Nonmodal stability analysis of extreme gust-airfoil encounters

Although many studies investigate the stability of flows over airfoils operating in statistically stationary or periodic conditions, few studies have explored the stability of flows over airfoils in unsteady conditions. Identifying the stability of unsteady flow structures is important for tasks such as determining if these structures trigger turbulence or if these structures break down. Here, we are particularly interested in uncovering types of perturbations that grow on top of extreme gust encounters (i.e., large gust ratios) that produce large, undesirable lift fluctuations. Thus, we aim to find what types of perturbations may alter these gust-airfoil encounters.



A major challenge with analyzing unsteady flows is that standard linear stability analysis only offers insight into the asymptotic behavior of perturbations. Instead, we use nonmodal stability analysis to identify the optimal perturbations and transient growth of these perturbations in gust-airfoil encounters. We perform this analysis using an adjoint formulation in which we compute the three-dimensional optimal perturbation on top of two-dimensional baseflows for various gust-airfoil encounters. We find that perturbations to gust-airfoil encounters can grow larger than perturbations to the flow over airfoils without a gust. Furthermore, we show the mechanisms that cause the growth of optimal perturbation during gust encounters.