Verification of local scattering theory as is applied to transition prediction in hypersonic boundary layers
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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.
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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 
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