明渠湍流速度的分形特征研究
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摘要
湍流运动广泛存在于自然界的各种明渠水流中,了解湍流运动的速度特征对于指导工程实际问题如泥沙运动的规律、河流污染物的扩散、高速水流的脉动压强等具有十分重要的现实意义。采用明渠水槽去模拟湍流,利用ADV去测量各测线点的湍流流速,结合空间位置和小波理论,探究明渠断面湍流速度的分形特征。结果表明:湍流速度和及其经小波包多尺度分解的各个频段能量谱具有分形特征和自相似性,湍流空间流速分数维并不是某一个固定值,在空间范围内呈现一定波动的规律性,考虑雷诺数对湍流分数维的影响时,要具体对同一流态三个方向的湍流速度信号分别来探讨,低雷诺数下,湍流的分数维主要受到的是小尺度涡耗散影响。
Turbulent motion exists widely in nature in a variety of open channel flows, and a good understanding of its velocity behaviors is practically of great significance helping solve the engineering problems related to sediment movement, pollutant diffusion in rivers, and fluctuating pressure in highspeed flows. This study conducts a flume experiment of the turbulent flows in an open channel using the ADV technique to measure turbulent velocities at the points of sampling lines, and adopts the wavelet theory to analyze the measurements and the characteristics of turbulence. Results show that fractal dimension and self-similarity feature the turbulent velocities measured and the energy spectrum on each band obtained through multi-scale wavelet packet decomposition, and that this fractal dimension is not a fixed value but varies in space with certain trends and volatility. When we consider the flow Reynolds number as a factor of the fractional dimension, the turbulence velocity signals of the same sampling point are discussed separately for each space direction. At low Reynolds numbers, the fractal dimensions depend mainly on the dissipation of small scale eddies.
Turbulent motion exists widely in nature in a variety of open channel flows, and a good understanding of its velocity behaviors is practically of great significance helping solve the engineering problems related to sediment movement, pollutant diffusion in rivers, and fluctuating pressure in highspeed flows. This study conducts a flume experiment of the turbulent flows in an open channel using the ADV technique to measure turbulent velocities at the points of sampling lines, and adopts the wavelet theory to analyze the measurements and the characteristics of turbulence. Results show that fractal dimension and self-similarity feature the turbulent velocities measured and the energy spectrum on each band obtained through multi-scale wavelet packet decomposition, and that this fractal dimension is not a fixed value but varies in space with certain trends and volatility. When we consider the flow Reynolds number as a factor of the fractional dimension, the turbulence velocity signals of the same sampling point are discussed separately for each space direction. At low Reynolds numbers, the fractal dimensions depend mainly on the dissipation of small scale eddies.
引文
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[19]Ziaei A N,Keshavarzi A R,Homayoun E.Fractal scaling and simulation of velocity components and turbulent shear stress in open channel flow[J].Chaos Solitons&Fractals,2005,24(4):1031-1045.
[20]李蕊言.明渠湍流的分形特征研究[J].科技创新与应用,2015(8):23-24.LI Ruiyan.Fractal characteristics of open channel turbulence[J].Innovation and Application of Science and Technology,2015(8):23-24.(in Chinese)
[21]靳秀青.基于小波变换和FFT及HHT的壁湍流能量传递的实验研究[C]//第八届全国实验流体力学学术会议.广州,2010.JIN Xiuqing.Experimental study of wall turbulence energy transfer based on wavelet transform and FFT and HHT[C]//Chinese Society of Mechanics.Guangzhou,2010.(in Chinese)
[22]马晓光,胡非.大气湍流能谱的精细结构及能量级串[J].地球物理学报,2004,47(2):195-199.MA Xiaoguang,HU Fei.The fine structure and energy series of atmospheric turbulence spectrum[J].Chinese Journal of Geophysics,2004,47(2):195-199.(in Chinese)
[23]周伟.MATLAB小波分析高级技术[M].西安:西安电子科技大学出版社,2006.ZHOU Wei.MATLAB wavelet analysis of advanced technology[M].Xi'an:Xi'an University of Electronic Science and Technology Press,2006.(in Chinese)
[2]Kolmogorov N A.The local structure of turbulence in an incompressible viscou s fluid at very high Reynolds numbers[J].Physics-Uspekhi,1968,10(6):734-746.
[3]Kline S J,Reynolds W C,Schraub F A,et al.The structure of turbulent boundary layers[J].Journal of Fluid Mechanics,1982,85(2):273-303.
[4]Mandelbrot B B.Intermittent turbulence in self-similar cascades:divergence of high moments and dimension of the carrier[J].Journal of Fluid Mechanics,1974,62(2):331-358.
[5]Frisch U,Sulem P L,Nelkin M.A simple dynamical model of intermittent fully developed turbulence[J].Journal of Fluid Mechanics,2006,87(4):719-736.
[6]汤一波,金忠青.脉动压力的紊流分形特征[J].水科学进展,1998,9(4):361-366.TANG Yibo,JIN Zhongqing.Fractal characteristics of turbulence pressure[J].Advances in Water Science,1998,9(4):361-366.(in Chinese)
[7]黄真理.湍流的分形特征[J].力学进展,2000,30(4):581-596.HUANG Zhenli.Fractal characteristics of turbulence[J].Mechanics Progress,2000,30(4):581-596.(in Chinese)
[8]赵玉新,易仕和,田立丰,等.超声速湍流混合层实验图像的分形度量[J].中国科学:物理学力学天文学,2008(5):562-571.ZHAO Yuxin,YI Shihe,TIAN Lifeng,et al.Fractal measurement of experimental image of supersonic turbulence mixed layer[J].Chinese Journal of Science,2008(5):562-571.(in Chinese)
[9]Burton G C,Dahm W J A.Multifractal subgrid-scale modeling for large-eddy simulation.I.Model development and a priori testing[J].Physics of Fluids,2005,17(7):75111.
[10]Burton G C,Dahm W J A.Multifractal subgrid-scale modeling for large-eddy simulation.II.Backscatter limiting and a posteriori evaluation[J].Physics of Fluids,2005,17(7):75112.
[11]万涛.明渠弯道速度的马尔可夫及分形特性研究[D].天津:天津大学,2012.WAN Tao.Research on Markov and fractal characteristics of open channel curvature[D]Tianjin:Tianjin University,2012.(in Chinese)
[12]沈学会,陈举华.分形与混沌理论在湍流研究中的应用[J].河南科技大学学报(自然科学版),2005,26(1):27-30.SHEN Xuehui,CHEN Juhua.Fractal and chaos theory in turbulence research[J].Journal of Henan University of Science and Technology(Natural Science Edition),2005,26(1):27-30.(in Chinese)
[13]袁全勇,李春,杨阳,等.基于分形学的湍流风谱特性对比研究[J].热能动力工程,2017(5):118-124.YUAN Quanyong,LI Chun,YANG Yang,et al.Comparison of characteristics of turbulent wind spectrum based on fractal theory[J].Thermal Power Engineering,2017(5):118-124.(in Chinese)
[14]黄才安,周济人,赵晓冬,等.基于分形理论的流速及含沙量垂线分布规律研究[J].水利学报,2013,44(9):1044-1049.HUANG Cai'an,ZHOU Jiren,ZHAO Xiaodong,et al.Study on vertical distribution of flow velocity and sediment concentration based on fractal theory[J].Journal of Hydraulic Engineering,2013,44(9):1044-1049.(in Chinese)
[15]舒小红.明渠挟沙水流垂线流速的分形特征研究[J].中国水运月刊,2010,10(7):160-161.SHU Xiaohong.Fractal characteristics of flow velocity in vertical channel with sediment[J].China Water Monthly,2010,10(7):160-161.(in Chinese)
[16]吴光文,王昌明,包建东,等.基于自适应阈值函数的小波阈值去噪方法[J].电子与信息学报,2014,36(6):1340-1347.WU Guangwen,WANG Changming,BAO Jiandong,et al.Based on adaptive threshold function wavelet threshold denoising method[J].Journal of Electronics&Information Technology,2014,36(6):1340-1347.(in Chinese)
[17]孙洪泉.分形几何与分形插值[M].北京:科学出版社,2011.SUN Hongquan.Fractal geometry and fractal interpolation[M].Beijing:Science Press,2011.(in Chinese)
[18]张鹏.明渠湍流涡运动尺度分布特性[J].水科学进展,2015,26(1):91-98.ZHANG Peng.Characteristics of turbulent eddy motion in open channels[J].Advances in Water Science,2015,26(1):91-98.(in Chinese)
[19]Ziaei A N,Keshavarzi A R,Homayoun E.Fractal scaling and simulation of velocity components and turbulent shear stress in open channel flow[J].Chaos Solitons&Fractals,2005,24(4):1031-1045.
[20]李蕊言.明渠湍流的分形特征研究[J].科技创新与应用,2015(8):23-24.LI Ruiyan.Fractal characteristics of open channel turbulence[J].Innovation and Application of Science and Technology,2015(8):23-24.(in Chinese)
[21]靳秀青.基于小波变换和FFT及HHT的壁湍流能量传递的实验研究[C]//第八届全国实验流体力学学术会议.广州,2010.JIN Xiuqing.Experimental study of wall turbulence energy transfer based on wavelet transform and FFT and HHT[C]//Chinese Society of Mechanics.Guangzhou,2010.(in Chinese)
[22]马晓光,胡非.大气湍流能谱的精细结构及能量级串[J].地球物理学报,2004,47(2):195-199.MA Xiaoguang,HU Fei.The fine structure and energy series of atmospheric turbulence spectrum[J].Chinese Journal of Geophysics,2004,47(2):195-199.(in Chinese)
[23]周伟.MATLAB小波分析高级技术[M].西安:西安电子科技大学出版社,2006.ZHOU Wei.MATLAB wavelet analysis of advanced technology[M].Xi'an:Xi'an University of Electronic Science and Technology Press,2006.(in Chinese)