槽道湍流中应变率张量的拉格朗日时间自相关
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摘要
已有的研究证实,在均匀各向同性湍流中速度梯度张量(VGT)演化的无量纲时间是当地Kolmogorov时间。本文使用大涡模拟的方法,计算了一个雷诺数7 000的槽道流场,以到壁面的无量纲距离的大小将流场分为不同区间,使用当地Kolmogorov时间对不同区间的应变率张量的拉格朗日时间自相关函数进行无量纲化。发现不同区间自相关函数的下降曲线不完全重合:在对数区中不同区间自相关函数的下降曲线基本重合,但在靠近壁面的黏性底层和过渡层中则无此现象。因此,当地Kolmogorov时间不是槽道中速度梯度张量演化的普适无量纲时间。
It is confirmed that the dimensionless time for evolution of velocity gradient tensor( VGT) is local Kolmogorov time scale in homogeneous isotropic turbulence. The channel flow at Reynolds number 7 000 was calculated using large-eddy simulation in this paper. The flow field was divided into different regions according to the size of the dimensionless distance to the wall and the auto-correlation functions of different regions were normalized by local Kolmogorov time scale. The decline curves of auto-correlation functions in different regions were found not really the same. In logarithmic layer,the decline curves of auto-correlation functions in different regions almost overlapped,while the similar phenomenon did not exist in viscous bottom layer near the wall and buffer layer. The results show that local Kolmogorov time scale is not the universal dimensionless time of evolution of VGT in channel flow.
It is confirmed that the dimensionless time for evolution of velocity gradient tensor( VGT) is local Kolmogorov time scale in homogeneous isotropic turbulence. The channel flow at Reynolds number 7 000 was calculated using large-eddy simulation in this paper. The flow field was divided into different regions according to the size of the dimensionless distance to the wall and the auto-correlation functions of different regions were normalized by local Kolmogorov time scale. The decline curves of auto-correlation functions in different regions were found not really the same. In logarithmic layer,the decline curves of auto-correlation functions in different regions almost overlapped,while the similar phenomenon did not exist in viscous bottom layer near the wall and buffer layer. The results show that local Kolmogorov time scale is not the universal dimensionless time of evolution of VGT in channel flow.
引文
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[2]OOI A,SORIA J,CHONG M S,et al.A study of the evolution and characteristics of the invariants of the velocity-gradient tensor in isotropic turbulence[J].Journal of Fluid Mechanics,1999,381(1):141-174.
[3]ATKINSON C,CHUMAKOV S,BRRMEJO-MORENO I,et al.Lagrangian evolution of the invariant of the velocity gradient tensor in a turbulent boundary layer[J].Physics of Fluids,2012,24(10):677-686.
[4]MENEVEAU C.Lagrangian dynamics and models of the velocity gradient tensor in turbulent flows[J].Annual Review of Fluid Mechanics,2011,43(1):219-245.
[5]KERR R M.Histograms of helicity and strain in numerical turbulence[J].Physical Review Letters,1987,59(7):783-786.
[6]ASHURST W T,KERSTEIN A R,KERR R M,et al.Alignment of vorticity and scalar gradient with the strain rate in simulated Navier-Stokes turbulence[J].Physics of Fluids,1987,30(8):2343-2353.
[7]SREENIVASAN K R,ANTONIA R A.The phenomenology of small-scale turbulence[J].Annual Review of Fluid Mechanics,1997,29(1):435-472.
[8]GIRIMAJI S S,POPE S B.A diffusion model for velocity gradients in turbulence[J].Physics of Fluids A:Fluid Dynamics,1990,2(2):242-256.
[9]MARTIN J,DOPAZO C,VALION L.Dynamics of velocity gradient invariants in turbulence:Restricted Euler and linear diffusion models[J].Physics of Fluids,1998,10(8):2012-2025.
[10]JEONG E,GIRIMAJI S S.Velocity-gradient dynamics in turbulence:Effect of viscosity and forcing[J].Theoretical and Computational Fluid Dynamics,2003,16(6):421-432.
[11]FANG L,BOS W J T,JIN G D.Short-time evolution of Lagrangian velocity gradient correlations in isotropic turbulence[J].Physics of Fluids,2015,27(12):457-472.
[12]FANG L,ZHANG Y J,FANG J,et al.Relation of the fourth-order statistical invariants of velocity gradient tensor in isotropic turbulence[J].Physical Review E,2016,94(2):023114.
[13]YU H,MENEVEAU C.Lagrangian refined Kolmogorov similarity hypothesis for gradient time-evolution in turbulence flows[J].Physical Review Letters,2010,104(8):084502.
[14]TENNEKES H,LUMLEY J.湍流初级教程[M].施红辉,林培锋,金浩哲,译.北京:科学出版社,2015:14-15.TENNEKES H,LUMLEY J.A first course in turbulence[M].SHI H H,LIN P F,JIN H Z,translated.Beijing:Science Press,2015:14-15(in Chinese).
[15]张兆顺,崔桂香,许春晓.湍流理论与模拟[M].北京:清华大学出版社,2005:11.ZHANG Z S,CUI G X,XU C X.Theory and modeling of turbulence[M].Beijing:Tsinghua University Press,2005:11(in Chinese).
[16]STOLOVITZKY G,KAILASNATH P,SREENIVASAN K R.Kolmogorov’s refined similarity hypothesis[J].Physical Review Letters,1992,69(8):1178-1181.
[17]张兆顺,崔桂香,许春晓.湍流大涡模拟的理论与应用[M].北京:清华大学出版社,2008:101-104.ZHANG Z S,CUI G X,XU C X.Theory and application of large eddy simulation of turbulence[M].Beijing:Tsinghua University Press,2008:101-104(in Chinese).
[18]周海兵.标量湍流的数值研究[D].北京:清华大学,2003:39-45.ZHOU H B.Numerical research of scalar turbulence[D].Beijing:Tsinghua University,2003:39-45(in Chinese).
[19]XU C X,ZHANG Z S,TOONDER J M J,et al.Origin of high kurtosis levels in the viscous sublayer.Direct numerical simulation and experiment[J].Physics of Fluids,1996,8(7):1938-1944.
[20]FANG L,SHAO L,BERTOGLIO J P,et al.The rapid-slow decomposition of the subgrid flux in inhomogeneous scalar turbulence[J].Journal of Turbulence,2011,12(8):1-23.