Compressible turbulent channel flow with impedance boundary conditions

Abstract

OATAO is an open access repository that collects the work of some Toulouse researchers and makes it freely available over the web where possible. This is an author's version published in : http://oatao.univ-toulouse.fr/13597 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.

Surface Impedance Determination via Numerical Resolution of the Inverse Helmholtz Problem

“…The impedance of a geometrically complex acoustically absorptive toy cavity is then considered (section §V), validated against time-domain pore-resolved unstructured Navier-Stokes simulations under both harmonic ( §V.A) and pulsed ( §V.B) excitation and with direct comparison against time-domain impedance boundary conditions (TDIBC) one-dimensional simulations . [15][16][17]…”

“…al 2015. 16 Test cases in the following subsections assume planar wave propagation and normal incidence in a viscous medium at atmospheric base pressure and temperature T 0 = 300 K for air, modeled as an ideal gas. Dynamic viscosity is evaluated using Sutherland's law using µ ref = 1.827 × 10 −3 kg m −1 s −1 to reduce computational costs associated to Stokes layer resolution.…”

“…Finally, application of the iHS methodology in the modeling of acoustic cavities as lumped impedance boundaries [16,18] is discussed and demonstrated ( §5.3). To this end, a broadband pulse reflection is studied, first off the pore resolved cavity, and then off an equivalent time domain impedance boundary condition (TDIBC) utilizing the iHS data, following the procedure in [17].…”

“…The latter shows that the total acoustic energy entering the duct (given by the area under the negative parts of the curve) is larger than the energy leaving the duct (given by the area under the positive parts of the curve), consistent with absorption of acoustic energy by the toy cavity. There is a small overall mismatch between the results from the two simulations, which can be attributed to the surface averaging of two-dimensional iHS data, and the use of a single-oscillator fit [16,17,18] as opposed to a more accurate multi-oscillator fit [23] in the evaluation of the TDIBC. The latter analysis will be deferred to future work.…”

Mach-number scaling of individual azimuthal modes of subsonic co-flowing jets

“…For the different jet Mach numbers, the liner parameters were set as listed in table 2. Scalo, Bodart & Lele (2015) note that a damping ratio ζ (defined in eq. 25b of Scalo et al 2015) greater than unity results in "inadmissible (or anti-causal)…”