雷诺应力与涡黏性模型的分离流预测对比分析

doi:10.7527/S1000-6893.2022.27619

Abstract

Abstract:

The demand for accurate prediction of flow separation in modern aircraft design is becoming increasingly urgent， yet the prediction results of the widely used eddy viscosity model are not satisfactory. With its solid theoretical foundation， the Reynolds stress model may obtain more reliable results； however， its performance advantages still need to be further evaluated and explored. In this paper， the shear stress transport model and stress baseline model are selected as the representatives of the eddy viscosity model and Reynolds stress model， respectively， and numerical simulations are carried out for two-dimensional hump， two-dimensional transonic bump and three-dimensional transonic ONERA M6 wing. Compared with the experimental values， the prediction results of the two models show that the flow separation point is ahead of time and the reattachment point lags behind， while the prediction error of the Stress BSL model is smaller， showing the advantage of separation flow prediction under strong reverse pressure gradient. It is found that the two models underestimate the Reynolds stress， resulting in a large separation zone. Specifically， the Bradshaw hypothesis introduced into the SST model limits the generation of turbulent kinetic energy， reduces the eddy viscosity coefficient calculated by the model， underestimates the Reynolds stress in the boundary layer under strong adverse pressure gradient， and leads to early flow separation. The smaller Reynolds stress prediction value at the upper edge of the separation zone is considered to be the main cause for the lag of flow reattachment. For the Reynolds stress model， the error mainly originates from the inaccurate modeling of the redistribution term of the Reynolds stress transport equation. Finally， aiming at the above causes， we recalibrate and preliminarily verify the key closure parameters of the SST model. The results show that the modified model performs better than the original model.

Key words: Reynolds stress model, eddy viscosity model, Reynolds stress, separation flow, shock induced separation

CLC Number:

V211.3

Yatian ZHAO, Zhiyuan SHAO, Chao YAN, Xinghao XIANG. Comparative analysis of Reynolds stress and eddy viscosity models in separation flow prediction[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(11): 127619-127619.

Figures/Tables 19

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References 32

1	DRIVER D M， SEEGMILLER H L， MARVIN J G. Time-dependent behavior of a reattaching shear layer［J］. AIAA Journal， 1987， 25（7）： 914-919.
2	BUSH R H， CHYCZEWSKI T S， DURAISAMY K， et al. Recommendations for future efforts in RANS modeling and simulation［C］∥AIAA Scitech 2019 Forum. Reston： AIAA， 2019： 0317.
3	EISFELD B， RUMSEY C， TOGITI V. Verification and validation of a second-moment-closure model［J］. AIAA Journal， 2016， 54（5）： 1524-1541.
4	RUMSEY C L. Application of Reynolds stress models to separated aerodynamic flows［M］∥EISFELD B. Differential Reynolds Stress Modeling for Separating Flows in Industrial Aerodynamics. Cham： Springer， 2015： 19-37.
5	RUMSEY C L， RIVERS S M， MORRISON J H. Study of CFD variation on transport configurations from the second drag-prediction workshop［J］. Computers & Fluids， 2005， 34（7）： 785-816.
6	WILCOX D C. Turbulence Modeling for CFD［M］. 3rd edition. San Diego： DCW Industries， 2006.
7	董义道，王东方，王光学，等. 雷诺应力模型的初步应用［J］. 国防科技大学学报， 2016， 38（4）： 46-53.
	DONG Y D， WANG D F， WANG G X， et al. Preliminary application of Reynolds stress model［J］. Journal of National University of Defense Technology， 2016， 38（4）： 46-53 （in Chinese）.
8	阎超，屈峰，赵雅甜，等. 航空航天CFD物理模型和计算方法的述评与挑战［J］. 空气动力学学报， 2020， 38（5）： 829-857.
	YAN C， QU F， ZHAO Y T， et al. Review of development and challenges for physical modeling and numerical scheme of CFD in aeronautics and astronautics［J］. Acta Aerodynamica Sinica， 2020， 38（5）： 829-857 （in Chinese）.
9	SLOTNICK J， KHODADOUST A， ALONSO J， et al. CFD vision 2030 study： A path to revolutionary computational aerosciences： NASA/CR-2014-218178［R］. Hampton： NASA Langley Research Center， 2014.
10	RUMSEY C， VATSA V. A comparison of the predictive capabilities of several turbulence models using upwind and central-difference computer codes［C］∥31st Aerospace Sciences Meeting. Reston： AIAA， 1993： 192.
11	WANG S Y， DONG Y D， DENG X G， et al. High-order simulation of aeronautical separated flows with a reynold stress model［J］. Journal of Aircraft， 2018， 55（3）： 1177-1190.
12	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）： 487-502.
	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）： 487-502 （in Chinese）.
13	熊莉芳，林源，李世武. k⁃ε湍流模型及其在FLUENT软件中的应用［J］. 工业加热， 2007， 36（4）： 13-15.
	XIONG L F， LIN Y， LI S W. k⁃ε turbulent model and its application to the FLUENT［J］. Industrial Heating， 2007， 36（4）： 13-15 （in Chinese）.
14	MENTER F R， EGOROV Y. The scale-adaptive simulation method for unsteady turbulent flow predictions. Part 1： Theory and model description［J］. Flow， Turbulence and Combustion， 2010， 85（1）： 113-138.
15	刘宏康，陈坚强，向星皓，等. 改进k⁃ω⁃γ转捩模式对不同雷诺数下HIAD的转捩预测［J］. 航空学报， 2022， 43（12）： 126868.
	LIU H K， CHEN J Q， XIANG X H， et al. Transition prediction for HIAD at different Reynolds number by improved k⁃ω⁃γ transition model［J］. Acta Aeronautica et Astronautica Sinica，2022，43（12）：126868 （in Chinese）.
16	GREENBLATT D， PASCHAL K B， YAO C S， et al. Experimental investigation of separation control part 1： baseline and steady suction［J］. AIAA Journal， 2006， 44（12）： 2820-2830.
17	GREENBLATT D， PASCHAL K B， YAO C S， et al. Experimental investigation of separation control part 2： Zero mass-flux oscillatory blowing［J］. AIAA Journal， 2006， 44（12）： 2831-2845.
18	BACHALO W D， JOHNSON D A. Transonic， turbulent boundary-layer separation generated on an axisymmetric flow model［J］. AIAA Journal， 1986， 24（3）： 437-443.
19	Mayeur J， Dumont A， Destarac D， et al. RANS simulations on TMR test cases and M6 wing with the Onera elsA flow solver［J］. AIAA Paper， 2015， 1745： 2015.
20	DEMUREN A， SARKAR S. Systematic study of Reynolds stress closure models in the computations of plane channel flows［R］. Hampton： Institute for Computer Applications in Science and Engineering， 1992.
21	PANDA J P， WARRIOR H V， MAITY S， et al. An improved model including length scale anisotropy for the pressure strain correlation of turbulence［J］. Journal of Fluids Engineering， 2017， 139（4）： 044503.
22	LAUNDER B E， REECE G J， RODI W. Progress in the development of a Reynolds-stress turbulence closure［J］. Journal of Fluid Mechanics， 1975， 68（3）： 537-566.
23	SPEZIALE C G， SARKAR S， GATSKI T B. Modelling the pressure–strain correlation of turbulence： an invariant dynamical systems approach［J］. Journal of Fluid Mechanics， 1991， 227： 245-272.
24	CÉCORA R D， RADESPIEL R， EISFELD B， et al. Differential Reynolds-stress modeling for aeronautics［J］. AIAA Journal， 2014， 53（3）： 739-755.
25	王圣业，符翔，杨小亮，等. 高阶矩湍流模型研究进展及挑战［J］. 力学进展， 2021， 51（1）： 29-61.
	WANG S Y， FU X， YANG X L， et al. Progresses and challenges of high-order-moment turbulence closure［J］. Advances in Mechanics， 2021， 51（1）： 29-61 （in Chinese）.
26	MENTER F R. Two-equation eddy-viscosity turbulence models for engineering applications［J］. AIAA Journal， 1994， 32（8）： 1598-1605.
27	GALVÁN S， REGGIO M， GUIBAULT F. Assessment study of K-ɛ turbulence models and near-wall modeling for steady state swirling flow analysis in draft tube using fluent［J］. Engineering Applications of Computational Fluid Mechanics， 2011， 5（4）： 459-478.
28	TOMINAGA Y， STATHOPOULOS T. Numerical simulation of dispersion around an isolated cubic building： comparison of various types of k⁃ɛ models［J］. Atmospheric Environment， 2009， 43（20）： 3200-3210.
29	WILCOX D C. Formulation of the k-w turbulence model revisited［J］. AIAA Journal， 2008， 46（11）： 2823-2838.
30	BRADSHAW P， FERRISS D H， ATWELL N P. Calculation of boundary-layer development using the turbulent energy equation［J］. Journal of Fluid Mechanics， 1967， 28（3）： 593.
31	KAEWBUMRUNG， TANGSOPA， THONGSRI. Investigation of the trailing edge modification effect on compressor blade aerodynamics using SST k⁃ω turbulence model［J］. Aerospace， 2019， 6（4）： 48.
32	ZHAO Y T， YAN C， WANG X Y， et al. Uncertainty and sensitivity analysis of SST turbulence model on hypersonic flow heat transfer［J］. International Journal of Heat and Mass Transfer， 2019， 136： 808-820.

模型及实验	分离点位置/c	再附点位置/c
SST	0.658	1.23
Stress-BSL	0.659	1.19
实验	0.665	1.10

模型及实验	分离点位置/c	再附点位置/c
SST	0.646	1.168
Stress-BSL	0.664	1.052
实验	0.700	1.100

网格质量	网格分辨率（流向×展向×法向）	第1层网格高度ΔX/m	网格雷诺数Re_Δ_X
粗网格	129×206×67	1×10^-5	32
中网格	169×226×87	5×10^-6	16
细网格	209×246×107	2×10^-6	8
极细网格	239×266×127	1×10^-6	5

模型	机翼升力系数C_L	机翼阻力系数C_D
Stress-BSL	0.270 1	0.030 4
SST	0.195 4	0.027 1

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[8]	WANG Bin, LI Huaxing. Control of flow turbulent kinetic energy by plasma [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015, 36(12): 3809-3821.
[9]	Xiang Xiaorong;Liu Bo;Wang Qingwei;Chen Yunyong. Flow Characteristics of Stator Wake in Small Axial Compressor [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2009, 30(11): 2045-2051.
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[11]	Xiao Po;Li Yuchun;Xu Liping. A METHOD FOR MEASURING UNSTEADY SEPARATION TURBULKNT FLOW USING SPLIT-FILM [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 1994, 15(12): 1438-1444.
[12]	E Qin;LiLi;YangMenghui. AN IMPROVED INTEGRAL METHOD FOR TWO-DIMENSIONAL COMPRESSIBLETURBULENT BOUNDARY-LAYER [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 1994, 15(11): 1375-1378.
[13]	Lu Xi-yun;Zhuang Li-xian;Yin Xie-yuan;Tong Bing-gang. NUMERICAL SIMULATION OF FLOWS PAST A LONGITUDINALLY OSCILLATING AIRFOIL AT HIGH INCIDENCES [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 1993, 14(11): 632-635.
[14]	Li Feng;Wang Yi-yun;Cui Er-jie. AERODYNAMIC INVESTIGATION ON INTERACTION OF VORTEX WITH STATIONARY AIRFOIL [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 1993, 14(11): 625-628.
[15]	Zhou Wei-jiang;Ma Han-dong;Ma Yan-wen. NUMERICAL STUDY OF SUPERSONIC FLOW OVER A BACKWARD STEP WITH TRANSVERSE INJECTION [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 1993, 14(1): 14-19.

Comparative analysis of Reynolds stress and eddy viscosity models in separation flow prediction

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