Low-Order Modeling and Sensor-Based Prediction of Stalled Airfoils at Moderate Reynolds Number

Abstract

We present analysis from planar time-resolved particle image velocimetry fields in the streamwise surface-normal plane of turbulent flow surrounding NACA 0012 and NACA 65-410 airfoils at focusing on stall phenomena at intermediate to high angles of attack . Dominant flow frequencies, identified from the lift spectra obtained from a load cell mounted to the foils, highlight the presence of bluff-body shedding [ of , where is the frequency, the airfoil chord, and the freestream velocity] for all cases and prominent low frequencies [ of ] for cases in transient stall (TS). A data-driven modeling framework via the proper orthogonal decomposition (POD) reveals that the low frequencies are associated to flow separation and reattachment driven by underlying expansion and contraction normal to the suction surface. Further, the ability to predict the low-order features from (pseudo) pressure probes at the leading, midchord, and trailing edges for both TS and deep stall (DS) cases is quantified using linear stochastic estimation (LSE). The framework pinpoints the centroid of the region of reverse flow with error on the order of 5 and 20% for DS and TS regimes, respectively. Notably, it is found that LSE coefficients governing the low-order POD correlations do not strongly depend on the airfoil geometry. This is demonstrated by the comparative performance of training the LSE using the probes of the NACA 0012 cases to predict the NACA 65-410 velocity fields and vice versa. This work demonstrates the insight afforded by the POD on the low-order features of turbulent stalled airfoils as well as the similarity of such features across geometries toward predicting flow features for potentially any airfoil geometry without the need to retrain an LSE library.