We perform the acoustic characterization of a model-scale wind turbine, including the tower and a fully reflective ground surface. The study constitutes the natural extension of the research presented in Rismondo et al. ( J. Fluid Mech. , 2025, vol. 1024, p. A33), where the isolated rotor (IR) was analysed. We use large-eddy simulation and acoustic analogy. The analysis of pressure over the solid surfaces shows that the rotor produces broadband trailing-edge fluctuations modulated at the blade passing frequency (BPF) by the blade–tower interaction, while the tower exhibits predominantly tonal behaviour at the BPF and its harmonics, as well as low-frequency tower vortex shedding. The tower increases wake asymmetry and turbulent mixing, producing a less coherent wake compared with the IR case. Two main mechanisms rule the near-to-far wake transition: tip-vortex instability and nonlinear interactions between the rotor and the tower induced wakes, enhancing asymmetry and mixing. These dynamics reduce the nonlinear low-frequency acoustic levels in the near wake compared with the IR case, while increasing the sound pressure level and the tonal character in the lateral direction, related to the tower pressure field. In addition, the presence of the tower shapes distinct directivity patterns: radiation in the horizontal plane is nearly isotropic, whereas the rotor-plane directivity is more dipole-shaped, related to the tower, and becomes more pronounced considering the reflective surfaces. Overall, the complete configuration differs significantly from the IR, with measurable differences in surface pressure, wake development and acoustic radiation, emphasizing the role of the tower in both aerodynamics and aeroacoustics.

The present paper deals with the relevant problem of prediction and understanding of physical mechanisms of noise generated in a fluid and propagated in another fluid through a thin solid interface. This is a problem of practical importance in both marine engineering and hydraulic engineering. Sound transmission through different materials involves complex wave interactions at interfaces, where impedance mismatches govern reflection and transmission processes. We first developed a numerical model able to reproduce noise propagation across sharp interfaces; it is based on a multi-domain finite-volume solution of the acoustic wave equation. The model was validated against analytical benchmarks. In addition, a dimensional framework was established to identify the key non-dimensional parameters controlling acoustic transmission across layered media. The methodology was applied to the case of waterborne noise transmitted into air through a thin solid layer, considering two types of acoustic sources, namely a monochromatic monopole at varying frequencies and a broadband signal generated by turbulent channel flow. Two materials were examined for the solid layer: one representative of steel and the other of fiberglass. Acoustic pressure fields and spectra were computed for the different case studies. The results demonstrate consistent attenuation of transmitted sound and highlight the frequency-selective behavior of the solid layers, thereby revealing the physical mechanisms governing waterborne noise transmission across heterogeneous media. Overall, the study shows that the proposed methodology, under particular conditions, is a robust and versatile tool for analyzing hydroacoustic noise in layered systems.

The study of wavebreakers is an important field of research in maritime and coastal engineering. These devices are widely in use for a number of applications; among the others, they are used for protection of harbors, marina, offshore petroleum platforms or other kinds of marine infrastructure from the action of waves and storms. The big impact of their use on the economy and industrial progress of a country gives these infrastructures a very important role Sadeghi(2008). They are also employed for reduction of coastal erosion, which in recent years has particularly intensified due to anthropogenic activities Van(2011). Also, they may be used as Wave Energy Conversion (WEC) systems, devices that convert the energy of the waves in zero-emission electric energy. In particular, the integration of different types of clean energy devices (for example the WECs with floating wind turbines, platforms and the wavebreakers) is crucial to reduce the total Levelised Cost of Energy (LCoE). The operation principle of a wavebreaker consists in reflection of the incident wave and dissipation of a fraction of the wave energy through the formation of a swirling and dissipative fluid motion. As a result, the wave energy transmitted behind the body, is a small portion of the energy of the incident wave. Here we focus on floating wavebreakers (FB) which represent a subset of the general class of wavebreakers and are used in a number of situations. The key parameter to be quantified in the analysis of wavebreakers is the transmission coefficient, defined as the ration between the height of the wave transmitted behind the obstacle and that of the incident wave.

We present an acoustic characterisation of a model-scale wind turbine using large eddy simulation and the acoustic analogy. The analysis is representative of medium-sized turbines with low tip Mach number ( ${\sim} 0.10$ ). The fluid dynamic analysis revealed: a turbulent boundary layer over the blades, together with a trailing edge vortex sheet; a complex near-wake structure, including tip and root vortices; an intermediate wake with vortex instabilities triggering leap-frogging and vortex grouping mechanisms; and a far wake characterised by fully developed turbulence. Two primary noise generation mechanisms were identified. The unsteady pressure field over the turbine surface generates tonal noise at the blade passing frequency and a high-frequency broadband noise, associated with the trailing edge vortex sheet (linear-noise contribution). The turbulent wake generates broadband low-frequency noise, driven by the complex fluid-dynamic processes outlined previously (nonlinear noise contribution). The linear part of the noise was found to dominate over the nonlinear one in the acoustic far field, while the opposite is true in the acoustic near field. As a composition of the two contributions to the noise, the directivity exhibits a non-symmetric dipole shape oriented along the flow direction, with lobes recovering symmetry moving from the near to the far field. Finally, analysis of the acoustic decay rates reveals that the linear term in the near field decays according to an $r<^>{-(n+1)}$ law within the rotor plane, where n is the number of blades, consistent with recent findings on the acoustics of rotating sources.

In the present paper we investigate, through numerical analysis, the hydrodynamic behavior of wavebreakers both in static and in floating configuration. The aim is to evaluate and compare the performance of wavebreakers in regular waves in the range of intermediate depth waters. The analysis is performed through evaluation of the waves transmitted downward and reflected back and the dissipative behavior of the wavebreaker. We simulate numerically the fluid dynamic field using the Unsteady Reynolds Averaged Navier Stokes equations (URANS) with the k−ϵ turbulence model, both for the water and the air phases, using the Volume of Fluid (VOF) method to detect the interface. We simulate a numerical wave tank, generating the waves at a lateral boundary of the domain and allowing its own propagation into the domain. First we study the static configuration of the wavebreaker, so it is considered fixed in space. Afterward, we consider the wavebreaker as a rigid body with a Single Degree of Freedom (SDOF) in the vertical direction and we analyze the interaction between the wave system and the structure. With this purpose we use the URANS equations over a dynamic mesh in conjunction with a Fluid–Structure-Interaction (FSI) algorithm, where the mesh displacement is associated to the body’s motion through a diffusive Laplace equation; the motion of the solid body is evaluated using the momentum equation of a rigid body subject to hydrodynamic loading. We study two different wavebreakers, the rectangular one and the Π shape one, and evaluate the differences in terms of transmitted, reflected and dissipated energy. First we assess the algorithm of generation and propagation of the regular waves comparing numerical results with analytical data. Afterward, we evaluate the performance of the two wavebreakers in terms of coefficients of transmission, reflection and dissipation and we compare our numerical results with data from the standard Wiegel Theory, 1960 and successive modifications. Finally, we study the performance of the wave system in presence of the floating body. This is done in two steps: we initially validate the results with those of the analytical solution of the governing equation of a SDOF rigid body forced by regular wave trains; successively we calculate the transmission coefficients for a number of waves with different length and height and compare the results with literature empirical formulas.

Underwater radiated noise from ship propellers is one of the major contributors to the increase in overall noise levels in marine environments. The development of numerical tools for the computation of noise propagation is of paramount importance for the assessment of the noise impact on the environment. Hybrid approaches, based on the decoupling of the computation of the fluid flow and the successive evolution of the noise using an acoustic analogy, are typically conducted in open-water conditions, which do not correspond to a realistic environment. The Full Acoustic Analogy, which couples a propagation model based on the solution of the acoustic wave equation to the hybrid approach, enables the propagation of the noise generated by a marine propeller in a confined heterogeneous domain. The near-field scattering characteristics of a simplified hull positioned in front of a ship's propeller are analyzed in shallow and deep water, in the presence of the free surface, and compared to the open water case. The analysis determines the directivity of the propeller noise and how this may affect how the noise propagates in the marine environment.

This paper discusses the acoustic mitigation properties of an air-water mixture excited by a monopole source. The numerical study reproduces a flat plate immersed in water and covered by an air film, acting as a sound barrier. This configuration mimics a mitigation device potentially in use for ship noise reduction, considering the flat plate as archetypal of a portion of the ship hull that works as a non-negligible scattering surface. The film, in this case, may also be used as an isolator with respect to the noise produced by the engines operating within the hull and propagating in the water. The study uses a homogeneous mixture model to reproduce the fluid dynamic field of air injected into the water. Once the air-water mixture is fully developed, the density and speed of sound distributions are extrapolated and used as input parameters for the acoustic propagation model. The monopole source exits the mixture layer, and the attenuation properties are assessed by recording the time signal on a probe positioned on the reflecting wall. The results show the difference in the transmission of acoustic pressure considering different frequencies and distributions of the mixture. These findings have significant practical implications, as they demonstrate how the air film can effectively attenuate the signal, with the mitigation effectiveness varying with the source's frequency and the distribution of the mixture of air and water in space.

In this paper, we focus on methodologies to inject a noise source in a numerical model of noise propagation in confined domains. This is a problem of primary importance when dealing with propagation of fluid-dynamic induced noise in confined basins, like ships at sea or wind farms. We first assess the performance of the literature hard source (HS) and transparent source methods; successively, we propose a novel method named the non-reflective HS (NRHS) method. It takes advantage of the linearity of the equation governing the propagation of acoustic waves in fluids and is based on the decomposition of the total signal in the sum of direct and reflected signals. It presents the advantages of the hard source method removing the main drawback consisting of the well-known problem of spurious reflections. To check the reliability of the HS vs the NRHS, a non-dimensional parameter (the encumbrance) has been defined, which gives a measure of the extension of the generation domain with respect to the propagation domain in relation to the principal wavelength of the acoustic waves and the presence of reflecting surfaces. The method herein developed gives accurate results in the case of a single-point source, where the literature methods behave well; more importantly, the NRHS method maintains its own accuracy when a noise source needs to be represented by a large number of points in space, situations of very practical importance where the standard methods may exhibit inaccuracy. This is a point of importance since the use of large generation domains is in favor of the accuracy of the source characterization, which can exhibit a complex directivity. The new method has been tested in a number of archetypal situations characterized by the presence of a reflecting plane, a scattering body close to the source location, and two sources placed side by side. In all cases, the method has shown its own superiority with respect to the standard HS method, still preserving the flexibility and simplicity of the latter.

The estimation of fluid dynamic noise generated by anthropogenic sources in realistic marine basins and on land is paramount for human safety and environmental protection. Classical acoustic analogies have limited capabilities when considering the natural variability and peculiarities of the acoustic propagation domain. The Full Acoustic Analogy (FAA), based on the combination of an acoustic analogy for source characterization and a propagation model for far-field transmission, allows the estimation of detailed soundmaps, practical when assessing the risk associated with exposure to fluid-dynamic noise, both impulsive and continuous. The verification of the methodology, consisting of comparing of the far-field acoustic pressure signal obtained with the FAA and with the Ffowcs-Williams and Hawkings equation (classical acoustic analogy for moving immersed bodies), is proven for the first time for the quadrupole non-linear terms. The latter may contribute significantly to the total noise field at small-to-medium distances from the source. In conjunction, the ability of the FAA method to predict the acoustic pressure distribution within the three-dimensional propagation domain is highlighted.

The homogeneous mixture model (HMM) is widely in use for simulation of cavitating flows. The mass transfer is typically ruled by simplified models whose efficiency is strictly dependent on the empirical choice of vaporization/condensation constants. In the present paper, we formulate a physically based mass-transfer model relying on the solution of the complete Rayleigh–Plesset (RP) equation. The latter can model the elasticity of the bubbles and non-linear interaction with the external pressure field. The model is tested in different configurations, also considering comparisons with the Schnerr–Sauer model (SSm) and the linearized version of the RP equation. The preliminary simplified tests show that the SS model responds statically to pressure variations and thus in not able to reproduce the actual dynamics of cavitation, under certain circumstances. On the other hand, the linearized RP model (RPl), although dynamically responsive to pressure variations, produces unrealistic small-amplitude bubble fluctuations, whereas the complete RP model (RPc) gives more realistic results. Tests on the performance of the SSm and RP models were carried out considering the turbulent flow in a convergent–divergent Venturi channel, already tested in numerical and experimental reference research. Here, we use the incompressible HMM. The study highlights various crucial aspects of the RPc model, emphasizing its own ability in replicating the shedding cycle as a three-dimensional, and non-stationary phenomenon. On the other hand, the SSm model results as a valid approximation for initial growth stages but fails to capture complex dynamics during the collapse phase. The results are consistent with recent literature findings, and refinements in grid resolution enhance accuracy in capturing the non-stationary sheet-to-cloud vapor dynamics. Neglecting compressibility may account for disparities between numerical and experimental outcomes, especially concerning shock waves generation and propagation. The RPc model emerges as a good candidate in reproducing bubble cloud dynamics and, in the next future, can be implemented in compressible HMM.

In the present work, we develop a new methodology to investigate the propagation of acoustic noise originating from a naval propeller, in a bounded marine environment. The propagation in a realistic environment is achieved by coupling the Ffowcs-Williams and Hawkings (FW-H) equation with the acoustic wave equation, overcoming some intrinsic limitations of the FW-H equation. First, the FW-H equation applied to the hydrodynamics field obtained from Large Eddy Simulation, accurately characterizes the propeller source in the acoustic near-field. Then, the propagation in the acoustic far-field is evaluated in an arbitrary domain by solving the acoustic wave equation. After validating the new proposed methodology, we investigate the propagation of the linear part of the noise generated by a naval propeller within a canal. The results show complex interaction between the noise source and the environment: the decay rate of the acoustic energy is strictly related to the distance of the source from the boundaries of the canal; local maxima and minima of the acoustic energy are observed resulting from the superposition of direct and reflected waves; the water–air interface introduces a peculiar asymmetry of the acoustic field associated with the interaction between the acoustic waves.

The present paper contains the results of the numerical analysis of the interaction between a Newtonian incompressible turbulent flow and a linear elastic slender body, together with the influence of the fluid–structure interaction (FSI) on the noise generation and propagation. The purpose is to evaluate the differences in term of acoustic pressure between the case where the solid body is rigid (infinite stiffness) and the case where it is elastic (finite stiffness). A partitioned and implicit algorithm with the arbitrary Lagrangian–Eulerian method (ALE) is used for the interaction between the fluid and solid. For the evaluation of the turbulent fluid motion, we use a large eddy simulation (LES) with the Smagorinsky subgrid scale model. The equation for the solid is solved through the Lagrangian description of the momentum equation and the second Piola–Kirchoff stress tensor. In addition, the acoustic analogy of Lighthill is used to characterize the acoustic source (the slender body) by directly using the fluid dynamic fields. In particular, we use the Ffowcs Williams and Hawkings (FW-H) equation for the evaluation of the acoustic pressure in the fluid medium. As a first numerical experiment, we analyze a square cylinder immersed in a turbulent flow characterized by two different values of stiffness: one infinite (rigid case) and one finite (elastic case). In the latter case, the body stiffness and mean flow velocity are such that they induce the lock-in phenomenon. Finally, we evaluate the differences in terms of acoustic pressure between the two different cases.

In the present work we perform the numerical characterization of the hydrodynamic and the hydroacoustic field of a notional submarine geometry (the BB2 submarine). Starting from a model-scale CFD simulation, the full scale acoustic signature of the submarine is derived. We use large eddy simulation with a wall-layer model and perform laboratory-scale numerical experiments at a value of Reynolds number equal to 1.2×106. The conditions are those of a wind-tunnel test. The study is carried out focusing on the submarine in its own basic configuration without propeller to highlight the acoustic properties of the hull by itself and to replicate the silent advancing running (where all the non-essential source of noise are shut down and the speed is minimum to minimize the propeller noise). In this configuration, the wake is the main source of noise. The computational hydroacoustic analysis is based on the Ffowcs-Williams and Hawkings equation, here considered in advective form, which is the most suitable form for wind-tunnel-like problems. The results show that the acoustic spectrum is broadband in the far field and the SPL evaluated in the near field contains the signature of coherent structures associated to the presence of the sail and appendages.

The need to understand how complex acoustic sources propagate noise in a realistic environment is of growing interest. In this work, we propose a numerical model for the simulation of noise generated by sources with directivity and propagating in ocean waveguides. The numerical model solves the wave equation for the acoustic pressure in the physical space using a second-order accurate finite difference method (FDTD). The source is implemented using an improved form of the hard-source method, which implicitly takes into consideration the reflection of acoustic waves associated to the presence of the ocean free surface, through the use of the method of images. This novel method is shown to improve the results with respect to the standard hard source implementation. We first validate the numerical method considering both analytical solutions and benchmark cases for the case of a monopole and then explore the acoustic energy patterns developed in the case of dipole and quadrupole sources. Specifically, the algorithm and the implementation of complex sources are evaluated first in a semi-infinite fluid layer and then considering two classical waveguides: the Ideal one and the Pekeris one. The comparison with analytical results shows the numerical method's accuracy and that incorporating free surface effects in the hard source implementation improves results. In addition, the study shows that the acoustic response in the near field, of the order of few kilometers from the source, is strongly influenced by the source's directivity and orientation relative to the free surface. The results of this paper have implications for future research aimed at characterizing and quantifying ship propeller noise in realistic waveguides. Indeed, this preliminary work is necessary to proceed to more complex numerical experiments, such as considering a real propeller signal as a source or considering stratification of the medium or propagation in confined domains such as experimental tanks.

The acoustic analogy is adopted to characterise the signature of a seven-bladed submarine propeller, relying on a high-fidelity large-eddy simulation, performed on a computational grid consisting of 840 million points. Results demonstrate that the nonlinear terms of the Ffowcs-Williams and Hawkings equation quickly become dominant moving away from the propeller along the direction of its wake development. While the linear terms experience a decay moving downstream, the nonlinear terms grow in the near wake, as a result of the development of wake instability. In particular, this growth affects frequencies lower than the blade frequency. Therefore, the acoustic signature of the propeller is mainly tonal in the near field only, due to the thickness and loading components of noise from the surface of the propeller and the periodic perturbation caused by its tip vortices. They develop instability at a faster rate, compared with the hub vortex, triggering the process of energy cascade towards higher frequencies and contributing in this way to broadband noise.

The present paper contains preliminary results obtained from coupling the Ffowcs-Williams and Hawkings (FW-H) acoustic model with the wave equation solved in the time domain using finite differences.The purpose is to study the propagation of complex noise sources in realistic water basins.The acoustic analogy is used to accurately characterize the source (an isolated marine propeller), whose propagation is then evaluated in an arbitrary domain through the wave equation.Differently from the FW-H equation, which assumes that the pressure disturbance propagates in an open, quiescent, and homogeneous medium, the general wave equation can deal with reflection on the boundaries of the basin and density variations along the water column.As a first experiment, we analyze the propeller signal propagating in a simplified canal, and we show the differences with respect to the open-sea case in terms of sound pressure level.

We present results of numerical simulations of a stratified reservoir with a three-layer stratification, subject to an oscillating surface shear stress. We investigate the effect of sloped endwalls on mixing and internal wave adjustment to forcing within the basin, for three different periods of forcing. The simulations are carried out at a laboratory scale, using large-eddy simulation. We solve the three-dimensional Navier–Stokes equations under the Boussinesq approximation using a second-order-accurate finite-volume solver. The model was validated by reproducing experimental results for the response of a reservoir to surface shear stress and resonant frequencies of internal waves. We find interesting combinations of wave modes and mixing under variation of the forcing frequencies and of the inclination of the endwalls. When the frequency of the forcing is close to the fundamental mode-one wave frequency, a resonant internal seiche occurs and the response is characterized by the first vertical mode. For forcing periods twice and three times the fundamental period, the dominant response is in terms of the second vertical mode. Adjustment to forcing via the second vertical mode is accompanied by the cancellation of the fundamental wave and energy transfer to higher-frequency waves. The study shows that the slope of the endwalls dramatically affects the location of mixing, which has a feedback on the wave field by promoting the generation of higher vertical modes.

Cavitation is often simulated using a mixture model, which considers the transport of an active scalar, namely the vapor fraction αv. Source and sink terms of the transport equation of αv, namely vaporization and condensation terms, rule the dynamics of the cavity and are described through different models. These models contain empirical coefficients generally calibrated through optimization processes. The purpose of this paper is to propose an analytical approach for the calculation of the coefficients, based on the time scales of vaporization and condensation processes. Four different models are compared considering as a test-case a two-dimensional flow around a cylinder. Some relevant quantities are analyzed both for standard value of coefficients, as found in the literature, and the coefficients calculated through the analytical approach. The study shows that the analytical computation of the coefficients of the model substantially improve the results, and the models considered give similar results, both in terms of cavitation regime and mean vapor fraction produced.

We perform a scaling analysis of the terms composing the Ffowcs-Williams and Hawkings (FWH) equation, which rules the propagation of noise generated by a rigid body in motion. Our analysis extends the seminal work of Lighthill (Proc. R. Soc. Lond.A, vol. 211, 1952, pp. 564–587) and the dimensional analysis of classical sources (monopole, dipole and quadrupole) considering all the FWH integral terms. Scaling properties are analysed in light of perfect/imperfect similarity when laboratory-scale data are used for full-scale predictions. As a test case we consider a hydrodynamic example, namely a laboratory-scale ship propeller. The data, obtained numerically in a previous study, were post-processed according to the scaling analysis presented herein. We properly scale the speed of sound to obtain perfect similarity and quantify the error with respect to the imperfect scaling. Imperfect similarity introduces errors in the acoustic response related both to the linear terms and to the nonlinear terms, the latter of great importance when the wake is characterized by robust and organized vorticity. Successively, we analyse the effect of a free surface, often present in hydrodynamic applications. We apply the method of images to the FWH equation. The free surface may generate a frequency-dependent constructive/destructive interference. The analysis of an archetypal acoustic field (monopole) provides robust explanation of these interference effects. Finally, we find that imperfect similarity and the absence of a free surface may introduce errors when model-scale data are used to obtain the full-scale acoustic pressure. The error is small for microphones placed in the near field and becomes relevant in the far field because of the nonlinear terms.