This dissertation studies the aerodynamic behavior of turbulent flow over acoustic liners— permeable surfaces installed inside aircraft engine nacelles to reduce noise. While these liners are highly effective at attenuating sound, they are also known to increase drag. Most prior research has focused on their acoustic performance, often simplifying or overlooking their aerodynamic impact. This work shifts that focus, using fully resolved, high-fidelity direct numerical simulations (DNS) to study flow over realistic liner geometries. Unlike many earlier studies that rely on simplifying assumptions such as impedance boundary models, this study avoids those simplifications by directly resolving the geometry of the acoustic liners.

The study explores key questions: which geometric features of acoustic liners most influence their aerodynamic behavior, how do these surfaces compare to traditional rough walls surfaces, and what additional effects are introduced by acoustic excitation. Although acoustic liners are flush with the surface and lack protrusions, we find that they still behave like canonical rough surfaces due to their permeability. The aerodynamic impact is governed by the non-linear Forchheimer permeability—a parameter that we show is closely linked to strong wall-normal velocity fluctuations in the near-wall region. These fluctuations are the primary driver of the drag penalty: the higher the wall-normal velocity fluctutations, the higher is the drag penalty compared to the reference smooth wall case. Importantly, the findings show that by limiting these wall-normal motions through geometric modifications—such as tapered orifices, or alternative shapes like elliptical orifices—it is possible to reduce drag. Tapered holes in particular show potential, as they decrease permeability without significantly affecting sound absorption. More aggressive changes, like parallel slots, tend to degrade acoustic performance, highlighting a necessary trade-off. However, certain designs, such as perpendicular slots, appear to offer a favorable balance.

Using the first fully resolved spatially developing turbulent boundary layer simulation over an acoustic liner array, this dissertation further shows that, for the conditions studied, acoustic excitation—modeled as a planar upstream-propagating monochromatic wave—does not significantly affect aerodynamic behavior. However, this does not rule out more complex interactions under realistic engine conditions, where acoustic fields are broadband and multidirectional. Limitations in the numerical setup, particularly in acoustic modeling, mean that the full impact of sound waves remains an open question.

The work also touches on broadband acoustic liner geometries, which are becoming increasingly relevant. These designs are more permeable—not just in the wall-normal direction—but across multiple directions. Higher permeability typically correlates with higher drag, and this trend holds for acoustic liners as well. Still, the study shows that with careful design, broadband liners can be engineered to avoid additional drag penalties, achieving comparable aerodynamic performance to conventional designs.

In summary, this dissertation offers a detailed aerodynamic analysis of flow over acoustic liners, explaining the mechanisms behind drag increase and establishing the central role of permeability. It shows that aerodynamic optimization is possible without compromising acoustic effectiveness and highlights the need for fully resolved simulations when studying such complex surfaces. The findings lay the groundwork for the design of next-generation acoustic liners that better balance noise control and aerodynamic efficiency.

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 direct numerical simulations (DNS) of turbulent flows grazing over acoustic liners with aerodynamically and/or acoustically optimised orifice configurations. Our DNS explore a large parameter space, studying different families of orifice geometries including the influence of orifice shape, orientation, and number. All flow cases show an increase in drag compared to the smooth wall. However, the added drag can be reduced by as much as ∼60%, as compared to conventional acoustic liners by simply changing the shape of the orifice or the orientation in the case of a non-circular orifice. Complementary acoustic simulations show that this drag reduction can be achieved while retaining the same noise reduction properties.

Pore-resolved direct numerical simulations (DNS) of turbulent flows grazing over acoustic liners with aerodynamically and/or acoustically optimized orifice configurations are presented. The DNS explore a large parameter space, studying various families of orifice geometries, including the influence of orifice shape, orientation, and the number of orifices. All flow cases show an increase in drag compared to the smooth wall. However, the added drag can be reduced by as much as approximately 55% as compared to conventional acoustic liners by simply altering the shape of the orifice or its orientation, in the case of a noncircular orifice. Complementary acoustic simulations demonstrate that this reduced drag may be achieved while maintaining the same noise reduction properties over a wide range of frequencies.

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.

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.

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.

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

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.