基于结构系综理论发展可靠工程转捩模型的一种新思路

毕卫涛; 唐帆; 胡永煌; 佘振苏

doi:10.7638/kqdlxxb-2020.0123

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基于结构系综理论发展可靠工程转捩模型的一种新思路

专栏——国家数值风洞自主可控关键技术 | 更新时间：2026-05-28

- 基于结构系综理论发展可靠工程转捩模型的一种新思路
- New perspective for developing reliable engineering transition model based on the structural ensemble dynamics theory
- 空气动力学学报 2020年38卷第6期页码：1136-1148
- 作者机构：
  
  1. 北京大学工学院力学与工程科学系,北京,100871
  2. 湍流与复杂系统国家重点实验室,北京,100871
- 作者简介：
  
  毕卫涛(1974-), 男, 陕西人, 副研究员, 研究方向:湍流.E-mail:weitaobi@pku.edu.cn
  佘振苏(1962-), 教授, 研究方向:湍流与复杂系统.E-mail:she@pku.edu.cn
- 基金信息：
  
  国家数值风洞工程;国家自然科学基金重大研究计划重点项目（91952201）
- DOI：10.7638/kqdlxxb-2020.0123
  中图分类号： O357.4
- 纸质出版：2020
- 稿件说明：
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毕卫涛, 唐帆, 胡永煌, 佘振苏. 基于结构系综理论发展可靠工程转捩模型的一种新思路[J]. 空气动力学学报, 2020, 38(6): 1136-1148.

BI Weitao, TANG Fan, HU Yonghuang, et al. New perspective for developing reliable engineering transition model based on the structural ensemble dynamics theory[J]. 2020, 38(6): 1136-1148.
毕卫涛, 唐帆, 胡永煌, 佘振苏. 基于结构系综理论发展可靠工程转捩模型的一种新思路[J]. 空气动力学学报, 2020, 38(6): 1136-1148. DOI： 10.7638/kqdlxxb-2020.0123.

BI Weitao, TANG Fan, HU Yonghuang, et al. New perspective for developing reliable engineering transition model based on the structural ensemble dynamics theory[J]. 2020, 38(6): 1136-1148. DOI： 10.7638/kqdlxxb-2020.0123.

摘要

边界层转捩是一个科学与工程难题。当代工程转捩模型建立在间歇因子的唯象演化基础上，包含大量的经验参数和关联函数，其物理意义模糊导致适用范围不明确。随着高速流动的物理新因素的增加，出现了模型复杂性迅速增长，而可靠性越来越低的尴尬状况。根本性的瓶颈在于缺乏完整的湍流边界层理论，这一状况在壁湍流的结构系综理论诞生后出现了显著变化。该理论将固壁对湍流脉动形成的对称性约束表述为形成少数个结构系综，利用结构系综的广义拉伸对称性假设，完成了对于规范边界层平均速度和湍动能的完整剖面的统一描述，与大量实验和计算数据精确符合。将该理论应用于描述边界层的流向变化，便自然形成了从层流到过渡区再到湍流充分发展区的三系综刻画，实现了对转捩全过程的完整描述。本文提出了一个构建典型工程边界层转捩模型的新思路：依据实验和可靠的计算数据确定转捩边界层的流向结构系综，提炼反映转捩边界层物理状态和相似性的多层结构参数，进而形成物理图像清晰、定量描述精确的新型转捩模型。针对自由来流湍流诱发的平板边界层强迫转捩和有攻角的高超声速尖锥转捩两类流动，证明了上述思路的可行性，获得了对大湍流度下平板转捩的全分量、全流域的精准理论描述。将所发展的SED-SL代数转捩模型应用到高超声速尖锥的计算，得到了与实验一致的计算结果。通过细致刻画边界层流动的多层结构系综，有望推动转捩模型研究进入一个物理化、精确化的新阶段。

Abstract

Current engineering transition models are built upon the concept of intermittency factor whose streamwise evolution is described by phenomenology of dimensional analysis with numerous physically insignificant coefficients which are not invariant with varying physical conditions

especially for supersonic and hypersonic flows. The major bottleneck is the lack of a complete theor

y for turbulent boundary layer (TBL) beyond the log law

and the situation begins to change after the proposal of the structural ensemble dynamics (SED) theory

which is based on the analysis of wall-induced dilation symmetry constraint on the momentum and energy balance equations. The key assumption of the SED theory is that TBL flow domain is self-organized into a finite number of sub-regions

in each of which a structural ensemble is so formed that eddies responsible for momentum and energy transport have characteristic (stress) lengths which locally behave in power laws with wall distance (

) to preserve dilation symmetry. With a generalized dilation invariance assumption describing a universal transition across different sub-regions

the theory yields analytic multi-layer expression of the stress lengths from which the mean velocity and turbulence intensity distributions can be derived

in excellent agreement with data of canonical wall turbulence from both experiments and computations. More recent extension of the SED theory in describing streamwise evolving TBL by introducing dilation of the distance to leading edge (

) yields in a straightforward way an accurate description of laminar-turbulent transition. Here

we present a new perspective to build a reliable engineering transition model from the SED theory

which consists in specifying the streamwise variation of the multi-layer parameters before solving the Reynolds averaged Navier-Stokes equations. The model is successfully validated by computational results for free-stream turbulence induced transitional flows passing flat plate and hypersonic flows passing sharp cone with varying attack angles. New kind of promising transition model may arise with advantage of being stable and transparency for adjusting parameters which are all physically meaningful.

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