Non-modal stability analysis of low-Re separated flow around a NACA 4415 airfoil in ground effect

Abstract

In this numerical–theoretical study, we perform a linear non-modal stability analysis of the separated flow around a NACA 4415 airfoil over a no-slip ground at low Reynolds numbers (300⩽Re⩽500) and high angles of attack (12∘⩽α⩽20∘). We find that: (i) the strength of the recirculation zone behind the airfoil is a key parameter controlling the absolute/convective nature of the instability in the boundary layer downstream; (ii) when Re, α or the ground clearance increases, the energy gain also increases, with the optimal perturbations switching from being three dimensional to two dimensional; and (iii) classical hairpin vortices, or Klebanoff modes, can be produced by three-dimensional optimal perturbations on a two-dimensional steady base flow containing a laminar separation bubble. Knowledge of the spatiotemporal features of the optimal mode could aid the design of advanced strategies for flow control. This study offers new insight into the transient growth behavior of airfoil–ground flow systems at low Re and high α, contributing to a better understanding of the ground-effect aerodynamics of small insects and micro aerial vehicles.