用平均速度剖面法测量湍流边界层壁面摩擦速度的对比研究
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摘要
基于不同雷诺数平板湍流边界层平均速度剖面,分别采用黏性底层拟合、对数律区拟合以及Spalding公式拟合算法计算了壁面摩擦速度,并对平均速度剖面进行无量纲化。通过比较无量纲化的平均速度剖面与理论规律曲线,验证了三种拟合计算方法的有效性。通过比较三种拟合算法所得的壁面摩擦速度与油膜干涉法直接测得的壁面摩擦速度之间的误差,并分析不同拟合算法误差形成的内在机制,验证了三种拟合算法计算结果的准确性与可靠性。结果表明Spalding拟合算法计算结果的准确性和可靠性都要优于其他两种拟合算法。
Based on average velocity profile of plate turbulent boundary layer with different Reynolds numbers,the wall friction velocity was calculated by using the viscous bottom layer fitting algorithm,the logarithmic law region fitting algorithm and Spalding formula fitting algorithm,respectively,and the average velocity profile was non-dimensionalized.By comparing the dimensionless average velocity profile with the theoretical curve,the validity of above three fitting methods was verified.Then the wall friction velocity error obtained by above three fitting algorithms was compared with that measured directly by oil film interference method,and the internal mechanism of the error formation of different fitting algorithms was analyzed.The accuracy and reliability of above three fitting algorithms were verified.Results show that the accuracy and reliability of Spalding fitting algorithm are better than the other two fitting algorithms.
Based on average velocity profile of plate turbulent boundary layer with different Reynolds numbers,the wall friction velocity was calculated by using the viscous bottom layer fitting algorithm,the logarithmic law region fitting algorithm and Spalding formula fitting algorithm,respectively,and the average velocity profile was non-dimensionalized.By comparing the dimensionless average velocity profile with the theoretical curve,the validity of above three fitting methods was verified.Then the wall friction velocity error obtained by above three fitting algorithms was compared with that measured directly by oil film interference method,and the internal mechanism of the error formation of different fitting algorithms was analyzed.The accuracy and reliability of above three fitting algorithms were verified.Results show that the accuracy and reliability of Spalding fitting algorithm are better than the other two fitting algorithms.
引文
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[2]Shen J Q,Pan C,Wang J J.Accurate measurement of wall skin friction by single-pixel ensemble correlation[J].Science China Physics Mechanics&Astronomy,2014,57(7):1352-1362.
[3]潘光,黄明明,胡海豹,等.Spalding公式在脊状表面湍壁摩擦力测量中的应用[J].力学学报,2009,41(1):15-20(PAN Guang,HUANG Mingming,HU Haibao,et al.Application of spalding formula in wall friction stress measurement on riblet surface[J].Chinese Journal of Theoretical and Application Mechanics,2009,41(1):15-20(in Chinese))
[4]樊星,姜楠.用平均速度剖面法测量壁湍流摩擦阻力[J].力学与实践,2005,27(1):28-30(FAN Xing,JIANGNan.Skin friction measurement in turbulent boundary layer by mean velocity profile method[J].Mechanics in Engineering,2005,27(1):28-30(in Chinese))
[5]Spalding D B.A single formula for the“Law of the wall”[J].Journal of Applied Mechanics,1961,28(3):455.
[6]Shen J Q,Pan C,Wang J J.Accurate measurement of wall skin friction by single-pixel ensemble correlation[J].Science China Physics Mechanics&Astronomy,2014,57(7):1352-1362.
[7]张兆顺,崔桂香,许春晓.湍流理论与模拟[M].清华大学出版社,2005(ZHANG Zhaoshun,CUI Guixiang,XU Chunxiao.Turbulence theory and simulation[M].Tsinghua University Press,2005(in Chinese))
[8]Mckeon B J,Li J,Jiang W,et al.Further observations on the mean velocity distribution in fully developed pipe flow[J].Journal of Fluid Mechanics,2004,501:135-147.
[9]rlüR.Experimental studies in jet flows and zero pressuregradient turbulent boundary layers(Ph.D.thesis)[D].Royal Institute of Technology,Stockholm,Sweden,2009.
[10]Philipp S,rlüR.Assessment of direct numerical simulation data of turbulent boundary layers[J].Journal of Fluid Mechanics,2010,659(4):116-126.
[11]Kendall A,Koochesfahani M.A method for estimating wall friction in turbulent wall-bounded flows[J].Experiments in Fluids,2008,44(5):773-780.
[12]Nagib H M,Christophorou C,Monkewitz P A.High reynolds number turbulent boundary layers subjected to various pressure-gradient conditions[M].IUTAM Symposium on One Hundred Years of Boundary Layer Research.Springer Netherlands,2006:383-394.
[13]Boiko A V,Kornilov V I.Hot-wire anemometer measurement of local skin friction coefficient[J].Thermophysics&Aeromechanics,2010,17(4):577-586.
[14]sterlund J M,Johansson A V,Nagib H M,et al.A note on the overlap region in turbulent boundary layers[J].Physics of Fluids,2000,12(1):1-4.
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