Flow acceleration statistics: a new paradigm for wind-driven loads, towards probabilistic turbine design
Authors: Kelly Mark 
Published: July 2024

Abstract. A method is developed to identify load-driving events based on filtered flow accelerations, regardless of the event-generating mechanism or specific temporal signature. Low-pass filtering enables calculation of acceleration statistics per characteristic turbine response time; this circumvents the classic problem of small-scale noise dominating the observed accelerations or extremes, while providing a way to deal with different turbines and controllers. Not only is the flow acceleration physically meaningful, but its use also removes the need for de-trending. Through consideration of the 99th percentile (P99) of filtered acceleration per each 10-minute period, we avoid assumptions about distributions of fluctuations or turbulence, and derive statistics of load-driving accelerations for offshore conditions from 'fast' (10 and 20 Hz) measurements spanning more than 16 years. These statistics scale with low-pass filter frequency (reciprocal turbine response time), but in a nontrivial manner varying with height due to the influence of the atmospheric boundary-layer’s capping inversion as well as the surface. We find long-term probability distributions of 10-minute P99 of filtered accelerations, which drive loads ranging from fatigue to ultimate; this also includes joint distributions of the P99 with 10-minute mean wind speed (U) or standard deviation of horizontal wind speed fluctuations (σu). The long-term mean and mode of the P99 of streamwise accelerations, conditioned on σu and U, are found to vary monotonically with σs and U respectively; this corroborates the IEC 61400-1 prescriptions for fatigue design-load cases. An analogous relationship is also seen between lateral (directional) accelerations and standard deviation of direction, particularly for sub-mesoscale fluctuations. The largest (extreme) P99 of filtered accelerations are seen to be independent of 10-minute mean speeds, and with only limited connection to 10-minute σu ; traditional 10-minute statistics cannot be translated into extreme load-driving acceleration statistics. From measurement heights of 100 m and 160 m, timeseries of the 10 most extreme acceleration events per 1 m s–1 wind speed bin were further investigated; events of diverse character were found to arise from numerous mechanisms, ranging from non-turbulent to turbulent regimes, also depending on the filter scale. Different behaviors were noted in the lateral and streamwise directions at different heights, though a fraction of these events exhibited extreme amplitudes for both horizontal acceleration components and/or were observed at both heights within a given 10-minute window. Via fits to the tails of the marginal P99 distributions, curves of offshore extreme P99 of filtered accelerations for return periods up to 50 years were calculated, for three characteristic turbine response times (filter scales) at the observation heights of 100 m and 160 m. To drive aeroelastic simulations, Mann-model parameters were also calculated from the timeseries of the most extreme events, allowing constrained simulations embedding the recorded events. To facilitate this for typical industrial measurements which lack three-dimensional anemometry, a new technique for obtaining Mann-model turbulence parameters was also created; this was employed to find the parameters corresponding to the background flow behind the identified extremes and their timeseries. Further, a method was created to use the extreme acceleration statistics in stochastic simulations for application to loads, including interpretation within the context of the IEC 61400-1 standard. Preliminary parallel work has documented aeroelastic simulations conducted using the extreme event timeseries identified here, as well as Monte Carlo simulations based on the extreme statistics and new method for stochastic generation of acceleration events.