Trapped waves in supersonic and hypersonic turbulent channel flow over porous walls. (11th June 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 [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.