ACTA AERONAUTICAET ASTRONAUTICA SINICA >
Improvement of shock wave and compressibility effects in SST turbulence model
Received date: 2023-03-14
Revised date: 2023-04-11
Accepted date: 2023-05-07
Online published: 2023-05-12
Supported by
National Natural Science Foundation of China(11925207)
Lack of consideration of certain important flow characteristics leads to obvious limitations in supersonic flow description by the standard SST turbulence model developed for incompressible flow. To improve the prediction accuracy of the SST model in complex supersonic flows involved in hypersonic propulsion systems， the shock wave and compressibility effects were introduced based on the flow characteristics. The shock/turbulent boundary layer discriminant function and compressible effect discriminant function were used to locate the region where the model parameters or modeling assumptions of the standard SST model failed， and the turbulence model was improved directionally. Examples of supersonic plate boundary layer flow， supersonic compression corner separation flow， supersonic complex shock train flow in an isolator and HIFiRE-2 supersonic internal flow were used for testing. The results show that the improved model has the same prediction ability as the standard SST model for turbulent boundary layers， but significantly improves the prediction ability of shock-wave involved flows and adverse-pressure-gradient induced separating flows.
Key words： SST; turbulence model; shock wave; compressibility; structure characteristics
Hongbo WANG , Yu ZENG , Dapeng XIONG , Yixin YANG , Mingbo SUN . Improvement of shock wave and compressibility effects in SST turbulence model[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2024 , 45(3) : 128694 -128694 . DOI: 10.7527/S1000-6893.2023.28694
| 1 | MENTER F R. Two-equation eddy-viscosity turbulence models for engineering applications［J］. AIAA Journal， 1994， 32（8）： 1598-1605. |
| 2 | 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）. | |
| 3 | URZAY J. Supersonic combustion in air-breathing propulsion systems for hypersonic flight［J］. Annual Review of Fluid Mechanics， 2018， 50： 593-627. |
| 4 | PENG Y P， BARZEGAR GERDROODBARY M， SHEIKHOLESLAMI M， et al. Mixing enhancement of the multi hydrogen fuel jets by the backward step［J］. Energy， 2020， 203： 117859. |
| 5 | 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）. | |
| 6 | 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. |
| 7 | 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. |
| 8 | HUANG X B， YANG W， LI Y J， 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. |
| 9 | BRADSHAW P. Turbulence modeling with application to turbomachinery［J］. Progress in Aerospace Sciences， 1996， 32（6）： 575-624. |
| 10 | 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. |
| 11 | 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）. | |
| 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 | 童福林， 段俊亦， 周桂宇， 等. 激波/湍流边界层干扰压力脉动特性数值研究［J］. 力学学报， 2021， 53（7）： 1829-1841. |
| TONG F L， DUAN J Y， ZHOU G Y， et al. Statistical characteristics of pressure fluctuation in shock wave and turbulent boundary layer interaction［J］. Chinese Journal of Theoretical and Applied Mechanics， 2021， 53（7）： 1829-1841 （in Chinese）. | |
| 15 | POPE S B. A more general effective-viscosity hypothesis［J］. Journal of Fluid Mechanics， 1975， 72（2）： 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 | 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. |
| 18 | BARROUILLET B， LAURENDEAU é， YANG H. Calibration of the transitional k?ω?γ-Reθt turbulence model［J］. AIAA Journal， 2022， 60（7）： 4140-4148. |
| 19 | MANCEAU R， HANJALI? K. Elliptic blending model： A new near-wall Reynolds-stress turbulence closure［J］. Physics of Fluids， 2002， 14（2）： 744-754. |
| 20 | BISWAS R， DURBIN P A， MEDIC G. Development of an elliptic blending lag k-ω ［J］. International Journal of Heat and Fluid Flow， 2019， 76： 26-39. |
| 21 | SHANG W J， AGARWAL R K. Development and validation of an elliptic blending lag SST k?ω turbulence model［C］∥ Proceedings of the AIAA Aviation 2020 Forum. Reston： AIAA， 2020. |
| 22 | 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. |
| 23 | 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. |
| 24 | MENTER F， KUNTZ M， LANGTRY R. Ten years of industrial experience with the SST turbulence model［J］. Turbulence， Heat and Mass Transfer， 2003， 4（1）： 625-632. |
| 25 | DURBIN P A. Some recent developments in turbulence closure modeling［J］. Annual Review of Fluid Mechanics， 2018， 50： 77-103. |
| 26 | 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）. | |
| 27 | RAJE P， SINHA K. Anisotropic SST turbulence model for shock-boundary layer interaction［J］. Computers & Fluids， 2021， 228： 105072. |
| 28 | 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. |
| 29 | SMITS A J， DUSSAUGE J P. Turbulent shear layers in supersonic flow［M］. 2nd ed. New York： Springer， 2006： 35-41. |
| 30 | 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）. | |
| 31 | SARKAR S. The pressure?dilatation correlation in compressible flows［J］. Physics of Fluids A： Fluid Dynamics， 1992， 4（12）： 2674-2682. |
| 32 | 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. |
| 33 | WILCOX D C. Dilatation-dissipation corrections for advanced turbulence models［J］. AIAA Journal， 1992， 30（11）： 2639-2646. |
| 34 | BROWN J. Turbulence model validation for hypersonic flows［C］∥ Proceedings of the 8th AIAA/ASME Joint Thermophysics and Heat Transfer Conference. Reston： AIAA， 2002. |
| 35 | MA G W， SUN M B， ZHAO G Y， et al. Effect of injection scheme on asymmetric phenomenon in rectangular and circular scramjets［J］. Chinese Journal of Aeronautics， 2023， 36（1）： 216-230. |
| 36 | LIU M J， SUN M B， ZHAO G Y， et al. Effect of combustion mode on thrust performance in a symmetrical tandem-cavity scramjet combustor［J］. Aerospace Science and Technology， 2022， 130： 107904. |
| 37 | ZHANG C， DUAN L A， CHOUDHARI M M. Direct numerical simulation database for supersonic and hypersonic turbulent boundary layers［J］. AIAA Journal， 2018， 56（11）： 4297-4311. |
| 38 | RINGUETTE M J， BOOKEY P， WYCKHAM C， et al. Experimental study of a Mach 3 compression ramp interaction at Reθ = 2400［J］. AIAA Journal， 2009， 47（2）： 373-385. |
| 39 | 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. |
| 40 | 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. |
| 41 | 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. |
| 42 | 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. |
| 43 | 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. |
| 44 | MIDDLETON T F， BALLA R， BAURLE R， et al. The NASA Langley isolator dynamics research LAB［C］∥ Proceedings of the 31st Airbreathing Joint Meeting， 2010. |
| 45 | BAURLE R， MIDDLETON T F， WILSON L G. Reynolds-averaged turbulence model assessment for a highly back-pressured isolator flowfield［C］∥ 33rd Airbreathing Propulsion Joint Subcommittee Meeting， 2012. |
| 46 | TIAN Y F， ZHU J J， SUN M B， et al. Enhancement of blowout limit in a Mach 2.92 cavity-based scramjet combustor by a gliding arc discharge［J］. Proceedings of the Combustion Institute， 2023， 39（4）： 5697-5705. |
| 47 | STORCH A， BYNUM M， LIU J W， et al. Combustor operability and performance verification for HIFiRE flight 2［C］∥ Proceedings of the 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference. Reston： AIAA， 2011. |
| 48 | HASS N， CABELL K， STORCH A， et al. HIFiRE direct-connect rig （HDCR） phase I scramjet test results from the NASA Langley arc-heated scramjet test facility［C］∥ Proceedings of the 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference. Reston： AIAA， 2011. |
| 49 | JACKSON K， GRUBER M， BUCCELLATO S. HIFiRE flight 2 project overview and status update 2011［C］∥ Proceedings of the 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference. Reston： AIAA， 2011. |
| 50 | 王力军， 袁韦韦， 徐义俊， 等. 基于HIFiRE-2超燃发动机内流道的激波边界层干扰分析［J］. 航空发动机， 2020， 46（3）： 14-19. |
| WANG L J， YUAN W W， XU Y J， et al. Analysis of shock wave boundary layer interactions based on internal flowpath of HIFiRE-2 scramjet［J］. Aeroengine， 2020， 46（3）： 14-19 （in Chinese）. |
/
| 〈 |
|
〉 |
CJA