A ray-based numerical model for aircraft noise propagation that accounts for source motion, ground effects, and atmospheric effects as recently proposed (Kayser et al., 2024, Acta Acustica, 8, 62) is evaluated against measurements. Prior to this comparison, an extension of the model is introduced to incorporate coherence loss due to atmospheric turbulence scattering. To capture realistic conditions, noise of aircraft flyovers was recorded on-site, along with aircraft trajectory and meteorological data, including wind and temperature profiles. The spectrograms at 1.2 m above the ground are extrapolated from the measured spectrograms at the ground level using a transfer function computed from both the proposed ray-tracing model and an existing heuristic model from the literature, which neglects refraction. Comparison with the spectrograms measured at 1.2 m shows that both models are capable of reproducing the spectrograms with good accuracy. However, the ray-based model demonstrates greater precision in capturing interference patterns, particularly when the aircraft is not directly overhead relative to the receiver (i.e., for slant propagation), where refraction plays a more significant role.

A formulation to introduce acoustic waves from a control surface using volumetric source terms is proposed for numerical simulations. A general expression of the source terms is derived from the non-linear Euler equations. The method is validated through three academic configurations: the injection of oblique plane waves and the radiation of a monopole source in two and three dimensions, in uniform flow. The governing equations are solved in a Cartesian grid using a low-dispersion and low-dissipation high order finite-difference numerical scheme. However, the control surface has an arbitrary shape, as demonstrated here with the use of a cylindrical surface. Numerical results show good agreement with analytical solutions in both phase and amplitude. The method is then applied to an open-fan aircraft engine configuration. The source terms are computed from a cylindrical control surface enclosing the rotor, based on data extracted from a previous fluid mechanics simulation. The radiated acoustic field is compared with the one obtained using the Ffowcs Williams-Hawkings integral formulation. The two solutions are again found in good agreement for this more realistic configuration.

A low-order immersed boundary method (IBM) is proposed for the simulation of acoustic scattering by obstacles. The IBM formulation, based on generalized functions, introduces source terms distributed along the obstacle surfaces through a Dirac delta function. For implementation using finite-difference methods, the delta function is smoothed using a Gaussian function. The proposed IBM can accommodate perfectly reflecting, impedance, and non-reflecting boundary conditions (BCs). Analytical investigations demonstrate that, when the delta function is employed, the IBM reproduces the exact reflection and transmission coefficients for oblique wave incidence and recovers the exact scattered field for the canonical problem of acoustic scattering by a cylinder. When a Gaussian function is used instead, the method achieves first-order accuracy for impedance and non-reflecting BCs, and second-order accuracy for perfectly reflecting BCs. Several numerical test cases confirm these theoretical findings.

This study demonstrates the influence of wind farm flow on noise generation and downstream propagation through numerical simulations. Time averaged flow fields, modeled using large-eddy simulations, serve as input to acoustic models that predict wind turbine noise. In the first turbine row, turbulent inflow noise and trailing-edge noise contribute equally, with turbulent inflow noise dominating at low frequencies and trailing-edge noise at higher frequencies. Farther downstream in the wind farm, trailing-edge noise's relative contribution decreases because the wind speed is lower, while turbulent inflow noise persists because turbulence levels remain high. These effects are more pronounced in aligned wind farms than in staggered layouts, given stronger wake interactions. However, staggered farms produce more noise overall because turbines operate at higher wind speeds. Additionally, wind farm flow significantly affects sound propagation downwind. Wake superposition changes sound focusing, modifying amplification areas compared to an isolated turbine. For a staggered layout, it particularly shows enhanced sound focusing downwind. This leads to higher sound levels and amplitude modulation downwind of the wind farm, compared to an aligned layout. These phenomena are not captured by models based on isolated turbines. These findings underscore the importance of integrating flow and acoustic models to more accurately assess the environmental impact of wind farms.

The influence of turbine-turbine interactions on sound propagation is investigated using numerical simulations. Three configurations are examined: turbines aligned downstream of each other, placed side by side, and arranged in a staggered pattern. The simulation framework combines large-eddy simulations for aerodynamic interactions, an aeroacoustic source model to simulate turbine sound emission, and parabolic equation methods for sound propagation. When a second turbine is positioned directly downstream, wake-induced flow focusing enhances sound pressure levels (SPLs) and amplitude modulation (AM) by several decibels downwind. In side-by-side and staggered configurations, SPL increases are limited (<2 dBA), and AM is generally reduced because of spatial averaging. Distinct AM patterns emerge in regions where acoustic contributions from both turbines are comparable. For identical rotor speeds, AM is strongly affected by the angular offset between rotors. When rotor speeds differ slightly, beating effects occur, resulting in intermittent AM. These findings highlight the sensitivity of AM to rotor dynamics, a key factor influencing sound perception, with implications for environmental impact and turbine siting.

Acoustic wave propagation in inhomogeneous media such as the atmosphere and ocean can be efficiently modelled with parabolic equations. This presentation overviews recently derived narrow- and wide-angle parabolic equations for sound propagation in motionless and moving media, along with algorithms for their numerical implementation. These parabolic equations preserve the phase of the sound wave and are valid for arbitrary variations in the sound speed and arbitrary (subsonic) Mach number of the medium velocity. Within the ranges of their applicability, the parabolic equations considered exactly describe sound propagation in stratified moving media. These features are particularly important for long-range multipath sound propagation when the phase increments along different arrivals should be calculated accurately. Despite their generality, the narrow- and wide-angle parabolic equations are relatively simple. Moreover, they can be efficiently solved with available Crank-Nicholson numerical techniques. Example calculations are provided that demonstrate the numerical implementation of the narrow- and wide-angle parabolic equations and their accuracy as compared to parabolic equations based on the effective sound speed approximation.

Prediction of the acoustic performance of 3D printed materials is investigated at normal and grazing incidence. A direct numerical (microscopic) simulation that solves the full set of Navier-Stokes equations is used as a reference. It is compared with a macroscopic approach in which the material is represented by an equivalent fluid. The materials have a periodic microstructure, consisting either of a single network of spherical or cubic cavities connected by cylindrical channels or of a double-nested network. The samples are printed using the stereolithography technique and are tested using an impedance tube and a duct test bench. For single network geometries, the results of sound absorption at normal and grazing incidence predicted using the equivalent fluid approach are in good agreement with those obtained by the microscopic approach. Comparisons with impedance tube measurements confirm that both approaches can accurately predict the absorption coefficient of the samples. For the in-duct liner configuration, the transmission loss measurements and predictions show similar evolution with frequency change, despite the discrepancy in amplitude. For the double network geometry, the equivalent fluid approach cannot exactly reproduce the results obtained with the direct numerical simulation. Finally, while the predictions with the microscopic approach provide a good match with the impedance tube measurements, only a poor agreement is obtained using the duct testing bench.

The impact of leakage on sound properties of open porosity 3D printed samples with a periodic microstructure is investigated at normal and grazing incidence. For that, direct numerical simulations (DNS) accounting for leakage are performed. In addition, an extension of the model proposed by Cummings [(1991). J. Sound Vib. 151, 63-75] is developed to predict the surface impedance of a sample surrounded by an air space at normal impedance accounting for dissipation in the leak. Experiments in a Kundt tube are performed for three series of 3D printed samples with different external diameter. Overall, leakage is responsible for a shift of the absorption peak toward higher frequencies and to an increase in its amplitude. Comparison of the measurements with the DNS and the extended Cummings model shows that both approaches predict satisfactorily the impact of leakage on the absorption coefficient. In addition, a duct wall configuration is studied for three geometries of 3D printed samples. DNS results reveal that the impact of leakage on transmission loss varies significantly depending on the 3D printed sample unit cell. Finally, discrepancies between the measured and predicted transmission loss are shown to be attributable to leakage for two of the three geometries.

The influence of three-dimensional (3D) wind turbine wake effects on sound propagation is investigated. To study this, numerical simulations are conducted using a 3D parabolic equation model at low frequencies, with comparisons made to a two-dimensional (2D) approach that neglects transverse horizontal propagation. Three atmospheric stability conditions are investigated using analytical wind profiles that incorporate the wake effects. The wind turbine noise source is specified using an aeroacoustic extended source model. 3D effects due to the wake are shown to be significant, especially for the stable atmosphere. Indeed, horizontal refraction induces focusing that a 2D approach fails at predicting. As the wind turbine blades are rotating, the focal zones are moving accordingly, yielding large variations of the sound levels. Downstream the turbine, amplitude modulation can locally reach values as high as 16.5 dB over long distances. In addition, higher average SPL are predicted by 3D simulations compared to 2D ones, with deviations up to 4.5 dB. For neutral and unstable conditions differences in 2D and 3D sound propagation approaches are smaller, as velocity gradients in the wind turbine wake are smaller.

Parabolic equations are among the most popular numerical techniques in many fields of physics. This article considers extra-wide-angle parabolic equations, wide-angle parabolic equations, and narrow-angle parabolic equations (EWAPEs, WAPEs, and NAPEs, respectively) for sound propagation in moving inhomogeneous media with arbitrarily large variations in the sound speed and Mach number of the (subsonic) wind speed. Within their ranges of applicability, these parabolic equations exactly describe the phase of the sound waves and are, thus, termed the phase-preserving EWAPE, WAPE, and NAPE. Although variations in the sound speed and Mach number are often relatively small, omitting the second-order terms pertinent to these quantities can result in large cumulative phase errors for long propagation ranges. Therefore, the phase-preserving EWAPE, WAPE, and NAPE can be preferable in applications. Numerical implementation of the latter two equations can be performed with minimal modifications to existing codes and is computationally efficient. Numerical results demonstrate that the phase-preserving WAPE and NAPE provide more accurate results than the WAPE and NAPE based on the effective sound speed approximation.

Wind turbine noise propagation in a hilly terrain is studied through numerical simulation in different scenarios. Linearized Euler equations are solved in a moving frame that follows the wavefront, and wind turbine noise is modeled with an extended moving source. We employ large-eddy simulations to simulate the flow around the hill and the wind turbine. The sound pressure levels (SPLs) obtained for a wind turbine in front of a 2D hill and a wind turbine on a hilltop are compared to a baseline flat case. First, the source height and wind speed strongly affect sound propagation downwind. We find that topography influences the wake shape, inducing changes in the sound propagation that drastically modify the SPL downwind. Placing the turbine on the hilltop increases the average sound pressure level and amplitude modulation downwind. For the wind turbine placed upstream of a hill, a strong shielding effect is observed. But, because of the refraction by the wind gradient, levels are comparable with the baseline flat case just after the hill. Thus, considering how terrain topography alters the flow and wind turbine wake is essential to accurately predict wind turbine noise propagation.

Engineering solutions for the modeling of aircraft noise often rely on simplified approaches that consider quasi-static sources and homogenous propagation conditions. These hypothesis may lead to significant inaccuracies on sound pressure level predictions in certain configurations, especially for source traveling at high mach number and at several hundred meters from the receiver. In order to overcome these limitations, an efficient numerical model based on the coupling of a heuristic formulation and a ray-tracing model is proposed. The modeling takes into account source motion effect (Doppler effect and convective amplification), as well as the sound propagation phenomena in inhomogeneous media (waves refraction and scattering by atmospheric turbulence). Several case study related to aircraft noise are presented, for which wind and temperature profiles correspond to experimental measurements. The influence of atmospheric turbulence for such configuration is finally discussed. This work is part of the program MAMBO (Advanced methods for engine and aicraft noise modelling" coordinated by Airbus SAS and supported by the Direction Générale de l'Aviation Civile (DGAC).

The acoustic regulations are increasingly stringent for aircraft noise.Aircraft manufacturers must therefore be able to predict accurately aircraft noise for certification scenarios as early as the design phase.Acoustic propagation models used in the industry are however based on simplified approaches.Thus, we use a heuristic model for a point source in arbitrary motion in a homogeneous atmosphere at rest above an absorbing ground proposed in the literature.It removes most of the simplification of existing approaches, but has however not been validated and applied for aircraft noise.These are the two goals of this study.The heuristic expression is first validated satisfactorily for several test cases against a numerical solution from a time-domain solver of the Linearized Euler equations.Then, a parametric study on ground properties (i.e.absorption, thickness and roughness) is performed to analyze ground effects on sound pressure levels estimation.

The objective of this study is to model and characterize the behaviour of different materials made with 3D printing when they are placed in the wall of a duct.The considered materials present a periodic structure of a volume linked to the volumes of other cells by small channels.Cubic and spherical volumes are used.Two model of the materials are studied.The first is based on a macroscopic description using an equivalent fluid by its dynamic characteristic functions.The semi-phenomenological parameters of the JCALP model are obtained using a hybrid multi-scale approach.The second model consists in describing the material as a whole at the microscopic scale and solving the Linearized Navier-Stokes equations in the material.The results of the two models are compared in normal incidence and in a duct wall.The behavior of the various materials is also investigated experimentally.Measurements at normal incidence are conducted in a circular Kundt Tube.The measurements in the wall of a duct are performed in the MATISSE experimental bench.The experimental and model results show a correct agreement.Finally, the potential differences between the model and the experiment are discussed.

Parabolic equations are among most popular numerical techniques in many fields of physics including atmospheric and ocean acoustics.This article considers extra-wide-angle, wide-angle, and narrow-angle parabolic equations (EWAPE, WAPE, and NAPE, respectively) that are valid for sound propagation in motionless and moving inhomogeneous media, and with arbitrary variations in the sound speed and arbitrary (subsonic) Mach numbers.Within the ranges of their applicability, these parabolic equations exactly describe the phase of the sound waves and are therefore termed the phase-conserving EWAPE, WAPE, and NAPE.On the other hand, WAPEs and NAPEs from the literature are valid for low Mach numbers and/or small variations in sound speed; they correctly describe the phase of a sound wave only within these approximations.Although the variations in sound speed and Mach number are often relatively small, omitting second-order small terms pertinent to these quantities can result in large cumulative phase errors for long propagation ranges.Therefore, the phase-conserving EWAPE, WAPE and NAPE can be preferable in applications.Numerical implementation of the latter two equations can be done with minimal modifications of existing PE codes.

A coupled approach is proposed for predicting sound radiation from a monopole in arbitrary motion in a moving and inhomogeneous atmosphere. It is based on a heuristic model proposed in the literature for sound radiation by a moving source in a homogeneous atmosphere at rest above an absorbing ground and a ray-tracing code, which takes into account meteorological effects. Validation of the model is performed with a reference three-dimensional finite-difference time-domain solution of the linearized Euler equations for several test-cases with different source trajectories and atmospheric conditions. We show that neglecting convective amplification or the source motion between the emission and reception times can lead to significant errors in the predictions. Finally, an application case for aircraft noise is presented. The importance of ground and meteorological effects on the sound pressure levels is highlighted.

The propagation of shock waves generated by a transonic flow at the tip of a propeller blade is numerically calculated in order to determine the pressure footprint on an aircraft fuselage. An academic case is first proposed to validate the methodology. An incoming signal is built up as oblique harmonic plane waves. The signal is introduced in the computational domain using a Gaussian volume forcing term in the conservation of mass and energy equations. The Euler equations are solved in two dimensions using finite-difference schemes with low dispersion and dissipation. Selective filtering has also been integrated in the algorithm to remove grid-to-grid oscillations. The numerical solution is compared to an analytical solution based on the tailored Green function. An illustration for a realistic open rotor is then considered. The pressure signal near the blade tip, determined from a preliminary RANS simulation, is introduced using a volume source in a solver of the Euler equations.

Noise generated by wind turbines is significantly impacted by its propagation in the atmosphere. Hence, for annoyance issues, an accurate prediction of sound propagation is critical to determine noise levels around wind turbines. This study presents a method to predict wind turbine sound propagation based on linearized Euler equations. We compare this approach to the parabolic equation method, which is widely used since it captures the influence of atmospheric refraction, ground reflection, and sound scattering at a low computational cost. Using the linearized Euler equations is more computationally demanding but can reproduce more physical effects as fewer assumptions are made. An additional benefit of the linearized Euler equations is that they provide a time-domain solution. To compare both approaches, we simulate sound propagation in two distinct scenarios. In the first scenario, a wind turbine is situated on flat terrain; in the second, a turbine is situated on a hilltop. The results show that both methods provide similar noise predictions in the two scenarios. We find that while some differences in the propagation results are observed in the second case, the final predictions for a broadband extended source are similar between the two methods.