Early detection of self-sustained low-frequency flow oscillations over an airfoil

We perform output-only system identification for early detection of self-sustained low-frequency flow oscillations (LFOs) over a prototypical airfoil near stall conditions. We treat the LFO statistics as a Markov process and model the lift force fluctuations with a Van der Pol oscillator subjected to stochastic intrinsic noise representing freestream turbulence. Using time-series data acquired with a load cell, we estimate the first two Kramers-Moyal coefficients (drift and diffusion coefficients) of the corresponding Fokker-Planck equation via an adjoint-based optimization algorithm. By reconstructing the probability distribution of the oscillation amplitude with the identified model parameters, we validate this modeling approach and confirm that the LFOs emerge via a supercritical Hopf bifurcation. Crucially, we show that even when equipped with only pre-bifurcation data, one can forecast the location of the Hopf point as well as the amplitude of the post-bifurcation limit cycle. This approach to early detection of LFOs could find use in future stall-avoidance strategies.