In the hypersonic boundary layer, the streamwise instability modes are mainly the Mack first mode and the Mack second mode. After the Mach number exceeds 4.0, the Mack second mode becomes the dominant instability mode for boundary layer transition. Currently, there is no complete analytical method to establish an amplification factor transport equation for the second mode. In order to improve the application of the amplification factor transport (AFT) model in hypersonic boundary layer transition prediction, this paper employs boundary layer similarity solutions to conduct stability analysis on the second mode and introduces a function to calculate the growth rate of disturbances. Additionally, a transport equation for the amplification factor of the second mode is formulated. For the non-local variables appearing in the equation, a local calculation method is provided. Combined with the intermittency factor transport equation, a transition prediction model for the second mode is formed. Hypersonic flat plate, wedge, and flared wedge are selected for model validation. The computed results show good agreement with standard stability analysis or experimental results, demonstrating the rationality of the transition model and its high prediction accuracy and reliability.

中文翻译：

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高超声速边界层麦克模态扰动的放大因子输运方程建模


在高超声速边界层，流向不稳定模态主要为麦克第一模态和麦克第二模态。马赫数超过4.0后，麦克第二模态成为边界层转变的主要不稳定模态。目前，还没有完整的分析方法来建立第二模态的放大因子输运方程。为了提高放大因子输运（AFT）模型在高超声速边界层转捩预测中的应用，本文采用边界层相似解对第二模态进行稳定性分析，并引入计算扰动增长率的函数。此外，还制定了第二模式的放大系数的传输方程。对于方程中出现的非局部变量，提供了局部计算方法。结合间歇因子输运方程，形成了第二模式的转变预测模型。选择高超声速平板、楔块和扩口楔块进行模型验证。计算结果与标准稳定性分析或实验结果吻合良好，证明了转变模型的合理性及其较高的预测精度和可靠性。