On the effect of airfoil geometry on extreme vortex-gust encounters

TL;DR

This paper investigates the effect of airfoil geometry on extreme vortex-gust encounters in two-dimensional incompressible flows at $Re_c=100$. A systematic numerical study using the immersed boundary projection method spans gust parameters ($G$, $R_v$, $y_0$, $\alpha$) and airfoil geometry ($\tau$, $\eta$) across multiple 4-digit NACA profiles. The authors introduce force-element analysis and vorticity-production diagnostics to relate gust-induced surface pressure changes and curvature-driven vorticity production to lift transients, finding that increasing thickness attenuates the leading-edge vorticity flux and lift fluctuations via reduced curvature effects. Key contributions include quantitative trends linking $|G|$, $R_v$, and $y_0$ to lift and drag fluctuations, and the demonstration that airfoil geometry can serve as a lever to mitigate unsteady gust loads. This work advances design principles for gust-resilient small aerial vehicles by connecting geometry, vorticity production, and nonlinear gust dynamics.

Abstract

Historically, investigations on gust encounters have been limited to thin airfoils. In this work, we examine vortex-gust encounters by a family of airfoils at a chord-based Reynolds number Re_c=100, which includes variations in the gust ratio, initial gust position, gust radius, angle of attack, airfoil thickness, and airfoil camber. We examine differences in the flow fields, lift-element distributions, and aerodynamic responses across several airfoil-gust interactions. We observe a large deviation of the flow fields and aerodynamic responses with respect to the baseline flows for increasing gust ratios and gust sizes. The initial position of the vortex gust influences the magnitude of the velocity gradients observed near the leading edge, effectively heightening or mitigating the amplitude of the lift response. Moreover, the lift fluctuation increases with the angle of attack until it flattens around $10^\circ$, reminiscent of an unsteady stall-like regime. Furthermore, we report a decrease in the amplitude of the gust-induced lift fluctuations for thicker airfoils, which we attribute to a decrease in the vorticity production levels from the leading edge. The exploration of a sensitive subset of the parameter space uncovers relevant trends, shedding light on regions that have received limited attention in past studies, with special focus on the influence of airfoil geometry.

Figures (17)

• Figure 1: (Left) Diagram of the flow and airfoil variables included in the parameter space explored in this work. All variables of interest are highlighted in red. (Right) Schematic of the airfoil geometry parameters of 4-digit NACA profiles.
• Figure 2: Baseline streamlines and vorticity (colored contours) fields of three symmetric airfoils at different angles of attack $\alpha$. Red markers indicate the bounds of the separated region, and its chordwise extent is denoted by $l$.
• Figure 3: Baseline lift $C_{L,b}$ (first column) and drag $C_{D,b}$ (second column) coefficients of symmetric and cambered 4-digit NACA profiles at different angles of attack $\alpha$.
• Figure 4: Lift $C_L(t)$ and drag $C_D(t)$ coefficients, kinetic energy $k$, velocity $(u,v)$, vorticity $\omega$, and lift-element $f_L$ fields, along with vorticity production fluxes ($J_{n,0},J_{n,0}^c$), observed during a during a vortex gust encounter by a NACA 0018 and $(G,R_v,y_0,\alpha)=(2,0.25,-0.1,5^\circ)$.
• Figure 5: Influence of $G$ on $C_L(t)$ and $C_D(t)$, kinetic energy $k$, velocity (streamlines), vorticity $\omega$, and lift-element $f_L$ fields, observed during a vortex gust encounter by a NACA 0018 and $(R_v,y_0,\alpha)=(0.25,-0.1,5^\circ)$.