Three compressible-flow direct numerical simulations (DNS) of aerofoils were conducted at a chord based Reynolds number of $R{e}_c=150,000$: a Controlled-Diffusion (CD) aerofoil at two incidences and an untripped NACA 6512-63 aerofoil at 0${}^{\circ }$ angle of attack (AoA). The aim of the simulations was to help improve the understanding of the generation mechanisms of aerofoil self-noise. To this end, the time-averaged flows around the aerofoils were investigated using a multi-dimensional global stability analysis based on the response to very low-amplitude hydrodynamic initial pulses. For the CD aerofoil at 5${}^{\circ }$ AoA and the untripped NACA 6512-63 aerfoil at 0${}^{\circ }$ AoA, the base flows are found to be globally unstable and an acoustic feedback loop occurs regardless of the perturbation locations. For the CD aerofoil at a slightly higher incidence (8${}^{\circ }$ AoA) where a laminar separation bubble appears at the leading edge and a turbulent attached boundary layer is present at the trailing edge, the initial perturbations decay with time for all initial pulse locations indicating that the base flow is globally stable. The results confirm that for cases where a laminar separation bubble is present on the aerofoil suction side at the trailing edge, independent of whether tones in the DNS exist or not, an unstable feedback loop exists. The laminar separation bubble at the aerofoil trailing edge on the suction side seems to be the only required prerequisite for triggering the acoustic feedback loop.

在基于弦的雷诺数的基础上进行了翼型的三个可压缩流直接数值模拟（DNS）。 $\mathrm{[R}{Ë}_C=150，000$：两种情况下的受控扩散（CD）机翼，零时未脱扣的NACA 6512-63机翼${}^{\circ }$迎角（AoA）。模拟的目的是帮助增进对翼型自噪声产生机理的理解。为此，基于对非常低振幅流体动力初始脉冲的响应，使用多维全局稳定性分析对翼型周围的时间平均流量进行了研究。对于5的CD翼型${}^{\circ }$ AoA和0时未绊倒的NACA 6512-63机翼${}^{\circ }$AoA，发现基本流量整体不稳定，并且无论扰动位置如何，都会发生声反馈回路。对于CD机翼，发病率略高（8${}^{\circ }$AoA），其中层流分离气泡出现在前缘，而湍流附着的边界层出现在后缘，所有初始脉冲位置的初始扰动随时间衰减，表明基本流量是全局稳定的。结果证实，对于在后缘的翼型吸入侧存在层状分离气泡的情况，与DNS中是否存在音调无关，存在不稳定的反馈回路。进气侧翼型后缘处的层流分离气泡似乎是触发声反馈回路的唯一必要先决条件。