面向精准工程湍流模型的理论研究
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摘要
长期以来,工程湍流模型建立在量纲分析和经验修正的基础上,绝对预测能力不足而且模型参数的意义不明确。关于湍流边界层的理论研究一直平行地在两条路线上前行,或是经验性地构造有关平均速度或动能的分布,或是利用数值模拟等技术对于湍流脉动结构进行精细刻画。二者之间的分割导致对湍流边界层物理图像的不完整,从而限制了对一系列相似性关系的揭示。新近发展的结构系综理论,立足于探索由于固壁对于流场的雷诺应力各个分量所表现的拉伸对称性约束,完成了一个对于平均速度和动能剖面的统一描述,从而形成了一个构建工程湍流模型的新思路:一方面,理论指导如何开展湍流DNS(Direct Numerical Simulation)和LES(Large Eddy Simulation)的大数据分析,提炼对定量描述复杂流动有物理意义的多层结构参数;另一方面,指导开发物理图像清晰、定量描述精确的新型湍流(代数)模型。结构系综理论揭示了壁湍流所共有的普适多层结构,完整地刻画了边界层湍流的雷诺数、马赫数相似性,有望推动理论空气动力学研究进入一个定量化、精确化的新阶段。
For decades,turbulence models are built upon dimensional arguments with numerous empirical coefficients,which yield two problems:absence of physical interpretation for parameters(thus limited adaptability to complex flows)and poor prediction accuracy(relying on experimental calibration).Only a deep understanding of the similarity principle in realistic engineering flows can make a fundamental change.After a review of current research on wall turbulence,we suggest a new symmetry-based approach,the so-called structure ensemble dynamics(SED)theory,which aims at discovering universal symmetry principle imposed by the presence of wall.The theory gives rise to a universal multi-layer description of all Reynolds stresses(hence a unified description for both the mean velocity and turbulence intensities)for canonical wall-bounded turbulent flows,based on the concepts of length order function,generalized dilation-invariance ansatz under a novel Lie-group analysis framework.Five steps of the SED analysis are proposed to renovate the aerodynamics studies,including collecting data,verifying symmetry, defining order functions, determining multi-layer parameters, and developing adequate turbulence models,respectively.The framework opens a new avenue for analyzing empirical data from experiments and numerical simulations,then developing new turbulence models with a physical parameterization and much more accurate prediction.
For decades,turbulence models are built upon dimensional arguments with numerous empirical coefficients,which yield two problems:absence of physical interpretation for parameters(thus limited adaptability to complex flows)and poor prediction accuracy(relying on experimental calibration).Only a deep understanding of the similarity principle in realistic engineering flows can make a fundamental change.After a review of current research on wall turbulence,we suggest a new symmetry-based approach,the so-called structure ensemble dynamics(SED)theory,which aims at discovering universal symmetry principle imposed by the presence of wall.The theory gives rise to a universal multi-layer description of all Reynolds stresses(hence a unified description for both the mean velocity and turbulence intensities)for canonical wall-bounded turbulent flows,based on the concepts of length order function,generalized dilation-invariance ansatz under a novel Lie-group analysis framework.Five steps of the SED analysis are proposed to renovate the aerodynamics studies,including collecting data,verifying symmetry, defining order functions, determining multi-layer parameters, and developing adequate turbulence models,respectively.The framework opens a new avenue for analyzing empirical data from experiments and numerical simulations,then developing new turbulence models with a physical parameterization and much more accurate prediction.
引文
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[5]高正红,王超.飞行器气动外形设计方法研究与进展[J].空气动力学学报,2017,35(4):516-528.GAO Z H,WANG G C.Aerodynamic shape design methods for air craft:status and trends[J].Acta Aerodynamica Sinica,2017,35(4):516-528.
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[8]SPALARTP R,ALLMARAS S.A one-equation turbulence model for aerodynamic flows[J].La Recherche Aérospatiale,1992,439(1):5-21.
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[18]CHEN X,SHE Z S,HUSSAIN F.Quantifying wall turbulence via a symmetry approach:Part II.Reynolds stresses[J].Journal of Fluid Mechanics,accepted.
[19]SHE Z S,HU N,WU Y.SED based closure model for wall bounded turbulent flow[J].Acta Mech Sin,2009,25:731-736.
[20]SHE Z S,CHEN X,WU Y,et al.New perspective in statistical modeling of wall-bounded turbulence[J].Acta Mech Sin,2010,26:847-861.
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[23]CHEN X,SHE Z S.Analytic prediction for planar turbulent boundary layers[J].Science China-Physics Mechanics Astronomy,2016,59(11):57-63.
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[27]CHEN X,HUSSAIN F,SHE Z S.Predictions of canonical wall bounded turbulent flows via a modified k-ωequation[J].Journal of Turbulence,2017,18(1):1-35.
[28]SHE Z S,WU Y,CHEN X,et al.A multi-state description of roughness effects in turbulent pipe flow[J].New Journal of Physics,2012,14:093054-1-16.
[29]WU B,BI W T,HUSSAIN F,et al.On the invariant mean velocity profile for compressible turbulent boundary layers[J].Journal of Turbulence,accepted.
[30]SHE Z S,CHEN X,ZOU H Y,et al.Prediction of temperature distribution in turbulent Rayleigh-Benard convection[J].arXiv:1401.2138,2014
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[33]RUMSEY C L,RIVERS S M,MORRISON J H.Study of CFDvariation on transport configurations from the second dragprediction workshop[R].AIAA 2004:0394.
[34]DURBIN P A.Some recent developments in turbulence closure modeling[J].Annual Review of Fluid Mechanics,2018,50:77-103.
[35]EMMONS H W.The laminar-turbulent transition in a boundary layer-Part I[J].Journal of the Aeronautical Sciences,1951,18(7):490-498.
[36]MENTER F R,LANGTRY R,VLKER S.Transition modelling for general purpose CFD codes[J].Flow,Turbulence and Combustion,2006,77(1):277-303.
[37]符松,王亮.基于雷诺平均方法的高超声速边界层转捩模拟[J].中国科学:物理学力学天文学,2009,39:617-626.FU S,WANG L.Simulation of transition in hypersonics boundary layers based on RANS method[J].Sci Sin-Phys Mech Astron,2009,39:617-626.(in Chinese)
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[40]SCHNEIDER S P.Flight data for boundary layer transition at hypersonic and supersonic speeds[J].Journal of Spacecraft Rockets,1999,36(1):8-20.
[41]SCHUBAUER G B,KLEBANOFF P S.Contributions on the mechanics of boundarylayer transition[J].Technical Report Archive and Image Library,1955,39:411-415.
[42]SAVILL A M.Further progress in the turbulence modelling of by-pass transition[C]//Engineering Turbulence Modelling&Experiments,1993:583-592
[43]BRANDT L,SCHLATTER P,HENNINGSON D S.Transition in boundary layers subject to free-stream turbulence[J].Journal of Fluid Mechanics,2004,517:167-198.
[44]VALLIKIVI M,HULTMARK M,SMITS A J.Turbulent boundary layer statistics at very high Reynolds number[J].Journal of Fluid Mechanics,2015,779:371-389.
[45]SHE Z S,ZOU H Y,XIAO M J,et al.Fazle Hussain,Prediction of compressible turbulent boundary layer via a symmetry-based length model[J].Journal of Fluid Mechanics,accepted.
[46]COOK P H,MCDONALD M A,FIRMIN M C P.Aerofoil RAE 2822-pressure distributions,and boundary layer and wake measurements[R].Experimental Data Base for Computer Program Assessment,AGARD Report AR 138,1979:A6-1-77.
[47]THIBERT J J,GRANDJACQUES M.NACA 0012AIRFOIL-ONERA[R].Experimental Data Base for Computer Program Assessment,AGARD Report AR 138,1979:A6-1-36.
[48]https://turbmodels.larc.nasa.gov/naca4412sep_val.html
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[50]MEE D J.Boundary-layer transition measurements in hypervelocity flows in a shock tunnel[J].AIAA Journal,2002,40(8):1542-1548.
[51]许春晓.壁湍流相干结构和减阻控制机理[J].力学进展,2015,45:111-140.XU C X.Coherent structures and drag-reduction mechanism in wall turbulence[J].Adv Mech,2015,45:111-140.(in Chinese)
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[2]周恒,张涵信.号称经典物理留下的世纪难题“湍流问题”的实质是什么?[J].中国科学:物理学力学天文学,2012,42:1-5.ZHOU H,ZHANG H X.What is the essence of the so-called century lasting difficult problem in classic physics,the“problem of turbulence”?[J].Sci Sin-Phys Mech Astron,2012,42:1-5.(in Chinses)
[3]阎超,于剑,徐晶磊,等.CFD模拟方法的发展成就与展望[J].力学进展,2011,41:562-589.YAN C,YU J,XU J L,et al.On the achievements and prospects for the methods of computational fluid dynamics[J].Adv Mech,2011,41:562-589.(in Chinese)
[4]王振国,孙明波.超声速湍流流动、燃烧的建模与大涡模拟[J].北京:科学出版社,2013:3-4.WANG Z G,SUN M B.Model for combustion and LES in supersonic turbulence flow[M].Beijing:Science Press,2013:3-4.(in Chinese)
[5]高正红,王超.飞行器气动外形设计方法研究与进展[J].空气动力学学报,2017,35(4):516-528.GAO Z H,WANG G C.Aerodynamic shape design methods for air craft:status and trends[J].Acta Aerodynamica Sinica,2017,35(4):516-528.
[6]WILCOX D C.Turbulence modeling for CFD[M].DCWIndustries,2006:124-127.
[7]佘振苏,陈曦,未波波,等.应用结构系综理论发展壁湍流工程湍流模型[J].中国科学:物理学力学天文学,2015,45:26-34.SHE Z S,CHEN X,WEI B B,et al.SED-based studies of turbulence models for wall flows[J].Sci Sin-Phys Mech Astron,2015,45:26-34.(in Chinese)
[8]SPALARTP R,ALLMARAS S.A one-equation turbulence model for aerodynamic flows[J].La Recherche Aérospatiale,1992,439(1):5-21.
[9]佘振苏.复杂系统学新框架[M].北京:科学出版社,2012:97-99.SHE Z S.New theory for complex system[M].Beijing:Science Press,2012:97-99.(in Chinese)
[10]佘振苏.什么是湍流世纪难题?[M].教育部,科学技术部,中国科学院,国家自然科学基金委员会.10000个科学难题:物理学卷.北京:科学出版社,2009.SHE Z S.What is the century-old difficult turbulence problem?[M].Ministry of Education,Ministry of Science and Technology,CSA,National Natural Science Foundation of China.10000Problem of Science:Phys.Beijing:Science Press,2009:163-174.
[11]PRANDTL L.Berichtüber die entstehung der turbulenz[J].ZAngew Math Mech,1925,5:136-139.
[12]MARUSIC I,MCKEON B J,MONKEWITZ P A,et al.Wallbounded turbulent flows at high Reynolds numbers:Recent advances and key issus[J].Physics of Fluids,2010,22:24-30.
[13]BODENSCHATZ E Prandtl,GOETTINGEN School.A voyage through turbulence[M].Cambridge:Cambridge University Press,2011:40-100.
[14]von Krmn′T H.Mechanische ahnlichkeit und turbulenz[J].Nachrichten von der Gesellschaft der Wissenschaften zu G9ttingen Fachgruppe I(Mathematik),1930,5:58-76.
[15]邓小刚,刘昕,毛枚良,等.高精度加权紧致非线性格式的研究发展[J].力学进展,2007,37:417-427.DENG X G,LIU X,MAO M L,et al.Advances in high-order accurate weighted compact nonlinear schemes[J].Adv Mech,2007,37:417-427.(in Chinese)
[16]王光学,邓小刚,刘化勇,等.高阶精度格式WCNS在三角翼大迎角模拟中的应用研究[J].空气动力学学报,2012,30(1):28-33.WANG G X,DENG X G,LIU H Y,et al.Study of DSMC of algorithm and model for hypersonic multiphase rarefied flow[J].Acta Aerodynamica Sinica,2012,30(1):28-33.(in Chinese)
[17]SHE Z S,CHEN X,HUSSAIN F.Quantifying wall turbulence via a symmetry approach:A Lie group theory[J].Journal of Fluid Mechanics,2017,827:322-356.
[18]CHEN X,SHE Z S,HUSSAIN F.Quantifying wall turbulence via a symmetry approach:Part II.Reynolds stresses[J].Journal of Fluid Mechanics,accepted.
[19]SHE Z S,HU N,WU Y.SED based closure model for wall bounded turbulent flow[J].Acta Mech Sin,2009,25:731-736.
[20]SHE Z S,CHEN X,WU Y,et al.New perspective in statistical modeling of wall-bounded turbulence[J].Acta Mech Sin,2010,26:847-861.
[21]SHE Z S,CHEN X,HUSSAIN F.A Lie-group derivation of a multi-layer mixing length formula for turbulent channel and pipe flow[A].In“Turbulence colloquium Marseille 2011”,p.436-455,Ed.Farge,Moffatt,Schneider,ISBN 978-2-7598-1145-8.
[22]陈曦.壁湍流的结构系综理论[D].北京大学博士学位论文,2012:92-99.CHEN X.The structural ensemble dynamics theory of wall turbulence[D].PHD dissertation of Peking university,2012:92-99.(in Chinese)
[23]CHEN X,SHE Z S.Analytic prediction for planar turbulent boundary layers[J].Science China-Physics Mechanics Astronomy,2016,59(11):57-63.
[24]WU Y,CHEN X,SHE Z S,et al.On the Karman constant in turbulent channel flow[J].Physica Scripta T,2013,155:014009-1-4.
[25]CHEN X,HUSSAIN F,SHE Z S.Bulk flow scaling for turbulent channel and pipe flows[J].Euro Phys Lett,2016,115:34001-1-5.
[26]CHEN X,WEI B,HUSSAIN F,et al.Anomalous dissipation and kinetic energy distribution in very high Reynolds number pipes[J].Phys Rev E,2016,93:011102-1-5.
[27]CHEN X,HUSSAIN F,SHE Z S.Predictions of canonical wall bounded turbulent flows via a modified k-ωequation[J].Journal of Turbulence,2017,18(1):1-35.
[28]SHE Z S,WU Y,CHEN X,et al.A multi-state description of roughness effects in turbulent pipe flow[J].New Journal of Physics,2012,14:093054-1-16.
[29]WU B,BI W T,HUSSAIN F,et al.On the invariant mean velocity profile for compressible turbulent boundary layers[J].Journal of Turbulence,accepted.
[30]SHE Z S,CHEN X,ZOU H Y,et al.Prediction of temperature distribution in turbulent Rayleigh-Benard convection[J].arXiv:1401.2138,2014
[31]XIAO M J,SHE Z S.A new algebraic transition model based on stress length function[C]//The 69th Annual Meeting of American Physical Society-Division of Fluid Dynamics.H29.00002.Portland,Oregon,U.S.A.20-22,Nov.2016.
[32]HASSANM Nagib,KAPIL A Chauhan.Variations of von Karman coefficient in canonical flows[J].Physics of Fluids,2008,20:101518.
[33]RUMSEY C L,RIVERS S M,MORRISON J H.Study of CFDvariation on transport configurations from the second dragprediction workshop[R].AIAA 2004:0394.
[34]DURBIN P A.Some recent developments in turbulence closure modeling[J].Annual Review of Fluid Mechanics,2018,50:77-103.
[35]EMMONS H W.The laminar-turbulent transition in a boundary layer-Part I[J].Journal of the Aeronautical Sciences,1951,18(7):490-498.
[36]MENTER F R,LANGTRY R,VLKER S.Transition modelling for general purpose CFD codes[J].Flow,Turbulence and Combustion,2006,77(1):277-303.
[37]符松,王亮.基于雷诺平均方法的高超声速边界层转捩模拟[J].中国科学:物理学力学天文学,2009,39:617-626.FU S,WANG L.Simulation of transition in hypersonics boundary layers based on RANS method[J].Sci Sin-Phys Mech Astron,2009,39:617-626.(in Chinese)
[38]ANDERSON J D.Hypersonic and high temperature gas dynamics[M].McGraw-Hill Book Company,1989:219-228.
[39]陈坚强,涂国华,张毅锋,等.高超声速边界层转捩研究现状与发展趋势[J].空气动力学学报,2017,35(3):311-337.CEN J Q,TU G H,ZHANG Y F,et al.Hypersonic boundary layer transition:what we know,where shall we go[J].Acta Aerodynamics Sinica,2017,35(3):311-337.
[40]SCHNEIDER S P.Flight data for boundary layer transition at hypersonic and supersonic speeds[J].Journal of Spacecraft Rockets,1999,36(1):8-20.
[41]SCHUBAUER G B,KLEBANOFF P S.Contributions on the mechanics of boundarylayer transition[J].Technical Report Archive and Image Library,1955,39:411-415.
[42]SAVILL A M.Further progress in the turbulence modelling of by-pass transition[C]//Engineering Turbulence Modelling&Experiments,1993:583-592
[43]BRANDT L,SCHLATTER P,HENNINGSON D S.Transition in boundary layers subject to free-stream turbulence[J].Journal of Fluid Mechanics,2004,517:167-198.
[44]VALLIKIVI M,HULTMARK M,SMITS A J.Turbulent boundary layer statistics at very high Reynolds number[J].Journal of Fluid Mechanics,2015,779:371-389.
[45]SHE Z S,ZOU H Y,XIAO M J,et al.Fazle Hussain,Prediction of compressible turbulent boundary layer via a symmetry-based length model[J].Journal of Fluid Mechanics,accepted.
[46]COOK P H,MCDONALD M A,FIRMIN M C P.Aerofoil RAE 2822-pressure distributions,and boundary layer and wake measurements[R].Experimental Data Base for Computer Program Assessment,AGARD Report AR 138,1979:A6-1-77.
[47]THIBERT J J,GRANDJACQUES M.NACA 0012AIRFOIL-ONERA[R].Experimental Data Base for Computer Program Assessment,AGARD Report AR 138,1979:A6-1-36.
[48]https://turbmodels.larc.nasa.gov/naca4412sep_val.html
[49]ZHANG Y S,BI W T,HUSSAIN F,et al.A generalized Reynolds analogy for compressible wall-bounded turbulentflows[J].Journal of Fluid Mechanics,2014,739:392-420.
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