Controlling fluidic oscillator flow dynamics by elastic structure vibration

Abstract

In this study, we introduce a design of a feedback-type fluidic oscillator with elastic structures surrounding its feedback channel. By employing phase reduction theory, we extract the phase sensitivity function of the complex fluid–structure coupled system, which represents the system’s oscillatory characteristics. We show that the frequency of the oscillating flow inside the fluidic oscillator can be modulated by inducing synchronization with the weak periodic forcing from the elastic structure vibration. This design approach adds controllability to the fluidic oscillator, where conventionally, the intrinsic oscillatory characteristics of such device were highly determined by its geometry. The synchronization-induced control also changes the physical characteristics of the oscillatory fluid flow, which can be beneficial for practical applications, such as promoting better fluid mixing without changing the overall geometry of the device. Furthermore, by analyzing the phase sensitivity function, we demonstrate how the use of phase reduction theory gives good estimation of the synchronization condition with minimal number of experiments, allowing for a more efficient control design process. Finally, we show how an optimal control signal can be designed to reach the fastest time to synchronization.

Optimal waveform for fast synchronization of airfoil wakes

“…The phase reduction approach expresses the perturbation dynamics using a single scalar phase variable. Recently, it has been used for studying periodic flows to reveal the phase sensitivity fields (Kawamura & Nakao 2013, 2015Khodkar & Taira 2020;Iima 2021;Loe et al 2021;Kawamura, Godavarthi & Taira 2022), synchronization characteristics to external forcing (Taira & Nakao 2018;Khodkar & Taira 2020;Khodkar, Klamo & Taira 2021;Skene & Taira 2022) and flow control (Nair et al 2021;Loe et al 2023) in a computationally inexpensive way.…”