Structural ensemble dynamics theory for engineering turbulenc models

SHE Zhensu; TANG Fan; XIAO Mengjuan

doi:10.7638/kqdlxxb-2018.0249

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Structural ensemble dynamics theory for engineering turbulenc models

更新时间：2026-05-28

- Structural ensemble dynamics theory for engineering turbulenc models
- Vol. 37, Issue 1, Pages: 1-18(2019)
- 作者机构：
  
  湍流与复杂系统国家重点实验室, 北京大学工学院,北京,100871
- 作者简介：
- 基金信息：
- DOI：10.7638/kqdlxxb-2018.0249
  CLC： V211.3
- Published：2019
- 稿件说明：
移动端阅览
佘振苏, 唐帆, 肖梦娟. 面向精准工程湍流模型的理论研究[J]. 空气动力学学报, 2019, 37(1): 1-18.

SHE Zhensu, TANG Fan, XIAO Mengjuan. Structural ensemble dynamics theory for engineering turbulenc models[J]. 2019, 37(1): 1-18.
佘振苏, 唐帆, 肖梦娟. 面向精准工程湍流模型的理论研究[J]. 空气动力学学报, 2019, 37(1): 1-18. DOI： 10.7638/kqdlxxb-2018.0249.

SHE Zhensu, TANG Fan, XIAO Mengjuan. Structural ensemble dynamics theory for engineering turbulenc models[J]. 2019, 37(1): 1-18. DOI： 10.7638/kqdlxxb-2018.0249.

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。

Abstract

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.

关键词

Keywords

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