A physics-based reduced-order dynamic model for fluidic oscillators with a mixing chamber and dual-feedback channels

To facilitate the rapid approximate prediction of the oscillation characteristics of a fluidic oscillator featuring a mixing chamber and two feedback channels, this study develops a nonlinear reduced-order model based on its underlying oscillation mechanism. By analysing the horizontal momentum of fluid parcels in the main jet, the feedback mechanism and jet attachment within the mixing chamber are separately modelled, resulting in a reduced-order equation analogous to the van der Pol equation. The model parameters are categorised into two types: shape parameters, which are derived directly from the oscillator geometry, and characteristic parameters, which are obtained from simulations or experimental data. Based on the reduced-order model, a theoretical formula of the Strouhal number ( St ) is proposed for fluidic oscillators with a mixing chamber and dual-feedback channels. This formula predicts St values of approximately 0.0150 and 0.0189 for typical curved and angled fluidic oscillators, respectively, showing close agreement with experimental values of 0.015 and 0.019, respectively. It also accurately captures the linear relationship between frequency and jet velocity under incompressible conditions. In addition, the model satisfactorily predicted the variation in the jet sweeping angle over time. This study offers further insights into the oscillation mechanism of fluidic oscillators and establishes a foundation for developing more accurate reduced-order models in the future.