Analysis of Dynamic Stall on a Pitching Airfoil With Spectral Proper Orthogonal Decomposition

In the field of Helicopter Engineering the need for a simultaneous variation of the pitch angle of the blade during its rotation about the hub is the cause of a major issue known as dynamic stall. This event is responsible for significant structural problems due to the periodic presence of augmented loads conditions that may couple with the rotor dynamics and cause the earlier failure of the blade. A deeper knowledge of the phenomenon is necessary to devise methods for controlling or preventing its occurrence. A particular attention was paid and different approaches applied by the aerodynamics community to analyze it. Among others, the Proper Orthogonal Decomposition (POD) has shown to provide an unbiased tool for the identification of coherent structures underlying the flow evolution. In this work the spectral variation of the decomposition (SPOD), based on the formulation from Sieber (2016) et al., is used to analyze the flow. According to this method, the application of a filter modifies the original formulation in order to extract new structures otherwise interpreted as noise of the considered data. The case study discussed here is a 2D pitching NACA 0012 airfoil, under deep stall conditions. The numerical data obtained by the CFD simulation with the DLR TAU code are decomposed with the stochastic tool. In particular two fields are decomposed: the vector-valued velocity field and the scalar-valued pressure field. In order to compare POD and SPOD results for dynamic stall, either pure and spectral variations are applied to the two fields; two different filter sizes are chosen according to the time scales of the flow features. New coherent structures are identified through the application of SPOD and the comparison between the analysis of the two fields provides a criterion for choosing a proper filter in order to approach the phenomenon. The dynamics underlying the most correlated structures shows a higher sensitivity towards the filter adopted when one analyzes the pressure field, which depicts lower responses at higher frequencies if compared with the velocity field. In fact, the flow evolution of the pressure field is dominated by the low frequency event related to the dynamic stall vortex, while in the velocity field even flow structures at higher frequencies can be clearly identified. Furthermore, aerodynamic loads are computed from a partial reconstruction of the pressure field previously decomposed with either pure and spectral POD, retaining a number of modes that contained the same cumulative energy in the two analysis. Original loads coefficients obtained from CFD simulations are compared with the ones reconstructed from the two decompositions in order to discuss the possible applicability of the spectral variation in the context of reduced order modeling. This analysis shows that the reconstruction from POD better recovers the original peak values, while the reconstruction from SPOD better predicts the fluctuations of coefficients curves.