两种SST湍流模型改进方法适用性分析

doi:10.7527/S1000-6893.2024.30574

Abstract

Abstract:

The Reynolds-averaged turbulence model has high computational efficiency， and is of great significance in engineering applications. The purpose of the improvement of the traditional and the new data-driven modes of turbulence model is to improve the prediction accuracy. However， the new data-driven mode is mainly for the low-speed flow， and there are less reports on the application， evaluation and promotion of the mode for the high-speed flow. The lack of comparative study of the two modes also causes problems for their rational use. Under the frame of the standard Reynolds Shear Stress Transport （SST） model， the traditional mode is adopted to introduce the compressibility effect into the dissipative term of the transport equation， and the new data-driven mode is used to modify the dissipative term. The improvement in the two modes mainly acts on the shear layer in the flow field. The test results of supersonic compression corner and supersonic cavity ramp show that the new data-driven mode can obtain a preliminary and explainable nonlinear relationship between different physical characteristics， but can only be applied after adjustment and re-optimization of the traditional mode. It has a certain generalization and is better than the traditional mode in capturing some turbulence details， but the accuracy still needs to be improved.

Key words: turbulence model, SST, data-driven technology, compressible, separated flow, symbolic regression

CLC Number:

V211.3

Yu ZENG, Hongbo WANG, Chengyue LIAN, Yixin YANG, Dapeng XIONG, Mingbo SUN, Weidong LIU. Applicability analysis of two improved methods of SST turbulence model[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(S1): 730574.

Figures/Tables 14

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References 33

1	曾宇，汪洪波，孙明波，等. SST湍流模型改进研究综述［J］. 航空学报， 2023， 44（9）： 027411.
	ZENG Y， WANG H B， SUN M B， et al. SST turbulence model improvements： Review［J］. Acta Aeronautica et Astronautica Sinica， 2023， 44（9）： 027411 （in Chinese）.
2	RINGUETTE M J， BOOKEY P， WYCKHAM C， et al. Experimental study of a Mach 3 compression ramp interaction at Re_θ = 2400［J］. AIAA Journal， 2009， 47（2）： 373-385.
3	WU M， MARTIN M P. Direct numerical simulation of supersonic turbulent boundary layer over a compression ramp［J］. AIAA Journal， 2007， 45（4）： 879-889.
4	DI STEFANO M A， HOSDER S， BAURLE R A. Effect of turbulence model uncertainty on scramjet isolator flowfield analysis［J］. Journal of Propulsion and Power， 2020， 36（1）： 109-122.
5	GROSS N， BLAISDELL G， LYRINTZIS A. Analysis of modified compressibility corrections for turbulence models［C］∥ Proceedings of the 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. Reston： AIAA， 2011.
6	SETTLES G S， WILLIAMS D R， BACA B K， et al. Reattachment of a compressible turbulent free shear layer［J］. AIAA Journal， 1982， 20（1）： 60-67.
7	HORSTMAN C C， SETTLES G S， WILLIAMS D R， et al. A reattaching free shear layer in compressible turbulent flow［J］. AIAA Journal， 1982， 20（1）： 79-85.
8	BERESH S J， WAGNER J L， CASPER K M. Compressibility effects in the shear layer over a rectangular cavity［J］. Journal of Fluid Mechanics， 2016， 808： 116-152.
9	TU G H， DENG X G， MAO M L. Assessment of two turbulence models and some compressibility corrections for hypersonic compression corners by high-order difference schemes［J］. Chinese Journal of Aeronautics， 2012， 25（1）： 25-32.
10	BRADSHAW P. Turbulence modeling with application to turbomachinery［J］. Progress in Aerospace Sciences， 1996， 32（6）： 575-624.
11	汪洪波，曾宇，熊大鹏，等. SST湍流模型的激波与可压缩效应改进［J］. 航空学报， 2024， 45（3）： 128694.
	WANG H B， ZENG Y， XIONG D P， et al. Improvement of shock wave and compressibility effects in SST turbulence model［J］. Acta Aeronautica et Astronautica Sinica， 2024， 45（3）： 128694 （in Chinese）.
12	PICKLES J D， METTU B R， SUBBAREDDY P K， et al. On the mean structure of sharp-fin-induced shock wave/turbulent boundary layer interactions over a cylindrical surface［J］. Journal of Fluid Mechanics， 2019， 865： 212-246.
13	GAITONDE D V. Progress in shock wave/boundary layer interactions［J］. Progress in Aerospace Sciences， 2015， 72： 80-99.
14	RAJE P， SINHA K. Anisotropic SST turbulence model for shock-boundary layer interaction［J］. Computers & Fluids， 2021， 228： 105072.
15	POPE S B. A more general effective-viscosity hypothesis［J］. Journal of Fluid Mechanics， 1975， 72： 331-340.
16	GATSKI T B， JONGEN T. Nonlinear eddy viscosity and algebraic stress models for solving complex turbulent flows［J］. Progress in Aerospace Sciences， 2000， 36（8）： 655-682.
17	BISWAS R， DURBIN P A， MEDIC G. Development of an elliptic blending lag k-ω model［J］. International Journal of Heat and Fluid Flow， 2019， 76： 26-39.
18	阎超. 航空CFD四十年的成就与困境［J］. 航空学报， 2022， 43（10）： 026490.
	YAN C. Achievements and predicaments of CFD in aeronautics in past forty years［J］. Acta Aeronautica et Astronautica Sinica， 2022， 43（10）： 026490 （in Chinese）.
19	WEATHERITT J， SANDBERG R. A novel evolutionary algorithm applied to algebraic modifications of the RANS stress-strain relationship［J］. Journal of Computational Physics， 2016， 325： 22-37.
20	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.
21	赵耀民，徐晓伟. 基于基因表达式编程的数据驱动湍流建模［J］. 力学学报， 2021， 53（10）： 2640-2655.
	ZHAO Y M， XU X W. Data-driven turbulence modelling based on gene-expression programming［J］. Chinese Journal of Theoretical and Applied Mechanics， 2021， 53（10）： 2640-2655 （in Chinese）.
22	张伟伟，朱林阳，刘溢浪，等. 机器学习在湍流模型构建中的应用进展［J］. 空气动力学学报， 2019， 37（3）： 444-454.
	ZHANG W W， ZHU L Y， LIU Y L， et al. Progresses in the application of machine learning in turbulence modeling［J］. Acta Aerodynamica Sinica， 2019， 37（3）： 444-454 （in Chinese）.
23	KAANDORP M L A， DWIGHT R P. Data-driven modelling of the Reynolds stress tensor using random forests with invariance［J］. Computers & Fluids， 2020， 202： 104497.
24	SPALART P. An old-fashioned framework for machine learning in turbulence modeling［DB/OL］. arXiv preprint： 2308.00837， 2023.
25	CRANMER M， SANCHEZ-GONZALEZ A， BATTAGLIA P， et al. Discovering symbolic models from deep learning with inductive biases［J］. Advances in Neural Information Processing Systems， 2020， 33： 17429-17442.
26	CRANMER M. Interpretable machine learning for science with PySR and SymbolicRegression.jl［DB/OL］. arXiv preprint： 2305.01582， 2023.
27	SAHOO S S， LAMPERT C H， MARTIUS G. Learning equations for extrapolation and control［C］∥Proceedings of the International Conference on Machine Learning， 2018.
28	WU C Y， ZHANG Y F. Enhancing the shear-stress-transport turbulence model with symbolic regression： A generalizable and interpretable data-driven approach［J］. Physical Review Fluids， 2023， 8（8）： 084604.
29	MENTER F R. Two-equation eddy-viscosity turbulence models for engineering applications［J］. AIAA Journal， 1994， 32（8）： 1598-1605.
30	WILCOX D C. Dilatation-dissipation corrections for advanced turbulence models［J］. AIAA Journal， 1992， 30（11）： 2639-2646.
31	LIOU W W， HUANG G， SHIH T H. Turbulence model assessment for shock wave/turbulent boundary-layer interaction in transonic and supersonic flows［J］. Computers & Fluids， 2000， 29（3）： 275-299.
32	HOLDEN M S， WADHAMS T P， MACLEAN M G. Measurements in regions of shock wave/turbulent boundary layer interaction from Mach 4 to 10 for open and “blind” code evaluation/validation［C］∥ Proceedings of the 21st AIAA Computational Fluid Dynamics Conference. Reston： AIAA， 2013.
33	MARVIN J， BROWN J L， GNOFFO P. Experimental database with baseline CFD solutions： 2-D and axisymmetric hypersonic shock-wave/turbulent-boundary-layer interactions： NASA/TM-2013-216604 ［R］. Washington， D.C.： NASA， 2013.

方法	Ma_∞	U_∞/（m·s^-1）	T_∞ /K	ρ_∞ /（kg·m^-3）	Re_θ
实验^［2］	2.9	604.5	108.1	0.074	2 400
DNS^［3］	2.9	609.1	107.1	0.07	2 300

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Applicability analysis of two improved methods of SST turbulence model

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