Hydro-Acoustic Instabilities in Transonic and Supersonic Turbulent Channel Flows Over Impedance*

This study focuses on flow instabilities in transonic and supersonic turbulent channel flows over assigned wall impedance. Such investigation is carried out via the Time-Domain Impedance Boundary Condition (TDIBC) technique [Fung and Ju 2004; Scalo, Bodart, and Lele 2015] that enables exact representation of the acoustic response of the wall in high-fidelity simulations. The study is an extension of previous work by Scalo, Bodart, and Lele in 2015, in which numerical simulations of bulk Mach numbers up to 0.5 were conducted. A resonance buffer layer consisting of spanwise Kelvin-Helmholtz rollers is observed near the wall, as a result of the interaction between the mean shear and the transpiration velocity controlled by the imposed normal impedance. In the current work we investigate bulk Mach numbers up to 1.5, extending the previous study to the transonic and supersonic flow regimes. A three-parameter impedance acting as a damped Helmholtz resonator is adopted; simulations are performed for varying acoustic resistance, damping ratio and resonant angular frequency. The latter is tuned to the characteristic time scale of energy containing eddies.