SST湍流模型改进研究综述

doi:10.7527/S1000-6893.2022.27411

Abstract

Abstract:

The k-ω Shear Stress Transport （SST） turbulence model， one of the best eddy viscosity models with comprehensive performance， has been widely used in recent years. However， with the increase of problem complexity and simulation accuracy requirements， the standard SST turbulence model shows clear limitations in certain aspects， eliciting extensive improvement research. This paper reviews the improvement research of the SST model from six aspects： rotation/curvature effect， compressibility effect， shock wave unsteadiness effect， effect of anisotropy Reynolds stress， effect of stress-strain deviation， and laminar/turbulent transition effect. Meanwhile， it also briefly introduces the model improvement based on the data-driven technology in recent years， sorts out the ideas and development trends of various improvement research， expounds their applicability and limitations， and analyzes the reasons and problems affecting the improvement effect. Finally， some suggestions for future work are given.

Key words: turbulence model, SST, rotation/curvature, compressibility, shock wave unsteadiness, anisotropy Reynolds stress, laminar/turbulent transition

CLC Number:

V211.3

Yu ZENG, Hongbo WANG, Mingbo SUN, Chao WANG, Xu LIU. SST turbulence model improvements: Review[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(9): 27411.

Figures/Tables 9

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References 161

1	MENTER F R. Zonal two equation k-ω turbulence models for aerodynamic flows［C］∥ 23rd Fluid Dynamics， Plasmadynamics， and Lasers Conference. Reston： AIAA， 1993.
2	MENTER F R. Two-equation eddy-viscosity turbulence models for engineering applications［J］. AIAA Journal， 1994， 32（8）： 1598-1605.
3	JONES W P， LAUNDER B E. The prediction of laminarization with a two-equation model of turbulence［J］. International Journal of Heat and Mass Transfer， 1972， 15（2）： 301-314.
4	JOHNSON D A， KING L S. A mathematically simple turbulence closure model for attached and separated turbulent boundary layers［J］. AIAA Journal， 1985， 23（11）： 1684-1692.
5	SPALART P R. Strategies for turbulence modelling and simulations［J］. International Journal of Heat and Fluid Flow， 2000， 21（3）： 252-263.
6	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）.
7	LAURENCE D. Large eddy simulation of industrial flows？［M］∥LAUNDER B E， SANDHAM N D. Closure strategies for turbulent and transitional flows. Cambridge： Cambridge University Press， 2001： 392-406.
8	HANJALIC K. Will RANS survive LES？ A view of perspectives［J］. Journal of Fluids Engineering， 2005， 127（5）： 831-839.
9	SLOTNICK J， KHODADOUST A， ALONSO J， et al. CFD vision 2030 study： A path to revolutionary computational aerosciences： NASA/CR-2014-218178［R］. Washington， D.C.： NASA， 2014.
10	DURBIN P A. Some recent developments in turbulence closure modeling［J］. Annual Review of Fluid Mechanics， 2018， 50： 77-103.
11	CEBECI T， SMITH A M O， LIBBY P A. Analysis of turbulent boundary layers［J］. Journal of Applied Mechanics， 1976， 43（1）： 189.
12	BALDWIN B， LOMAX H. Thin-layer approximation and algebraic model for separated turbulent flows［C］∥ 16th Aerospace Sciences Meeting. Reston： AIAA， 1978.
13	BALDWIN B， BARTH T. A one-equation turbulence transport model for high Reynolds number wall-bounded flows［C］∥ 29th Aerospace Sciences Meeting. Reston： AIAA， 1991.
14	SPALART P， ALLMARAS S. A one-equation turbulence model for aerodynamic flows［C］∥ 30th Aerospace Sciences Meeting and Exhibit. Reston： AIAA， 1992.
15	HELLSTEN A， LAINE S. Explicit algebraic Reynolds-stress modelling in decelerating and separating flows［C］∥ Fluids 2000 Conference and Exhibit. Reston： AIAA， 2000.
16	MENTER F， KUNTZ M， LANGTRY R. Ten years of industrial experience with the SST turbulence model［J］. Heat and Mass Transfer， 2003， 4（1）： 625-632.
17	KOLMOGOROV A N. Equations of turbulent motion in an incompressible fluid［J］. Proceedings of the USSR Academy of Sciences， 1941， 30（4）： 299-303.
18	BRADSHAW P. Effects of streamline curvature on turbulent flow［R］. Paris： Advisory Group for Aerospace Reserch and Development， 1973.
19	AILLAUD P， GICQUEL L Y M， DUCHAINE F. Investigation of the concave curvature effect for an impinging jet flow［J］. Physical Review Fluids， 2017， 2（11）： 114608.
20	BARLOW R S， JOHNSTON J P. Structure of a turbulent boundary layer on a concave surface［J］. Journal of Fluid Mechanics， 1988， 191： 137-176.
21	WANG Q C， WANG Z G， ZHAO Y X. The impact of streamwise convex curvature on the supersonic turbulent boundary layer［J］. Physics of Fluids， 2017， 29（11）： 116106.
22	MOKHTARZADEH-DEHGHAN M R， YUAN Y M. Measurements of turbulence quantities and bursting period in developing turbulent boundary layers on the concave and convex walls of a 90° square bend［J］. Experimental Thermal and Fluid Science， 2002， 27（1）： 59-75.
23	HUANG X， YANG W， LI Y， et al. Review on the sensitization of turbulence models to rotation/curvature and the application to rotating machinery［J］. Applied Mathematics and Computation， 2019， 341： 46-69.
24	LAUNDER B E， LOIZOU P A. Laminarization of three-dimensional accelerating boundary layers in a curved rectangular-sectioned duct［J］. International Journal of Heat and Fluid Flow， 1992， 13（2）： 124-131.
25	HOFFMANN P H， MUCK K C， BRADSHAW P. The effect of concave surface curvature on turbulent boundary layers［J］. Journal of Fluid Mechanics， 1985， 161： 371-403.
26	DURBIN P. Adapting scalar turbulence closure models for rotation and curvature［J］. Journal of Fluids Engineering， 2011， 133（6）： 061205.
27	BRETHOUWER G. The effect of rotation on rapidly sheared homogeneous turbulence and passive scalar transport. Linear theory and direct numerical simulation［J］. Journal of Fluid Mechanics， 2005， 542： 305-342.
28	KRISTOFFERSEN R， ANDERSSON H I. Direct simulations of low-Reynolds-number turbulent flow in a rotating channel［J］. Journal of Fluid Mechanics， 1993， 256： 163-197.
29	LAMBALLAIS E， MÉTAIS O， LESIEUR M. Spectral-dynamic model for large-eddy simulations of turbulent rotating channel flow［J］. Theoretical and Computational Fluid Dynamics， 1998， 12（3）： 149-177.
30	GRUNDESTAM O， WALLIN S， JOHANSSON A V. Direct numerical simulations of rotating turbulent channel flow［J］. Journal of Fluid Mechanics， 2008， 598： 177-199.
31	WILCOX D C. Turbulence modeling for CFD［M］. 3rd ed. La Cãnada： DCW Industries， Inc.， 2006： 125-129.
32	SPALART P R， SHUR M. On the sensitization of turbulence models to rotation and curvature［J］. Aerospace Science and Technology， 1997， 1（5）： 297-302.
33	SHUR M L， STRELETS M K， TRAVIN A K， et al. Turbulence modeling in rotating and curved channels─Assessing the Spalart-Shur correction［J］. AIAA Journal， 2000， 38（5）： 784-792.
34	SMIRNOV P E， MENTER F R. Sensitization of the SST turbulence model to rotation and curvature by applying the Spalart-Shur correction term［J］. Journal of Turbomachinery， 2009， 131（4）： 041010.
35	MUSA O， ZHOU C S， CHEN X， et al. Prediction of swirling cold flow in a solid-fuel ramjet engine with a modified rotation/curvature correction SST turbulence model［J］. Applied Thermal Engineering， 2016， 105： 737-754.
36	MUSA O， CHEN X， ZHOU C S. Combustion characteristics and turbulence modeling of swirling reacting flow in solid fuel ramjet［J］. Acta Astronautica， 2017， 139： 1-17.
37	BRADSHAW P. The analogy between streamline curvature and buoyancy in turbulent shear flow［J］. Journal of Fluid Mechanics， 1969， 36（1）： 177-191.
38	HOWARD J H G， PATANKAR S V， BORDYNUIK R M. Flow prediction in rotating ducts using Coriolis-modified turbulence models［J］. Journal of Fluids Engineering， 1980， 102（4）： 456-461.
39	LAUNDER B E， PRIDDIN C H， SHARMA B I. The calculation of turbulent boundary layers on spinning and curved surfaces［J］. Journal of Fluids Engineering， 1977， 99（2）： 435-437.
40	KHODAK A， HIRSCH C. Second-order non-linear k-ε models with explicit effect of curvature and rotation［C］∥ECCOMAS Computational Fluid Dynamics Conference， 1996： 690-696.
41	HELLSTEN A. Some improvements in Menter’s k-omega SST turbulence model［C］∥ 29th AIAA Fluid Dynamics Conference. Reston： AIAA， 1998.
42	任芸，吴登昊，牟介刚，等. 考虑旋转和曲率的湍流模型修正及应用［J］. 西安交通大学学报， 2016， 50（9）： 25-30.
	REN Y， WU D H， MU J G， et al. Modification for turbulence model considering rotation and curvature with applications［J］. Journal of Xi’an Jiaotong University， 2016， 50（9）： 25-30 （in Chinese）.
43	TRITTON D J. Stabilization and destabilization of turbulent shear flow in a rotating fluid［J］. Journal of Fluid Mechanics， 1992， 241： 503-523.
44	BERTOGLIO J P. Homogeneous turbulent field within a rotating frame［J］. AIAA Journal， 1982， 20（9）： 1175-1181.
45	REIF B A P， DURBIN P A， OOI A. Modeling rotational effects in eddy-viscosity closures［J］. International Journal of Heat and Fluid Flow， 1999， 20（6）： 563-573.
46	AROLLA S K， DURBIN P A. Modeling rotation and curvature effects within scalar eddy viscosity model framework［J］. International Journal of Heat and Fluid Flow， 2013， 39： 78-89.
47	GATSKI T B， SPEZIALE C G. On explicit algebraic stress models for complex turbulent flows［J］. Journal of Fluid Mechanics， 1993， 254： 59-78.
48	YORK W D， WALTERS D K， LEYLEK J H. A simple and robust linear eddy-viscosity formulation for curved and rotating flows［J］. International Journal of Numerical Methods for Heat & Fluid Flow， 2009， 19（6）： 745-776.
49	DHAKAL T P， WALTERS D K. Curvature and rotation sensitive variants of the k-omega SST turbulence model［C］∥ Proceedings of ASME 2009 Fluids Engineering Division Summer Meeting. New York： ASME， 2009： 2221-2229.
50	DURBIN P A. Near-wall turbulence closure modeling without “damping functions”［J］.Theoretical and Computational Fluid Dynamics， 1991， 3（1）： 1-13.
51	DHAKAL T P， WALTERS D K. A three-equation variant of the SST k-ω model sensitized to rotation and curvature effects［J］. Journal of Fluids Engineering， 2011， 133（11）： 111201.
52	LELE S K. Compressibility effects on turbulence［J］. Annual Review of Fluid Mechanics， 1994， 26： 211-254.
53	MORKOVIN M V. Effects of compressibility on turbulent flows［J］. Mécanique de la Turbulence， 1962， 367（380）： 26.
54	GATSKI T B， ERLEBACHER G. Numerical simulation of a spatially evolving supersonic turbulent boundary layer： NASA/TM-2002-211934［R］. Washington， D.C.： NASA， 2002.
55	PIROZZOLI S， GRASSO F， GATSKI T B. Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at M=2.25［J］. Physics of Fluids， 2004， 16（3）： 530-545.
56	BRADSHAW P. Turbulence modeling with application to turbomachinery［J］. Progress in Aerospace Sciences， 1996， 32（6）： 575-624.
57	COLEMAN G N， KIM J， MOSER R D. A numerical study of turbulent supersonic isothermal-wall channel flow［J］. Journal of Fluid Mechanics， 1995， 305： 159-183.
58	WILCOX D. Progress in hypersonic turbulence modeling［C］∥ 22nd Fluid Dynamics， Plasma Dynamics and Lasers Conference. Reston： AIAA， 1991.
59	SARKAR S. The pressure-dilatation correlation in compressible flows［J］. Physics of Fluids A： Fluid Dynamics， 1992， 4（12）： 2674-2682.
60	ZEMAN O. Dilatation dissipation： The concept and application in modeling compressible mixing layers［J］. Physics of Fluids A： Fluid Dynamics， 1990， 2（2）： 178-188.
61	SHYY W， KRISHNAMURTY V S. Compressibility effects in modeling complex turbulent flows［J］. Progress in Aerospace Sciences， 1997， 33（9-10）： 587-645.
62	ZEMAN O. A new model for super/hypersonic turbulent boundary layers［C］∥ 31st Aerospace Sciences Meeting. Reston： AIAA， 1993.
63	El BAZ A M， LAUNDER B E. Second-moment modelling of compressible mixing layers［M］∥ RODI W， MARTELLI F. Engineering turbulence modelling and experiments 2. Amsterdam： Elsevier， 1993： 63-72.
64	WILCOX D C. Dilatation-dissipation corrections for advanced turbulence models［J］. AIAA Journal， 1992， 30（11）： 2639-2646.
65	ERDEM E， KONTIS K. Numerical and experimental investigation of transverse injection flows［J］. Shock Waves， 2010， 20（2）： 103-118.
66	BROWN J. Turbulence model validation for hypersonic flows［C］∥ 8th AIAA/ASME Joint Thermophysics and Heat Transfer Conference. Reston： AIAA， 2002.
67	TU G H， DENG X， MAO M. 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.
68	SUZEN Y， HOFFMANN K. Investigation of supersonic jet exhaust flow by one- and two-equation turbulence models［C］∥ 36th AIAA Aerospace Sciences Meeting and Exhibit. Reston： AIAA， 1998.
69	康宏琳. 高超声速湍流气动加热的数值模拟研究［D］. 北京：北京航空航天大学， 2007： 51-58.
	KANG H L. Numerical simulation of aerodynamic heating in hypersonic turbulent flows［D］. Beijing： Beihang University， 2007： 51-58 （in Chinese）.
70	FUJIWARA H， ARAKAWA C. Modelling of compressible turbulent flows with emphasis on pressure-dilatation correlation［M］∥RODI W， BERGELES G. Engineering turbulence modelling and experiments 3. Amsterdam： Elsevier， 1996： 151-160.
71	El BAZ A M. Modelling compressibility effects on free turbulent shear flows［C］∥5th Biennial Colloquium on Computational Fluid Dynamics， 1992： 27-28.
72	KRISHNAMURTY V S， SHYY W. Study of compressibility modifications to the k-ε turbulence model［J］. Physics of Fluids， 1997， 9（9）： 2769-2788.
73	KRISHNAMURTY V S， SHYY W. Treatment of inviscid fluxes in compressible turbulent flow computations［J］. Numerical Heat Transfer， Part B： Fundamentals， 1998， 33（2）： 139-152.
74	RISTORCELLI J R. A representation for the turbulent mass flux contribution to Reynolds-stress and two-equation closures for compressible turbulence： No. NAS 1.26： 191569［R］. 1993.
75	GAVIGLIO J， DUSSAUGE J P， DEBIEVE J F， et al. Behavior of a turbulent flow， strongly out of equilibrium， at supersonic speeds［J］. Physics of Fluids， 1977， 20（10）： S179-S192.
76	RUBESIN M W. Extra compressibility terms for Favre-averaged two-equation models of inhomogeneous turbulent flows： NASA-CR-177556［R］. Washington， D.C.： NASA， 1990.
77	CHASSAING P. The modeling of variable density turbulent flows： A review of first-order closure schemes［J］. Flow， Turbulence and Combustion， 2001， 66（4）： 293-332.
78	刘景源. SST二方程湍流模型在高超声速绕流中的可压缩修正［J］. 宇航学报， 2012， 33（12）： 1719-1726.
	LIU J Y. Compressibility correction for the SST two-equation turbulence model in hypersonic flows［J］. Journal of Astronautics， 2012， 33（12）： 1719-1726 （in Chinese）.
79	甘文彪，周洲，许晓平，等. 基于改进SST模型的分离流动数值模拟［J］. 推进技术， 2013， 34（5）： 595-602.
	GAN W B， ZHOU Z， XU X P， et al. Investigation on improving the capability of predicting separation in modified SST turbulence model［J］. Journal of Propulsion Technology， 2013， 34（5）： 595-602 （in Chinese）.
80	SARKAR S. The stabilizing effect of compressibility in turbulent shear flow［J］. Journal of Fluid Mechanics， 1995， 282： 163-186.
81	HEINZ S. A model for the reduction of the turbulent energy redistribution by compressibility［J］. Physics of Fluids， 2003， 15（11）： 3580-3583.
82	NIU D S， HOU L Y. Comparison study on different compressibility modifications of turbulence model in supersonic combustion simulation［J］. Advances in Mechanical Engineering， 2014， 6： 238250.
83	韩省思. 超声速燃烧中湍流模型的研究［D］. 合肥：中国科学技术大学， 2009： 59-66.
	HAN X S. Turbulence modeling for supersonic combustion［D］. Hefei： University of Science and Technology of China， 2009： 59-66 （in Chinese）.
84	DURBIN P A. On the k-ε stagnation point anomaly［J］. International Journal of Heat and Fluid Flow， 1996， 17（1）： 89-90.
85	DUAN L， BEEKMAN I， MARTÍN M P. Direct numerical simulation of hypersonic turbulent boundary layers. Part 3. Effect of Mach number［J］. Journal of Fluid Mechanics， 2011， 672： 245-267.
86	ROSE W C， MURPHY J D. Ratio of Reynolds shear stress to turbulence kinetic energy in a boundary layer［J］. Physics of Fluids， 1973， 16（6）： 935-937.
87	刘景源. SST湍流模型在高超声速绕流中的改进［J］. 航空学报， 2012， 33（12）： 2192-2201.
	LIU J Y. An improved SST turbulence model for hypersonic flows［J］. Acta Aeronautica et Astronautica Sinica， 2012， 33（12）： 2192-2201 （in Chinese）.
88	GEORGIADIS N， YODER D. Recalibration of the shear stress transport model to improve calculation of shock separated flows［C］∥ 51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. Reston： AIAA， 2013.
89	EVANS S， LARDEAU S. Validation of a turbulence methodology using the SST k-ω model for adjoint calculation［C］∥ 54th AIAA Aerospace Sciences Meeting. Reston： AIAA， 2016.
90	KNIGHT D， YAN H， PANARAS A G， et al. Advances in CFD prediction of shock wave turbulent boundary layer interactions［J］. Progress in Aerospace Sciences， 2003， 39（2-3）： 121-184.
91	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.
92	YAN L， WU H， HUANG W， et al. Shock wave/turbulence boundary layer interaction control with the secondary recirculation jet in a supersonic flow［J］. Acta Astronautica， 2020， 173： 131-138.
93	SETTLES G S， DODSON L J. Supersonic and hypersonic shock/boundary-layer interaction database［J］. AIAA Journal， 1994， 32（7）： 1377-1383.
94	ANDREOPOULOS Y， AGUI J H， BRIASSULIS G. Shock wave-turbulence interactions［J］. Annual Review of Fluid Mechanics， 2000， 32： 309-345.
95	DOLLING D S. Fifty years of shock-wave/boundary-layer interaction research： What next？［J］. AIAA Journal， 2001， 39（8）： 1517-1531.
96	CLEMENS N T， NARAYANASWAMY V. Low-frequency unsteadiness of shock wave/turbulent boundary layer interactions［J］. Annual Review of Fluid Mechanics， 2014， 46： 469-492.
97	GAITONDE D V. Progress in shock wave/boundary layer interactions［J］. Progress in Aerospace Sciences， 2015， 72： 80-99.
98	张昊元，孙东，邱波，等. 湍动能在激波/边界层干扰流动中的影响［J］. 航空学报， 2022， 43（7）： 125504.
	ZHANG H Y， SUN D， QIU B， et al. Influence of turbulent kinetic energy on shock wave/boundary layer interaction［J］. Acta Aeronautica et Astronautica Sinica， 2022， 43（7）： 125504 （in Chinese）.
99	范孝华，唐志共，王刚，等. 激波/湍流边界层干扰低频非定常性研究评述［J］. 航空学报， 2022， 43（1）： 625917.
	FAN X H， TANG Z G， WANG G， et al. Review of low-frequency unsteadiness in shock wave/turbulent boundary layer interaction［J］. Acta Aeronautica et Astronautica Sinica， 2022， 43（1）： 625917 （in Chinese）.
100	程剑锐，施崇广，瞿丽霞，等. 二维弯曲激波/湍流边界层干扰流动理论建模［J］. 航空学报， 2022， 43（9）： 125993.
	CHENG J R， SHI C G， QU L X， et al. Theoretical model of 2D curved shock wave/turbulent boundary layer interaction［J］. Acta Aeronautica et Astronautica Sinica， 2022， 43（9）： 125993 （in Chinese）.
101	BENEK J. Lessons learned from the 2010 AIAA shock boundary layer interaction prediction workshop［C］∥ 28th AIAA Applied Aerodynamics Conference. Reston： AIAA， 2010.
102	VIEIRA R F， AZEVEDO J L F. Turbulence model assessment for simulation of shock wave-boundary layer interaction flows［C］∥ 31st AIAA Applied Aerodynamics Conference. Reston： AIAA， 2013.
103	HIRSCH C. Lessons learned from the first AIAA-SWBLI workshop CFD simulations of two test cases［C］∥ 28th AIAA Applied Aerodynamics Conference. Reston： AIAA， 2010.
104	SINHA K， MAHESH K， CANDLER G V. Modeling shock unsteadiness in shock/turbulence interaction［J］. Physics of Fluids， 2003， 15（8）： 2290-2297.
105	SINHA K， MAHESH K， CANDLER G V. Modeling the effect of shock unsteadiness in shock/turbulent boundary-layer interactions［J］. AIAA Journal， 2005， 43（3）： 586-594.
106	PASHA A A， SINHA K. Simulation of hypersonic shock/turbulent boundary-layer interactions using shock-unsteadiness model［J］. Journal of Propulsion and Power， 2012， 28（1）： 46-60.
107	VEMULA J B， JOSHI T K， SINHA K. Application of shock-unsteadiness model to interaction of transverse sonic jet and supersonic crossflow［C］∥ AIAA Aviation 2021 Forum. Reston： AIAA， 2021.
108	ROY S， PATHAK U， SINHA K. Variable turbulent Prandtl number model for shock/boundary-layer interaction［J］. AIAA Journal， 2018， 56（1）： 342-355.
109	RAJE P， SINHA K. Anisotropic SST turbulence model for shock-boundary layer interaction［J］. Computers & Fluids， 2021， 228： 105072.
110	RAJE P， SINHA K. Formulation of advanced SST turbulence model for shock-boundary layer interaction［C］∥ AIAA Aviation 2021 Forum. Reston： AIAA， 2021.
111	韩省思，叶桃红，朱旻明，等. 一个新的可压缩性修正的k-ε模型［J］. 空气动力学学报， 2009， 27（6）： 677-682.
	HAN X S， YE T H， ZHU M M， et al. A new k-ε turbulence model with compressibility modifications［J］. Acta Aerodynamica Sinica， 2009， 27（6）： 677-682 （in Chinese）.
112	LARSSON J， LELE S K. Direct numerical simulation of canonical shock/turbulence interaction［J］. Physics of Fluids， 2009， 21（12）： 126101.
113	JAMME S， CAZALBOU J B， TORRES F， et al. Direct numerical simulation of the interaction between a shock wave and various types of isotropic turbulence［J］. Flow， Turbulence and Combustion， 2002， 68（3）： 227-268.
114	POPE S B. A more general effective-viscosity hypothesis［J］. Journal of Fluid Mechanics， 1975， 72（2）： 331-340.
115	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.
116	THIVET F. Lessons learned from RANS simulations of shock-wave/boundary-layer interactions［C］∥ 40th AIAA Aerospace Sciences Meeting & Exhibit. Reston： AIAA， 2002.
117	WILCOX D， RUBESIN M W. Progress in turbulence modeling for complex flow fields including effects of compressibility： NASA-TP-1517［R］. Washington， D.C.： NASA， 1980.
118	SHIH T H， ZHU J， LUMLEY J L. A realizable Reynolds stress algebraic equation model［M］. Washington， D.C.： NASA， 1993： 235-241.
119	CRAFT T J， LAUNDER B E， SUGA K. Development and application of a cubic eddy-viscosity model of turbulence［J］. International Journal of Heat and Fluid Flow， 1996， 17（2）： 108-115.
120	APSLEY D D， LESCHZINER M A. A new low-Reynolds-number nonlinear two-equation turbulence model for complex flows［J］. International Journal of Heat and Fluid Flow， 1998， 19（3）： 209-222.
121	舒博文，杜一鸣，高正红，等. 典型航空分离流动的雷诺应力模型数值模拟［J］. 航空学报， 2022， 43（11）： 526385.
	SHU B W， DU Y M， GAO Z H， et al. Numerical simulation of Reynolds stress model of typical aerospace separated flow［J］. Acta Aeronautica et Astronautica Sinica， 2022， 43（11）： 526385 （in Chinese）.
122	WALLIN S， JOHANSSON A V. An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows［J］. Journal of Fluid Mechanics， 2000， 403： 89-132.
123	RUNG T， LÜBCKE H， FRANKE M， et al. Assessment of explicit algebraic stress models in transonic flows［M］∥RODI W， LAURENCE D. Engineering turbulence modelling and experiments 4. Amsterdam： Elsevier， 1999： 659-668.
124	REVELL A J， CRAFT T J， LAURENCE D R. Turbulence modelling of unsteady turbulent flows using the stress strain lag model［J］. Flow， Turbulence and Combustion， 2011， 86（1）： 129-151.
125	LARDEAU S， BILLARD F. Development of an elliptic-blending lag model for industrial applications［C］∥ 54th AIAA Aerospace Sciences Meeting. Reston： AIAA， 2016.
126	MANCEAU R， HANJALIĆ K. Elliptic blending model： A new near-wall Reynolds-stress turbulence closure［J］. Physics of Fluids， 2002， 14（2）： 744-754.
127	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.
128	SHANG W J， AGARWAL R K. Development and validation of an elliptic blending lag SST k-ω turbulence model［C］∥ AIAA Aviation 2020 Forum. Reston： AIAA， 2020.
129	SHANG W J， AGARWAL R K. Development and validation of an elliptic blending lag wall-distance-free SST k-ω turbulence model［C］∥ AIAA Scitech 2021 Forum. Reston： AIAA， 2021.
130	GOLDBERG U C， BATTEN P. A wall-distance-free version of the SST turbulence model［J］. Engineering Applications of Computational Fluid Mechanics， 2015， 9（1）： 33-40.
131	WALKER G J. The role of laminar-turbulent transition in gas turbine engines： A discussion［J］. Journal of Turbomachinery， 1993， 115（2）： 207-216.
132	MAYLE R E， SCHULZ A. The path to predicting bypass transition［J］. Journal of Turbomachinery， 1997， 119（3）： 405-411.
133	MALKIEL E， MAYLE R E. Transition in a separation bubble［J］. Journal of Turbomachinery， 1996， 118（4）： 752-759.
134	MENTER F R， ESCH T， KUBACKI S. Transition modelling based on local variables［M］∥RODI W， FUEYO N. Engineering turbulence modelling and experiments 5. Amsterdam： Elsevier， 2002： 555-564.
135	MENTER F R， LANGTRY R B， LIKKI S R， et al. A correlation-based transition model using local variables—Part I： Model formulation［J］. Journal of Turbomachinery， 2006， 128（3）： 413-422.
136	MENTER F R， LANGTRY R， VÖLKER S. Transition modelling for general purpose CFD codes［J］. Flow， Turbulence and Combustion， 2006， 77（1）： 277-303.
137	LANGTRY R B， MENTER F R. Correlation-based transition modeling for unstructured parallelized computational fluid dynamics codes［J］. AIAA Journal， 2009， 47（12）： 2894-2906.
138	孟德虹，张玉伦，王光学，等. γ-Re_θ 转捩模型在二维低速问题中的应用［J］. 航空学报， 2011， 32（5）： 792-801.
	MENG D H， ZHANG Y L， WANG G X， et al. Application of γ-Re_θ transition model to two-dimensional low speed flows［J］. Acta Aeronautica et Astronautica Sinica， 2011， 32（5）： 792-801 （in Chinese）.
139	HOU Y， WRAY T， AGARWAL R K. Application of SST k-ω transition model to flow past smooth and rough airfoils［C］∥ 47th AIAA Fluid Dynamics Conference. Reston： AIAA， 2017.
140	HELLSTEN A， LAINE S， HELLSTEN A， et al. Extension of the k-omega-SST turbulence model for flows over rough surfaces［C］∥ 22nd Atmospheric Flight Mechanics Conference. Reston： AIAA， 1997.
141	ENDO S， SUJISAKULVONG T， KUYA Y， et al. Laminar-turbulent transition modeling with a Reynolds stress model for anisotropic flow characteristics［C］∥ AIAA Scitech 2020 Forum. Reston： AIAA， 2020.
142	BARROUILLET B， LAURENDEAU É， YANG H. Calibration of the transitional k⁃ω⁃γ⁃Re_θt turbulence model［J］. AIAA Journal， 2022， 60（7）： 4140-4148.
143	PIOTROWSKI M， ZINGG D W. Investigation of a local correlation-based transition model in a Newton-Krylov algorithm［C］∥ AIAA Scitech 2019 Forum. Reston： AIAA， 2019.
144	DURBIN P. An intermittency model for bypass transition［J］. International Journal of Heat and Fluid Flow， 2012， 36： 1-6.
145	GE X， AROLLA S， DURBIN P. A bypass transition model based on the intermittency function［J］. Flow， Turbulence and Combustion， 2014， 93（1）： 37-61.
146	MENTER F R， SMIRNOV P E， LIU T， et al. A one-equation local correlation-based transition model［J］. Flow， Turbulence and Combustion， 2015， 95（4）： 583-619.
147	KATO M. The modeling of turbulent flow around stationary and vibrating square cylinders［C］∥Proceedings of 9th Symposium on Turbulence and Shear Flows， 1993： 4-10.
148	WANG J Y， SHENG C H. A comparison of a local correlation-based transition model coupled with SA and SST turbulence models［C］∥ 53rd AIAA Aerospace Sciences Meeting. Reston： AIAA， 2015.
149	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.
150	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.
151	OLIVER T A， MOSER R. Uncertainty quantification for rans turbulence model predictions［C］∥APS Division of Fluid Dynamics Meeting Abstracts， 2009.
152	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.
153	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.
154	米俊亦. 湍流模式理论的机器学习研究［D］. 哈尔滨：哈尔滨工业大学， 2017： 41-43.
	MI J Y. Research on turbulence modeling theory with machine learning［D］. Harbin： Harbin Institute of Technology， 2017： 41-43 （in Chinese）.
155	孙亮. 基于机器学习的代数湍流模型建模［D］. 南京：南京航空航天大学， 2019.
	SUN L. An algebraic turbulence model based on machine learning［D］. Nanjing： Nanjing University of Aeronautics and Astronautics， 2019 （in Chinese）.
156	BANKO A J， EATON J K. Estimating performance bounds of machine-learning Reynolds-stress models via optimal tensor basis expansions［C］∥Center for Turbulence Research Annual Research Briefs， 2020.
157	叶舒然，张珍，王一伟，等. 基于卷积神经网络的深度学习流场特征识别及应用进展［J］. 航空学报， 2021， 42（4）： 524736.
	YE S R， ZHANG Z， WANG Y W， et al. Progress in deep convolutional neural network based flow field recognition and its applications［J］. Acta Aeronautica et Astronautica Sinica， 2021， 42（4）： 524736 （in Chinese）.
158	张伟伟，寇家庆，刘溢浪. 智能赋能流体力学展望［J］. 航空学报， 2021， 42（4）： 524689.
	ZHANG W W， KOU J Q， LIU Y L. Prospect of artificial intelligence empowered fluid mechanics［J］. Acta Aeronautica et Astronautica Sinica， 2021， 42（4）： 524689 （in Chinese）.
159	WEATHERITT J， SANDBERG R D. The development of algebraic stress models using a novel evolutionary algorithm［J］. International Journal of Heat and Fluid Flow， 2017， 68： 298-318.
160	TAGHIZADEH S， WITHERDEN F D， GIRIMAJI S S. Turbulence closure modeling with data-driven techniques： Physical compatibility and consistency considerations［J］. New Journal of Physics， 2020， 22（9）： 093023.
161	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.

案例	分离长度1/mm	分离长度2/mm
实验数据	22.3	15.1
Menter SST， a₁=0.31	52.9	43.1
Menter SST， a₁=0.34	30.6	19.6
Menter SST， a₁=0.355	24.6	13.5
Menter SST， a₁=0.37	21.2	9.7
Menter BSL	16.0	0

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SST turbulence model improvements: Review

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