**1. Introduction**

At the present time, wind energy is a renewable, sustainable source of power, and one of the most rapidly developing electricity production fields worldwide [1]. Based on the European Union's (EU's) report of the gross electricity consumption from wind power, a more than threefold increase between 2004 and 2014 took place, and to fulfill EU climate goals for 2030 it can be expected that this trend will continue in the future [2]. Wind energy increase will mean that many more wind turbines will be installed, inevitably closer to more people and their residences. Wind turbine noise is one of the major hindrances for the widespread use of wind energy. Surveys [3] show that noise from a wind turbine is annoying to people and that is perceived to be more annoying than other forms of industrial noise at

the same level. To accommodate the expected increase in the number of installed wind farms and to reduce public disquiet, there is need to reduce wind turbines' noise.

In Western Europe alone, an estimated 1.0–1.6 million healthy life years are lost each year because of environmental noise based on the report of the World Health Organization [4]. The wind turbine noise is playing a more and more important role in environmental noise as wind turbines are increasingly installed worldwide [5]. The sleep disturbance of the wind turbine noise is the greatest influence to long-term health [2]. Wind turbine noise has aerodynamic and mechanical origins. For a modern, large-scale wind turbine, aerodynamic noise from the blades is generally considered to be the dominant noise source, in which the turbulent flow around an airfoil that induces aerodynamic noise typically has a high Reynolds number flow at a low Mach number [6]. Empirical or semi-empirical models have been developed to predict the overall noise emitted by a wind turbine. However current empirical or semi-empirical models do not contain an accurate description of the wind turbine blade geometry and its relations to emitted noise. Furthermore, wind turbine blade manufacturers are interested in small modifications of given blade geometries and their exact influences on the aerodynamic noise. It is, therefore, necessary to develop techniques that take the correct blade geometry into account to predict the aerodynamic noise. As a result, computational fluid dynamics (CFD) and computational aeroacoustics (CAA) have become useful tools to numerically simulate the complex flow and aerodynamic noise for engineering applications. Various numerical investigations of aerodynamic wind turbine noise using CFD and CAA have been conducted [7–10]. Since the pioneering paper of Lighthill [11,12], computational techniques to deal with flow-induced noise have been classified into two categories: direct methods [13] and indirect methods [14–17]. In a direct method, sound sources and sound propagations are obtained as a result of the numerical simulation based on the compressible Navier–Stokes equations. The direct method can to reproduce the sound generation mechanism exactly and is suitable when a strong interaction between the flow and acoustic fields exists. This means that the order of magnitude of the pressure fluctuation of the flow field closes to the sound pressure; namely, the case of high Mach number flows. However, for the objective of the present research, a large-scale wind turbine blade, use of the direct method is inappropriate due to the low Mach number. Furthermore, it is also very difficult for practical applications to apply the direct method in the industry due to the high computational cost.

On the other hand, Lighthill–Curle acoustic analogy [18] has been widely used for predicting a far-field sound in engineering practice. In this sort of indirect method, unsteady flows are simulated by the incompressible scheme, usually with Reynolds averaged numerical simulation (RANS), large eddy simulation (LES), or LES/RANS hybrid method. Then, the acoustic field is predicted based on the theoretically estimated sound source; e.g., Lighthill–Curle acoustic analogy [18] and Powell [19]. Thus, there is no mutual interaction between the flow field and the sound field; that is, it is assumed that the noise is determined by the information of the flow field, and the sound generated does not influence the flow field. This assumption is valid in low Mach number flow since the sound pressure is small compared to the pressure fluctuation of the flow field. Actually, in the case that the effect of feedback from the sound field to the flow field is not important, this method has been widely used in industrial applications, since the far-field sound is reproduced successfully.

For estimation of the acoustic field around objects in fluid flows, the Lighthill–Curle acoustic analogy [18] is most widely used; see Amiet [20] and Wang [21]. In this method, a pressure fluctuation of the object surface obtained from the incompressible flow field is used as a sound source, and then a far-field sound is estimated separately. This method, however, makes it difficult to understand the relationship between the behavior of the sound source in the flows field and the radiated sound. As a result, this method can not guide engineers and manufacturers to optimize the large-scale wind turbine blade for the reduction of the aerodynamic noise. On the other hand, the theory of vortex sound proposed by Powell [19] and then extended by Howe [22] is also widely used: take for example, Mohring [23], Takaishi et al. [24], and Ewert et al. [25]. In this method, the sound source is estimated from the behavior of vortices, and the far-field sound pressure is computed by using the compact

green's function [22]. Although the prediction accuracy of the far-field sound is affected by the range of volume integral regions, this method is able to treat the sound source that is distributed to the space, qualitatively. The behavior of vortex might be a true sound source so that this method is probably suitable for predicting the aerodynamic noise generated from large-scale wind turbine blades and then guiding manufacturers in optimizing the blade geometry. However, there is an important assumption for this method; i.e., the sound source is derived under the assumption of incompressible flows. The compressibility effect that appears even in low Mach number, weakly compressible turbulent flows is, therefore, not taken into account. However, even a small fluctuation of density affects the flow filed and the flow-induced sound field around the object, such as that from an airfoil. Hutcheson et al. [26,27] showed that the peak frequency in the profile of sound pressure level is different from the change of Mach number even in the low Mach number range. Since this characteristic is not reproduced by the classical indirect method mentioned above, this sort of indirect method becomes less accurate in low Mach number turbulent flows, especially with increasing Mach numbers. In order to predict the acoustic field accurately for applications in low Mach number turbulent flow, such as for large-scale wind turbine, it is necessary to improve the acoustic model of considering the compressibility effect even in low Mach number flows.

The purpose of this study was to seek for a more accurate acoustic model for large-scale wind turbine blade manufacturers to optimize the blade geometry for aerodynamic noise reduction. To attain that end, an new acoustic model was required, one that not only understood what kind of fluctuations of the flow field cause the aerodynamic noise but also accounted for the small fluctuation of density in the noise source (namely, compressibility effect). In the derivation of the new acoustic theory, we rearranged the continuity and Navier–Stokes equations as a wave equation with a lump of source terms including the material derivative and square of the velocity divergence. These source terms are used for sound source detection and the estimation of the far-field sound.

In this study, our acoustic model was applied to low Mach number, weakly compressible turbulent flows around NACA0012 airfoil. For the computation of flow fields and considering the weak compressibility in flow fields, an LES with the dynamic Smagorinsky model [28,29] and the cubic interpolated pseudo particle (CIP)-combined unified numerical procedure method [30] were conducted. Our LES technique was verified by comparison its results with the experimental results performed by Miyazawa et al. [31]. The reproduced turbulent flow around NACA0012 airfoil was in good agreement with the experimental data. For the estimation of acoustic fields, different acoustic models were performed using our LES database. The distribution of the sources obtained by our acoustic model was compared with classical sound source models, such as Lighthill [11] and Powell [19], in the case of very low fluctuation of density. Then, the sound pressure level (SPL) predicted based on the above-mentioned LES and our newly derived acoustic model was compared with the SPLs obtained by the Lighthill–Curle's equation [18] using our LES database and the experimental data by Miyazawa et al. [31]. Finally, our acoustic source model was verified to treat the influence of Mach numbers on the acoustic field, and the influence of the increase of Mach number on the acoustic field was investigated.

#### **2. LES of Low Mach Number Turbulent Flows around NACA0012 Airfoil**
