Pr数对湍流被动标量输运的影响  

THE EFFECT OF TRANSPORTATION OF PASSIVE SCALAR IN THE HOMOGENEOUS TURBULENCE WITH DIFFERENT MOLECULAR PRANDTL NUMBERS

作　　者：周海兵[1] 崔桂香[1] 张兆顺[1] L.Shao 

机构地区：[1]清华大学工程力学系,北京100084 [2]Laboratory of Fluid Mechanics and Acoustics,Ecole Centrale de Lyon,France

出　　处：《力学学报》2002年第6期847-855,共9页Chinese Journal of Theoretical and Applied Mechanics

基　　金：清华大学基础研究基金;中法实验室(LIAMA);探索108集群计算机应用基金的资助项目.

摘　　要：采用直接数值模拟的方法,研究分子Pг数对湍流被动标量输运的影响,并提供充分的证据证明,湍流Pг数明显依赖于分子Pг数.在算例中,湍流雷诺平均PгT数与分子Pг数的倒数呈线性关系;湍流亚格子Pгt数与分子Pг数的关系较为复杂,在分子Pг数为1附近时,湍流亚格子Pгt数出现极小值.This paper studies the transportation of passive scalar in statistically stationary isotropic turbulence with different molecular Prandtl numbers by direct numerical simulation (DNS). The mean gradient of scalar is constant. Two cases of grid resolution are computed, i.e. 1283 and 2563 with several Taylor-scale Reynolds numbers respectively in order to see the Reynolds number effect. The molecular Prantdl numbers are given at 0.1, 0.5, 0.8, 1.0, 1.2 and 3.0. The results of DNS are in good agreement with available experimental data, including the decay of the longitudinal variance and cross-stream variance, the ratio of velocity to scalar timescale, etc. This paper provides sound evidence that the turbulence Prandtl number depends on molec-ular Prandtl number. The turbulence Prandtl number PrT varies linearly with the reciprocal of molecular Prandtl number in Reynolds average. So the study on the turbulent Prandtl number is particularly important for lower molecular Prandtl number. We applied dynamic procedure to obtain subgrid Prandtl number in large eddy simulation. The relationship between subgrid-scale turbulence Prandtl number Prt and molecular Prandtl number is more complicated, the mini-mum Prt occurs around Pr = 1.0. The paper investigates the reason for the minimum of subgrid Prandtl number. The statistical quantities dominated by small scale turbulence are weakly depen-dent on the molecular Prandtl number, but it is of stronger dependence on the molecular Prandtlnumber for the quantities dominant by great scale turbulence. Based on the analysis of transferspectrum of scalar flux the appearance of minimum subgrid Prandtl number around Pr ?1 can be well understood. The production of subgrid scalar flux clearly shows a maximum of around Pr = 1.0. This is the further explanation of why the subgrid Prandtl number takes a minimum around Pr=1.0.

关 键 词：湍流 被动标量 PR数 雷诺平均 亚格子模式 

分 类 号：O357.5[理学—流体力学]