Abstract The present paper investigates the fluid–structure interaction (FSI) of a wing with two degrees of freedom (DOF), i.e., pitch and heave, in the transitional Reynolds number regime. This 2-DOF setup marks a classic configuration in aeroelasticity to demonstrate flutter stability of wings. In the past, mainly analytic approaches have been developed to investigate this challenging problem under simplifying assumptions such as potential flow. Although the classical theory offers satisfying results for certain cases, modern numerical simulations based on fully coupled approaches, which are more generally applicable and powerful, are still rarely found. Thus, the aim of this paper is to provide appropriate experimental reference data for well-defined configurations under clear operating conditions. In a follow-up contribution these will be used to demonstrate the capability of modern simulation techniques to capture instantaneous physical phenomena such as flutter. The measurements in a wind tunnel are carried out based on digital-image correlation (DIC). The investigated setup consists of a straight wing using a symmetric NACA 0012 airfoil. For the experiments the model is mounted into a frame by means of bending and torsional springs imitating the elastic behavior of the wing. Three different configurations of the wing possessing a fixed elastic axis are considered. For this purpose, the center of gravity is shifted along the chord line of the airfoil influencing the flutter stability of the setup. Still air free-oscillation tests are used to determine characteristic properties of the unloaded system (e.g. mass moment of inertia and damping ratios) for one (pitch or heave) and two degrees (pitch and heave) of freedom. The investigations on the coupled 2-DOF system in the wind tunnel are performed in an overall chord Reynolds number range of 9 . 66 × 1 0 3 ≤ Re ≤ 8 . 77 × 1 0 4 . The effect of the fluid-load induced damping is studied for the three configurations. Furthermore, the cases of limit-cycle oscillation (LCO) as well as diverging flutter motion of the wing are characterized in detail. In addition to the DIC measurements, hot-film measurements of the wake flow for the rigid and the oscillating airfoil are presented in order to distinguish effects originating from the flow and the structure.

中文翻译：

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基于数字图像相关测量的 2-DOF 翼型在过渡 Re 数状态下的动态行为的实验研究

摘要 本文研究了具有两个自由度 (DOF) 的机翼在过渡雷诺数状态下的流固耦合 (FSI)，即俯仰和升沉。这种 2-DOF 设置标志着气动弹性的经典配置，以证明机翼的颤振稳定性。过去，主要是开发分析方法来在简化假设（例如潜在流量）下研究这一具有挑战性的问题。尽管经典理论在某些情况下提供了令人满意的结果，但仍然很少发现基于全耦合方法的现代数值模拟更普遍适用和强大。因此，本文的目的是在明确的操作条件下为明确定义的配置提供适当的实验参考数据。在后续的贡献中，这些将用于展示现代模拟技术捕捉瞬时物理现象（如颤动）的能力。风洞中的测量是基于数字图像相关 (DIC) 进行的。研究的设置包括使用对称 NACA 0012 翼型的直机翼。在实验中，模型通过模拟机翼弹性行为的弯曲和扭转弹簧安装到框架中。考虑了具有固定弹性轴的机翼的三种不同配置。为此，重心沿翼型的弦线移动，影响装置的颤振稳定性。静止空气自由振荡测试用于确定卸载系统的特性（例如 一（俯仰或升沉）和两个（俯仰和升沉）自由度的惯性质量矩和阻尼比）。风洞中耦合 2-DOF 系统的研究是在 9 的总弦雷诺数范围内进行的。66 × 1 0 3 ≤ Re ≤ 8 。77 × 1 0 4 。研究了三种配置的流体载荷诱导阻尼的影响。此外，详细描述了极限循环振荡（LCO）以及机翼发散颤振的情况。除了 DIC 测量之外，还提供了刚性和振荡翼型尾流的热膜测量，以区分源自流动和结构的影响。风洞中耦合 2-DOF 系统的研究是在 9 的总弦雷诺数范围内进行的。66 × 1 0 3 ≤ Re ≤ 8 。77 × 1 0 4 。研究了三种配置的流体载荷诱导阻尼的影响。此外，详细描述了极限循环振荡（LCO）以及机翼发散颤振的情况。除了 DIC 测量之外，还提供了刚性和振荡翼型尾流的热膜测量，以区分源自流动和结构的影响。风洞中耦合 2-DOF 系统的研究是在 9 的总弦雷诺数范围内进行的。66 × 1 0 3 ≤ Re ≤ 8 。77 × 1 0 4 。研究了三种配置的流体载荷诱导阻尼的影响。此外，详细描述了极限循环振荡（LCO）以及机翼发散颤振的情况。除了 DIC 测量之外，还提供了刚性和振荡翼型尾流的热膜测量，以区分源自流动和结构的影响。详细描述了极限循环振荡 (LCO) 以及机翼发散颤振的情况。除了 DIC 测量之外，还提供了刚性和振荡翼型尾流的热膜测量，以区分源自流动和结构的影响。详细描述了极限循环振荡 (LCO) 以及机翼发散颤振的情况。除了 DIC 测量外，还提供了刚性和振荡翼型尾流的热膜测量，以区分源自流动和结构的影响。