标题： 涡流脉动与机翼相互作用的最优时间依赖模式 显示英文标题

标题： Optimally time-dependent modes of vortex gust-airfoil interactions

摘要： 我们找到了关于由强阵风涡旋影响NACA 0012机翼产生的时变流场的最优时间依赖（OTD）正交模态。 这种OTD分析揭示了扰动在非定常基流中的放大特性及其随时间演化的放大时空结构。 我们考虑了四种时变层流基流，在这些流场中，一个强度对应于阵风比$G$的涡旋以攻角$12^\circ$的角度撞击机翼前缘，其强度为$\{-1,-0.5,0.5,1\}$。 在这些情况下，强阵风涡旋的撞击导致机翼周围在两个对流时间单位内出现大规模分离和大尺度涡旋的生成。 这些涡旋-机翼相互作用的高度非定常性需要一种能够捕捉瞬态扰动动力学的先进分析技术。 对于每个考虑的阵风比，OTD分析确定了对扰动最放大的区域，该区域的位置随着尾流的不同演化而变化。 对于中等正涡旋阵风（$G=0.5$）与机翼的相互作用，扰动被放大的区域从机翼前缘涡旋片转移到正在形成的前缘涡旋。 之后，这个最放大的结构直接位于机翼尾缘后方的尾流中。 相比之下，机翼遇到的强涡旋阵风（$G=\pm 1$）显示最放大的OTD模态出现在脱落涡旋的核心附近。 本研究提供了一种分析技术和对更广泛的非定常空气动力学问题的基本见解。 显示英文摘要

摘要： We find the optimally time-dependent (OTD) orthogonal modes about a time-varying flow generated by a strong gust vortex impacting a NACA 0012 airfoil. This OTD analysis reveals the amplification characteristics of perturbations about the unsteady base flow and their amplified spatiotemporal structures that evolve over time. We consider four time-varying laminar base flows in which a vortex with a strength corresponding to the gust ratio $G$ of $\{-1,-0.5,0.5,1\}$ impinges on the leading edge of the airfoil at an angle of attack of $12^\circ$. In these cases, the impingement of the strong gust vortex causes massive separation and the generation of large-scale vortices around the airfoil within two convective time units. The highly unsteady nature of these vortex-airfoil interactions necessitates an advanced analytical technique capable of capturing the transient perturbation dynamics. For each of the considered gust ratios, the OTD analysis identifies the most amplified region to perturbations, the location of which changes as the wake evolves differently. For interactions between a moderate positive vortex gust ($G=0.5$) and the airfoil, the area where perturbations are amplified transitions from the leading-edge vortex sheet to the forming leading-edge vortex. Later, this most amplified structure becomes supported in the airfoil wake directly behind the trailing edge. In contrast, a strong vortex gust ($G=\pm 1$) encountered by the airfoil shows the most amplified OTD mode to appear around the core of the shed vortices. This study provides an analysis technique and fundamental insights into the broader family of unsteady aerodynamic problems.