A transformation-acoustic (TA) design approach for flow-adaptive gradient-index (GRIN) metamaterial liners is presented in this research. This architecture helps reduce broadband noise in the ducts of high-speed jet engines. Starting with a Mach-dependent coordinate mapping, the effective acoustic parameters ρ(x) and c(x) are combined to keep the local impedance approximately constant all along the liner. The resulting TA-GRIN profile ensures adiabatic impedance matching between the freestream and the backing wall, allowing for broadband reflection suppression without excessive damping. To calculate the reflection coefficient in the frequency and Mach-number domains, a transfer-matrix method is developed that incorporates the convective wavenumber correction Formula: see text and the complex sound speed Formula: see text. Parameter sweeps show the best factor Formula: see text and liner length Formula: see text, indicating strong broadband reflection suppression across the 300-3000 Hz band, particularly for finite Mach numbers (M = 0.2 and 0.4). The results demonstrate that spatial impedance grading, rather than resistive loss, is the primary physical mechanism governing broadband, flow-adaptive noise attenuation in TA-based metamaterial liners. Beyond regulatory noise reduction, the proposed TA-GRIN liner has direct implications for passenger acoustic comfort. In aircraft with tail-mounted engines, such as the McDonnell Douglas MD-80 and DC-9 families, the close proximity of the propulsion system to the fuselage leads to enhanced acoustic coupling and elevated cabin noise levels, particularly in the rear sections. By suppressing internal reflections and mitigating standing-wave formation in aero-ducts, the present design can contribute to reducing duct-transmitted noise and improving the onboard acoustic environment.
Sadeghi et al. (Thu,) studied this question.