Ground effects on the stability of separated flow around a NACA 4415 airfoil at low Reynolds numbers

We perform a linear BiGlobal modal stability analysis on the separated flow around a NACA 4415 airfoil at low Reynolds numbers (Re=300-1000) and a high angle of attack (α=20°), with a focus on the effect of the airfoil's proximity to two different types of ground: a stationary ground and a moving ground. The results show that the most dominant perturbation is a Kelvin-Helmholtz mode, which gives rise to a supercritical Hopf bifurcation to a global mode, leading to large-scale vortex shedding at a periodic limit cycle. As the airfoil approaches the ground, this mode can become more unstable or less unstable, depending on the specific type of ground: introducing a stationary ground to an otherwise groundless system is destabilizing but introducing a moving ground is stabilizing, although both effects weaken with increasing Re. By performing a Floquet analysis, we find that short-wavelength secondary instabilities are damped by a moving ground but are amplified by a stationary ground. By contrast, long-wavelength secondary instabilities are relatively insensitive to ground type. This numerical-theoretical study shows that the ground can have an elaborate influence on the primary and secondary instabilities of the separated flow around an airfoil at low Re. These findings could be useful for the design of micro aerial vehicles and for improving our understanding of natural flyers such as insects and birds.