Wake transition and aerodynamics of a dragonfly-inspired airfoil

TL;DR

This study explores the flow dynamics and stability of a dragonfly-inspired airfoil across various angles of attack and Reynolds numbers, revealing different bifurcation modes and vortex behaviors affecting aerodynamics.

Contribution

It provides a comprehensive analysis of flow stability and bifurcations for a corrugated dragonfly-inspired airfoil using linear stability and nonlinear simulations, highlighting new flow regimes and instability mechanisms.

Findings

Primary instability is a Hopf bifurcation leading to periodic flow.

Different flow bifurcation modes depend on angle of attack and Reynolds number.

Vortex shedding and secondary instabilities vary with flow parameters.

Abstract

We investigate the dynamics and the stability of the incompressible flow past a corrugated dragonfly-inspired airfoil in the two-dimensional (2D) $\alpha-Re$ parameter space, where $\alpha$ is the angle of attack and $Re$ is the Reynolds number. The angle of attack is varied between $-5^\circ \le \alpha \le 10^\circ$, and $Re$ (based on the free-stream velocity and the airfoil chord) is increased up to $Re=6000$. The study relies on linear stability analyses and three-dimensional (3D) nonlinear direct numerical simulations. For all $\alpha$ the primary instability consists of a Hopf bifurcation towards a periodic regime. The linear stability analysis reveals that two distinct modes drive the flow bifurcation for positive and negative $\alpha$, being characterised by a different frequency and a distinct triggering mechanism. The critical $Re$ decreases as $|\alpha|$ increases, and scales as a power law for large positive/negative $\alpha$. At intermediate $Re$, different limit cycles arise depending on $\alpha$, each one characterised by a distinctive vortex interaction, leading thus to secondary instabilities of different nature. For intermediate positive/negative $\alpha$ vortices are shed from both the top/bottom leading- and trailing-edge shear layers, and the two phenomena are frequency locked. By means of Floquet stability analysis, we show that the secondary instability consists of a 2D subharmonic bifurcation for large negative $\alpha$, of a 2D Neimark--Sacker bifurcation for small negative $\alpha$, of a 3D pitchfork bifurcation for small positive $\alpha$, and of a 3D subharmonic bifurcation for large positive $\alpha$. The aerodynamic performance of the dragonfly-inspired airfoil is discussed in relation to the different flow regimes emerging in the $\alpha-Re$ space of parameters.