Turbulence-interaction noise arises from unsteady surface pressure fluctuations caused by the interaction of incoming turbulence with an aerofoil or rotor. This type of flow induced noise is relevant across a range of diverse applications. Consequently, multiple physical mechanisms must be examined and analytically modelled for use in low-fidelity prediction methods. Such models are particularly valuable during the design and optimisation phases due to their low computational cost. However, their accuracy is critically dependent on the fidelity of the underlying physical assumptions. One of the most widely used and robust approaches, Amiet’s model, has been shown to produce inaccurate results for thick blades, as it was originally developed for flat plates. This limitation is likely due to the distortion of the incoming turbulent structures and the alteration of the noise radiation caused by aerodynamic surfaces of non-negligible thickness. Comparable limitations affect its application to rotors, where an accurate representation of the inflow conditions is essential to ensure the reliability of the prediction. The present study seeks to address the following three research questions:
1. How does turbulence distortion affect noise generation and prediction?
2. How can turbulence-distortion effects be included in Amiet’s model?
3. How does this apply to rotors?

This study examines the role of turbulence distortion in predicting inflow turbulence (IT) noise generation from large wind turbines via Amiet's theory. Two subsequent distortion mechanisms are investigated: (i) the streamtube expansion in the rotor induction zone and (ii) the interaction with the surface of thick-blade profiles. Large-eddy simulations reveal that the turbulence spectra, which reflect distortion effects, remain largely unaffected by rotor induction within the frequency range relevant for noise generation. As for the other mechanism, the distortion of the turbulence approaching a blade leading edge is modeled with a simplified closed-form solution of Goldstein's rapid distortion theory. This model, based on vorticity deflection, is extended here beyond the high-frequency approximation and integrated into an analytical Amiet-based IT noise tool. Applications to representative test cases show that while distortion effects are minimal for current turbine sizes, they become relevant for future configurations featuring larger rotor sizes and thicker airfoils. The developed model reveals that IT noise levels do not necessarily scale with rotor size but are shaped by spectral changes induced by the blade geometry, operational parameters, and inflow conditions. This model offers a physically consistent, computationally efficient framework for the aeroacoustic assessment of next-generation wind turbine design.

When applied to aerofoils with non-negligible thickness, Amiet’s theory for turbulence-interaction noise prediction does not account for the alterations in the velocity field and acoustic response induced by the surface, resulting in an overestimation of the radiated noise. This study proposes a semi-analytical method that models turbulence distortion in the immediate vicinity of the surface starting from upstream flow conditions and considers the resulting effects on the acoustic response of the aerofoil. The distorted spectrum of the upwash velocity component is calculated using the asymptotic results of the rapid distortion theory (RDT) for very large- and small-scale turbulence, overcoming the need to define a representative location where turbulence characteristics are sampled. This distorted spectrum is characterised by an increased energy content that is encompassed in the model by scaling the analytical flat-plate formulation of the aeroacoustic transfer function. The proposed approach relies on defining the aerofoil geometrical feature that affects distortion mechanisms, required to extend the RDT results to such geometries. This parameter is identified as the path travelled by the turbulent eddies from the stagnation point to the position of maximum surface-pressure fluctuations, which is, in turn, related to flow acceleration and leading-edge sharpness. The accuracy of this methodology in enhancing noise prediction is demonstrated using numerical and experimental data of grid-generated turbulence interacting with different aerofoils.

Turbulence-ingestion noise, caused by the interaction between incoming turbulence and rotors, is currently a key area of research in the rapidly expanding field of Urban Air Mobility. This is due to the highly turbulent flows characterizing urban environments, where acoustic optimization is especially critical, and to the complexity and diversity of the physical mechanisms involved in noise generation. This makes the analytical modeling for low-fidelity prediction – favored over computationally expensive numerical simulations in the optimization phase — particularly challenging. This study proposes two key modifications to Amiet’s model aimed at enhancing the assessment of inflow-conditions effects on noise generation and prediction. The first allows strip theory to be incorporated to account for radially-varying inflow while preserving the modeling of blade-blade correlation. The second enables the replacement of the original three-dimensional turbulence input, particularly challenging to measure both experimentally and numerically, with a one-dimensional one. This allows probe measurements to be directly used as input to assess the effects of inflow conditions. Additionally, it paves the way for the extension of turbulence-distortion models from rectilinear motion to rotating systems, potentially enhancing prediction accuracy. The approach is validated against experimental acoustic data obtained for a two-bladed propeller under various operating conditions.

Ingested turbulence affects propeller noise at frequencies above the 2nd Blade Passing Frequency. The extension of the Amiet model to rotating structures is a useful tool to predict this phenomenon. However, comparison with the experimental results reveal discrepancies between predicted and measured acoustic spectra. A likely explanation for this mismatch lies in turbulence distortion.This paper investigates the effects of the propeller-induced flow field on incoming turbulence to obtain a comprehensive description of the flow physics and enhance, in future studies, Amiet’s prediction model.Lattice Boltzmann Very Large Eddy Simulations of a reference propeller operating at low-Reynolds number and subjected to turbulent inflow are performed. The spatial and temporal evolution of isotropic grid-generated turbulence approaching the propeller plane is characterized . The analysis shows that the leading edge interacts with anisotropic turbulence. This is due to the rotational flow induced by the propeller, streamtube contraction, and leading edge distortion.In addition, the effect of turbulence on the laminar separation bubble, conventionally present in flow at low Reynolds number, whose dynamics affects the acoustics at high frequencies, is analyzed. Acoustic spectra, obtained through the Ffowcs-Williams and Hawkings analogy applied to the propeller surface, are then linked to the aerodynamic sources.

Amiet's model for turbulence-ingestion noise prediction for rotors is adapted to incorporate pointwise velocity measurements as input. This is accomplished by using an inverse strip theory approach and transforming the three-dimensional turbulence spectrum, which models inflow conditions, into a one-dimensional term. This latter modification enhances the low-fidelity prediction tool in two key ways. First, it enables its application in cases where turbulence modeling is unavailable, or detailed inflow characterization is impractical. In this way, for example, hot-wire anemometry measurements of the incoming turbulence can be used to compute the acoustic prediction. Second, since the conversion of the turbulence term entails introducing two new functions describing spanwise and axial turbulence correlations; this approach establishes a framework for Amiet's theory in which the contributions to turbulence alteration and noise scattering are separated and represented individually. This “modular” structure enables independent analysis and modeling of these contributions, facilitating the application of Amiet's model to complex flow configurations and rotor geometries. The proposed methodology is successfully validated through experimental measurements of a simplified axial-flight turbulence-interaction setup, where a two-bladed propeller interacts with grid-generated turbulence at three different advance ratios.

The distortion of turbulence interacting with thick airfoils is analyzed with scale-resolved numerical simulations to elucidate its impact on leading-edge-noise generation and prediction. The effect of the leading-edge geometry is investigated by considering two airfoils with different leading-edge radii subjected to grid-generated turbulence. The velocity field is shown to be altered near the stagnation point, in a region whose extension does not depend on the leading-edge radius. Here, the deformation of large-scale turbulence causes the amplitude of the upwash velocity fluctuations to increase in the low-frequency range of the spectrum because of the blockage exerted by the surface. Conversely, the distortion of small-scale structures leads to an exponential decay of the spectrum at high frequencies due to the alteration of the vorticity field. The prevalence of a distortion mechanism over the other is found to depend on the size of the turbulent structures with respect to the curvilinear length from the stagnation point to the location where surface-pressure fluctuations and pressure gradient peak. This occurs at the curvilinear abscissa where the curvature changes the most. The same high-frequency exponential-decay slope observed for the upwash velocity is retrieved for surface-pressure spectra in the leading-edge region, suggesting that the airfoil unsteady response is induced by the distorted velocity field. This physical mechanism can be accounted for in Amiet's model by using a distorted turbulence spectrum as input and accounting for the increased amplitude of the distorted gust in the aeroacoustic transfer function, retrieving an accurate noise prediction for both airfoils.

This study analyzes the alteration undergone by turbulent eddies as they approach a propeller operating at low Reynolds number, with the purpose of investigating the resulting effects on the noise emitted by the propeller. The two mechanisms affecting turbulence distortion, the streamtube contraction and the interaction between the turbulent structures and the blade, have been investigated experimentally. The set-up consists of a propeller with a diameter of 30 cm operating at a 75% chord-based Reynolds number of 10.8 × 104 interacting with the turbulence produced by a rectangular grid. The flow behavior has been studied by particle image velocimetry (PIV) and hot-wire anemometry (HWA), while a microphone arc was installed for the acoustic analysis. The results reveal that the interaction between incoming turbulence and the propeller plays a dominant role in the alteration of turbulence with respect to the streamtube contraction. This is due to the relatively low contraction ratio of the propeller at this regime, equal, in this case, to C.R.=1.3. Turbulence characteristics are used as input for two different analytical noise-prediction models, both based on Amiet’s theory for turbulence-impingement noise. The first implements the original formulation of Amiet for propeller noise, which requires a position along the blade to be specified to define all the inputs. The second has been developed in the present work to account for the variations of the blade geometry and turbulence conditions in the radial direction. The comparison between the noise predictions and the experimental measurements shows that a better agreement can be obtained with the second model. This reveals that noise generation is strongly dependent on the variation of the flow conditions and propeller geometry along the radial direction, confirming that the description of these characteristics can enhance the accuracy of low-fidelity noise-prediction methods.

A physical analysis has been conducted to assess the effects of turbulence distortion on leading-edge noise generation and low-fidelity modeling in the framework of Amiet's theory. This model retrieves the power spectral density (PSD) of far-field noise using as input the upwash velocity spectrum of incoming turbulent flow and an aeroacoustic transfer function modeling the aerodynamic and acoustic response of the airfoil to the perturbation. The study has been carried out by investigating the interaction of grid-generated turbulence with a NACA 0012 and a NACA 0012-103, featuring the same thickness but different leading-edge shape. The alteration of the velocity field has been shown to occur in agreement with the analytical findings of the rapid distortion theory (RDT), identifying in particular an exponential decay for the upwash-velocity component spectrum at high frequencies. The same decay is observed for the surface-pressure spectra close to the leading edge, suggesting that sound is generated by a pressure distribution induced by the altered velocity field and hence proving that turbulence-distortion effects should be included to enhance the noise-prediction accuracy of low-fidelity models. This has been further demonstrated by using as input in Amiet's model the altered upwash velocity spectrum sampled in the immediate vicinity of the leading edge: an improved prediction of the high-frequency decay is yielded, but the evident overestimation of the noise levels with respect to the results provided by the Ffowcs-Williams and Hawkings' (FWH) analogy indicates the necessity of correcting the aeroacoustic transfer function as well.

The present study assesses the ability to numerically predict turbulence-interaction noise of a NACA0012 airfoil with grid-generated turbulence by utilizing the Lattice Boltzmann solver PowerFLOW. Both the near-field flow characteristics and far field noise are bench-marked against an existing experimental study. The grid was chosen to match that from the experiment to provide evidence that the present numerical approach in physically placing a grid upstream of the airfoil can reproduce the turbulence characteristics observed from the benchmark experiment and thus accurately capture the turbulence-interaction noise generated. The comparison of the results show that the turbulence statistics, including turbulence intensity, integral length scales and anisotropy are highly consistent with the experiment. Moreover, far field acoustics of the turbulence interaction as well as the near-field flow properties near the leading-edge and the unsteady wall pressure fluctuations of the airfoil are also analyzed and the results agreed well with the experimental measurements. The present study confirms that the grid-generated approach is suitable for numerical investigation of turbulence-interaction noise and its potential mitigation strategies.

The analytical model for leading-edge noise prediction formulated by Amiet, developed for a flat plate, relates the far-field acoustic pressure to the upstream inflow conditions, modeled by canonical turbulence spectra. The inaccurate results provided by this low-fidelity method when applied to thick airfoils has been attributed to the distortion experienced by turbulent structures when approaching the airfoil, not modeled in the original formulation of Amiet. The first attempts to account for the effects of this physical mechanism consisted of modifying the term representing the incoming turbulence by means of the analytical results of the rapid distortion theory, obtaining a promising improvement of the noise-prediction accuracy. This paper aims to set up the physical framework to investigate the relation between turbulence distortion and noise-generation mechanisms with the purpose of enhancing inflow-turbulence noise modeling. A numerical database obtained for a rod-airfoil configuration has been chosen to allow the analysis of the vortex dynamics when interacting with a body. The analysis of the velocity field near the leading edge has highlighted that the extension of the region where turbulence distortion occurs depends on the size of the incoming turbulence structures. Furthermore, surface pressure fluctuations have been observed to peak at the same position along the airfoil where the pressure gradient in the streamwise direction is maximum. A novel approach has been proposed to account for turbulence distortion in Amiet's model by using as input the turbulence spectrum directly sampled in this position. A satisfactory agreement with the prediction provided by the solid formulation of the Ffowcs-Williams and Hawkings analogy has been obtained.