Compressible turbulent channel flow with impedance boundary conditions

We have performed large-eddy simulations of isothermal-wall compressible turbulent channel flow with linear acoustic impedance boundary conditions (IBCs) for the wall-normal velocity component and no-slip conditions for the tangential velocity components. Three bulk Mach numbers, M-b = 0.05, 0.2, 0.5, with a fixed bulk Reynolds number, Re-b = 6900, have been investigated. For each M-b, nine different combinations of IBC settings were tested, in addition to a reference case with impermeable walls, resulting in a total of 30 simulations. The adopted numerical coupling strategy allows for a spatially and temporally consistent imposition of physically realizable IBCs in a fully explicit compressible Navier-Stokes solver. The IBCs are formulated in the time domain according to Fung and Ju ["Time-domain impedance boundary conditions for computational acoustics and aeroacoustics," Int. J. Comput. Fluid Dyn. 18(6), 503-511 (2004)]. The impedance adopted is a three-parameter damped Helmholtz oscillator with resonant angular frequency,omega(r), tuned to the characteristic time scale of the large energy-containing eddies. The tuning condition, which reads omega(r) = 2 pi M-b (normalized with the speed of sound and channel half-width), reduces the IBCs' free parameters to two: the damping ratio, zeta, and the resistance, R, which have been varied independently with values, zeta = 0.5, 0.7, 0.9, and R = 0.01, 0.10, 1.00, for each M-b. The application of the tuned IBCs results in a drag increase up to 300% for M-b = 0.5 and R = 0.01. It is shown that for tuned IBCs, the resistance, R, acts as the inverse of the wall-permeability and that varying the damping ratio, zeta, has a secondary effect on the flow response. Typical buffer-layer turbulent structures are completely suppressed by the application of tuned IBCs. A new resonance buffer layer is established characterized by large spanwise-coherent Kelvin-Helmholtz rollers, with a well-defined streamwise wavelength. lambda(x), traveling downstream with advection velocity c(x) = lambda(x) M-b. They are the effect of intense hydroacoustic instabilities resulting from the interaction of high-amplitude wall-normal wave propagation (at the tuned frequency f(r) = omega(r)/2 pi = M-b) with the background mean velocity gradient. The resonance buffer layer is confined near the wall by structurally unaltered outer-layer turbulence. Results suggest that the application of hydrodynamically tuned resonant porous surfaces can be effectively employed in achieving flow control. (C) 2015 AIP Publishing LLC.