Abstract

The ability to accurately predict the forces on an aerofoil in real-time when large flow variations occur is important for a wide range of applications such as, for example, for improving the manoeuvrability and control of small aerial and underwater vehicles. Closed-form analytical formulations are only available for small flow fluctuations, which limits their applicability to gentle manoeuvres. Here we investigate large-amplitude, asymmetric pitching motions of a NACA 0018 aerofoil at a Reynolds number of \(3.2 \times 10^4\) using time-resolved force and velocity field measurements. We adapt the linear theory of Theodorsen and unsteady thin-aerofoil theory to accurately predict the lift on the aerofoil even when the flow is massively separated and the kinematics is non-sinusoidal. The accuracy of the models is remarkably good, including when large leading-edge vortices are present, but decreases when the leading and trailing edge vortices have a strong interaction. In such scenarios, however, discrepancies between the theoretically predicted and the measured lift are shown to be due to vortex lift that is calculated using the impulse theory. Based on these results, we propose a new limiting criterion for Theodorsen’s theory for a pitching aerofoil: when a coherent trailing-edge vortex is formed and it advects at a significantly slower streamwise velocity than the freestream velocity. This result is important because it extends significantly the conditions where the forces can be confidently predicted with Theodorsen’s formulation, and paves the way to the development of low-order models for high-amplitude manoeuvres characterised by massive separation.

Graphic abstract

中文翻译：

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高振幅俯仰翼型上的不稳定升力

摘要

当发生大的流量变化时，实时准确地预测翼型上的力的能力对于广泛的应用非常重要，例如，对于提高小型空中和水下飞行器的机动性和控制能力。封闭形式的分析配方仅适用于流量波动较小的情况，这限制了它们在轻柔操作中的适用性。在这里，我们研究了雷诺数为\（3.2 \乘以10 ^ 4 \）的NACA 0018机翼的大振幅，不对称俯仰运动。使用时间分辨力和速度场测量。我们采用Theodorsen的线性理论和非稳态薄翼型理论来精确预测翼型上的升力，即使在流动被大量分离且运动学不是正弦的情况下也是如此。该模型的准确性非常好，包括存在较大的前缘涡旋时，但在前缘和后缘旋涡具有强相互作用时会降低。但是，在这种情况下，理论上预测的升程和测得的升程之间的差异显示为使用脉冲理论计算出的涡旋升程。基于这些结果，我们为狄奥多尔森理论的翼型桨叶提出了一个新的极限准则：当形成一个连贯的后缘涡流时，它以比自由流速度慢得多的流向速度平流。这个结果很重要，因为它大大扩展了可以用Theodorsen公式可靠地预测力的条件，并为开发以大规模分离为特征的高振幅机动的低阶模型铺平了道路。

图形摘要