  The unsteady power generation of a wind turbine translating in the streamwise
direction is relevant to floating offshore wind turbines, kite-mounted airborne
wind turbines, and other non-traditional wind-energy systems. To study this
problem experimentally, measurements of torque, rotor speed, and power were
acquired for a horizontal-axis wind turbine actuated in periodic surge motions
in a fan-array wind tunnel at the Caltech Center for Autonomous Systems and
Technologies (CAST). Experiments were conducted at a diameter-based Reynolds
number of $Re_D=6.1\times10^5$ and at tip-speed ratios between 5.2 and 8.8.
Sinusoidal and trapezoidal surge-velocity waveforms with maximum surge
velocities up to 23% of the free-stream velocity were tested. A model in the
form of a linear ordinary differential equation (first-order in time) was
derived to capture the time-resolved dynamics of the surging turbine. Its
coefficients were obtained using torque measurements from a stationary turbine,
without the need for unsteady calibrations. Its predictions compared favorably
with the measured amplitude- and phase-response data. Furthermore, increases in
the period-averaged power of up to 6.4% above the steady reference case were
observed in the experiments at high tip-speed ratios and surge velocities,
potentially due to unsteady or nonlinear aerodynamic effects. Conversely,
decreases in mean power with increased surge velocity at low tip-speed ratios
were likely a result of the onset of stall on the turbine blades. These results
inform the development of strategies to optimize and control the unsteady power
generation of periodically surging wind turbines, and motivate further
investigations into the unsteady aerodynamics of wind-energy systems.
