Compressible turbulent channel flow with impedance boundary conditions

Abstract

We have performed large-eddy simulations (LES) 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 IBCs are formulated in the time domain according to Fung and Ju 1 . 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 impedance adopted is a three-parameter, damped Helmholtz oscillator with resonant angular frequency, ω r , tuned to the characteristic time scale of the large energy-containing eddies. The tuning condition, which reads ω r = 2πM b (normalized with the speed of sound and channel half-width), reduces the IBC’s free parameters to two: the damping ratio, ζ, and the resistance, R, which have been varied independently with values, ζ = 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, ζ, 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, λ x , traveling downstream with advection velocity c x = λ x M b . They are the effect of intense hydro-acoustic instabilities resulting from the interaction of high-amplitude wall-normal wave propagation at the tuned frequency f r = ω r /2π = M b with the background mean velocity gradient. The resonance buffer layer is confined near the wall by (otherwise) structurally unaltered outer-layer turbulence. Results suggest that the application of hydrodynamically tuned resonant porous surfaces can be effectively employed in achieving flow control.