Fully Passive Energy Harvesting from Heaving and Pitching Airfoils: Oscillation Response Patterns and Vortex Dynamics in Fluid Flow

Abstract

This study employs the Direct-Forcing Immersed Boundary (DFIB) method to model the flow-induced vibration (FIV) behavior of three types of airfoils—NACA0009, NACA0012, and NACA0015—within a flow field. The analysis investigates the vibration characteristics of these airfoils in a fully passive mode under specific conditions, including a fixed airfoil pitching center at $\frac{1}{2}c$, a mass ratio of 2.0, a Reynolds number of Re$=400$, and undamped conditions with both aerodynamic damping coefficients set to zero ($b_a^{\ast }=b_{a\theta }^{\ast }=0$). The stiffness of the linear spring ($k_a^{\ast }$) and the torsional spring ($k_{a\theta }^{\ast }$) are both defined as ${(2\pi /U_a^{\ast })}^2$. The study examines the oscillatory responses, vortex patterns, and energy conversion efficiencies of the three types of airfoils across 12 reduced velocities ($U_a^{\ast }$). Oscillation response patterns are categorized into three distinct regions: S-I, T-II, and S-III, while vortex patterns are classified into four types: ‘2P’, ‘2P + 2S’, ‘mP,’ and ‘P + S.’ Notably, all three airfoils achieve their peak energy conversion efficiency at $U_a^{\ast }=1.63$, with NACA0009 reaching 43.9%, NACA0012 achieving 44.2%, and NACA0015 reaching 36.3%.