A reduced-order model for the near wake dynamics of a wind turbine: Model development and uncertainty quantification

Wind turbine power production and its variability are affected by unsteady, turbulent structures that are induced in the wake and emerge over a range of disparate length scales. However, the inclusion of the unsteady dynamics in wake models remains difficult in kinematic modeling where steady-state conditions are assumed. We develop and quantify the uncertainty of an unsteady wake model by leveraging model-order reduction. The wake is modeled as a dynamical system based on dynamic mode decomposition and compressive sensing, where the system is reduced by designating an objective function to select energetic turbulent structures represented by dynamic modes. A series of large-eddy simulations are undertaken using the actuator line model and the actuator surface with nacelle model for training and testing data. Differences in the turbine parameterizations of near wake simulations are used to identify how modes are related to turbulent structures and are selected through compressive sensing. The results showed that the flow field can be constructed with few modes. The modes are the most energetic and have frequencies related to pertinent features such as tip and hub vortices. While the error in the training phase is dependent on the number of modes, the relative error remains less than 6% and is largely independent of the number of modes during the prediction phase if certain modes are retained. The error accumulates over time near the turbine blades. However, error accumulation does not have a significant impact on the prediction of instantaneous velocity in the wake further downwind.