With the wide application of curved compression configurations in internal/external flows, it presents a formidable challenge on perceiving shock wave/boundary layer interactions characterized by curvatures. Thus, to create new theories of Curved Shock Wave/turbulent Boundary Layer Interactions (CSWBLI) is of great importance. In this paper, an inviscid model of 2D incident curved shock wave/turbulent boundary layer interaction on a flat plate is built based on the curved shock theory and the free interaction theory. The flowfield is divided into three regions: the curved shock wave/expansion wave interaction region, the curved shock wave/separation shock interaction region and the boundary layer region, where the second order parameters behind the curved shock wave are used to describe the characteristics of the 2D CSWBLI flowfield. Thereafter, the accuracy of the model is verified by numerical simulations in five models with different Mach numbers and incident shocks, and the maximum error of the key point such as the separation point and the intersection point is less than 4.5%. Finally, the influences of incident shock, local boundary layer and downstream disturbance on the interaction are analyzed, and the rules of upstream influence length of the separation bubble in the 2D CSWBLI are summarized. The developed model is the fundamental of the flowfield structure of 3D CSWBLI, and also provides a new method for the research on CSWBLI in the future.
[1] FERRI A. Experimental results with airfoils tested in the high-speed tunnel at Guidonia: NACA-TM-946[R]. Washington, D.C. : NACA, 1940.
[2] 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). 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.
[3] SUN D, LIU P X, TONG F L. Effect of spanwise oscillation on interaction of shock wave and turbulent boundary layer[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(12): 124054 (in Chinese). 孙东, 刘朋欣, 童福林. 展向振荡对激波/湍流边界层干扰的影响[J]. 航空学报, 2020, 41(12): 124054.
[4] MATHEIS J, HICKEL S. On the transition between regular and irregular shock patterns of shock-wave/boundary-layer interactions[J]. Journal of Fluid Mechanics, 2015, 776: 200-234.
[5] WU H, WANG J H, HUANG W, et al. Research progress on shock wave/boundary layer interactions and flow controls induced by micro vortex generators[J]. Acta Aeronautica et Astronautica Sinica, 2021, 42(6): 025371 (in Chinese). 吴瀚, 王建宏, 黄伟, 等. 激波/边界层干扰及微型涡流发生器控制研究进展[J]. 航空学报, 2021, 42(6): 025371.
[6] DELERY J, MARVIN J G, RESHOTKO E. Shock-wave boundary layer interactions: AGARD-AG-280[R]. Washington, D.C. : NASA, 1986.
[7] YAO Y, GAO B. Flow structure of incident shock wave boundary layer interaction with separation[J]. ActaAerodynamica Sinica, 2019, 37(5): 740-747, 769 (in Chinese). 姚瑶, 高波. 入射激波边界层干扰分离流场结构研究[J]. 空气动力学学报, 2019, 37(5): 740-747, 769.
[8] TONG F L, SUN D, YUAN X X, et al. Direct numerical simulation of impinging shock wave/turbulent boundary layer interactions in a supersonic expansion corner[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(3): 123328 (in Chinese). 童福林, 孙东, 袁先旭, 等. 超声速膨胀角入射激波/湍流边界层干扰直接数值模拟[J]. 航空学报, 2020, 41(3): 123328.
[9] ZUO F Y, MEMMOLO A, HUANG G P, et al. Direct numerical simulation of conical shock wave-turbulent boundary layer interaction[J]. Journal of Fluid Mechanics, 2019, 877: 167-195.
[10] ZHANG K Y. Hypersonic curved compression inlet and its inverse design[M]. Beijing: National Defense Industry Press, 2019: 97-116 (in Chinese). 张堃元. 高超声速曲面压缩进气道及其反设计[M]. 北京: 国防工业出版社, 2019: 97-116.
[11] NEUMANN R, HAYES J. Prediction techniques for the characteristics of the three dimensional shock wave/turbulent boundary layer interaction[C]//15th Aerospace Sciences Meeting. Reston: AIAA, 1977.
[12] CAMBIER L, ESCANDE B. Calculation of a three-dimensional shock wave-turbulent boundary-layer interaction[J]. AIAA Journal, 1990, 28(11): 1901-1908.
[13] XUE L S, SCHRIJER FF J, VAN OUDHEUSDEN B W, et al. Theoretical study on regular reflection of shock wave-boundary layer interactions[J]. Journal of Fluid Mechanics, 2020, 899: A30.
[14] CHAPMAN D R, KUEHN D M, LARSON H K. Investigation of separated flows in supersonic and subsonic streams with emphasis on the effect of transition: NACA-TN-3869[R]. Washington, D.C. : NACA, 1957.
[15] GIEPMAN R H M, SCHRIJER F F J, VAN OUDHEUSDEN B W. A parametric study of laminar and transitional oblique shock wave reflections[J]. Journal of Fluid Mechanics, 2018, 844: 187-215.
[16] GROSSMAN I J, BRUCE P J K. Confinement effects on regular-irregular transition in shock-wave-boundary-layer interactions[J]. Journal of Fluid Mechanics, 2018, 853: 171-204.
[17] MÖLDER S. Curved shock theory[J]. Shock Waves, 2016, 26(4): 337-353.
[18] MÖLDER S. Flow behind concave shock waves[J]. Shock Waves, 2017, 27(5): 721-730.
[19] MÖLDER S. Reflection of curved shock waves[J]. Shock Waves, 2017, 27(5): 699-720.
[20] SHI C G, HAN W Q, DEITERDING R, et al. Second-order curved shock theory[J]. Journal of Fluid Mechanics, 2020, 891: A21.
[21] BABINSKY H, HARVEY J K. Shock wave-boundary-layer interactions[M]. Cambridge: Cambridge University Press, 2011: 60-61.
[22] ERDOS J, PALLONE A. Shock-boundary layer interaction and flow separation[C]//Proceedings of the 1962 Heat Transfer and Fluid Mechanics Institute. Stanford: Stanford University Press, 1962: 239-254.
[23] CHEN M Z. Fundamentals ofviscous fluid dynamics[M]. Beijing: Higher Education Press, 2002: 237-372 (in Chinese). 陈懋章. 粘性流体动力学基础[M]. 北京: 高等教育出版社, 2002: 237-372.
[24] EDNEY B. Anomalous heat transfer and pressure distributions on blunt bodies at hypersonic speeds in the presence of an impinging shock: NSA-22-049015[R]. Washington, D.C. : Office of Scientific and Technical Information, 1968.
[25] YANG J M, LI Z F, ZHU Y J. Shock waves and shock interactions in hypersonic flow[M]. Beijing: National Defense Industry Press, 2019: 51-79 (in Chinese). 杨基明, 李祝飞, 朱雨建. 高超声速流动中的激波及相互作用[M]. 北京: 国防工业出版社, 2019: 51-79.
[26] COLES D. The law of the wake in the turbulent boundary layer[J]. Journal of Fluid Mechanics, 1956, 1(2): 191-226.
[27] NEILAND V Y. Flow behind the boundary layer separation point in a supersonic stream[J]. Fluid Dynamics, 1971, 6(3): 378-384.
[28] RAMESH M D, TANNEHILL J C. Correlations to predict the streamwise influence regions in supersonic turbulent flows[J]. Journal of Aircraft, 2004, 41(2): 274-283.
[29] MILLER J, TANNEHILL J, LAWRENCE S. PNS algorithm for solving supersonic flows with upstream influences[J]. AIAA Journal, 2000, 38(10): 1837-1845.
[30] LU X G, YI S H, NIU H B, et al. Experimental study on shock and turbulent boundary layer interactions under different incident shock waves[J]. Scientia Sinica (Physica, Mechanica & Astronomica), 2020, 50(10): 61-72 (in Chinese). 陆小革, 易仕和, 牛海波, 等. 不同入射激波条件下激波与湍流边界层干扰的实验研究[J]. 中国科学: 物理学力学天文学, 2020, 50(10): 61-72.
[31] SPALART P, ALLMARAS S. A one-equation turbulence model for aerodynamic flows: AIAA-1992-0439[R]. Reston: AIAA, 1992.
[32] TAO Y, FAN X Q, ZHAO Y L. Viscous effects of shock reflection hysteresis in steady supersonic flows[J]. Journal of Fluid Mechanics, 2014, 759: 134-148.
[33] HE G. Investigation on the three-dimensional swept impinging oblique shock/turbulent boundary layer interactions[D]. Changsha: National University of Defense Technology, 2018 (in Chinese). 何刚. 三维后掠激波/湍流边界层干扰研究[D]. 长沙: 国防科技大学, 2018.
[34] WANG C P, XUE L S, CHENG K M. Application of the minimum entropy production principle to shock reflection induced by separation[J]. Journal of Fluid Mechanics, 2018, 857: 784-805.
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