Phase-oscillator-based modeling and control of multi-modal fluid flows

Analysis and control for time-periodic fluid flows have been performed using phase reduction analysis, wherein the high-dimensional periodic flow physics is described as a single scalar phase dynamics. However, most unsteady flows have several dominant frequencies and flow control is challenging owing to the nonlinear interactions. In the present work, we capture the dynamics of unsteady flows with a coupled phase oscillator model, where each dominant mode is represented with an oscillator and the coupling terms quantify the triadic interactions. We demonstrate this approach on a compressible laminar flow over a rectangular cavity with strong triadic interactions. Such flows are characterized by violent pressure fluctuations. Using the developed coupled phase oscillator model, we can identify the phase sensitivity function and the optimal actuation waveform for a rapid shift of the dominant frequency. An actuation jet is introduced at the leading edge using this optimal waveform to modify the dominant physics, which results in a reduction in the triadic interactions, and a 20 percent reduction in pressure fluctuations in the cavity.

This work is supported by the US Air Force Office of Scientific Research (FA9550-21-1-0178) and the US National Science Foundation (2129639).