Physics informed DMD for periodic Dynamic Induction Control of Wind Farms

Dynamic Induction Control (DIC) is a novel, exciting branch of Wind Farm Control. It makes use of time-varying control inputs to increase wake mixing, and consequently improve the velocity recovery rate of the flow and the power production of downstream turbines. The Pulse and the Helix are two promising DIC strategies that rely on sinusoidal excitations of the collective pitch and individual pitch of the blades, respectively. While their beneficial effects are evident in simulations and wind tunnel tests, we do not yet fully understand the physics behind them. We perform a systematic analysis of the dynamics of pulsed and helicoidal wakes by applying a data-driven approach to the analysis of data coming from Large Eddy Simulations (LES). Specifically, Dynamic Mode Decomposition (DMD) is used to extract coherent patterns from high-dimensional flow data. The periodicity of the excitation is exploited by adding a novel physics informed step to the algorithm. We then analyze the power spectral density of the resulting DMD modes as a function of the Strouhal number for different pitch excitation frequencies and amplitudes. Finally, we show the evolution in time and space of the dominant modes and comment on the recognizable patterns. By focusing on the modes that contribute the most to the flow dynamics, we gather insight on what causes the increased wake recovery rate in DIC techniques. This knowledge can then be used for the optimization of the signal parameters in complex layouts and conditions.