Gust encounters of rigid wings: Taming the parameter space

One of the primary challenges in the study of gust encounters lies in isolating, defining, and parametrizing a specific problem in a highly unsteady, three-dimensional, and multiscale flow. Recent efforts have decomposed the complex gusty environment typical of atmospheric turbulence and wakes into three canonical gust types: transverse gusts, vortex gusts, and streamwise gusts. By applying analytical, experimental, and numerical methods, a comprehensive picture of the flow fields and force histories typical of gust encounters has been achieved, shedding light on how the defining parameters in the problem affect unsteady forcing. The focus of the current work is on vortex formation and lift production on rigid two-dimensional wings. Despite these simplifications, analytical and low-order modeling of gust encounters resulting in massively separated flows remains a challenge, largely because the force response of the wing is highly sensitive to the growth and motion of vorticity in the flow. It also remains to be seen how well canonical gusts represent real-world gust encounters, and whether there is some region of the parameter space where linear superposition of these inherently nonlinear flows results in a reasonable approximation of the true problem. This article provides an overview of a limited selection of recent and classic work on large-amplitude gust encounters to motivate a discussion of current challenges in parametrizing and modeling these flows, as well as thoughts on working toward a long-term goal of mitigating gust responses.

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Figure 1

Schematic of three types of gust encounters. From Ref. [28]. (a) Transverse gust, (b) Vortex gust, (c) Streamwise gust.

Figure 2

Results from a top-hat transverse gust encounter in the University of Cambridge (CU) towing tank and a sine-squared gust encounter in the University of Maryland (UMD) towing tank. Both test models are a flat plate wing at zero incidence passing through a gust of $GR=1$. From Ref. [28]. (a) Lift coefficient histories from experimental measurements and analytical results from Küssner's model applied to sine-squared and top-hat gusts. (b) Color contours of vorticity (note inverted colors) overlaid on velocity fields as measured using time-resolved particle image velocimetry measurements of a sine-squared (left) and top-hat (right) gust encounter.

Figure 3

Numerical [32] and experimental [37] results for a vortex interacting with a 12% thick airfoil. From Ref. [32]. (a) Effect of inflow position on vortex trajectory over the wing. (b) Variations in vortex strength throughout the encounters due to boundary layer interaction.

Figure 4

Contours of streamwise velocity, and a time series of drag, lift, and velocity for a wing in a randomly varying freestream. Lift and drag vary in time with fluctuations in the streamwise velocity, but the suction parameter clearly rises from $\sigma =0.2$ to 0.23 when the flow reattaches. From Ref. [52].