Trapped waves in supersonic and hypersonic turbulent channel flow over porous walls. (10th August 2021) - Chen, Yongkai; Scalo, Carlo
Abstract: Abstract : This study investigates the effect of an isothermal wall with complex impedance on compressible turbulent channel flow up to bulk Mach numbers of $6.00$ . Such investigation is carried out via the time-domain impedance boundary conditions based on auxiliary differential equations method. A three-parameter complex impedance, modelling a frequency-selective porous wall, with tuneable resonating frequency $ω _{res}$ and variable resistance $R \in [0.10, 1.0]$ is employed. Higher resistance leads to lower wall permeability with $R → ∞$ representing the impermeable limit. Three bulk Mach numbers $M_b = \{1.50, 3.50, 6.00\}$ are investigated with a semi-local Reynolds number $Re_τ ^{*} ≈ 220$ . It is found that a sufficiently low $R$ could trigger flow instabilities, which comprise streamwise-travelling waves in the near-wall region, akin to spanwise rollers at low subsonic flow conditions and second-mode waves at hypersonic conditions. The probability density function of instantaneous wall-shear stress shows an enhancement in extreme positive cases of wall-shear stress fluctuations, leading to an increase in the mean wall-shear stress due to porous walls. The wave dynamically affects the turbulence, yielding a local peak near the wall in the pre-multiplied spectrum of the production term of turbulence kinetic energy. Linear stability analysis using the turbulent base flow profile confirmed that the finite wall permeability triggers the instability when $R$ is below a threshold $R_{{cr}}$, which shows a sub-linear proportionality on the bulk Mach number $M_b$ . The perturbed field exhibits more dilatational nature in high Mach number flows with low permeability.