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Description
This study investigates the aero-acoustic robustness of rainbow trapping structures (RTSs) with straight and coiled cavities in fully opened and flow-compliant convergent configurations under a low-speed grazing flow. A transfer matrix model is developed to predict dissipation, reflection, and transmission loss (TL), and validated against finite element simulations of the Linearized Navier–Stokes equations in the no-flow case. In the absence of flow, increasing the acoustic path length, particularly in convergent designs, broadens and downshifts the high-dissipation plateau through merging of quarter-wave resonances and improved impedance matching. The convergent straight (CS) and coiled (CC) RTSs exhibit the widest efficiency bandwidths, while the CS configuration provides the highest TL peak. Under grazing flow, all configurations remain robust, with reflection coefficients below 1.5% above 400 Hz. Upstream flow conditions (UPC) enhance attenuation relative to downstream flow conditions (DPC), yielding broader dissipation bandwidths and higher TLs, whereas DPC induce over-damping at the cavity mouths and reduced performance. In convergent designs, geometric acceleration of the flow increases the flow-induced modification of the cavity impedances. It triggers a low-frequency axial half-wavelength resonance that scales on the reduced sound speed. Overall, RTS performance is maximized in suction mode, confirming their robustness for flow-integrated noise control.