面向流体力学的多范式融合研究展望

张伟伟; 王旭; 寇家庆

doi:10.6052/1000-0992-22-050

面向流体力学的多范式融合研究展望

doi: 10.6052/1000-0992-22-050

张伟伟^{1, 2, ,},
王旭¹,
寇家庆³

1.
西北工业大学航空学院, 西安 710072
2.
西北工业大学流体力学智能化国际联合研究所, 西安 710072
3.
亚琛工业大学空气动力学所, 德国亚琛 52062

基金项目: 国家自然科学基金重大计划集成项目 (92152301) 、国家自然科学基金面上项目 (12072282) 、国家数值风洞项目 (NNW2018-ZT1B01, NNW2019ZT2-A05) 资助

详细信息

作者简介:
张伟伟，西北工业大学航空学院博士生导师，长江学者特聘教授，中国空气动力学会副理事长、流体力学智能化国际联合研究所中方负责人。主要从事智能空气动力学、气动弹性力学和飞行器设计研究，是国内智能流体力学研究的倡导者和主要推动者之一。发展了高效高精度的空气动力模型和气动弹性分析方法，揭示了复杂流固耦合问题的诱发机理，主持国家自然科学基金等国家级项目10余项，有力支撑了我国航空、航天、兵器等十多个单位20多个型号的研制，获得省部级科研成果奖5项。在PAS、JFM等国内外知名刊物发表论文100余篇，撰写著作3部。曾获得国家优秀青年基金、中国航空学会青年科技奖、中国空气动力学会青年科技奖等荣誉。担任中国空气动力学会智能流体力学专业组主任、空气弹性力学专业委员会副主任，中国力学学会流固耦合力学专业委员会副主任，智能流体力学产业联合体副理事长兼秘书长，《空气动力学学报》副主编，AST、TAML、AAMM、AIA等国际期刊编委

通讯作者:
aeroelastic@nwpu.edu.cn

中图分类号: V211
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出版历程
- 收稿日期: 2022-12-19
- 录用日期: 2023-03-16
- 网络出版日期: 2023-04-17
- 刊出日期: 2023-06-25

Prospects of multi-paradigm fusion methods for fluid mechanics research

ZHANG Weiwei^{1, 2
, ,},
WANG Xu¹,
KOU Jiaqing³

1.
School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China
2.
International Joint Institute of Artificial Intelligence on Fluid Mechanics, Northwestern Polytechnical University, Xi'an 710072, China
3.
Institute of Aerodynamics, RWTH Aachen University, Wüllnerstraße 5a, 52062, Aachen, Germany

Funds: The project was supported by the (12345678) and (9876543)

More Information

Corresponding author: aeroelastic@nwpu.edu.cn

摘要

摘要: 实验观测、理论研究以及数值模拟是包括流体力学在内很多学科的基本研究范式. 21世纪以来, 大数据驱动下的人工智能成为引领新一轮科技革命和产业变革的重要驱动力, 也被称为数据密集型科学研究范式, 即第四范式. 同样, 数据驱动的机器学习方法也成为流体力学的新兴方向, 并助推智能流体力学方向的发展. 然而, 与面向社会依赖“互联网 + 大数据”的数据密集型范式相比, 流体力学智能化研究有其特有的背景. 例如有限工程样本中产生的海量流动数据, 与流动状态、几何边界条件的高维度以及复杂流动固有的高维、跨尺度、随机、非线性特征相比, 数据驱动的流体力学研究面临着大数据小样本问题. 经典流体力学虽然有三大研究范式, 但融合度很低, 工程设计师通常只能对不同来源的数据进行拼凑使用或简单修正. 多源数据融合一定程度上可缓解单一样本量来源少、建模难, 以及低精度样本利用不充分等困境, 但仍未能实现基本范式中的理论模型或者专家知识和经验的充分利用. 因此, 在人工智能技术支撑的第四范式架构下, 有机融合实验、理论模型以及数值模拟三大手段, 发展“数据 + 知识”双驱动的流体力学多范式融合方法, 成为解决重大实际工程研制问题的迫切需求, 也是新时代流体力学学科内涵、特色发展的迫切需求.
- 数据驱动 /
- 人工智能 /
- 流体力学 /
- 智能流体力学 /
- 多范式融合
Abstract: Experimental observation, theoretical research and numerical simulation are the basic research paradigms in many disciplines, including fluid mechanics. Since the 21st century, artificial intelligence based on big data has become an important driving force, leading to new scientific and technological revolution and industrial transformation. This is known as the data-intensive scientific research paradigm, which forms the fourth research paradigm. Similarly, data-driven machine learning has also become an emerging research direction in fluid mechanics and promoted the progress in intelligent fluid mechanics. However, compared to traditional data-intensive research paradigm that relies on "Internet and big data", research on intelligent fluid mechanics has its own unique background. For example, compared to high-dimensional flow state, geometric boundary conditions, and the inherent high-dimensional, cross-scale, random, and nonlinear characteristics of complex flow, research in data-driven fluid mechanics essentially handles large data but small samples. Although there are three major research paradigms in fluid mechanics, the integration among research paradigms is very low, where engineering optimization simply corrects data from multiple sources. Multi-source data fusion can alleviate several dilemmas, like small data sample from a single source, difficulties in modelling, and the insufficient utilization of low-fidelity data, it still fails to fully integrate theoretical models, expert knowledge and experience from the basic paradigms.Therefore, based on the fourth paradigm driven by artificial intelligence, the organic combination of three major research topics including experiment, theoretical model and numerical simulation, developing date and knowledge jointly driven multi-paradigm fusion methods for fluid mechanics, have become urgent to solve major practical engineering problems, as well as to satisfy the need for the development of the connotation and the characteristics of fluid mechanics in the new era.
- data-driven /
- artificial intelligence /
- fluid mechanics /
- intelligent fluid mechanics /
- multi-paradigm fusion

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图 1 达芬奇对水流现象的描摹

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图 2 边界层内外流动(Anderson 2005)

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图 3 NACA63415翼型流场压力分布和速度分布结果与CFD样本数据结果对比 (Re=1900, α=7°) ( a、b: 压力场; c、d: 速度场; 左: CFD样本数据; 右: 神经网络模型预测结果) (Sekar et al. 2019)

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图 4 机器学习湍流模型预测周期山算例壁面湍流剪切应力分布(Wang et al. 2017)

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图 5 机器学习应用于湍流建模的主要研究方向及流程(张伟伟等 2021)

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图 6 不同流场快照下机器学习方法的湍流区域识别结果对比(Li B et al. 2020)

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图 7 基于遗传编程的无模型智能化控制设计思路(Duriez et al. 2017)

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图 8 层流状态下圆柱流动控制结果(Ren et al. 2021)

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图 9 多范式融合的研究脉络

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图 10 分布载荷稀疏重构流程(赵旋等 2022)

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图 11 不同试验数据驱动模型的预测能力对比(Holierhoek et al. 2013)

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图 12 基于随机森林的天地气动数据融合(王旭等 2023)

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图 13 第二与第四范式的关系(Karpatne et al. 2017)

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图 14 Ling等人的TBNN网络架构 (Ling et al. 2016)

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图 15 Zhu等人引入标度分析的网络架构(Zhu L Y et al. 2021)

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图 16 基于机器学习的湍流模型修正(Singh et al. 2017b)

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图 17 集成神经网络融合模型实现小样本动态失速预测(Wang X et al. 2022)

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图 18 基于深度学习的计算-试验范式融合(Li K et al. 2022)

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表 1 Zhu L Y等(2019)对涡粘建模的输入特征

Feature	Description	Sign
1	Horizontal	u
2	Density	ρ
3	Normal wall distance	d
4	Normal wall distance squared times the vorticity	${{\rm{d}}^2}\varOmega$
5	Exponential function	${F_s}$
6	Projection of free stream to normal direction of streamline	${{\rm{sgn}}} (y)[ - v + u\tan (\alpha )]$
7	Velocity direction	$\arctan [\left\| {v/u} \right\|]$
8	Entropy	${{{\boldsymbol{S}}'}}$
9	Normalized strain rate	$\left\\| {{{\boldsymbol{S}}}} \right\\|/(\left\\| {{{\boldsymbol{S}}}} \right\\| + \left\\| {\boldsymbol{\varOmega }} \right\\|)$

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表 2 Xiao等(2017)对雷诺应力建模的输入特征

Feature (${q_\beta }$)	Description	Raw feature(${\hat q_\beta }$)	Normalization factor ($ q{_\beta *_{}} $)
${q_1}$	Ratio of excess Rotation rate to strain rate (Q criterion)	$\dfrac{1}{2}({\left\\| {\boldsymbol{\varOmega }} \right\\|^2} - {\left\\| {{\boldsymbol{S}}} \right\\|^2})$	${\left\\| {{\boldsymbol{S}}} \right\\|^2}$
${q_2}$	Turbulence intensity	k	$\dfrac{1}{2}{U_i}{U_i}$
${q_3}$	Wall-distance based Reynolds number	$\min \left(\dfrac{ {\sqrt k {\rm{d}}} }{ {50v} },2\right)$	Not applicable ^a
${q_4}$	Pressure gradient along streamline	${U_k}\dfrac{{\partial P}}{{\partial {x_k}}}$	$ \sqrt {\dfrac{{\partial P}}{{\partial {x_j}}}\dfrac{{\partial P}}{{\partial {x_j}}}{U_i}{U_i}} $
$ {q_5} $	Ratio of turbulence time scale to mean strain time scale	$\dfrac{k}{\varepsilon }$	$\dfrac{1}{{\left\\| {S} \right\\|}}$
${q_6}$	Cratio of pressure normal stresses to shear stresses	$ \sqrt {\dfrac{{\partial P}}{{\partial {x_j}}}\dfrac{{\partial P}}{{\partial {x_j}}}} $	$\dfrac{1}{2}\rho \dfrac{{\partial U_k^2}}{{\partial {x_k}}}$
${q_7}$	Nonorthogonality between velocity and its gradient	$\left\| {{U_i}{U_j}\dfrac{{\partial {U_i}}}{{\partial {x_j}}}} \right\|$	$\sqrt {{U_l}{U_l}{U_i}\dfrac{{\partial {U_i}}}{{\partial {x_j}}}{U_k}\dfrac{{\partial {U_k}}}{{\partial {x_j}}}} $
${q_8}$	Ratio of convection to production of TKE	${U_i}\dfrac{{{\rm{d}}k}}{{{\rm{d}}{x_i}}}$	$ \left\| {\overline {{{u'}_j}{{u'}_k}} {S_{jk}}} \right\| $
${q_9}$	Ratio of total to normal Reynolds stresses	$ \left\\| {\overline {{{u'}_i}{{u'}_j}} } \right\\| $	k
${q_{10}}$	Streamline curvature	$ \begin{gathered} \left\| {\dfrac{{{\rm D}\varGamma }}{{{\rm D}s}}} \right\|where \to \varGamma \equiv {U} /\left\| {U} \right\|, \\ {\rm D}s = \left\| {U} \right\|{\rm D}t \\ \end{gathered} $	$\dfrac{1}{{{L_c}}}$
^a Normalization is not necessary as the Reynolds number is nondimensional.

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