Stochastic Wake Modeling Based on POD Analysis

Abstract. In this work, large eddy simulation data is analyzed to investigate a new stochastic modeling approach for the wake of a wind turbine. The data is generated by the LES model PALM combined with an actuator disk with rotation representing the turbine. After applying a proper orthogonal decomposition (POD), three different stochastic models for the weighting coefficients of the POD modes are deduced resulting in three wake models. Their performance is investigated mainly on the basis of aeroelastic simulations of a wind turbine in the wake. Three different load cases and their statistic characteristics are compared for the original LES, truncated PODs and the stochastic wake models including different numbers of POD modes. It is shown that approximately six POD modes are enough to capture the load dynamics on large temporal scales. Modeling the weighting coefficients as independent stochastic processes leads to similar load characteristics as in the case of the truncated POD. To complete this simplified wake description, we show evidence that the small-scale dynamics can be grasped by adding to our model a homogeneous turbulent field. In this way, we present a procedure how to derive stochastic wake models from costly CFD calculations or elaborated experimental investigations. These numerically efficient models provide the added value of possible long-term studies. Depending on the aspects of interest, different minimalized models may be obtained.