Data-Driven Optimal Basis Clustering To Characterize Cycle-to-Cycle Variations in Dynamic Stall Measurements

Pitching airfoil measurements are known to exhibit significant scatter at near- and post-stall angles of attack. Applying data-driven algorithms revealed the presence of bimodal distribution within the data scatter, suggesting that the statistical mean and standard deviation often used to represent cycle-to-cycle variations are incorrect. Considering the historical significance of dynamic stall measurements, a thorough assessment was undertaken to ascertain that the observed furcation in the data is not a result of facility or post processing error. Once confirmed, cluster-averages, associated variances, and group probability were identified as the best alternative to represent groups in the data. Several existing clustering techniques were tested, however, their shortcomings led to the development of two new data-driven algorithms. A uniqueness that is common to both of the new algorithms is that the clustering process is based on the flow phenomena that contribute the most energy to the overall flow variations. By operating in the optimal basis that maximizes the variance in the measurements, separation of clusters became efficient. When applied to several test cases, the clusters revealed the causes for such grouping, such as the variations in the separation location, occurrence of LE/TE stall, presence/absence of a dynamic stall vortex (or vortices), reattachment angle, etc. In all the cases, the physical processes and their effects were obscured by the phase-average curves. Further analyses to study the effects of Mach number, reduced frequency, mean angle and amplitude of oscillation revealed trends in the group probability. Aerodynamic damping, peak values of pitching moment and lift were substantially different between the clusters, as well as with the phase-average. Considering future semi-empirical models that need to account for cycle switching from one group to another, Markov process (and chain) was studied.