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基于当地变量的横流转捩预测模式研究进展

徐家宽,  段毅,  杨家盛,  乔磊,  刘建新,  白俊强

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文章导航 > 气体物理  > 2023 >  8(3): 19-34
徐家宽, 段毅, 杨家盛, 乔磊, 刘建新, 白俊强. 基于当地变量的横流转捩预测模式研究进展[J]. 气体物理, 2023, 8(3): 19-34. doi: 10.19527/j.cnki.2096-1642.1012
引用本文: 徐家宽, 段毅, 杨家盛, 乔磊, 刘建新, 白俊强. 基于当地变量的横流转捩预测模式研究进展[J]. 气体物理, 2023, 8(3): 19-34. doi: 10.19527/j.cnki.2096-1642.1012
shu
XU Jia-kuan, DUAN Yi, YANG Jia-sheng, QIAO Lei, LIU Jian-xin, BAI Jun-qiang. Progress on Prediction Models for Crossflow Instabilities Dominated Transition Based on Local Variables[J]. PHYSICS OF GASES, 2023, 8(3): 19-34. doi: 10.19527/j.cnki.2096-1642.1012
Citation: XU Jia-kuan, DUAN Yi, YANG Jia-sheng, QIAO Lei, LIU Jian-xin, BAI Jun-qiang. Progress on Prediction Models for Crossflow Instabilities Dominated Transition Based on Local Variables[J]. PHYSICS OF GASES, 2023, 8(3): 19-34. doi: 10.19527/j.cnki.2096-1642.1012
shu

基于当地变量的横流转捩预测模式研究进展

doi: 10.19527/j.cnki.2096-1642.1012
  • 1.

    西北工业大学, 陕西西安 710072

  • 2.

    中国运载火箭技术研究院空间物理重点实验室, 北京 100076

  • 3.

    天津大学, 天津 300072

基金项目: 

国家自然科学基金 12102361

中央高校基本科研业务费 G2021KY05101

详细信息
    作者简介:

    徐家宽(1989-) 男, 副教授, 主要研究方向为转捩-湍流预测模式、流动稳定性分析。E-mail: jk.xu@nwpu.edu.cn

  • 中图分类号: V211

Progress on Prediction Models for Crossflow Instabilities Dominated Transition Based on Local Variables

  • 1.

    Northwestern Polytechnical University, Xi'an 710072, China

  • 2.

    Science and Technology on Space Physics Laboratory, China Academy of Launch Vehicle Technology, Beijing 100076, China

  • 3.

    Tianjin University, Tianjin 300072, China

    摘要
  • 摘要: 边界层转捩预测一直是流体力学领域的研究热点和难点。其中, 横流转捩是飞行器表面转捩现象中关键的一种。由于受到来流扰动、壁面粗糙度、壁面压力梯度、当地后掠角、横流特征Reynolds数、边界层边缘Mach数、壁面曲率和温度等因素的影响, 横流转捩的预测非常复杂且困难。近年来诸多研究机构都针对该问题提出了不同思路的预测方法, 从根本上分为两大类: 一类是建立临界转捩Reynolds数准则, 通过与当地的特征尺度Reynolds数进行比较判定是否发生转捩; 另一类则是模式化的线性稳定性理论, 计算得到横流扰动增长因子与转捩阈值相比较判定是否发生转捩。将系统回顾和总结低速边界层和高速边界层的几类典型的基于当地变量的横流转捩预测模式, 并展望下一步的研究方向。

     

    Abstract: Boundary layer transition prediction has always been a hot and difficult research topic in the field of fluid mechanics. Among them, the crossflow induced transition plays a crucial role in the transition phenomenon on the surface of the aircraft, which is affected by the freestream disturbance, wall surface roughness, wall pressure gradient, local sweep angle, crossflow characteristic Reynolds number, Mach number, wall curvature and temperature. All those factors make the prediction of the cross-flow transition very complicated and difficult. In recent years, many research institutions have proposed various prediction methods for this problem, which are basically divided into two categories: one is to establish the critical transition Reynolds number criterion, and to determine whether transition occurs; the other type is the modeled linear stability theory, which calculates the cross-flow disturbance amplification factor and compares it with the transition threshold to determine whether transition occurs. Several typical prediction models of crossflow dominated transition based on local variables of low-speed boundary layer and high-speed boundary will be systematically reviewed and summarized, and the future research directions will be prospected.

     

    • HTML全文

  • 图  1  横流速度型示意图

    Figure  1.  Diagram of crossflow velocity profile

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    图  2  Blasuis边界层和βH=0.2时FSC边界层中非当地变量与当地变量的函数关系[20]

    Figure  2.  Relationship between non-local and local variables in the Blasuis boundary layer and the FSC boundary layer with βH=0.2[20]

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    图  3  横流驻涡失稳动量厚度Reynolds数与粗糙度的关系[36]

    Figure  3.  Relationship between Reynolds number of stationary crossflow vortices instability momentum thickness and roughness[36]

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    图  4  临界螺旋度Reynolds数与形状因子之间的经验关系式[20]

    Figure  4.  Empirical relationship between the critical helicity Reynolds number and shape factor[20]

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    图  5  两种转捩模式对镰刀翼的摩擦力系数云图预测结果与实验数据的对比

    Figure  5.  Comparison between the prediction results of the skin friction coefficient contour of the sickle wing by the two transition models and the experimental data

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    图  6  O-S方程分析所得不同形状因子下的空间放大因子曲线[41]

    Figure  6.  Spatial amplification factor curves obtained by O-S equation analysis under different shape factors[41]

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    图  7  NLF(2)-0415算例中NCF模式预测结果与标准LST结果的对比[48]

    Figure  7.  Comparison of the prediction results by NCF model and the standard LST in NLF(2)-0415[48]

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    图  8  NCF模式在镰刀翼上表面的预测结果[48]

    Figure  8.  Prediction results of NCF model on upper surface of sickle wing[48]

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    图  9  NCF模式在6:1椭球上的预测结果(α=20°, ReL=6.5×106)[49]

    Figure  9.  Prediction results of NCF model on surface of 6:1 ellipsoid (α=20°, ReL=6.5×106)[49]

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    图  10  壁温修正后的横流Reynolds数与最大横流速度分量之间的函数关系[52]

    Figure  10.  Relationship between crossflow Reynolds number with wall temperature correction and maximal crossflow velocity component[52]

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    图  11  Ma=3.5直圆锥在2°迎角时的转捩模式预测所得间歇因子分布[56]

    Figure  11.  Distribution of the intermittency factors by Fu & Wang′s transition model over Ma=3.5 straight cone at 2° of attack[56]

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    图  12  HIFiRE-5构型在不同Reynolds数下的风洞试验结果(左列)和模式预测结果(右列)[58]

    Figure  12.  Wind tunnel test results (left column) and model prediction results (right column) of HIFiRE-5 configuration at different Reynolds numbers[58]

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    图  13  Ma=3.5直圆锥和HIFiRE-5构型在不同Reynolds数下的风洞试验结果和模式预测结果的对比[60]

    Figure  13.  Comparison between wind tunnel test results and model predicition results of Ma=3.5 straight cone and HIFiRE-5 configuration at different Reynolds numbers[60]

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    图  14  有迎角超声速圆锥在静止状态下和高速旋转运动状态下的风洞试验结果和模式预测结果的对比[60]

    Figure  14.  Comparison between wind tunnel test results and model prediction results of angle-of-attack supersonic cone in stationary state and high-speed rotating state[60]

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    图  15  X33表面的转捩预测结果与试验结果的对比[64]

    Figure  15.  Comparison between prediction results and test results of transition on the upper surface of X33[64]

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    图  16  HIFiRE-5构型在来流Reynolds数均为10.2×106/m时的预测结果与试验结果的对比[67]

    Figure  16.  Comparison between prediction results and test results of HIFiRE-5 configuration at Re=10.2×106/m[67]

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    图  17  Purdue 3°迎角直圆锥在静风洞的试验结果与模式预测结果的对比[67]

    Figure  17.  Comparison between quiet wind tunnel test results and model prediction results of Purdue straight cone with angle-of-attack of 3°[67]

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    图  18  HIFiRE-5构型在来流Reynolds数均为10.2×106/m时的预测结果与试验结果的对比[68]

    Figure  18.  Comparison between prediction results and test results of HIFiRE-5 configuration[68] when Reynolds numbers of incoming flow are all 10.2×106/m

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    图  19  Ma=6工况下横流Reynolds数与壁面粗糙高度之间的函数关系[70]

    Figure  19.  Relationship between crossflow Reynolds number and wall roughness height under Ma=6 condition[70]

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    图  20  HIFiRE-5构型在静音风洞下的风洞试验结果和模式预测结果的对比[70]

    Figure  20.  Comparison between test results and model prediction results of HIFiRE-5 configuration in quiet wind tunnel[70]

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    • 参考文献(70)
  • [1] 周恒, 赵耕夫. 流动稳定性[M]. 北京: 国防工业出版社, 2004.

    Zhou H, Zhao G F. Flow stability[M]. Beijing: National Defence Industry Press, 2004(in Chinese).
    [2] 李存标, 吴介之. 壁流动中的转捩[J]. 力学进展, 2009, 39(4): 480-507. https://www.cnki.com.cn/Article/CJFDTOTAL-LXJZ200904013.htm

    Lee C B, Wu J Z. Transition in boundary flows[J]. Progress in Mechanics, 2009, 39(4): 480-507(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-LXJZ200904013.htm
    [3] 周恒, 苏彩虹, 张永明. 超声速/高超声速边界层的转捩机理及预测[M]. 北京: 科学出版社, 2015.

    Zhou H, Su C H, Zhang Y M. Transition mechanism and prediction of supersonic/hypersonic boundary layer[M]. Beijing: Science Press, 2015(in Chinese).
    [4] Lee C, Chen S Y. Recent progress in the study of transition in the hypersonic boundary layer[J]. National Science Review, 2019, 6(1): 155-170. doi: 10.1093/nsr/nwy052
    [5] 陈坚强, 涂国华, 张毅锋, 等. 高超声速边界层转捩研究现状与发展趋势[J]. 空气动力学学报, 2017, 35(3): 311-337. https://www.cnki.com.cn/Article/CJFDTOTAL-KQDX201703001.htm

    Chen J Q, Tu G H, Zhang Y F, et al. Hypersonic boundary layer transition: what we know, where shall we go[J]. Acta Aerodynamica Sinica, 2017, 35(3): 311-337(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-KQDX201703001.htm
    [6] 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. https://www.cnki.com.cn/Article/CJFDTOTAL-KQDX202005001.htm

    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). https://www.cnki.com.cn/Article/CJFDTOTAL-KQDX202005001.htm
    [7] 解少飞, 杨武兵, 沈清. 高超声速边界层转捩机理及应用的若干进展回顾[J]. 航空学报, 2015, 36(3): 714-723. https://www.cnki.com.cn/Article/CJFDTOTAL-HKXB201503002.htm

    Xie S F, Yang W B, Shen Q. Review of progresses in hypersonic boundary layer transition mechanism and its applications[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(3): 714-723(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-HKXB201503002.htm
    [8] Radeztsky Jr R H, Reibert M S, Saric W S, et al. Effect of micron-sized roughness on transition in swept-wing flows[R]. AIAA 1993-0076, 1993.
    [9] 徐国亮, 符松. 可压缩横流失稳及其控制[J]. 力学进展, 2012, 42(3): 262-273. https://www.cnki.com.cn/Article/CJFDTOTAL-LXJZ201203005.htm

    Xu G L, Fu S. Compressible transverse flow stability and its control[J]. Progress in Mechanics, 2012, 42(3): 262-273(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-LXJZ201203005.htm
    [10] 赵磊. 高超声速后掠钝板边界层横流定常涡失稳的研究[D]. 天津: 天津大学, 2016.

    Zhao L. Study on instability of stationary crossflow vortices in hypersonic swept blunt plate boundary layer[D]. Tianjin: Tianjin University, 2016(in Chinese).
    [11] Obremski H, Morkovin M, Landahl M, et al. A portfolio of stability characteristics of incompressible boundary layers[R]. AGARD-No. 134, 1969.
    [12] Klebanoff P S, Tidstrom K D, Sargent L M. The three-dimensional nature of boundary-layer instability[J]. Journal of Fluid Mechanics, 1962, 12(1): 1-34.
    [13] 向星皓, 张毅锋, 陈坚强, 等. 横流转捩模型研究进展[J]. 空气动力学学报, 2018, 36(2): 254-264, 180. https://www.cnki.com.cn/Article/CJFDTOTAL-KQDX201802010.htm

    Xiang X H, Zhang Y F, Chen J Q, et al. Progress in transition models for crossflow instabilities[J]. Acta Aerodynamica Sinica, 2018, 36(2): 254-264, 180(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-KQDX201802010.htm
    [14] 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, 2004, 128(3): 413-422.
    [15] Langtry R B, Menter F R, Likki S R, et al. A correlation-based transition model using local variables—part Ⅱ: test cases and industrial applications[J]. Journal of Turbomachinery, 2004, 128(3): 423-434.
    [16] Menter F R, Langtry R, Völker S. Transition modelling for general purpose CFD codes[J]. Flow, Turbulence and Combustion, 2006, 77(1/4): 277-303.
    [17] 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.
    [18] 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.
    [19] Menter F R, Matyushenko A, Lechner R, et al. An algebraic LCTM model for laminar-turbulent transition prediction[J/OL]. Flow, Turbulence and Combustion, 2022. https://link.springer.com/article/10.1007/s10494-022-00336-8.
    [20] 徐家宽. 基于RANS方程的多速域边界层转捩模式构造方法及应用研究[D]. 西安: 西北工业大学, 2017.

    Xu J K. Modelling methods and application research of boundary layer transition in multi-speed range based on RANS equations[D]. Xi'an: Northwestern Polytechnical University, 2017(in Chinese).
    [21] Grabe C, Krumbein A. Correlation-based transition transport modeling for three-dimensional aerodynamic configurations[R]. AIAA 2012-0448, 2012.
    [22] Grabe C, Krumbein A. Correlation-based transition transport modeling for three-dimensional aerodynamic configurations[J]. Journal of Aircraft, 2013, 50(5): 1533-1539.
    [23] Grabe C, Krumbein A. Extension of the γ-Reθt model for prediction of crossflow transition[R]. AIAA 2014-1269, 2014.
    [24] Krumbein A, Krimmelbein N, Grabe C, et al. Development and application of transition prediction techniques in an unstructured CFD Code[R]. AIAA 2015-2476, 2015.
    [25] Grabe C, Nie S Y, Krumbein A. Transition transport modeling for the prediction of crossflow transition[R]. AIAA 2016-3572, 2016.
    [26] Grabe C, Nie S Y, Krumbein A. Transport modeling for the prediction of crossflow transition[J]. AIAA Journal, 2018, 56(8): 3167-3178.
    [27] Nie S Y, Krimmelbein N, Krumbein A, et al. Extension of a Reynolds-stress-based transition transport model for crossflow transition[J]. Journal of Aircraft, 2018, 55(4): 1641-1654.
    [28] Nie S Y, Krimmelbein N, Krumbein A, et al. Coupling of a Reynolds stress model with the γ-Reθt transition model[J]. AIAA Journal, 2018, 56(1): 146-157.
    [29] Choi J H, Kwon O J. Enhancement of a correlation-based transition turbulence model for simulating crossflow instability[R]. AIAA 2014-1133, 2014.
    [30] Choi J H, Kwon O J. Recent improvement of a correlation-based transition turbulence model for simulating three-dimensional boundary layers[R]. AIAA 2015-2762, 2015.
    [31] 徐家宽, 白俊强, 乔磊, 等. 后掠翼边界层横流不稳定转捩预测模型[J]. 航空动力学报, 2015, 30(4): 927-935. https://www.cnki.com.cn/Article/CJFDTOTAL-HKDI201504021.htm

    Xu J K, Bai J Q, Qiao L, et al. Prediction model of cross-flow instability transition in swept wing boundary layers[J]. Journal of Aerospace Power, 2015, 30(4): 927-935(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-HKDI201504021.htm
    [32] 徐家宽, 白俊强, 乔磊, 等. 横流不稳定性转捩预测模型[J]. 航空学报, 2015, 36(6): 1814-1822. https://www.cnki.com.cn/Article/CJFDTOTAL-HKXB201506009.htm

    Xu J K, Bai J Q, Qiao L, et al. Transition model for predicting crossflow instabilities[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(6): 1814-1822(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-HKXB201506009.htm
    [33] Arnal D, Juillen J. Three-dimensional transition studies at ONERA/CERT[R]. AIAA 1987-1335, 1987.
    [34] Xu J K, Bai J Q, Qiao L, et al. Correlation-based transition transport modeling for simulating crossflow instabilities[J]. Journal of Applied Fluid Mechanics, 2016, 9(5): 2435-2442.
    [35] Müeller C, Herbst F. Modelling of crossflow-induced transition based on local variables[C]. 6th European Conference on Computational Fluid Dynamics (ECFD), 2014.
    [36] Langtry R B, Sengupta K, Yeh D T, et al. Extending the γ-Reθt local correlation based transition model for crossflow effects[R]. AIAA 2015-2474, 2015.
    [37] Carnes J, Coder J G. Effects of crossflow transition on the S-76 and PSP rotors in hover[R]. AIAA 2020-0773, 2020.
    [38] Petzold R, Radespiel R. Transition on a wing with spanwise varying crossflow and linear stability analysis[J]. AIAA Journal, 2015, 53(2): 321-335.
    [39] Smith A M, Gamberoni N. Transition, pressure gradient and stability theory[R]. Douglas Aircraft Company Report ES-26388, 1956.
    [40] Van Ingen J L. A suggested semi-empirical method for the calculation of the boundary-layer transition region[R]. Delft University of Technology Report VTH-74, 1956.
    [41] Drela M, Giles M B. Viscous-inviscid analysis of transonic and low Reynolds number airfoils[J]. AIAA Journal, 1987, 25(10): 1347-1355.
    [42] Coder J G, Maughmer M D. A CFD-compatible transition model using an amplification factor transport equation[R]. AIAA 2013-0253, 2013.
    [43] Coder J G, Maughmer M D. Computational fluid dynamics compatible transition modeling using an amplification factor transport equation[J]. AIAA Journal, 2014, 52(11): 2506-2512.
    [44] Coder J G, Maughmer M D. Application of the amplification factor transport transition model to the shear stress transport model[R]. AIAA 2015-0588, 2015.
    [45] Coder J G. Enhancement of the amplification factor transport transition modeling framework[R]. AIAA 2017-1709, 2017.
    [46] Coder J G. Further development of the amplification factor transport transition model for aerodynamic flows[R]. AIAA 2019-0039, 2019.
    [47] Xu J K, Bai J Q, Zhang Y, et al. Transition study of 3D aerodynamic configures using improved transport equations modeling[J]. Chinese Journal of Aeronautics, 2016, 29(4): 874-881.
    [48] Xu J K, Han X, Qiao L, et al. Fully local amplification factor transport equation for stationary crossflow instabilities[J]. AIAA Journal, 2019, 57(7): 2682-2693.
    [49] Xu J K, Qiao L, Bai J Q. Improved local amplification factor transport equation for stationary crossflow instability in subsonic and transonic flows[J]. Chinese Journal of Aeronautics, 2020, 33(12): 3073-3081.
    [50] Xu J K. Linear amplification factor transport equation for stationary crossflow instabilities in supersonic boundary layers[J]. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2021, 235(6): 703-717.
    [51] 王玉轩, 徐家宽, 张扬, 等. 横流驻波增长因子模式在跨声速边界层的应用[J]. 空气动力学学报, 2022, 40(6): 108-116. https://www.cnki.com.cn/Article/CJFDTOTAL-KQDX202206012.htm

    Wang Y X, Xu J K, Zhang Y, et al. Applications of transition model based on amplification factor of stationary crossflow waves in transonic boundary layers[J]. Acta Aerodynamica Sinica, 2022, 40(6): 108-116(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-KQDX202206012.htm
    [52] Reed H L, Haynes T S. Transition correlations in three-dimensional boundary layers[J]. AIAA Journal, 1994, 32(5): 923-929.
    [53] Wang L, Fu S. Modelling flow transition in a hypersonic boundary layer with Reynolds-averaged Navier-Stokes approach[J]. Science in China Series G: Physics, Mechanics and Astronomy, 2009, 52(5): 768-774.
    [54] Wang L, Fu S. Development of an intermittency equation for the modeling of the supersonic/hypersonic boundary layer flow transition[J]. Flow, Turbulence and Combustion, 2011, 87(1): 165-187.
    [55] 王亮. 高超音速边界层转捩的模式研究[D]. 北京: 清华大学, 2008.

    Wang L. Modelling flow transition in hypersonic boundary layer[D]. Beijing: Tsinghua University, 2008(in Chinese).
    [56] Fu S, Wang L. RANS modeling of high-speed aerodynamic flow transition with consideration of stability theory[J]. Progress in Aerospace Sciences, 2013, 58: 36-59.
    [57] Wang L, Fu S, Carnarius A, et al. A modular RANS approach for modelling laminar-turbulent transition in turbomachinery flows[J]. International Journal of Heat and Fluid Flow, 2012, 34: 62-69.
    [58] Zhang Y F, Zhang Y R, Chen J Q, et al. Numerical simulations of hypersonic boundary layer transition based on the flow solver chant 2.0[R]. AIAA 2017-2409, 2017.
    [59] 刘清扬, 雷娟棉, 刘周, 等. 适用于可压缩流动的γ-Reθt-fRe转捩模型[J]. 航空学报, 2022, 43(8): 125794.

    Liu Q Y, Lei J M, Liu Z, et al. γ-Reθt-fRe transition model for compressible flows[J]. Acta Aeronautica et Astronautica Sinica, 2022, 43(8): 125794(in Chinese).
    [60] Xu J K, Wang Y X, Liu N, et al. An improved physics-informed transition-turbulence model for asymmetric transition over supersonic rotating projectiles[J]. Computers & Fluids, 2022, 238: 105366.
    [61] Xu J K, Bai J Q, Qiao L, et al. Fully local formulation of a transition closure model for transitional flow simulations[J]. AIAA Journal, 2016, 54(10): 3015-3023.
    [62] Xu J K, Bai J Q, Qiao L, et al. Development of a computational fluid dynamics compatible mathematical model for boundary layer transitional flows in low-disturbance environment[J]. Aerospace Science and Technology, 2019, 86: 487-496.
    [63] Xu J K, Bai J Q, Fu Z Y, et al. Parallel compatible transition closure model for high-speed transitional flow[J]. AIAA Journal, 2017, 55(9): 3040-3050.
    [64] Zhou L, Li R F, Han Z H, et al. Improved k-ω-γ model for crossflow-induced transition prediction in hypersonic flow[J]. International Journal of Heat and Mass Transfer, 2017, 115: 115-130.
    [65] Zhou L, Zhao R, Li R F. A combined criteria-based method for hypersonic three-dimensional boundary layer transition prediction[J]. Aerospace Science and Technolo-gy, 2018, 73: 105-117.
    [66] Zhou L, Zhao R, Yuan W. Application of improved k-ω-γ transition model to hypersonic complex configurations[J]. AIAA Journal, 2019, 57(5): 2214-2221.
    [67] Qiao L, Xu J K, Bai J Q, et al. Fully local transition closure model for hypersonic boundary layers considering crossflow effects[J]. AIAA Journal, 2021, 59(5): 1692-1706.
    [68] Liu Z J, Lu Y H, Li J P, et al. Local correlation-based transition model for high-speed flows[J]. AIAA Journal, 2022, 60(3): 1365-1381.
    [69] Liu Z J, Lu Y H, Xiao F S, et al. Further developments to a local correlation-based transition model for hypersonic flows[J]. AIAA Journal, 2022, 60(6): 3909-3916.
    [70] Xiang X H, Chen J Q, Yuan X X, et al. Cross-flow transition model predictions of hypersonic transition research vehicle[J]. Aerospace Science and Technology, 2022, 122: 107327.
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