Phase-averaged dynamics of a periodically surging wind turbine

Abstract

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 = 6.1 × 10 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.

Power-generation enhancements and upstream flow properties of turbines in unsteady inflow conditions

“…Dabiri (2020) recently relaxed that assumption and suggested that the contribution of an unsteady velocity potential could lead to theoretical efficiencies in excess of the so-called Betz limit. In parallel with this prediction, several studies have shown relative power enhancements over the steady operating power for turbines in surge motions or unsteady flows, both experimentally (Farrugia, Sant & Micallef 2014;El Makdah et al 2019;Mancini et al 2020;Wei & Dabiri 2022) and in simulations of varying fidelity (Farrugia, Sant & Micallef 2016;Wen et al 2017;Johlas et al 2021). However, the extent to which unsteady flow physics contributed to these observed power enhancements is unclear.…”

“…The model can therefore yield numerical predictions of the time-varying and time-averaged rotation rate, torque and power of a turbine under surge motions or dynamic inflow conditions. This stands in contrast to the linearized model developed by Wei & Dabiri (2022), which can be written as a transfer function for convenient analysis but is unable to capture changes in time-averaged quantities.…”

“…We build upon the linear modelling approach of Wei & Dabiri (2022), who describe the time-varying dynamics of a turbine using the swing equation (i.e. Newton's second law for rotation)…”

“…Deviations from equilibrium between the aerodynamic and generator torques τ aero and τ gen produce changes in the turbine rotation rate. Wei & Dabiri (2022) model the generator torque using the ordinary differential equation for the torque from a permanent-magnet motor,…”

“…These parameters can be established empirically for a given generator over a range of resistive loads. While Wei & Dabiri (2022) utilized a linearized model for the aerodynamic torque, in this work we include explicitly the nonlinear relationship between the turbine coefficient of power,…”