面向精准工程湍流模型的理论研究

佘振苏; 唐帆; 肖梦娟

doi:10.7638/kqdlxxb-2018.0249

面向精准工程湍流模型的理论研究

doi: 10.7638/kqdlxxb-2018.0249

湍流与复杂系统国家重点实验室, 北京大学工学院, 北京 100871

基金项目:

国家自然科学基金项目 11452002

国家自然科学基金创新研究群体项目 11521091

详细信息

作者简介:
佘振苏^*(1962-), 讲座教授, 研究方向:湍流, 复杂系统.E-mail:she@pku.edu.cn

中图分类号: V211.3
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- 被引次数: 0
出版历程
- 收稿日期: 2018-10-17
- 修回日期: 2018-11-05
- 刊出日期: 2019-02-25

Structural ensemble dynamics theory for engineering turbulenc models

State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Engineering sciences, College of Engineering, Peking University, Beijing 100871, China

摘要

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。
- 壁湍流 /
- 对称性 /
- 结构系综理论 /
- 湍流模型
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.
- wall turbulence /
- symmetry /
- structural ensemble dynamics theory /
- turbulence model

HTML全文

图 1 SED-k-ω平均速度剖面预测结果与实验数据的比较，红色的点是普林斯顿超级圆管实验数据，黑色的线是模型计算结果^[7]

Figure 1. Comparison of the mean velocity profiles predicted by SED-k-ω model with experimental measurements. The red open symbols are from Princeton supper pipe experiment. The black lines are from the SED-k-ω model ^[7]

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图 2 SED-k-ω动能剖面预测结果与实验数据的比较，红色的点是普林斯顿超级圆管实验数据，黑色的线是模型计算结果^[27]

Figure 2. Comparison of the kinetic energy profiles predicted by SED-k-ω model with experimental measurements. The black open symbols are from Princeton supper pipe experiment. The red lines are from the SED-k-ω model^[27]

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图 3 SED-SL模型(红色线)对平板转捩流动摩阻系数的预测与实验(实心符号)和直接计算模拟(空心符号)^{[34, 41-42]}的比较

Figure 3. Comparison of the streamwise development of skin friction coefficient for transitional flat plate flows between the SED-SL prediction (red lines) with experimental (filled symbols) and direct numerical simulation (open symbols) data

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图 4 SED-SL模型(红线)对充分发展的湍流边界层平均速度剖面的预测与实验数据(黑色点)的比较。结果显示，模型对实验数据在雷诺数全范围内实现了精确刻画^[43]

Figure 4. Comparison of the mean velocity profiles for fully developed turbulent boundary layers at available Reynolds number between SED-SL's prediction (red lines) and experimental and numerical measurements (black filled symbols). Highly accurate descriptions cover the entire available range of the Reynolds number^[43]

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图 5 SED-SL模型(红线)对Ma=2.25可压缩平板流动的预测与直接数值模拟的比较。(a)流向不同位置处的平均速度剖面；(b)平均温度剖面。黑色点为实验结果，红色线为模型计算结果^[29]

Figure 5. Comparison of the mean velocity profiles (a) and mean temperature profiles (b) of compressible flat plate flow at Ma=2.25 between SED-SL's prediction (red lines and direct numerical simulation ^[29] (open symbols)

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图 6 RAE2822翼型不同迎角下的升阻力系数计算结果对比，黑点线是实验数据，红色是SED-SL计算结果，蓝色是SA模型计算结果，绿色是BL模型计算结果

Figure 6. Comparison of lift coefficients (C_L) and drag coefficients (C_D) for RA2822 airfoil flow under different attack angles. Black filled symbols are experimental measurements^[44]; red open symbols are from SED-SL model, green from BL model, and blue from SA mode

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图 7 NACA0012翼型不同迎角下的升阻力系数计算结果对比。图例同图 6

Figure 7. Comparison of lift coefficients (C_L) and drag coefficients (C_D) for NACA0012 airfoil flow under different attack angles. Legend is as same as Fig. 6

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图 8 SED-SL模型对NACA4412分离区流动(Ma=0.09, AOA=13.87°)的计算结果与实验和其它模型的比较^[46]

Figure 8. Comparison of NACA 4412 airfoil trailing edge separation under Ma=0.09, AOA=13.87°^[46]

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图 9 SED-SL模型对NACA0012大迎角非定常分离流动d的刻画(Ma=0.3, AOA=15.18°)^[47]

Figure 9. Comparison of NACA 0012 airfoil separation flow for Ma=0.3, AOA=15.18°^[47]

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图 10 (a) M6机翼表面压力系数分布；(b) SED-SL和SA模型计算的M6机翼在展向位置z=0.95的表面压力系数分布与实验^[48]的比较

Figure 10. (a) Sketch of M6 wing; (b) Comparison of surface pressure coefficient at z=0.95 between experiments^[48] and models (including SED-SL model and SA model)

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图 11 SED-SL模型(实线)对冷壁可压缩边界(Ma=4.5, T_wall/T_{_inf}=2.5)的预测结果与直接数值模拟结果(点)的比较^[29]

Figure 11. Comparison between the SED-SL's prediction (red lines), BA model (blue lines) and SA model (brown lines) with direct numerical simulation (symbols) of compressible flat plate flow under cold wall boundary condition^[29] (Ma=4.5, T_wall/T_{_inf}=2.5)

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图 12 SED-SL模型(实线)对冷壁可压缩边界层不同雷诺数下壁面热流的预测结果符号为实验数据^[50]; 红线为SED-SL模型的预测结果

Figure 12. Prediction of Stanton number for compressible transitional flat plate flow under cold wall boundary condition The black symbols are experimental measurements^[50]; the red lines are from SED-SL model

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图 13 SED-SL模型(实线)对超声速尖锥流动壁面热流的预测结果。符号为实验数据^[50]; 红线为SED-SL模型的计算结果

Figure 13. Prediction of wall heat flux for transitional supersonic straight cone flow. The black symbols are experimental measurements^[50]; the red lines are from SED-SL model

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表 1 超声速平板实验算例的参数设置

Table 1. Parameter setting for case of supersonic plate experiment

Case	1	2	3	4
Ma	6.3	6.2	6.1	5.5
Re/m	1.7×10⁶	2.6×10⁶	4.9×10⁶	1.6×10⁶
T_{_inf}	570	690	800	1560

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表 2 尖锥流动的参数设置

Table 2. Perameter setting for case of flow over straight cone

Case	Re	T₀/K	T_∞/K	T_wall/K
A	2.03×10⁷	519.26	63.32	306.36
B	1.77×10⁷	519.26	63.32	306.36
C	1.41×10⁷	505.37	61.63	298.16
D	1.05×10⁷	505.37	61.63	298.16
E	9.19×10⁶	505.37	61.63	298.16
F	9.19×10⁶	449.82	54.86	265.39
G	7.22×10⁶	505.37	61.63	298.16
H	3.61×10⁶	491.48	59.94	289.97

下载: 导出CSV

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