Extreme vortex gust encounters by a square wing

TL;DR

This study investigates extreme vortex gust encounters with a finite square wing at $Re=600$ using direct numerical simulation, modeling a Taylor-vortex gust of radius $R/c=0.25$ and gust ratios $G=\{-1.2,-3,1.2,3\}$. It reveals that TiVs and LEV interactions generate large lift fluctuations, but three-dimensional effects—arch vortices and gust-vortex distortion near the tips—attenuate these fluctuations relative to a 2D wing. Positive and negative gusts produce distinct vortex dynamics, with TiVs providing both lift-enhancing and lift-mitigating roles; the latter dominates, leading to smaller finite-wing lift changes. The study also shows that flying the wing above a positive gust or below a negative gust can reduce lift fluctuations, offering practical guidance for mitigating transient loads in severe gusts. These laminar-flow insights establish a foundation for higher-Re investigations and design strategies that leverage TiV dynamics to reduce gust-induced loads in small-scale aircraft.

Abstract

Extreme gust encounters by finite wings with disturbance velocity exceeding their cruise speed remain largely unexplored, while particularly relevant to miniature-scale aircraft. This study considers extreme aerodynamic flows around a square wing and the large, unsteady forces that result from gust encounters. We analyse the evolution of three-dimensional, large-scale vortical structures and their complex interactions with the wing by performing direct numerical simulations at a chord-based Reynolds number of 600. We find that a strong incoming positive gust vortex induces a prominent leading-edge vortex (LEV) on the upper surface of the wing, accompanied by tip vortices (TiVs) strengthened through the interaction. Conversely, a strong negative gust vortex induces an LEV on the lower surface of the wing and causes a reversal in TiV orientation. In both extreme vortex gust encounters, the wing experiences significant lift fluctuations. Furthermore, we identify two opposing effects of the TiVs on the large lift fluctuations. First, the enhanced or reversed TiVs contribute to significant lift surges or drops by generating large low-pressure cores near the wing. Second, the TiVs play a part in attenuating lift fluctuations through enhanced downwash or upwash, formation of an arch vortex, and distortion of vortical structure around the wing corners. The second effect outweighs the first, resulting in smaller transient lift changes on the finite wing compared to the 2D wing. We also show that flying above a positive gust vortex or flying below a negative one can mitigate lift fluctuations during encounters. The current findings provide potential guidance on how TiV dynamics and wing positions could be leveraged to alleviate large transient lift fluctuations experienced by finite wings in severe gust conditions.

Figures (11)

• Figure 1: $(a)$ NACA0015 square wing encountering a gust vortex modeled as a Taylor vortex. Q-criterion isosurface is shown. $(b)$ Circumferential velocity profile and spanwise vorticity distribution of a Taylor vortex with a positive orientation. $(c)$ Computational domain and discretization.
• Figure 2: Lift history for the 2D (dashed line) and square (solid line) wings with $G= \{-1.2,-3,1.2,3 \}$. Representative temporal instances are indicated with $\tau=\tau_1$, $\tau_2$, $\tau_3$, and $\tau_4$.
• Figure 3: Snapshots of spanwise vorticity $\omega_z$ for the 2D wing with $G= \{-1.2,-3,1.2,3 \}$ at four temporal instances $\tau=\tau_1$ through $\tau_4$ noted in figure \ref{['fig:fig2']}. Lift elements $L_e$ (green and purple contours) with lined contours of $\omega_z$ are inserted at the top right of each subplot.
• Figure 4: Top-port views for the square wing cases with $G=1.2$ and $3$ at the four temporal instances noted in figure \ref{['fig:fig2']}. Q-criterion iso-surface is shown in gray with three representative vortex lines coloured in black, aqua, and orange. Spanwise slices of lift elements $L_e$ (colour contours) with $\omega_z$ (line contours) along the root $z/c=0$ and near the tip $z/c=0.48$ are shown on the right of each subplot. Sectional lift distributions at $\tau_0=-0.6$ and $\tau=\tau_1$ through $\tau_4$ are presented at the bottom.
• Figure 5: Same isosurface, spanwise slices, and sectional lift distributions as in figure \ref{['fig:fig4']} for $G=-1.2$ and $-3$.