基于Liutex的数据驱动湍流模型修正

doi:10.7527/S1000-6893.2023.29579

Abstract

Abstract:

The current widely used turbulence models often exhibit significant discrepancies with experimental results for largely separated flows primarily due to the strong adverse pressure gradients present in the flows， which violate the fundamental assumptions of turbulence models. To enhance the computational accuracy for largely separated flow problems， it is necessary to modify the turbulence models. A combined approach of field inversion and data-driven methods is proposed to introduce a neural network for the correction of the Spalart-Allmaras （S-A） one-equation model based on Liutex. Initially， correction coefficients for the S-A one-equation model generation terms are obtained through field inversion with discrete adjoint. Feature selection indicates that Liutex exhibits the highest correlation with the correction coefficients for the S-A one-equation model generation terms and is suitable as an input for the neural network. Subsequently， Liutex and other variables are used as inputs to construct a neural network to approximate the correction coefficients for the S-A model generation terms， establishing the neural network structure for the generation term correction coefficients. This correction method is validated through separated flow results for the S809 and S814 airfoils， demonstrating the ability to significantly improve the computational accuracy of largely separated flows.

Key words: turbulence model, field inversion, neural network, separated flows, Liutex method

CLC Number:

V211.3

Jiajun LONG, Chenpiao LIU, Fei QIN, Jiale ZHANG, Shengguan XU, Yisheng GAO. Liutex based data-driven turbulence model correction[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(15): 129579-129579.

Figures/Tables 26

Fig.1

Fig.2

Fig.3

Fig.4

Table 1

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Fig.11

Fig.12

Fig.13

Fig.14

Fig.15

Fig.16

Fig.17

Fig.18

Fig.19

Fig.20

Fig.21

Fig.22

Fig.23

Fig.24

Fig.25

References 42

1	阎超. 航空CFD四十年的成就与困境［J］. 航空学报， 2022， 43（10）： 526490.
	YAN C. Achievements and predicaments of CFD in aeronautics in past forty years［J］. Acta Aeronautica et Astronautica Sinica， 2022， 43（10）： 526490 （in Chinese）.
2	MALIK M R， BUSHNELL D M. Role of computational fluid dynamics and wind tunnels in aeronautics R&D： NASA/TP-2012-217602［R］. Washington， D.C.： NASA， 2012.
3	HOLLAND J. Integrated field inversion and machine learning with embedded neural network training for turbulence modeling［D］. Maryland： University of Maryland， 2019.
4	朱文庆，肖志祥，符松. 使用IDDES方法预测飞行速度对喷流噪声的影响［J］. 空气动力学学报， 2018， 36（3）： 463-469.
	ZHU W Q， XIAO Z X， FU S. The effects of flight velocity on jet noise are simulated by improved delayed detached eddy simulation with the modification of grid scale definition［J］. Acta Aerodynamica Sinica， 2018， 36（3）： 463-469 （in Chinese）.
5	LOZANO-DURÁN A， BOSE S T， MOIN P. Performance of wall-modeled LES with boundary-layer-conforming grids for external aerodynamics［J］. AIAA Journal， 2021， 60（2）： 747-766.
6	WILCOX D C. Turbulence modeling for CFD［M］. 3rd ed. La Cãnada： DCW Industries， Inc.， 2006.
7	HEY T. The fourth paradigm-Data-intensive scientific discovery［M］∥KURBANOĞLU S， AL U， ERDOĞAN P L， et al. Communications in computer and information science. Berlin： Springer， 2012.
8	DURAISAMY K， SPALART P R， RUMSEY C L. Status， emerging ideas and future directions of turbulence modeling research in aeronautics： NASA/TM-2017-219682 ［R］. Washington， D.C.： NASA， 2017.
9	YARLANKI S， RAJENDRAN B， HAMANN H. Estimation of turbulence closure coefficients for data centers using machine learning algorithms［C］∥13th InterSociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems. Piscataway： IEEE Press， 2012： 38-42.
10	LING J， TEMPLETON J. Evaluation of machine learning algorithms for prediction of regions of high Reynolds averaged Navier Stokes uncertainty［J］. Physics of Fluids， 2015， 27（8）： 085103.
11	SINGH A P， MEDIDA S， DURAISAMY K. Machine-learning-augmented predictive modeling of turbulent separated flows over airfoils［J］. AIAA Journal， 2017， 55（7）： 2215-2227.
12	TRACEY B D， DURAISAMY K， ALONSO J J. A machine learning strategy to assist turbulence model development［C］∥53rd AIAA Aerospace Sciences Meeting. Reston： AIAA， 2015.
13	ZHANG Z J， DURAISAMY K. Machine learning methods for data-driven turbulence modeling［C］∥22nd AIAA Computational Fluid Dynamics Conference. Reston： AIAA， 2015.
14	WANG J X， WU J L， XIAO H. Physics-informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data［J］. Physical Review Fluids， 2017， 2（3）： 034603.
15	尹宇辉，李浩然，张宇飞，等. 机器学习辅助湍流建模在分离流预测中的应用［J］. 空气动力学学报， 2021， 39（2）： 23-32.
	YIN Y H， LI H R， ZHANG Y F， et al. Application of machine learning assisted turbulence modeling in flow separation prediction［J］. Acta Aerodynamica Sinica， 2021， 39（2）： 23-32 （in Chinese）.
16	LING J L， KURZAWSKI A， TEMPLETON J. Reynolds averaged turbulence modelling using deep neural networks with embedded invariance［J］. Journal of Fluid Mechanics， 2016， 807： 155-166.
17	ZHU L Y， ZHANG W W， KOU J Q， et al. Machine learning methods for turbulence modeling in subsonic flows around airfoils［J］. Physics of Fluids， 2019， 31（1）： 015105.
18	王铎，刘超群，蔡小舒，等. 基于流动仿真大数据应对旋涡-湍流的研究进展［J］. 力学季刊， 2022， 43（2）： 197-216.
	WANG D， LIU C Q， CAI X S， et al. Tackling vortex/turbulence challenges based on direct numerical simulation data in fluid science［J］. Chinese Quarterly of Mechanics， 2022， 43（2）： 197-216 （in Chinese）.
19	王述之，战林浩，曹博超，等. 基于直接数值模拟数据和神经网络的湍流封闭模型构建［J］. 水动力学研究与进展（A辑）， 2020， 35（2）： 141-154.
	WANG S Z， ZHAN L H， CAO B C， et al. Turbulence closure model based on neural network and direct numerical simulation data［J］. Chinese Journal of Hydrodynamics， 2020， 35（2）： 141-154 （in Chinese）.
20	张珍，叶舒然，岳杰顺，等. 基于组合神经网络的雷诺平均湍流模型多次修正方法［J］. 力学学报， 2021， 53（6）： 1532-1542.
	ZHANG Z， YE S R， YUE J S， et al. A combined neural network and multiple modification strategy for Reynolds-averaged Navier-Stokes turbulence modeling［J］. Chinese Journal of Theoretical and Applied Mechanics， 2021， 53（6）： 1532-1542 （in Chinese）.
21	DURAISAMY K， ZHANG Z J， SINGH A P. New approaches in turbulence and transition modeling using data-driven techniques［C］∥53rd AIAA Aerospace Sciences Meeting. Reston： AIAA， 2015.
22	RUMSEY C L， COLEMAN G N， WANG L. In search of data-driven improvements to RANS models applied to separated flows［C］∥AIAA SciTech 2022 Forum. Reston： AIAA， 2022.
23	何创新，邓志文，刘应征. 湍流数据同化技术及应用［J］. 航空学报， 2021， 42（4）： 524704.
	HE C X， DENG Z W， LIU Y Z. Turbulent flow data assimilation and its applications［J］. Acta Aeronautica et Astronautica Sinica， 2021， 42（4）： 524704 （in Chinese）.
24	闫重阳，张宇飞，陈海昕. 基于离散伴随的流场反演在湍流模拟中的应用［J］. 航空学报， 2021， 42（4）： 524695.
	YAN C Y， ZHANG Y F， CHEN H X. Application of field inversion based on discrete adjoint method in turbulence modeling［J］. Acta Aeronautica et Astronautica Sinica， 2021， 42（4）： 524695 （in Chinese）.
25	刘超群. Liutex-涡定义和第三代涡识别方法［J］. 空气动力学学报， 2020， 38（3）： 413-431， 478.
	LIU C Q. Liutex-third generation of vortex definition and identification methods［J］. Acta Aerodynamica Sinica， 2020， 38（3）： 413-431， 478 （in Chinese）.
26	LIU C Q， GAO Y S， DONG X R， et al. Third generation of vortex identification methods： Omega and Liutex/Rortex based systems［J］. Journal of Hydrodynamics， 2019， 31（2）： 205-223.
27	LIU C Q， GAO Y S， TIAN S L， et al. Rortex—A new vortex vector definition and vorticity tensor and vector decompositions［J］. Physics of Fluids， 2018， 30（3）： 035103.
28	GAO Y S， LIU C Q. Rortex and comparison with eigenvalue-based vortex identification criteria［J］. Physics of Fluids， 2018， 30（8）： 085107.
29	LIU C Q， XU H Y， CAI X S， et al. Liutex and its applications in turbulence research［M］. New York： Academic Press， 2021.
30	CHONG M S， PERRY A E， CANTWELL B J. A general classification of three-dimensional flow fields［J］. Physics of Fluids A： Fluid Dynamics， 1990， 2（5）： 765-777.
31	EPPSB P. Review of vortex identification methods［C］∥55th AIAA Aerospace Sciences Meeting. Reston： AIAA， 2017.
32	WANG Y Q， GAO Y S， LIU J M， et al. Explicit formula for the Liutex vector and physical meaning of vorticity based on the Liutex-Shear decomposition［J］. Journal of Hydrodynamics， 2019， 31（3）： 464-474.
33	YU Y F， SHRESTHA P， NOTTAGE C， et al. Principal coordinates and principal velocity gradient tensor decomposition［J］. Journal of Hydrodynamics， 2020， 32（3）： 441-453.
34	SPALART P R， ALLMARAS S R. A one-equation turbulence model for aerodynamic flows［C］∥30th Aerospace Sciences Meeting and Exhibit. Reston： AIAA， 1992.
35	SCHAEFER J A， CARY A W， MANI M， et al. Uncertainty quantification and sensitivity analysis of SA turbulence model coefficients in two and three dimensions［C］∥55th AIAA Aerospace Sciences Meeting. Reston： AIAA， 2017.
36	GILES M B， PIERCE N A. An introduction to the adjoint approach to design［J］. Flow， Turbulence and Combustion， 2000， 65（3）： 393-415.
37	BYRD R H， LU P H， NOCEDAL J， et al. A limited memory algorithm for bound constrained optimization［J］. SIAM Journal on Scientific Computing， 1995， 16（5）： 1190-1208.
38	SOMERS D M. Design and experimental results for the S809 airfoil［R］. Colorado： National Renewable Energy Laboratory， 1997.
39	ECONOMON T D， PALACIOS F， COPELAND S R， et al. SU2： An open-source suite for multiphysics simulation and design［J］. AIAA Journal， 2016， 54（3）： 828-846.
40	VIRTANEN P， GOMMERS R， OLIPHANT T E， et al. SciPy 1.0： Fundamental algorithms for scientific computing in python［J］. Nature Methods， 2020， 17（3）： 261-272.
41	PASZKE A， GROSS S， MASSA F， et al. PyTorch： An imperative style， high-performance deep learning library［EB/OL］. （2019-12-03）［2023-09-13］.
42	SOMERS D M. Design and experimental results for the S814 airfoil［R/OL］. （1997-01）［2023-09-13］. .

[1]	Fei MA, Qiong ZHANG, Peijun LAI, Yidi YUE. BP neural network⁃based quantitative classification model for safety in experimental flight training [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(5): 529957-529957.
[2]	Yude NI, Miaoyu YAN, Ruihua LIU. Short-term prediction of ionospheric TEC based on DOA-BP neural network [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(4): 328707-328707.
[3]	Hongbo WANG, Yu ZENG, Dapeng XIONG, Yixin YANG, Mingbo SUN. Improvement of shock wave and compressibility effects in SST turbulence model [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(3): 128694-128694.
[4]	Yanfang LIU, Jiayu SHE, Qiufan YUAN, Rui ZHOU, Naiming QI. Real⁃time small target detection networks for UAV remote sensing [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(14): 630119-630119.
[5]	Wentao LI, Yunqin HE, Wenbo LI, Yiyi ZHANG, Guozhu LIANG. 3D grain reverse design and shape optimization for solid rocket motor [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(11): 529089-529089.
[6]	Kailing ZHANG, Siyi LI, Yi DUAN, Chao YAN. Uncertainty quantification of parameters in SST turbulence model for inlet simulation [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(S2): 729429-729429.
[7]	Wu LIU, Yunyan WU, Wei LIU, Mingming TIAN, Tianpeng HUANG. Re-entry robust fault tolerant attitude control for RLVs considering unknown disturbances [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(S1): 727787-727787.
[8]	Chenyang LIU, Dawei WU, Yize GUO, Xinsai LV, Jiani ZHOU, Shuyi SHAO. Robust adaptive attitude control of quadrotor with uncertain strong coupling [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(S1): 727645-727645.
[9]	Zhongzhi LI, Jinyi MA, Jianliang AI, Yiqun DONG. Fault detection and classification of aerospace sensors using deep neural networks finetuned from VGG16 [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(S1): 727615-727615.
[10]	Yu ZENG, Hongbo WANG, Mingbo SUN, Chao WANG, Xu LIU. SST turbulence model improvements: Review [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(9): 27411-027411.
[11]	Zhikai WANG, Sheng CHEN, Wei FAN. Effect of neural network width on combustor emission prediction [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(5): 126816-126816.
[12]	Lei HE, Weiqi QIAN, Kangsheng DONG, Xian YI, Congcong CHAI. Aerodynamic characteristics modeling of iced airfoil based on convolution neural networks [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(5): 126434-126434.
[13]	Honglun WANG, Yanxiang WANG, Yiheng LIU. Recovery trajectory optimization for UAV towed aerial recovery based on trajectory mapping [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(20): 628775-628775.
[14]	Huailu LI, Xu WANG, Xiao WANG, Tong ZHAO, Weiwei ZHANG. Aerodynamic modeling and flight simulation of maneuver flight at high angle of attack [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(19): 128410-128410.
[15]	Xiangwei ZHU, Dan SHEN, Kai XIAO, Yuexin MA, Xiang LIAO, Fuqiang GU, Fangwen YU, Kefu GAO, Jingnan LIU. Mechanisms, algorithms, implementation and perspectives of brain⁃inspired navigation [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(19): 28569-028569.

Liutex based data-driven turbulence model correction

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 26

References 42

Related Articles 15

Recommended Articles

Metrics

Comments