Scaling unsteady load alleviation in airfoils with flexible trailing-edges

Unsteady load alleviation is crucial for engineering applications such as tidal turbines. Herein, we present an experimental study into the load alleviation capacities of constant-section airfoils with flexible trailing-edges. The trailing-edge studied here consists of two independent flexible skins, enabling large skin deformations and enhanced load alleviation compared to conventional flexible trailing-edge designs. We test high-amplitude plunging kinematics (up to peak-to-peak amplitude of one chord length) at reduced frequency <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>k</a:mi> <a:mo>=</a:mo> <a:mn>0.2</a:mn> </a:mrow> </a:math> and Reynolds numbers <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>Re</b:mi> <b:mo>=</b:mo> <b:mi mathvariant="script">O</b:mi> <b:mo>(</b:mo> <b:msup> <b:mn>10</b:mn> <b:mn>4</b:mn> </b:msup> <b:mo>)</b:mo> </b:mrow> </b:math> . To quantify the role of airfoil flexibility, we introduce two Cauchy numbers ( <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:msub> <d:mi>Ca</d:mi> <d:mi>u</d:mi> </d:msub> </d:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:msub> <e:mi>Ca</e:mi> <e:mi>v</e:mi> </e:msub> </e:math> ), which normalize the freestream and plunging velocities, respectively. We demonstrate that both the trailing-edge deflection and the resulting lift alleviation scale with these Cauchy numbers provide a fundamental framework for understanding flexible airfoil dynamics. Furthermore, we propose semi-empirical models for unsteady lift alleviation, which agree with our measurements. These findings lay the groundwork for fully predictive low-order models, advancing the design of passively morphing airfoils for efficient load control in unsteady flow environments.