Data Driven Modal Decomposition of the Wake behind an NREL-5MW Wind Turbine

The wake produced by a utility-scale wind turbine invested by a laminar, uniform inflow is analyzed by means of two different modal decompositions, the proper orthogonal decomposition (POD) and the dynamic mode decomposition (DMD), in its sparsity-promoting variant. The turbine considered is the NREL-5MW at tip-speed ratio l = 7 and a diameter-based Reynolds number of the order 108. The flow is simulated through large eddy simulation, where the forces exerted by the blades are modeled using the actuator line method, whereas tower and nacelle are modeled employing the immersed boundary method. The main flow structures identified by both modal decompositions are compared and some differences emerge that can be of great importance for the formulation of a reduced-order model. In particular, a high-frequency mode directly related to the tip vortices is found using both methods, but it is ranked differently. The other dominant modes are composed by large-scale low-frequency structures, but with different frequency content and spatial structure. The most energetic 200 POD modes account for similar to 20% only of the flow kinetic energy. While using the same number of DMD modes, it is possible to reconstruct the flow field to within 80% accuracy. Despite the similarities between the set of modes, the comparison between these modal-decomposition techniques points out that an energy-based criterion such as that used in the POD may not be suitable for formulating a reduced-order model of wind turbine wakes, while the sparsity-promoting DMD appears able to perform well in reconstructing the flow field with only a few modes.