The nacelle of aircraft engines is coated with acoustic liners to reduce engine noise emissions. An undesirable side effect of acoustic liners is that they increase aerodynamic drag. For the first time, the authors study this drag penalty through pore-resolved direct numerical simulation (DNS) of a flat-plate zero pressure gradient turbulent boundary layer at friction Reynolds number Re_τ ≈ 850–2600, which is high enough to be representative of liners in operating conditions. In the configuration under scrutiny, the turbulent boundary layer experiences a step change in surface topography passing from a smooth wall to an acoustic liner array, allowing one to study the streamwise adaptation length of the boundary layer. It is found that the mean velocity profile adjusts to the new surface condition in a nearly negligible distance (less than 10 local boundary-layer thicknesses), whereas turbulent fluctuations take much longer. DNS is also performed with external acoustic noise in the form of planar monocromatic waves grazing the boundary layer with an amplitude of 150 dB. In agreement with some earlier studies, it is found that sound waves do not affect aerodynamic drag at these flow conditions.

We present pore-resolved compressible direct numerical simulations of turbulent flows grazing over perforated plates, that closely resemble the acoustic liners found on aircraft engines. Our direct numerical simulations explore a large parameter space including the effects of porosity, thickness and viscous-scaled diameter of the perforated plates, at friction Reynolds numbers, which allows us to develop a robust theory for estimating the added drag induced by acoustic liners. We find that acoustic liners can be regarded as porous surfaces with a wall-normal permeability and that the relevant length scale characterizing their added drag is the inverse of the wall-normal Forchheimer coefficient. Unlike other types of porous surfaces featuring Darcian velocities inside the pores, the flow inside the orifices of acoustic liners is fully turbulent, with a magnitude of the wall-normal velocity fluctuations comparable to the peak in the near-wall cycle. We provide clear evidence of a fully rough regime for acoustic liners, also confirmed by the increasing relevance of pressure drag. Once the fully rough asymptote is reached, canonical acoustic liners provide an added drag comparable to that of sand-grain roughness with viscous-scaled height matching the inverse of the viscous-scaled Forchheimer permeability of the plate.

The nacelle of aircraft engines is coated with acoustic liners to reduce engine noise. An undesirable effect of these liners is that they increase aerodynamic drag. We study this drag penalty by performing Direct Numerical Simulations of a turbulent boundary layer over an acoustic liner array at friction Reynolds number, Re _τ ≈ 850–2500. We use this simulation to confirm several findings that we recently brought forward using a simpler channel flow setup [1]. We show that acoustic liners lead to high wall-normal velocity fluctuations that can be directly correlated with a modulation of the classical near-wall cycle and to an increase in drag. We also confirm that the acoustic liners act as permeable surface roughness and the non-linear Forchheimer coefficient is the relevant permeability parameter for scaling the drag increase.

In order to reduce the noise emitted by aircraft engines, the nacelle is coated with acoustic liners. An undesirable effect of these surfaces is that they increase the aerodynamic drag. In the present work, we characterize this type of surface roughness by performing Direct Numerical Simulations of fully resolved acoustic liner geometries. We find evidence of a fully rough regime, whose onset is determined by the value of the viscous-scaled Forchheimer coefficient. Moreover, the intensity of the wall-normal velocity fluctuations at the wall also scales with the viscous-scaled wall-normal permeability, leading to a relation between fluctuations and added drag.

We perform direct numerical simulations of turbulent flow at friction Reynolds number Re_τ≈ 500 - 2000 grazing over perforates plates with moderate viscous-scaled orifice diameter d⁺≈ 40 - 160 and analyse the relation between permeability and added drag. Unlike previous studies of turbulent flows over permeable surfaces, we find that the flow inside the orifices is dominated by inertial effects, and that the relevant permeability is the Forchheimer and not the Darcy one. We find evidence of a fully rough regime where the relevant length scale is the inverse of the Forchheimer coefficient, which can be regarded as the resistance experienced by the wall-normal flow. Moreover, we show that, for low porosities, the Forchheimer coefficient can be estimated with good accuracy using a simple analytical relation.

In this article the author name Stefan Hickel was incorrectly written as Hickel Stefan. The original article has been corrected.