Causal State-Space Reduced-Order Modeling of Sweeping Jet Actuators Using Internal Mixing-Chamber Dynamics

Sweeping jet (SWJ) actuators are widely used in active flow control, but explicitly resolving actuator-scale unsteadiness in full-configuration computational fluid dynamics (CFD) remains prohibitively expensive because of the small geometric scales and high-frequency oscillations involved. Existing reduced-order boundary-condition models constructed from exit-plane data alone can reproduce the observed switching waveform, but they treat the actuator as an input–output black box and provide limited insight into the internal dynamics that generate the response. This work develops a causal state-space reduced-order modeling framework that links internal mixing-chamber dynamics to time-resolved exit-plane boundary conditions. Proper orthogonal decomposition (POD) is used to obtain a low-dimensional representation of the internal flow, and a data-driven linear evolution operator is identified in the reduced space by least-squares regression of successive snapshot pairs. A POD truncation rank of r=60 is selected from cumulative-energy and validation-error sensitivity analyses, capturing well above 99% of the fluctuation energy while lying within the converged performance regime. A corresponding reduced operator is identified for the exit plane, and spectral comparison reveals near-neutrally stable oscillatory modes in both regions. Using a ±1% relative frequency-matching tolerance, the dominant reduced-operator modes exhibit a 28.3% frequency overlap, providing operator-level evidence that exit-plane oscillations are dynamically linked to internal coherent structures. This correspondence is further supported by cross-spectral coherence analysis between representative internal and exit-plane probe signals, which shows strong coherence at dynamically relevant frequencies. A delayed causal output mapping is then formulated in which the internal reduced state drives the exit-plane response after an identified lag of 149 time steps, corresponding to 2.98×10−3 s. This delay provides a physically interpretable convective transport timescale from the mixing chamber to the actuator exit. Over the validation interval, the model maintains a mean relative L2 error below 0.02, with maximum normalized errors below 0.04 for most of the prediction horizon, and localized increases are confined to rapid jet-switching events. Field-level reconstructions of streamwise velocity and total pressure show that the model captures both phases of the jet-switching cycle, with errors concentrated primarily in high-gradient shear-layer regions. Compared with exit-only reduced-order models, the proposed internal-driven formulation improves amplitude and phase fidelity over extended prediction horizons. The resulting framework provides a compact, interpretable, operator-based representation of SWJ actuator dynamics suitable for use as a CFD-embeddable dynamic boundary condition.