This manuscript presents a numerical investigation of an open-cell 3D-printed perme-able/porous insert used to reduce turbulent boundary layer-trailing edge (TBL-TE) noise. The matrix topology of the insert resembles the lattice of diamond atoms, and thus, it is also referred to as the diamond trailing edge (TE). The porous insert replaces the last 20 % of the chord of a NACA 0018 airfoil. The airfoil is set to zero angle of attack and the chord-based Reynolds number equals to 2.8 × 10 ⁵ . The geometrical details of the 3D-printed insert are replicated in the simulation to allow comparison with the corresponding experimental measurements. The diamond TE is found to reduce noise by up to 10 dB in the low frequency range. At higher frequencies however, the diamond TE causes a slight noise increase. Using a wake survey method, the porous insert is found to cause a minor drag increase compared to its solid counterpart. It is found that the diamond TE produces stronger surface pressure fluctuations, which would have resulted in higher noise intensity according to analytical models. However, by using a source localization method based on the vortex sound theory, it is observed that the increase in pressure fluctuations is primarily due to the exposed pores at the surface of the porous material, which is responsible for the high-frequency excess noise. These analyses also support the argument that a permeable TE produces different acoustic scattering characteristics with respect to the solid TE.

Abstract: The flow field on solid and porous airfoils subjected to turbulence shed by an upstream cylindrical rod and the corresponding far-field noise radiations are studied through particle image velocimetry (PIV) and microphone measurements, respectively. Three different Reynolds numbers based on the rod diameter are considered in a range between 2.7 × 10 ⁴ and 5.4 × 10 ⁴, and two porous airfoil models are tested to analyze the influence of the design elements of the permeable treatment. A standard proper orthogonal decomposition (POD) algorithm is employed to band filter the different length scales that characterize the turbulent flow, making it feasible to determine which turbulence scales are affected by porosity. The aeroacoustic results indicate that the porous treatment of the wing profile leads to a noise reduction at low frequencies and a noise regeneration at high frequencies due to surface roughness. The investigation on the flow field shows that the main effect of porosity is to mitigate the turbulent kinetic energy in the stagnation region, attenuating the distortion of turbulence interacting with the airfoil surface. The application of the POD algorithm indicates that this effect acts mainly on the largest scales of turbulence. Graphic abstract: [Figure not available: see fulltext.].

Lattice Boltzmann simulations were carried out to investigate the noise mitigation mechanisms of a 3-D printed porous trailing-edge insert, elucidating the link between noise reduction and material permeability. The porous insert is based on a unit cell resembling a lattice of diamond atoms. It replaces the last 20 % chord of a NACA 0018 at zero angle-of-attack. A partially blocked insert is considered by adding a solid partition between 84 % and 96 % of the aerofoil chord. The regular porous insert achieves a substantial noise reduction at low frequencies, although a slight noise increase is found at high frequencies. The partially blocked porous insert exhibits a lower noise reduction level, but the noise emission at mid-to-high frequency is slightly affected. The segment of the porous insert near the tip plays a dominant role in promoting noise mitigation, whereas the solid-porous junction contributes, in addition to the rough surface, towards the high-frequency excess noise. The current study demonstrates the existence of an entrance length associated with the porous material geometry, which is linked to the pressure release process that is responsible for promoting noise mitigation. This process is characterised by the aerodynamic interaction between pressure fluctuations across the porous medium, which is found at locations where the porous insert thickness is less than twice the entrance length. Present results also suggest that the noise attenuation level is related to both the chordwise extent of the porous insert and the streamwise turbulent length scale. The porous inserts also cause a slight drag increase compared to their solid counterpart.

Numerical simulations, using a lattice-Boltzmann technique, have been carried out to study the effect of aerodynamic loading and Reynolds number on the aeroacoustics of a porous trailing-edge insert. The airfoil is a National Advisory Committee for Aeronautics 0018 with the last 20% of its chord being replaceable with porous insert based on a Ni-Cr-Al metal foam with a mean pore diameter of 0.8 mm. The porous insert is modeled as an equivalent fluid region governed by the Darcy's law. The angle-of-attack is set to 7.8°, and the freestream Reynolds numbers based on the airfoil chord are 2.7 × 10⁵ and 5.4 × 10⁵. The amount of noise reduction produced by the porous insert generally decreases as the angle-of-attack or Reynolds number is increased, although the far-field noise directivity remains similar to that of the solid insert case. Unlike for a solid insert, in which noise sources are concentrated at the trailing edge, those on the porous insert are distributed across the porous medium surface, and they promote phase interference effect that causes noise attenuation. This mechanism is realized by the pressure release process, which refers to the interaction between surface pressure fluctuations on both sides of the trailing edge through the porous medium. It is found that the pressure release process is strongly present at the last 25% of the porous insert extent, and thus the upstream segment plays a relatively limited role in noise attenuation. The porous insert also causes velocity deficit, enhanced Reynolds shear stress, and lower convection velocity in the turbulent boundary layer. Nevertheless, since only the flow field surrounding the porous insert is affected, the overall aerodynamic penalty is relatively minor. It has also been found that the effect of mean cross-flow inside the porous medium is almost negligible in the present investigation due to the small surface pressure difference between the two sides of the porous insert.

Porous materials have been widely investigated as a mean for noise reduction. Numerical simulations can be used to investigate the physical mechanisms responsible for noise reduction; however, a correct modeling of the porous medium through an equivalent fluid model is essential to minimize the computational costs. This paper reports a detailed review of a few applications of the equivalent fluid model based on a three-layer approach, a method that is particularly useful to account for the variation of porous material thickness in aerospace applications. The multilayer approach has been applied in three relevant aerodynamic noise issues: leading-edge impingement noise, turbulent boundary-layer trailing-edge noise, and jet installation noise. Comparison with experiments is used to validate the simulation approach.

A lattice-Boltzmann method has been employed to study the aeroacoustics and aerodynamics of airfoils equipped with leading edge treatments, namely the porous leading edge and leading edge serrations. The present study aims to identify the differences in noise reduction mechanisms between the two treatments. Within the context of turbomachinery applications, the airfoils undergo aerodynamic excitation due to the impingement of turbulent wake shed by an upstream rod. Two airfoil profiles are considered: NACA 0012 and NACA 5406; the latter mimics geometrical features and aerodynamic loading distribution of the outlet-guide vane in a turbofan test rig. Simulations are carried out at a freestream Mach number of 0.22, corresponding to Reynolds number based on the rod diameter of 48 000. The serrations are designed to follow a sinusoidal planform shape, whereas the porous leading edge is based on a Ni-Cr-Al metal-foam with homogeneous and isotropic properties. It is found that the porous leading edge attenuates noise by dampening surface pressure fluctuations due to the reduced blockage effect compared to the solid one. Differently, the leading edge serrations promote destructive interference of noise sources along the span. When applied against turbulent inflow with tonal characteristic, such as that induced by the impingement of Kàrmàn vortex street in the rod wake, the latter is more effective. On the other hand, both treatments are found to produce similar broadband noise reduction. When comparing aerodynamic performances, it is found that under a lifting condition, cross-flow is present through the porous material which results in lift reduction and drag increase. A serrated porous leading edge is then proposed to combine the benefits of the two leading edge treatments. This results in optimal noise reduction performances and lower aerodynamic penalty with respect to the fully porous leading edge.

Open-cell porous materials have been reported as a promising concept for mitigating turbulent boundary-layer trailing-edge noise. This manuscript examines the aeroacoustics of a porous trailing edge to study its noise reduction mechanisms. Numerical investigations have been carried out for a NACA 0018 aerofoil with three different types of trailing edge: a baseline solid trailing edge, a fully porous trailing edge and a blocked-porous variant in which a solid core is added at the symmetry plane. The latter prevents flow interaction between the two sides of the aerofoil. Flow-field solutions are obtained by solving the explicit, transient and compressible lattice-Boltzmann equation, while the Ffowcs-Williams and Hawkings acoustic analogy has been used to compute far-field noise. The porous material is modelled using an equivalent fluid region governed by Darcy's law, in which the properties of a Ni-Cr-Al open-cell metal foam are applied. The simulation results are validated against reference data from experiments. The regular porous trailing edge reduces noise substantially, particularly at low frequency, whereas the blocked variant retains similar noise characteristics as the solid one. By employing a beamforming technique, the dominant source is found at the trailing edge for the solid and blocked trailing edges, while for the fully porous one, the dominant source is located near the solid-porous junction. The analysis of the scattered sound suggests that the permeability of the porous trailing edge allows for acoustic scattering along the porous medium surface that promotes destructive interference, and in turn, attenuates far-field noise intensity. The spectra and spanwise coherence of surface pressure fluctuations at the trailing edge are hardly affected by the presence of the porous material, which are found to be insufficient to justify the noise reduction. The flow field inside the porous medium is also examined to explain the differences between the fully porous and blocked-porous trailing edges. While the mean velocity components are similar for both, substantial difference is found for the velocity fluctuations. The impedance of the porous medium is computed as the ratio of velocity and pressure fluctuations. Unlike the blocked variant, the impedance in the fully porous trailing edge gradually decreases along the downstream direction, which leads to the distributed noise scattering along the porous medium surface. Additionally, the scattering efficiency at the actual trailing edge location is reduced due to the smaller impedance discontinuity.

This manuscript presents a rod-linear cascade model for emulating rotor-stator interaction noise. The model is intended as a test platform for studying noise mitigation techniques for a turbofan fan stage, while it also extends the classical rod-airfoil configuration by considering a row of blades based on realistic geometrical details. The rod-linear cascade model consists of a rod positioned upstream of a 7-blade linear cascade, such that the rod wake impinges onto the central blade. The rod is scaled to obtain a fundamental shedding frequency equal to the first blade passing frequency of the NASA-Glenn Source Diagnostics Test (SDT)fan stage at approach condition. The cascade blade profile is also based on the OGV of the SDT sampled at 90% of the radial span. Subsequently, numerical simulations are performed using lattice-Boltzmann Method on a computational setup comprised of a contraction and a test section enclosing the rod-linear cascade model. The integral length scales of the rod wake and the mean loading of the central blade have been found to be in good agreement with the trends observed in the SDT fan stage. The primary noise sources are localized at the central blade leading edge, although noise propagation to the far-field is influenced by additional diffraction by the other blades. Furthermore, the acoustic-blade row interaction causes intense pressure fluctuation within the inter-blade channels, including in those that are not directly affected by the rod wake.

This manuscript presents a numerical investigation of the turbulent boundary layer-trailing edge (TBL-TE) noise reduction with an open-cell porous material. The implementation of the porous media is verified by emulating a facility for characterizing the flow resistivity of the porous material. Subsequently, the porous media is applied on the trailing edge of a NACA 0018 airfoil to examine its capability to mitigate TBL-TE noise. The airfoil is set at zero angle of attack and the chord-based Reynolds number is 2.8 × 10 ⁵. Boundary layer profiles and integral boundary layer quantities have been compared with reference experimental data. The noise reduction obtained with the porous trailing edge at low to mid frequency ranges has been found to be in good agreement with the experiment. However, the simulation is unable to predict the noise increase at high frequency, which is considered due to the neglected surface roughness effects in the adopted porous media model. Conventional beamforming is also used to locate the dominant sound sources. In contrast with the solid trailing edge case, it has been found that the solid-porous interface is the location of the dominant sound source for the porous trailing edge case.

The rod-airfoil configuration has been widely used to gain more insights into turbulence impingement noise in aeroengines, such as periodic fan wake impingement onto outlet guide vane (OGV). To this scope, this paper investigates a linear cascade model, which replicates the baseline OGV of NASA-Glenn Source Diagnostic Test (SDT) rig. The rod, which is located upstream of the linear cascade, sheds turbulent Kármán vortex street at a frequency equal to the SDT’s first blade passage frequency (BPF). The vertical position of the rod is adjusted to achieve direct impingement of the vortex street along the span of the central blade leading edge. A suitable contraction and test section has been designed to allow freestream flow condition of about 100 m/s. Numerical simulations are performed using Lattice-Boltzmann solver Power- FLOW with the intent of reproducing the whole test rig and get preliminary insights into the aeroacoustics of the test rig before being manufactured. Subsequently, turbulence structures impinging on the OGV are characterized and found to be comparable to those measured in the actual SDT rig. However, the unsteadiness resulting from the rod wake impingement was observed to not only affecting the central blade, but also the neighboring blades and inter-blade channels. This results on a significant influence on the far-field noise characteristics.