Onset of absolute instability on a pitching airfoil

A transient linear stability analysis of the time-dependent flow around a natural laminar flow airfoil undergoing small-amplitude pitching motion is performed using the Optimally Time-Dependent (OTD) framework. The most salient linear instabilities associated with the instantaneous basic state are computed and tracked over time. The resulting OTD modes reflect the variations in the basic state and can be used as predictors of its evolution including the formation of a laminar separation bubble, its gradual spanwise modulation via primary global instability leading to secondary instability and finally rapid breakdown to turbulence. The study confirms and expands upon earlier stability analyses of the same case based on the local properties of span-wise averaged velocity profiles in the bubble that predicted the onset of absolute instability soon followed by rapid breakdown of the separation bubble. The three-dimensional structure of the most unstable OTD mode is extracted which compares well with both the locally absolutely unstable mode and the evolution of the basic state itself.
QC 20230511