Analysis of vortical gust impact on airfoils at low Reynolds number

The response of a NACA0012 airfoil impacted by vortical gusts is investigated perform-ing Direct Numerical Simulations of the two-dimensional incompressible flow. Taylorvortices of different diameter and intensity located at different vertical separationswith respect to the airfoil are deployed in the free stream. These vortices, which arecharacterized by its compact distribution of vorticity, are advected downstream tointeract with the airfoil, set at a fixed angle of attack. For the low Reynolds numberused in these simulations (Re=1000), the effect of the different parameters definingthe vortical gust and the impact is characterized. It is found that the change in thetime evolution of the variation of the lift coefficient with respect to the steady state,∆Cl(t), is fairly independent on the angle of attack, at least in the range ofαconsideredin this study. Furthermore, it is found that the time at which the peak in∆Clisproduced scales with the diameter of the viscous core of the vortex and the free-streamvelocity,D/U∞. On the other hand, the maximum value of∆Clis roughly proportionalto the non-dimensional vortex circulation, but varies non-linearly with the verticaldistance between the vortex and the airfoil. This dependency can be captured by scaling∆Clwith the relative intensity of the vertical velocity induced over the airfoil andthe free-stream velocity (wh/U∞), where the former is defined as an integral of thevortex velocity profile over the chord of the airfoil. Using this scaling, the profiles of∆Cl(tU∞/D)/(wh/U∞) collapse over a single curve for the different vortex intensities,sizesandverticalseparationsconsideredinthepresentstudy,speciallyduringtheinitialevolution of the vortical gust impact. The self-similar profile of∆Cl(tU∞/D)/(wh/U∞) isfound to depend on the velocity profile of the vortex (i.e., Taylor vortices versus Lamb–Oseenvortices).However,thepeakaerodynamicforceandthetimetopeakaerodynamicforce seem to scale withD/U∞andwh/U∞irrespective of the velocity profile of thevortex, suggesting that our definition ofwhis sufficiently robust