  Many traditional methods for wind turbine design and analysis assume
quasi-steady aerodynamics, but atmospheric flows are inherently unsteady and
modern turbine blades are susceptible to aeroelastic deformations. This study
therefore evaluates the effectiveness of simple analytical models for capturing
the effects of such unsteady conditions on wind-turbine blades. We consider a
pitching and plunging airfoil in a periodic transverse gust as an idealization
of unsteady loading scenarios on a blade section. A potential-flow model
derived from a linear combination of canonical problems is proposed to predict
the unsteady lift on a two-dimensional airfoil in the small-perturbation limit.
We then perform high-fidelity two-dimensional numerical simulations of a
NACA-0012 airfoil over a range of periodic pitch, plunge, and gust
disturbances, and quantify the amplitude and phase of the unsteady lift
response. Good agreement with the model predictions is found for low to
moderate forcing amplitudes and frequencies, while deviations are observed when
the angle-of-attack amplitudes approach the static flow-separation limit of the
airfoil. Potential explanations are given for the cases in which the ideal-flow
theory proves insufficient. This theoretical framework and numerical evaluation
motivate the inclusion of unsteady flow models in design and simulation tools
in order to increase the robustness and operational lifespans of wind turbine
blades in real flow conditions.
