Verification of local scattering theory as is applied to transition prediction in hypersonic boundary layers
-
摘要: eN方法是物理意义明确的转捩预测方法之一, 但它无法考虑边界层中的局部突变(如粗糙元、缝隙、台阶等)对转捩的影响. 而后者在飞行器表面经常出现. 近期发展的局部散射理论框架提供了该问题的有效解决途径. 该理论框架从转捩的物理机理出发, 定量刻画局部感受性和线性模态的局部散射两个机制, 并用参数化的感受性系数和透射系数修正转捩判据. 为了验证该理论框架的有效性, 设计了一套高超声速边界层的直接数值模拟方案: 分别在光滑壁与粗糙壁两种工况下引入相同的初始失稳模态, 计算它们触发转捩的过程, 并定量考察粗糙元对转捩的影响. 数值模拟结果与描述线性模态局部散射机制的理论预测吻合很好.Abstract: The eN method is one of the most widely used transition-prediction approaches with clear physical meaning, which however fails to take into account the effects of surface abrupt changes, such as roughness elements, gaps, steps, etc., in boundary-layer flows. However, the latter appears frequently on the surface of flying vehicles. A recently developed local scattering framework provides an effective means to address this issue. Based on the physical mechanisms of transition, the theoretical framework quantitatively describes two regimes, the local receptivity and the linear-mode scattering, leading to a modification of the transition criterion by the parameterized receptivity and transmission coefficients. In order to confirm the effectiveness of the theoretical framework, a set of direct numerical simulations of hypersonic boundary-layer flows are designed, namely, introducing the same inflow modal perturbations for two cases with a smooth surface and a rough surface, respectively. The transition processes are simulated, and the roughness effect on transition is quantified. The numerical results are found to agree well with the theoretical predictions of the linear-mode scattering regime.
-
A-2 扰动温度流向演化与Zhao 等 (2019)对比
表 1 模态扰动参数
$ i $ $\omega_i$ $\beta_i$ $A_0$ 1 0.6 0.7972 0.001 2 1 0 0.001 3 1.6 0 0.0005 4 1.8 0 0.0005 5 2.2 0 0.0005 
下载: 导出CSV
-
[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 in boundary layer transition prediction. Acta Aerodynamica Sinica, 38: 286-298). [2] 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 [3] 周恒, 张涵信. 2017. 有关近空间高超声速飞行器边界层转捩和湍流的两个问题. 空气动力学学报, 35: 151-155 (Zhou H, Zhang H X. 2017. Two problems in the transition and turbulence for near space hypersonic flying vehicles. Acta Aerodynamica Sinica, 35: 151-155). doi: 10.7638/kqdlxxb-2017.0016 [4] Cebeci T, Stewartson K. 1980. On stability and transition in three-dimensional flows. AIAA Journal, 18: 398-405. doi: 10.2514/3.50772 [5] Dong M. 2020. Scattering of Tollmien-Schlichting waves by localized roughness in transonic boundary layers. Applied Mathematics and Mechanics (English Edition) , 41: 1105-1124. doi: 10.1007/s10483-020-2622-6 [6] Dong M, Li C. 2021. Effect of two-dimensional short rectangular indentations on hypersonic boundary-layer transition. AIAA Journal, DOI: 10.2514/1.J059957 [7] 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 [8] Dong M, Luo J S. 2007. Mechanism of transition in a hypersonic sharp cone boundary layer with zero angle of attack. Applied Mathematics and Mechanics (English Edition) , 28: 1019-1028. doi: 10.1007/s10483-007-0804-2 [9] 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 [10] Duan L, Wang X W, Zhong X L. 2013. Stabilization of a Mach 5.92 boundary layer by two-dimensional finite-height roughness. AIAA Journal, 51: 266-270. doi: 10.2514/1.J051643 [11] Fong K D, Wang X W, Zhong X L. 2014. Numerical simulation of roughness effect on the stability of a hypersonic boundary layer. Computers and Fluids, 96: 350-367. doi: 10.1016/j.compfluid.2014.01.009 [12] Fong K D, Wang X W, Zhong X L. 2015. Parametric study on stabilization of hypersonic boundary layer waves using 2-D surface roughness//53rd AIAA Aerospace Sciences Meeting, 2015, Kissimmee, Florida. [13] Fujii K. 2006. Experiment of the two-dimensional roughness effect on hypersonic boundary-layer transition. Journal of Spacecraft and Rockets, 43: 731-738. doi: 10.2514/1.17860 [14] Kachanov Y S. 1994. Physical mechanisms of laminar-boundary-layer transition. Annual Review of Fluid Mechanics, 26: 411-482. doi: 10.1146/annurev.fl.26.010194.002211 [15] 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 [16] Schneider S P. 2008a. Effects of roughness on hypersonic boundary-layer transition. Journal of Spacecraft and Rockets, 45: 193-209. doi: 10.2514/1.29713 [17] Schneider S P. 2008b. Summary of hypersonic boundary-layer transition experiments on blunt bodies with roughness. Journal of Spacecraft and Rockets, 45: 1090-1105. doi: 10.2514/1.37431 [18] Smith A M O. 1956. Transition, pressure gradient, and stability theory//IX International Congress for Applied Mechanics, 1956, Brussels, Belgium. [19] Su C H, Zhou H. 2009. Transition prediction of a hypersonic boundary layer over a cone at small angle of attack with the improvement of e-N method. Science in China Series G: Physics, Mechanics and Astronomy, 52: 115-123. doi: 10.1007/s11433-009-0006-4 [20] Tang Q, Zhu Y D, Chen X, Lee C. 2015. Development of second-mode instability in a Mach 6 flat plate boundary layer with two-dimensional roughness. Physics of Fluids, 27: 064105. doi: 10.1063/1.4922389 [21] Wheaton B M, Schneider S P. 2010. Roughness-induced instability in a laminar boundary layer at Mach 6//48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, 2010, Orlando, Florida. [22] 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 [23] 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 -
下载:
点击查看大图
图(11) / 表(1)
计量
- 文章访问数: 719
- HTML全文浏览量: 221
- PDF下载量: 92
- 被引次数: 0
