究. 力学学报,2006,38(1):25-32(Li Ruixia, Liu Zhaohui, He Zhu, et al. Direct numerical simulation of inertial particle collisions in isotropic turbulence. Chinese Journal of Theoretical and Applied Mechanics, 2006, 38(1):25-32(in Chinese))

4 李新亮,傅德薰,马延文. 可压缩均匀各向同性湍流的直接数值模拟. 中国科学(A辑),2002,32(8):716-724(Li Xinliang, Fu Dexun, Ma Yanwen. Direct numerical simulation of compressible homogeneous isotropic turbulence. Science in China(Series A), 2002, 32(8):716-724(in Chinese))

5 张曙光,雷磊,何国威. 均匀各向同性湍流的频率波数能量谱. 力学学报,2003,35(3):317-320(Zhang Shuguang, Lei Lei, He Guowei. Frequency-wavenumber energy spectra in isotropic turbulence. Acta Mechanica Sinica, 2003, 35(3):317-320(in Chinese))

6 赵松年,胡非. 湍流问题:如何看待"均匀各向同性湍流"?中国科学:物理学力学天文学,2015,45(2):024701(Zhao Songnian, Hu Fei. Turbulence question:How do view "the homogeneous and isotropic turbulence"? Science China Physics, Mechanics & Astronomy, 2015, 45(2):024701(in Chinese))

7 方乐,杨云柯,王洪涛等. 全场离散Tophat过滤操作的快速算法. 数值计算与计算机应用,2009,30(3):218-224(Fang Le, Yang Yunke, Wang Hongwei, et al. A rapid algorithm for Tophat filter operation in discrete field. Journal on Numerical and Computer Applications, 2009, 30(3):218-224(in Chinese))

8 方乐,崔桂香,许春晓等. 标量湍流的能量传输特性. 计算物理, 2006,23(6):692-698(Fang Le, Cui Guixiang, Xu Chunxiao, et al. Energy transfer in scalar turbulence. Chinese Journal of Computational Physics, 2006, 23(6):692-698(in Chinese))

9 Stepanov R, Plunian F, Kessar M, et al. Systematic bias in the calculation of spectral density from a three-dimensional spatial grid. Physical Review E, 2014, 90(5):053309

10 Fang L, Cui GX, Xu CX, et al. Multi-scale analysis of energy transfer in scalar turbulence. Chinese Physics Letters, 2005, 22(11):2877

11 Cichowlas C, Bonaïti P, Debbasch F, et al. Effective dissipation and turbulence in spectrally truncated Euler flows. Physical Review Letters, 2005, 95(26):264502

12 Bos WJT, Bertoglio JP. Dynamics of spectrally truncated inviscid turbulence. Physics of Fluids, 2006, 18(7):071701

13 Brun C, Pumir A. Statistics of Fourier modes in a turbulent flow. Physical Review E, 2001, 63(5):056313

14 Qin ZC, Fang L, Fang J. How isotropic are turbulent flows generated by using periodic conditions in a cube? Physics Letters A, 2016, 380(13):1310-1317

15 Hinze JO. Turbulence, 2nd edn. New York:McGraw-Hill International Book Company, 1975

16 Fang L, Bos WJT, Jin GD. Short-time evolution of Lagrangian velocity gradient correlations in isotropic turbulence. Physics of Fluids, 2015, 27(12):125102

17 马威,方乐,邵亮等. 可解尺度各向同性湍流的标度律. 力学学报,2011, 43(2):267-276(MaWei, Fang Le, Shao Liang, et al. Scaling law of resolved-scale isotropic turbulence. Chinse Journal of Theoretical and Applied Mechanics, 2011, 43(2):267-276(in Chinese))

18 Fang L, Shao L, Bertoglio JP, et al. An improved velocity increment model based on Kolmogorov equation of filtered velocity. Physics of Fluids, 2009, 21(6):065108

19 Gotoh T, Fukayama D, Nakano T. Velocity field statistics in homogeneous steady turbulence obtained using a high-resolution direct numerical simulation. Physics of Fluids, 2002, 14(3):1065-1081

20 Cui GX, Zhou HB, Zhang ZS, et al. A new dynamic subgrid eddy viscosity model with application to turbulent channel flow. Physics of Fluids, 2004, 16(8):2835-2842

21 乔海军,李会元. 二维各向同性湍流直接数值模拟的六边形谱方法及GPU实现和优化. 数值计算与计算机应用,2013,34(6):147-160(Qiao Haijun, Li Huiyuan. Hexagonal spectral method for direct numerical simulation of two-dimensional homogeneous isotropic turbulence and their GPU implementation and optimization. Journal on Numerical Methods and Computer Applications, 2013, 34(6):147-160(in Chinese))

22 Rogallo RS. Numerical experiments in homogeneous turbulence. Technical Report 81315, NASA, 1981

23 Lesieur M. Turbulence in Fluids. Springer Science & Business Media, 2012

24 Fang L, Zhu Y, Liu YW, et al. Spectral non-equilibrium property in homogeneous isotropic turbulence and its implication in subgridscale modeling. Physics Letters A, 2015, 379(38):2331-2336

25 Fang L, Bos WJT, Shao L, et al. Time reversibility of Navier-Stokes turbulence and its implication for subgrid scale models. Journal of Turbulence, 2012(13):N3

26 Hearst RJ, Lavoie P. Velocity derivative skewness in fractalgenerated, non-equilibrium grid turbulence. Physics of Fluids, 2015, 27(7):071701

27 Fang L, Zhang YJ, Fang J, et al. Relation of the fourth-order statistical invariants of velocity gradient tensor in isotropic turbulence. Physical Review E, 2016, 94(2):023114

28 Zhao X, He GW. Space-time correlations of fluctuating velocities in turbulent shear flows. Physical Review E, 2009, 79(5):046316

29 He GW, Zhang JB. Elliptic model for space-time correlations in turbulent shear flows. Physical Review E, 2006, 73(5):055303

30 Vassilicos JC. Dissipation in turbulent flows. Annual Review of Fluid Mechanics, 2015, 47:95-114

施引文献

资源附件(0)

访问统计