Modal Analyses Of Rotor Wake By Means Of Time-Resolved PIV Measurements

Abstract

Data-driven decomposition methods, i.e., Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD), have been exploited for analyzing time-resolved PIV measurements of tip vortices shed by a four-bladed isolated rotor in hovering conditions. Two rotor speeds at either ω = 2π∙29.9 H z or 2π∙26.3 Hz have been explored, defining two test cases TC1 or TC2, respectively. Under these regimes, the corresponding aerodynamic loads, in terms of thrust coefficient, lead to CT = 5.5 × 10^-3 or 5.4 × 10^-3, and, of figures of merit, FM = 0.47 or 0.46, respectively. The travel of the tip vortices determines on average a wake contraction inward the radial direction, which effect is more pronounced as the thrust diminishes. During their evolution, momentum addition of the quiescent ambient air is imposed by the advection of the corotating vortex travel. This culminates further downstream where the pairing process of two consecutive vortices occurs. These dynamical mechanisms have been studied in detail using modal analyses. The dominance of the periodic shedding of the tip vortices was captured by both the modal decompositions. The first pair of POD modes describe the spatial organization of the tip vortices and the pairing region. The corresponding time coefficients include multiple frequency peaks discerning the most prominent contribution ascribed to the tip vortex shedding. Dually, the analysis by the DMD method indicates the tip vortices as the most dynamic flow feature. Secondary flow structures are found for TC1 in correspondence of the shear layer and the developed wake, having a characteristic frequency of the order of the rotor speed. Whereas for TC2 it is found that small vortical structures concur to the build-up of the complete vortical dynamic, they are characterized by a doubled frequency than that measured for the tip vortices.