Analysis of vortical gust impact on airfoils at low Reynolds number

Abstract

The response of a NACA0012 airfoil impacted by vortical gusts is investigated performing Direct Numerical Simulations of the two-dimensional incompressible flow. Taylor vortices of different diameter and intensity located at different vertical separations with respect to the airfoil are deployed in the free stream. These vortices, which are characterized by its compact distribution of vorticity, are advected downstream to interact with the airfoil, set at a fixed angle of attack. For the low Reynolds number used in these simulations (Re=1000), the effect of the different parameters defining the vortical gust and the impact is characterized. It is found that the change in the time evolution of the variation of the lift coefficient with respect to the steady state, ΔCl(t), is fairly independent on the angle of attack, at least in the range of α considered in this study. Furthermore, it is found that the time at which the peak in ΔCl is produced scales with the diameter of the viscous core of the vortex and the free-stream velocity, D∕U∞. On the other hand, the maximum value of ΔCl is roughly proportional to the non-dimensional vortex circulation, but varies non-linearly with the vertical distance between the vortex and the airfoil. This dependency can be captured by scaling ΔCl with the relative intensity of the vertical velocity induced over the airfoil and the free-stream velocity (wh∕U∞), where the former is defined as an integral of the vortex velocity profile over the chord of the airfoil. Using this scaling, the profiles of ΔCl(tU∞∕D)∕(wh∕U∞) collapse over a single curve for the different vortex intensities, sizes and vertical separations considered in the present study, specially during the initial evolution of the vortical gust impact. The self-similar profile of ΔCl(tU∞∕D)∕(wh∕U∞) is found to depend on the velocity profile of the vortex (i.e., Taylor vortices versus Lamb–Oseen vortices). However, the peak aerodynamic force and the time to peak aerodynamic force seem to scale with D∕U∞ and wh∕U∞ irrespective of the velocity profile of the vortex, suggesting that our definition of wh is sufficiently robust.