应用结构系综理论发展壁湍流工程湍流模型  

SED-based studies of turbulence models for wall flows

作　　者：佘振苏[1] 陈曦[1] 未波波[1] 邹鸿岳[1] 毕卫涛[1] 

机构地区：[1]湍流与复杂系统国家重点实验室、北京大学工学院力学与工程科学系,北京 100871

出　　处：《中国科学：物理学、力学、天文学》2015年第12期12-29,共18页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家重点基础研究发展规划(编号:2009CB724100);国家自然科学基金资助项目(编号:11221062,11452002)

摘　　要：本文综述结构系综理论(Structural Ensemble Dynamics,SED)在湍流模型研究上的进展.SED研究壁湍流在系综统计层面的对称性规律.借助反映系统对称性变化的序函数新概念,SED给出了壁湍流平均场的解析刻画,为分析和修正湍流模型奠定了基础.本文以k-?模型和Baldwin&Lomax(BL)模型为例,展示了将SED应用到发展壁湍流工程模型.新的SED-k-?模型首次实现了对圆管平均速度和(流向)湍动能剖面的同时精确预测(精度高于99%).该结果一方面支撑了新近提出的0.45的普适卡门常数,另一方面确认了存在一个中间层,对应于最近学界广泛关注的湍动能第二峰值.SED-stress-length模型给出了不同马赫数下平板湍流边界层平均速度和温度(密度)剖面的高精度预测,比BL模型提高了近十个百分点.以上结果提供了湍流模型研究的新框架,即通过参照SED对模型背后的多层结构图像进行定量修正,由此大幅提高预测精度,尤其是把模型经验参数用具有明确物理意义的多层结构参数解析表达,从而有望解决复杂流动计算时参数调节的核心困难.One of the greatest challenges in computational modeling of real engineering flows is to derive physically sound turbulence models and to determine their（numerous） coefficients from the understanding of turbulence physics, which has been a bottleneck in turbulence studies for several decades for the lack of a sound theoretical framework. Here, we present a new symmetry-based approach, called structural ensemble dynamics（SED）, and apply it to develop new turbulence models. The SED theory focuses on revealing the symmetry properties of wall-bounded flows including channel, pipe, turbulent boundary layer, RB convection, etc. We propose a concept of order function which preserves the dilation invariance due to the presence of wall, yielding a new parameterization for mean profiles in terms of physical multi-layer structure parameters（thickness, scaling, etc.）. The SED can be applied to study the Reynolds-averaged Navier-Stokes equation with turbulence models whose defect is easily revealed under the multi-layer picture. We report here the improvement of the k-？ model for pipe flow modeling, as well as the definition of a new algebraic model for compressible turbulent boundary layer（CTBL） modeling. The modified k-ω model, the so-called SED-k-？ model, has achieved, for the first time, accurate prediction of both mean velocity and（streamwise） kinetic energy for a wide range of Reynolds number, with a 99% accuracy when compared to the Princeton experimental data. In addition, this study has laid a solid support to the universal Karman constant 0.45. Moreover, it points out the existence of a meso-layer with anomaly in energy dissipation, which explains both the outer peak and the approximate logarithmic law in the kinetic energy profile. Secondly, we report a new algebraic model, SED-SL model, which performs clearly superior in both accuracy and simplicity to the Baldwin Lomax model for the modeling of CTBL. The SED-based models have two distinct features： the first is its accurate determinatio

关 键 词：结构系综理论 湍流模型 k-w模型 BL模型 壁湍流 

分 类 号：O357.5[理学—流体力学]