Study on the evolution of non-modal disturbances in hypersonic boundary layer based on HLNS approach
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摘要: 高超声速边界层转捩是航天飞行器设计中的基础难题, 发生在线性失稳区上游的亚临界转捩是常规风洞实验中常见的现象. 亚临界转捩一般是由非模态扰动的演化及二次失稳触发的, 为了揭示局部突变对高超声速边界层亚临界转捩的影响机理, 发展了基于谐波型线性化Navier-Stokes (HLNS) 方程及其伴随系统的描述非模态扰动演化的求解框架. 该框架的优点是不改变原始系统的椭圆型特性, 因而可以处理非模态扰动 (条带) 在局部突变附近的快速畸变. 针对马赫数为5.96、攻角为
$ - 4^\circ $ 的高超声速钝平板边界层, 研究了不同深度凹槽对条带幅值的影响. 数值结果表明凹槽对条带有促进作用, 这与实验中发现的规律定性相符, 且存在使促进作用最大的最优凹槽深度.Abstract: Laminar-turbulent transition in hypersonic boundary layers is of fundamental importance in the design of aerospace vehicles. Subcritical transition, occurring upstream of the linear instability region, appears frequently in conventional wind-tunnel experiments. The subcritical transition is usually triggered by the evolution of non-modal disturbances and their subsequent secondary instability. In order to reveal the inherent mechanisms governing the impact of abrupt changes on hypersonic subcritical transition, a numerical framework describing the evolution of non-modal disturbances based on the harmonic linearized Navier-Stokes (HLNS) equation and its adjoint system is developed. The advantage of this framework is that the elliptic nature of the original system is retained, leading to the ability to deal with the rapid distortion of the non-modal disturbances (streaks) in the vicinity of the local abrupt changes. For a hypersonic blunt-plate boundary layer with an oncoming Mach number 5.96 and an angle of attack$ - 4^\circ $ , the impact of the cavities with different depths on streak amplitude is studied. Numerical solutions indicate that streaks are enhanced by the cavities, which agrees with the experimental observations in quantity. Moreover, the enhancement effect peaks at a particular cavity depth.-
Key words:
- hypersonic boundary layer /
- cavity /
- optimal perturbation /
- subcritical transition
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[1] 董明. 2020. 边界层转捩预测中的局部散射理论. 空气动力学学报, 38: 286-298 (Dong M. 2020. Local scattering theory for transition prediction in boundary-layer flows. Acta Aerodynamica Sinica, 38: 286-298). [2] 李强, 赵磊, 陈苏宇, 江涛, 庄宇, 张扣立. 2020. 展向凹槽及泄流孔对高超声速平板边界层转捩影响的试验研究. 物理学报, 69: 024703 (Li Q, Zhao L, Chen S Y, Jiang T, Zhuang Y, Zhang K L. 2020. Experimental study on effect of transverse groove with/without discharge hole on hypersonic blunt flat-plate boundary layer transition. Acta Phys Sin, 69: 024703). doi: 10.7498/aps.69.20191155 [3] 李斯特, 董明. 2021. 局部散射理论在高超声速边界层转捩预测中应用的检验. 力学进展, 51: 364-375 (Li S T, Dong M. 2021. Verification of local scattering theory as is applied to transition prediction in hypersonic boundary layers. Advances in Mechanics, 51: 364-375). doi: 10.6052/1000-0992-21-016 [4] 赵磊. 2017. 高超声速后掠钝板边界层横流定常涡失稳的研究. [博士论文]. 天津: 天津大学Zhao L. 2017. Study on instability of stationary crossflow vortices in hypersonic swept blunt plate boundary layers. [PhD Thesis]. Tianjin: Tianjin University [5] Dong M, Li C. 2021. Effect of two-dimensional short rectangular indentations on hypersonic boundary-layer transition. AIAA Journal, 59: 7 DOI: 10.2514/1.J059957. [6] Dong M, Liu Y H, Wu X S. 2020. Receptivity of inviscid modes in supersonic boundary layers due to scattering of free-stream sound by localised wall roughness. Journal of Fluid Mechanics, 896: A23. doi: 10.1017/jfm.2020.358 [7] Dong M, Zhao L. 2021. An asymptotic theory of the roughness impact on inviscid Mack modes in supersonic/hypersonic boundary layers. Journal of Fluid Mechanics, 913: A22. doi: 10.1017/jfm.2020.1146 [8] Henningson D. 1995. Bypass transition and linear growth mechanisms. Advances in Turbulence V. Springer, 1: 190-204. [9] Leib S J, Wundrow D W, Goldstein M E. 1999. Effect of free-stream turbulence and other vortical disturbances on a laminar boundary layer. Journal of Fluid Mechanics, 380: 169-203. doi: 10.1017/S0022112098003504 [10] Liu Y H, Dong M, Wu X S. 2020. Generation of first Mack modes in supersonic boundary layers by slow acoustic waves interacting with streamwise isolated wall roughness. Journal of Fluid Mechanics, 888: A10. doi: 10.1017/jfm.2020.38 [11] Luchini P. 2000. Reynolds-number-independent instability of the boundary layer over a flat surface optimal perturbations. Journal of Fluid Mechanics, 404: 289-309. doi: 10.1017/S0022112099007259 [12] Paredes P, Choudhari M M, Li F, et al. 2016. Optimal growth in hypersonic boundary layers. AIAA Journal, 54: 3050-3061. doi: 10.2514/1.J054912 [13] Paredes P, Choudhari M M, Li F. 2017. Blunt-body paradox and transient growth on a hypersonic spherical forebody. Physical Review Fluids, 2: 053903. doi: 10.1103/PhysRevFluids.2.053903 [14] Paredes P, Choudhari M M, Li F, et al. 2018. Nose-tip bluntness effects on transition at hypersonic speeds. Journal of Spacecraft and Rockets, 56: 1-19. doi: 10.2514/1.A34277 [15] Ricco P, Luo J S, Wu X S. 2011. Evolution and instability of unsteady nonlinear streaks generated by free-stream vortical disturbances. Journal of Fluid Mechanics, 677: 1-38. doi: 10.1017/jfm.2011.41 [16] Song R, Zhao L, Huang Z. F. 2020. Improvement of the parabolized stability equation to predict the linear evolution of disturbances in three-dimensional boundary layers based on ray tracing theory. Physical Review Fluids, 5: . doi: 10.1103/PhysRevFluids.5.033901 [17] Tempelmann D, Hanifi A, Henningson D S. 2010. Spatial optimal growth in three-dimensional boundary layers. Journal of Fluid Mechanics, 646: 5-37. doi: 10.1017/S0022112009993260 [18] Tempelmann D, Hanifi A, Henningson D S. 2012. Spatial optimal growth in three-dimensional compressible boundary layers. Journal of Fluid Mechanics, 704: 251-279. doi: 10.1017/jfm.2012.235 [19] Trefethen L N, Trefethen A E, Reddy S C, et al. 1993. Hydrodynamic stability without eigenvalues. Science, 261: 578-584. doi: 10.1126/science.261.5121.578 [20] Tumin A, Reshotko E. 2001. Spatial theory of optimal disturbances in boundary layers. Physics of Fluids, 13: 2097-2104. doi: 10.1063/1.1378070 [21] Wu X S, Dong M. 2016. A local scattering theory for the effects of isolated roughness on boundary-layer instability and transition: transmission coefficient as an eigenvalue. Journal of Fluid Mechanics, 794: 68-108. doi: 10.1017/jfm.2016.125 [22] Zhang A Y, Dong M, Zhang Y M. 2018. Receptivity of secondary instability modes in streaky boundary layers. Physics of Fluids, 30: 114102. doi: 10.1063/1.5046136 [23] Zhao L, Zhang C B, Liu J X, Luo J S. 2016. Improved algorithm for solving nonlinear parabolized stability equations. Chinese Physics B, 25: 084701. doi: 10.1088/1674-1056/25/8/084701 [24] Zhao L, Dong M, Yang Y G. 2019. Harmonic linearized Navier-Stokes equation on describing the effect of surface roughness on hypersonic boundary-layer transition. Physics of Fluids, 31: 034108. doi: 10.1063/1.5086912 [25] Zhao L, Dong M. 2020. Effect of suction on laminar-flow control in subsonic boundary layers with forward-/backward-facing steps. Physics of Fluids, 32: 054108. doi: 10.1063/5.0007624 -
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