[论文解读] Receptivity and instability of the hypersonic flow over moderately blunt cones

N. d'Eprémesnil, C. Caillaud+3 more|arXiv (Cornell University)|Jan 5, 2026

Fluid Dynamics and Turbulent Flows被引用 0

一句话总结

论文使用全局求解分析来识别和表征在马赫数6的中等钝锥体之上流动的线性放大机制，揭示主导的条纹和熵层模态以及壁温对感受性与增长的影响。

ABSTRACT

With a view to identifying and understanding the linear receptivity and amplification mechanisms that underpin laminar-to-turbulent transition over blunt bodies in hypersonic flow, we use resolvent analysis to study the flow over a blunt cone with 7° half-angle at Mach number $M_{\infty} = 6$, zero angle of attack, and nose-radius-based Reynolds number $Re_{R_n} = 90000$. Optimal forcing and responses are obtained for frequencies up to 330 kHz and azimuthal wavenumbers between 0 and 200. Wall-temperature effects are accounted for by considering both isothermal ($T_w =$ 300 K) and adiabatic wall conditions. The resolvent analysis shows that stationary streak modes are the most amplified in the isothermal case, followed by entropy-layer modes between 20 and 140 kHz. In the adiabatic case, the $1^{st}$ Mack mode is the most amplified. The entropy layer, caused by the nose-tip bluntness, has a profound influence on the receptivity structures. For the optimal streak mode, the most intense receptivity structures lie deep in the entropy layer, further away from the boundary-layer edge compared to the equivalent sharp-cone streak mode. This indicates that atmospheric disturbances may excite streak-like instability without fully penetrating the boundary layer. For the entropy-layer modes, the dominant receptivity and fluctuation signatures are located within the entropy layer. An energy-budget analysis reveals that these modes are most susceptible to kinetic disturbances and they sign the most on temperature fluctuations. These modes are found to leverage a temperature mixing mechanism that exploits the baseflow's wall-normal temperature gradient in the entropy layer to grow.

研究动机与目标

• 理解钝端高超音速体上层流-湍流转变的线性感受性与放大机制的动机。
• 在广泛的频率和方位波数范围内计算最优强迫与响应（求解模态）。
• 评估壁温条件（等温与绝热）如何改变主导不稳定性机制。
• 对能量产生及熵层在模态激发中的作用给出物理解释。

提出的方法

• 求解可压缩Navier–Stokes方程，获得马赫数为6、半锥角为7°的钝锥基流的稳态解。
• 围绕基流线性化，并给出求解算子R=(iωI−J)−1以研究输入输出行为。
• 计算加权求解奇异值分解以获得最优强迫与响应模态及其增益μ^2(ω,m)。
• 使用Chu能量范数（动能、密度与温度项）来量化扰动能量。
• 考察等温与绝热壁条件，以研究壁温对感受性的影响。
• 在BROADCAST中实现数值框架，采用高阶空间离散化并使用TAPENADE进行线性化。

实验结果

研究问题

• RQ1 在高超音速流动中，哪些线性放大机制支配着在中等钝锥体上的流动？
• RQ2 最优强迫与响应结构（求解模态）在频率和方位波数上的变化模式是怎样的？
• RQ3 熵层动力学对感受性和模态增长有何影响？
• RQ4 壁温（等温与绝热）如何改变主导机制及其能量产生？

主要发现

• 钝化显著抑制Mack模态，与尖锥相比，最大求解增益降低超过六个数量级。
• 对于等温钝锥，静态条纹（f*=0，m≈57）是最强的放大模式，主导增益 μ^2≈10^7 s^2。
• 与熵层相关的模态（HAWEL）在20–140 kHz之间占主导地位，强烈的强迫与响应局域在熵层内。
• 在壁面为绝热的情况下，第一Mack模态成为最强放大模态，表明壁温显著重塑模态组成。
• 熵层模态表现出动能扰动易感性以及以温度为主导的能量产生，基流温度梯度被用于增长。
• 最优条纹结构位于熵层更深处，表明环境扰动可能激发类似条纹的不稳定性，而不必完全穿透边界层。