Acoustic investigation of rod vortex generators on a wind turbine rotor

c

= segment chord [m];

 c_f

= friction coefficient [-];

 c₀

= speed of sound [m/s];

 c_ref

= reference chord [m];

 c_T

= thrust coefficient [-];

d

= segment span for noise prediction [m];

dS

= elemental area [m²];

f

= frequency [Hz];

 f_s

= moving surface [-];

H

= boundary layer shape factor [-];

L

= turbulent integral length scale [m];

M

= Mach number [-];

 M_i

= unit Mach vector components [-];

 M_r

= Mach number in the direction of the observer [-];

 M_y, M_z

= Rotational matrices [-];

 n_i

= unit normal vector components [-];

p

= pressure [Pa];

 p_L

= loading noise [Pa];

 p_T

= thickness noise [Pa];

r

= distance between the source and the observer [m];

$r^i$

unit radiation vector;

 R_a

= radial location of the mid of each segment [m];

 R_0,WT

= observer position on the fixed reference frame of the wind turbine [(X_WT, Y_WT,Z_WT) [m];

 R_0,a

= observer position on the Amiet’s reference frame [(x_a, y_a, z_a)] [m];

 S_pp|seg

= Power spectral density (PSD) of the total noise produced by each segment in a specific angular position [Pa²/Hz];

 S_pp|LE

= PSD of the leading-edge noise produced by each segment in a specific angular position [Pa²/Hz];

 S_pp|blade

= PSD of the total noise produced by the blade in a specific angular position [Pa²/Hz];

 S_pp|WT

= PSD of the total noise produced by the wind turbine over one rotation [Pa²/Hz];

 S_pp|TE

= PSD of the trailing-edge noise produced by each segment in a specific angular position [Pa²/Hz];

t

= observer time [s];

 Tu_∞

= turbulence intensity (in the Z_WT direction) [m/s];

 U_t

= apparent tangential velocity of the segment (in the x_a direction) [m/s];

 U_∞

= inflow velocity (in the Z_WT direction) [m/s];

 v_n

= normal velocity [m/s];

 X_WT, Y_WT, Z_WT

= axes in the fixed reference frame of the wind turbine, Z_WT in downwind direction, Y_WT in hub direction [m];

x

= observer space [m];

 x_a, y_a, z_a

= axes in the Amiet’s reference frame, x_a in the chordwise direction, y_a in the spanwise direction [m];

 ω

= angular velocity [rad/s];

 ω_e

= emitted angular velocity [rad/s];

 Ψ

= azimuthal angle [rad];

 θ

= pitch angle of the wind turbine [rad];

 ϕ

= twist angle of each segment [rad];

 δ

= boundary layer thickness [m];

 δ^*

= boundary layer displacement thickness [m];

 τ

= emission time [s];

 θ^*

= boundary layer momentum thickness [m];

 u_τ

= friction velocity [-];

 Ω

= rotational speed [rad/seg]; and

 ρ

= air density [= 1.221 kg/m³].

The noise generated by wind turbines is a major concern for people residing near wind farms, often leading to opposition to widespread implementation of wind energy (Davies et al., 2015). This reluctance presents a significant challenge for the wind energy sector, while it aims to become the leading alternative to fossil fuels, amidst other renewable energy sources. To address this challenge, an increase in research efforts to reduce wind turbine noise thereby minimizing its environmental and psychological impact on communities has been undertaken. However, implementing effective noise mitigation strategies poses several challenges. The fundamental challenge is that the underlying physics of sound generation and propagation are not understood completely. Next, reducing noise without compromising turbine performance is complex. Additionally, factors such as feasibility, increased weight and maintenance demands act as practical constraints that further complicate the balance between efficient energy production and noise reduction.

Extensive research has been conducted on the flow and acoustic behavior of wind turbines operating under optimal design conditions (Oerlemans et al., 2007; Bowdler et al., 2012; Delbari et al., 2020). The rotor blades though, encounter non-uniform inflow conditions and significant variations in inflow angles, which result in adverse pressure gradients (Buck, 2018). This can lead to turbulent boundary layer separation, that causes aerodynamic inefficiencies, increased stall and higher fatigue loads (De Tavernier et al., 2021; Gad-el-Hak and Bushnell, 1991), consequently, diminishing wind turbine performance and increasing per unit energy costs. To address these challenges, different flow control devices have been explored including vane-type Vortex Generators (VGs) (Barzoki et al., 2021; Xu et al., 2018; Yu et al., 2023). A promising VG type namely the Rod Vortex Generators (RVGs), has been investigated by Tejero Embuena et al. (2018) for helicopter rotors, for wind turbines by Suresh et al. (2024). RVGs delay turbulent flow separation by generating streamwise vortices along the blade surface (Tiwari et al., 2023). Unlike traditional vane-type VGs, RVGs offer a distinct advantage, as they can be activated selectively during off-design conditions through micro-electro-mechanical systems technology.

Suarez et al. (2018a) have evaluated RVGs for National Renewable Energy Laboratory (NREL) Phase VI wind turbine blades, demonstrating their potential to mitigate turbulent boundary layer separation and enhance aerodynamic efficiency. The acoustic implications of incorporating RVGs on wind turbine rotor blades remain unexplored. This paper presents an original investigation into the acoustic effects of RVG implementation on the NREL wind turbine rotor, comparing its performance with and without these flow control devices.

With the reduction of separation, the RVGs improve aerodynamic performance. This is expected to reduce separation noise. However, they generate streamwise vortices that induce increased pressure fluctuations, impacting loading noise. Studies on the interplay between these two competing noise mechanisms are limited. The current work aims to provide more details regarding this. Both rotational noise and broadband noise analysis are conducted using two different approaches – Ffowcs-Williams Hawkings (FW–H) acoustic analogy (Ffowcs-Williams and Hawkings, 1969) and Amiet’s theory (Amiet, 1976) for the NREL rotor with RVGs. Steady pressure distribution obtained from a previous study (Suarez et al., 2018a) is used as input for both (FW–H and Amiet) models.

The FW-H solver can predict only rotational noise (harmonic), but not broadband noise. For the wind turbine application, the steady pressure data is the major factor that contributes to the rotational noise. The semi-empirical models such as Amiet’s theory – for attached boundary layer (Corcos (1964) and Lee et al. (2005) models) and separated boundary layer (Bertagnolio et al. (2017) and Cotté et al. (2022) model) are used to predict trailing-edge noise. These theories allow us to model the wall pressure fluctuations based on the boundary layer characteristics obtained from the steady simulations and use them as input to predict broadband noise.

The numerical methodology used to obtain the steady pressure data for the reference rotor (rotor without RVGs) has been validated against experimental data by Suarez et al. (2018a). The validated model is then used for the turbine blade with RVGs, consisting of grid refinement in the rod regions. The validation of the FW-H solver that is used in this work has already been published by Suresh et al. (2022).

The effect of the stream-wise vortices generated by the rods on the different types of noise (thickness noise, loading noise, trailing-edge noise) and its components (near- and far-field) is studied. Results show that the RVGs do not significantly impact the rotational noise emission. They do increase the broadband noise emitted in the higher frequency range. They reduce flow separation through the streamwise vortices generated, increasing aerodynamic performance. However, this leads to increased pressure fluctuations thus shifting peak pressure signals toward higher frequencies. There is an increase of ∼2 dB at the off-plane microphone locations. This facilitates a better understanding of the noise source mechanisms, thus enabling better design and optimization of flow control devices to achieve the desired aerodynamic performance without any significant acoustic penalty.

Section 1 of the paper introduces the background and motivation behind this research work. The theoretical background and methodology are detailed in Sections 2 and 3. The impact of the RVGs on the steady rotational noise emitted by the NREL Phase VI rotor is presented in Section 4.A followed by the effect of the rods on the trailing edge separation noise in Section 4.B. The main findings and conclusions of this research undertaking are summarized in the last Section.

The rotational noise (thickness and loading noise) prediction is obtained from an in-house aeroacoustic code (Suresh et al., 2022) based on the famous FW–H acoustic analogy for moving bodies in subsonic motion. The aeroacoustic code is a post-processing tool based on the linear integral solution derived by Farassat (2007) in the time domain (retarded time approach). The acoustic pressure signal is a summation of the sound emitted by the elementary sources (monopole and dipole). Farassat (1996) shows that the flow non-linearities are neglected for rotating bodies in subsonic motion thus the Lighthill’s stress tensor T_ij (quadrupole) is not computed. Among the various available solutions, Farassat’s integral formulations (Farassat, 2007) are among the most widely applied, particularly those designed for subsonic motion described by equations (1) and (2), known as Formulation 1A:

where, p_T represents the thickness noise component of the total acoustic pressure, (x, t) is an observer/listener time-space coordinates, f_s is the moving surface (f_s = 0 represents the control surface of the moving rotor body such that ∇f = n, n is the unit normal vector, f_s > 0 represents outside the moving surface), ρ₀ is the ambient density, v_n is the normal velocity of the moving surface, r is the distance between the source and the observer (radiation vector), M_r is Mach number in the direction of the observer, $r^i$ is the unit radiation vector, M_i represents Mach vector components, τ is acoustic source (moving surface) emission time, dS is the elemental area, c₀ is the speed of sound, M is the Mach number. The dot above the variable indicates source time differentiation:

where, p_L represents the loading noise component of the total acoustic pressure, p is the local pressure distribution on the moving surface, cos θ is the local angle between the normal to the surface and radiation vector at emission time and n_i represents the components of the normal vector. The relative motion between the sources (blade) and the microphone is expressed by the term (1 – M_r) which is present in the denominator of both the thickness and loading noise terms. This term is known as the Doppler effect and it accounts for the relative motion of the source concerning the microphone. The necessary input to predict thickness noise is rotor body kinematics and for predicting loading noise is surface pressure distribution obtained from numerical flow simulations. More details regarding this are described in Section 3.A.

Broadband noise analysis is performed using Amiet’s theory, a widely adopted approach for predicting trailing-edge noise (Amiet, 1976; Christophe et al., 2009). Amiet’s framework enables the calculation of the far-field power spectral density of a flat plate of chord c and span d based on boundary layer characteristics (wall-pressure spectrum and spanwise correlation length). This theory is based on several key assumptions, including a flat plate geometry with negligible thickness, a stationary observer and a uniform free-stream condition along the span. Amiet (1976) derived the mathematical formulation for the power spectral density of the trailing-edge noise given by:

where $L$ is the aeroacoustic transfer function that accounts for the sub-critical and super-critical gusts and for the scattering and back-scattering propagation of trailing and leading-edges, modeled according to Roger and Moreau (2005), Φ_pp is the wall-pressure spectrum close to the trailing edge, l_y is the spanwise correlation length, σ² is the flow-corrected radial distance defined as $σ2=xa2+(1−Mt2)(ya2+za2)$⁠, where M_t is the tangential Mach number, x_a, y_a and z_a are the coordinates of the observer location in the Amiet’s reference, ω is the angular velocity and b is the semi chord.

The wall-pressure spectrum and spanwise correlation length are used as input for Amiet’s theory. Different models are used to model these parameters depending on the state of the boundary layer. Standard methods for turbulent boundary layers are adopted for the sections where the boundary layer is attached. Corcos (1964) defined the spanwise correlation length as:

where U_c is the convection velocity, assumed as 0.7U and b_c is the Corcos’ constant equal to 1.47 (Stalnov et al., 2016). Lee et al. (2005) proposed the wall-pressure spectrum known as the TNO-Blake model. The inputs for this model are estimated from the velocity profiles obtained from RANS simulations (described in section 3.A) at 97% of the airfoil chord.

For the separated boundary layer case, the semi-empirical model proposed by Bertagnolio et al. (2017) and presented by Cotté et al. (2022) is adopted to predict the wall-pressure spectrum. This model is validated against wind tunnel experiments for the flow separated at around 50% of the airfoil chord. The wall-pressure spectrum is calculated as:

where x_meas is the location for the calculation of ϕ_pp, i.e. x_meas = 0.97c, where c is the local chord of the section, x_sep is the location of the separation, L_x is the streamwise correlation length, defined as:

where R_eM is the Reynolds number based on the airfoil chord divided by 10⁶. The spanwise correlation length l_y is defined as:

St_L is the Strouhal number based on L_x, and St_s = f (x_means – x_sep)/U_∞. A constant $CBStL$ is defined to avoid the discontinuity of the model with St_L = 0.02:

The thickness noise prediction for the NREL Phase VI rotor presented in this paper is based on the geometry, rotational speed, etc. the loading noise prediction is based on the blade surface pressure distribution obtained from RANS simulations, the trailing-edge noise prediction is based on flow separation location for attached boundary layer and on velocity profiles for separated boundary layer. This acoustic investigation is based on the flow simulations with a 2-equation Explicit Algebraic Reynolds Stress Turbulence Model (EARSM) conducted by Suarez et al. (2018a).

The steady RANS simulations were conducted using FINE/Turbo (Numeca). The wind turbine rotor blade is of radius 5.029 m. The computational domain is created from a half cylinder of 3 rotor diameters with periodic conditions to reduce computational effort. It consists of 8.8 million control volumes distributed into 76 hexahedral blocks. The first mesh cell is at a non-dimensional distance of the order of 1. For the rotor with the RVGs, the grid is refined in the regions close to the RVGs. The height of the first layer of cells from the blade wall (y_wall) is 5 × 10^–5 m, and y⁺ is of the order of 1. The RVG-included grid consists of 27.4 million control volumes distributed into 282 hexahedral blocks. The validation of the numerical model was performed against the measurement data (Hand et al., 2001) from the sequence S campaign of the Phase VI Unsteady Aerodynamics Experiment of NREL and presented by Suarez et al. (2018a) for the reference rotor blades (without RVGs). They compared the aerodynamic performance characteristics such as pressure coefficient (C_p), and the normal and torque coefficients (C_n, C_t) against measurements for different wind speeds and for different turbulence models. The geometric characteristics and RVG configuration are defined by Szwaba et al. (2019) and based on the optimum design guidelines that were established in previous studies. Suarez (2016) conducted numerical and experimental studies on the influence of the RVG diameter (D) and height (h) on the strength of the vortices generated. The chordwise location of the rods and the optimum spacing between two rods are based on the studies conducted by Suarez et al. (2018b) on a wind turbine airfoil (S809).

To study the effect of the flow control for the blades the rotor with a wind speed of 10 m/s is chosen. A row of 10 RVGs is implemented at discrete spanwise locations (Figure 1), from R_a /R = 0.738–0.775, covering a 3.7% of blade radius and at mid-chord. These rods are designed based on the mid-chord boundary layer thickness at the reference section (R_a/R = 0.75). The boundary layer thickness at this location is approximately equal to δ_ref = 0.024 c_ref. Hence, the orientation and dimensions are ϕ = 30°, θ = 45°, D = 0.2 δ_ref, h = 0.5 δ_ref with ϕ being the pitch angle, θ is the skew angle, D and h are the diameter and height of the rods respectively. A single blade is simulated, and the second blade is accounted for using rotational periodicity boundary conditions.

For the current acoustic analysis, the rotor operating at a wind speed of 10 m/s is specifically selected, as turbulent separation occurs on the suction side for almost the entire span R_a/R = 0.95. At this speed, the implementation of RVGs reduces separation volume (Figure 2), thereby increasing the torque by 0.54% and the thrust by 0.67%. The pressure distribution obtained from the steady simulations along with the grid is re-scaled back from the numerical chord of 1 m to the experimental chord of 0.482 m and fed as input to the aeroacoustic code. Suarez et al. (2018a) provide a comprehensive report on the numerical set-up and aerodynamic performance.

The FW–H code requires blade discretization (mesh) and rotor kinematics as input for thickness noise prediction and surface pressure distribution for loading noise prediction which are obtained from the RANS simulations (EARSM turbulence model) of the rotor with a wind speed of 10 m/s. The code computes the acoustic potential for each mesh cell which is considered as an acoustic source, at emission time. To obtain the total noise emitted the acoustic potential from all the source panels is linearly added at the correct listener/observer time. Sound analyses are conducted in time and frequency domains for a few chosen microphones to give an overall perspective on the impact of RVGs. Pressure signals for two out-of-plane and one in-plane microphone are presented in this section for the NREL wind turbine rotor with/without RVGs.

Grid and time dependency studies are conducted for the reference rotor. The time convergence study is conducted for T/90, T/180 and T/360 time steps and mesh dependency with coarse grid – 2877 mesh cells, medium grid – 9715 mesh cells and fine grid – 35716 mesh cell grids. The solution is considered to be the fine grid and fine time-step solution when the difference between the current grid and the fine grid, fine time-step solution is below 0.5% (relative error) for the selected sound metrics. The fine grid with 35716 mesh cells and time-step of T/360 solution is chosen for all further analysis. The microphones are defined using parameters such as the height of the wind turbine H = 12.2 m, rotor radius R = 5.022 m with reference to the ground (0, -H, 0). The two out-of-plane microphones are located at M2(0, -R, H), M3(0, -H, H) and the in-plane microphone at M1(0, -H, 0) as shown in Figure 3. All the signals presented in Section 4.A are without the constant shift known as the DC shift by experimentalists (mean amplitude of the waveform) (Farassat, 2007) and hence, vary around the ambient pressure (0 value in the figures). This is achieved by subtracting the mean values from each signal.

The Amiet-Schlinker strip theory for rotating noise sources (Schlinker and Amiet, 1981) is used for predicting the broadband noise emitted by the wind turbine rotor. The blade is divided into six segments, with more refinement on the tip. Amiet’s theory for 2D airfoils is used to calculate the trailing-edge noise for each segment. The theory takes into account the rotational velocity plus inflow velocity through the effective tangential velocity. The total noise for each segment is computed and then added up to form the total noise of the whole blade at each angular position Ψ.

For the noise prediction of each segment, the location of the observer is transformed in the coordinates of Amiet’s theory. The relative motion of the segment that induces a delay between the noise emission and observer location is considered by a Doppler effect (= ω_e /ω). The total noise of the blade at each azimuth location is calculated by summing the noise produced by all the segments as:

where S_pp|blade (ω,Ψ) is the total noise of the blade as a function of the angular frequency (ω) for each azimuthal angle (Ψ), and S_pp|seg (ω_e) is the total noise of each segment calculated in the emission angular frequency (ω_e) (Sinayoko et al., 2013). The noise of the segment is calculated as the noise generated by a 2D airfoil with a separated boundary layer, or as turbulent boundary layer trailing-edge noise. The difference between both predictions is during the calculation of the wall-pressure spectrum. The state of the boundary layer, separated or attached, is obtained from the numerical simulations described in Section 3.A.

The average noise produced by the wind turbine in one rotation (S_pp|WT (ω)) is then calculated as:

where B is the number of blades.

The coordinate system in the fixed reference frame of the wind turbine (Figure 4) is Z_WT located perpendicular to the rotor plane, positive in the downwind direction and Y_WT located in the vertical direction, positive upwards. Ψ = 0 is aligned with X_WT -axis. The origin of the coordinate system is the wind turbine hub.

To predict the noise of each segment, the observer location $R→0,WT$⁠, given in the reference frame of the wind turbine, needs to be transformed to the Amiet’s coordinate system (⁠$R→0,a$⁠). The first rotation is conducted in the Z_WT -axis to obtain R_0,WT in the blade reference frame $R→0,blade$ as: $R→0,blade=MzR→0,WT$⁠, where M_z is:

Later, a translation to the radial position of the segment (R_a) is conducted, i.e. $R→0,seg$ = $R→0,blade$ + $dr→$⁠, where $dr→$ is defined as:

R_a is the radial location of the segment located at the center of the segment.

Finally, a rotation in the y_seg-axis is conducted to align the coordinate system with the segment chord. The rotational angle is the sum of the pitch angle of the blade (α) plus the twist angle of the segment (β). The final vector of the observer in Amiet’s reference frame is $R→0,a=MyR→0,seg$⁠, where M_y is:

In Amiet’s reference frame, x_a is located in the chordwise direction and y_a in the spanwise direction.

To calculate the Doppler effect, the methodology proposed by Sinayoko et al. (2013) is adopted. They defined the Doppler effect as:

where $Mf→=[0,0,U∞/c0]$ is the flow Mach number and c₀ is the speed of sound, $Ms→$ is the segment Mach number (⁠$Ms→=(Ωra/c0)[−sinΨ,cosΨ,0]$⁠) and $C^O$ is the unitary vector between the convected noise source (⁠$xc→$⁠) and the observer location in the frame of the wind turbine (⁠$R→0,WT$⁠), calculated as:

where $xc→$ is the location of the convected noise source generated at $xe→$⁠, i.e. $xe→$ is located at the middle of the blade segment (⁠$xe→=−ra[−sinΨ,cosΨ,0]$⁠), where as $xc→$ accounts for the shift of the noise location because of the velocity, calculated as:

where c₀T_e is the propagation time of the noise defined as (Bresciani et al., 2023):

where $r→$ is the vector between the observer and the emission point (⁠$r→=R→0,WT−xe→$⁠), and r_z is the component of $r→$ in the Z_WT direction (⁠$rz=r→·[0,0,1]$⁠).

A comparison of various sound metrics between the wind turbine rotor with/without RVGs is presented for time and frequency domains in the following sections.

The acoustic pressure signal components, including their near-field and far-field contributions, are examined in the time domain for M1 [Figure 5(a)] and M2 [Figure 5(b)] microphones. Figure 5 presents the total thickness and loading noise for both the reference rotor and the rotor equipped with RVGs. The plots indicate that the loading noise is substantially greater than the thickness noise, with values approximately 6.8 times higher for the M1 microphone and 11.7 times higher for M2, which aligns with expectations for low-speed rotors. Due to the low rotational speed, thickness noise remains minimal, even for the in-plane M1 microphone. Furthermore, the signals from the RVG-equipped rotor closely align with those of the reference rotor, suggesting that the presence of RVGs has a negligible effect on the acoustic response at both microphone locations. The total pressure signal magnitude received by the in-plane microphone (M1) is an order of magnitude greater than that measured by the out-of-plane microphone (M2).

A more detailed examination of the near-field and far-field contributions to thickness noise for microphone M1 [Figure 6(a)], microphone M2 [Figure 6(b)] and predictions for loading noise components – M1 [Figure 7(a)] and M2 [Figure 7(b)] are presented. In both cases, near-field components dominate over far-field components, irrespective of the microphone positions. Furthermore, the structure and characteristics of the pressure signal components are comparable for both microphones.

With the exception of the loading near-field term for the in-plane M1 microphone [Figure 7(a)], the RVG case exhibits strong agreement with the baseline blade signals. A minor variation is observed in the loading near-field signals between the RVG and reference configurations, though it is not visible. The potential implications of this deviation will be explored in the section.

The total acoustic pressure including its components – thickness, and loading are presented for the in-plane M1 microphone and the out-of-plane M2, and M3 microphones, in time [Figures 8(a) and (b)] and frequency domains [Figures 9(a) and (b)], respectively. Figures 8(b) and 9(b) provide a comparison of the in-plane and out-of-plane microphones positioned on the ground. Results indicate that the peak amplitude of the pressure signals is higher for the in-plane M1 microphone compared to the out-of-plane microphones. Despite this difference in magnitude, the overall shape and trends of the signals remain consistent across all microphone positions. Additionally, the overall sound pressure levels (OASPL) recorded at M1 are higher than those at the out-of-plane locations.

A comparative analysis of sound levels for microphones M1, and M3 at ground level is conducted, as this is particularly relevant for residents living near wind farms. Results show that the pressure signals perceived by observers further from the turbine (M3) are significantly weaker than those near the tower (M1), with a peak amplitude approximately 3.7 times lower. This distinction is clearly illustrated in the pressure and SPL figures.

The influence of RVGs on the global/total acoustic pressure signals appears almost negligible from the current analysis. In these plots, the curves for the flow-controlled case overlap with the reference rotor blades in both the time and frequency domain as well as for all microphones. There is a very slight deviation (between Ref and RVGs) noticeable only in the observer M1 location in the time domain [Figure 8(a)]. RVGs decrease the sound levels slightly for the in-plane microphone. This reduction is quantified in the OASPL Table 1. The peaks in the frequency plots (Figure 9) are marked to denote the blade passing frequencies (BPF) which are computed based on the rotor’s rotational speed. BPF is the frequency at which the rotor blades pass a fixed point such as the tower. In this case, the wind turbine has a rotational speed of 71.86 RPM and consists of two blades thus leading to the first BPF of 2.4 Hz. All the three resolved harmonics in the case of M1 and the two harmonics for M2 and M3, all occur at very low frequencies below 20 Hz, which is out of the human audible range. However, these low-frequency sound waves travel longer distances and may affect some animals, hence, they are an important factor for wind farms.

Time domain signals (Figure 8) depict the pressure variations over time leading to a smooth continuous signal. The variations in pressure lead to variations in the amplitude of the pressure signal. The frequency domain signals (Figure 9) on the other hand depict energy content at each frequency thus showing variations in harmonic content. They also contain information about various noise sources such as tonal and broadband noise components. The Fourier fast transform processing conducted to the time signals discretizes the signal into certain bands of frequencies (bins) to allow for detailed study of various sources at all frequencies. The nature of the spectrum depends on the type of window function applied while processing.

The sound levels are quantified through OASPL values for the three microphones in Table 1. The OASPL values obtained from both time (P_rms) and frequency domain (SPL) are presented along with their difference Δ = OASPL_RVGs - OASPL_Ref. Results show that the in-plane observer (M1) records the loudest sound level of 73 dB compared to the out-of-plane listeners (M2, M3). Although the out-of-plane microphones are positioned equidistant from the rotor tower, the ground-level M3 microphone experiences a higher sound level of approximately 2.36 dB greater than the microphone located directly in front of the rotor hub (M2). This discrepancy is attributed to the directionality of the noise emitted by the rotor blades. The RVGs have no significant effect on the OASPL values at the out-of-plane microphone locations (Δ < 0.06 dB). For the in-plane microphone M1, the presence of RVGs results in a slight reduction in noise (∼0.16 dB) compared to the reference rotor. The sound levels estimated from both P_rms and SPL values are in close agreement across all microphone positions.

Since the impact of RVGs on overall acoustic emissions remains minimal in the pressure signals of the complete two-bladed rotor analyzed in the previous sections, a more localized analysis is conducted by examining the pressure signals emitted from specific sections of a single blade. Two key regions (Figure 10) are selected for this investigation – Region 1 is defined by the tip region near the trailing edge spanning from R_a/R = 0.79 to R_a/R = 1 and Region 2 is defined by the area where the RVGs are implemented, covering R_a/R = 0.63 to R_a/R = 0.79. These sections are chosen from approximately mid-chord to the trailing edge to focus on areas where flow modifications induced by RVGs, particularly streamwise vortices, were identified in the aerodynamic analysis (Figure 2). By narrowing the scope to these localized regions, the maximum variations between the reference rotor blade and the flow-controlled case can be assessed more effectively.

The thickness and loading noise components from these two regions are analyzed and compared in the time domain (Figure 11) for both the reference rotor and the rotor equipped with RVGs. It is important to note that the signals presented below represent localized values rather than the total acoustic emissions from the entire blade.

A detailed region-wise comparison of the components of the pressure signal is presented in this section. A slight variation in loading noise is observed in Region 1, with differences in magnitude approximately equivalent to a single line width in the plots. There is a reduction in the loading noise at the tip trailing edge area for the rotor with RVGs compared to the reference rotor. The contribution of thickness noise from both regions remains comparable, although the section containing RVGs (Region 2) exhibits a slightly higher loading noise than the tip region (Region 1). Also note that in this comparison, the magnitude of the thickness noise is much higher than the loading noise which is of opposite nature to the total signals presented in Figures 6 and 7. This is because, globally (the entire blade), the thickness noise gets canceled out due to destructive interference caused by the pressure signals from other parts of the blade and hence the total signal exhibits a different nature than what is observed in the local regions. The influence of constructive interference can be noticed for the thickness noise presented by the curve obtained by adding the signals from Regions 1 and 2 [Figure 11(a)]. Since the signals from both regions have the same sign, they add up to have a large magnitude. In contrast, for loading noise, the signals from these regions exhibit opposite phases (signs), resulting in destructive interference, which reduces the overall signal magnitude [Figure 11(b)].

The difference in acoustic characteristics between the flow-controlled (RVG-equipped) and reference rotor blades are quantified in Table 2 using sound metrics derived from time domain analysis. In terms of thickness noise, the presence of RVGs leads to only a minor reduction in emitted noise. There is no significant variation in sound metrics for the two regions considered. For loading noise, a small reduction of ∼ 0.1 dB is observed in the tip (Region 1), whereas Region 2 (RVG-implemented section) exhibits a slight increase of ∼ 0.01 dB. The OASPL values exhibit the effects of constructive and destructive interference. Specifically, thickness noise reaches a higher level of ∼ 76 dB when signals from both regions are combined, compared to the contributions from individual regions. On the contrary, loading noise from both regions collectively registers a lower value of ∼ 47 dB than the noise emitted from Region 2 alone (∼48 dB).

The local pressure signal analysis further confirms that RVGs introduce no significant variations in acoustic emissions. Although these rods positively influence flow characteristics by reducing turbulent boundary layer separation (Figure 2), their impact on rotational noise remains minimal. Since the implemented RVGs are submerged within the boundary layer they do not create significant additional pressure fluctuations (because of cylindrical surfaces sticking out of the blade surface) that would otherwise contribute to rotational noise. While the current study focuses on steady pressure variations (based on RANS flow data), incorporating unsteady pressure distribution may provide deeper insights into the flow characteristics and subsequently noise emissions. The following section examines the impact of reduced boundary layer flow separation on trailing-edge noise emissions.

To predict the total trailing-edge noise over one blade rotation, the rotor blade is divided into five segments at R_a/R = [0.46, 0.7, 0.75, 0.78, 0.95]. The noise estimation accounts for contributions from both the suction and pressure sides of the blade at each segment. Depending on the state of the boundary layer – attached flow or separated flow, different models are implemented. On the suction side, the outermost segment (R_a/R = 0.95) maintains an attached boundary layer, whereas at the remaining segments, the boundary layer is separated. Conversely, on the pressure side, the boundary layer remains attached along the entire blade span for both the reference and RVG-equipped cases.

A reduction in the separation zone size is observed through the implementation of RVGs. The separation locations along the blade for both the reference rotor and the rotor with RVGs, which are based on the skin friction coefficient obtained from RANS simulations (Suarez et al., 2018a) are presented in Figure 12. Near the first rod location R_a/R = 0.7, the effect of the RVGs in reducing the separation zone is small as the streamwise vortices generated by the rod need to develop further. However, as additional rods are introduced, their effectiveness in suppressing separation improves, shifting the separation point closer to the trailing edge. This influence reaches its peak at the outermost rod position R_a/R = 0.78, where the separation location is shifted to x_sep /c = 0.95. Upstream of the rods at R_a/R = 0.46, there is no significant change in the flow characteristics. A separated boundary layer generates a broadband far-field noise spectrum characterized by a hump in the low-frequency range. This feature is generated by the large turbulent structures that develop when the boundary layer separates (Brooks et al., 1989; Bertagnolio et al., 2017). In the case of a 2D airfoil, delaying separation shifts this hump toward higher frequencies attributed to the reduction in turbulent structure size, while the high-frequency component is barely affected. The far-field noise produced at chosen segments (where the rods exhibit the strongest influence) at R_a/R = 0.75 and 0.78 is presented in Figure 13(a) and (b), respectively. At both locations, the introduction of RVGs results in a shift in the hump for the blade equipped with RVGs toward higher frequencies and a reduction in the low-frequency range. Specifically, at R_a/R = 0.78, an increase in far-field noise is observed in the 0.4–3 kHz, corresponding to the shift of the hump, which contributes to an increase in the total noise output of the wind turbine rotor [Figure 17(a)]. It is important to note that the empirical model used for predicting the wall-pressure spectrum of separated boundary layers was developed for cases where separation occurs significantly upstream of the trailing edge. In the flow-controlled case, the separation zone is reduced close to the trailing edge (at 95%) of the airfoil chord by the RVGs. This may lead to a potential over-prediction of the wall-pressure spectrum level for higher frequencies.

Near the tip, where the flow is attached, the wall-pressure spectrum is predicted using the boundary layer velocity profile obtained from RANS simulations (Suarez et al., 2018a). Figure 14(a) shows the mean velocity profile across the boundary layer. RVGs do not change the flow near the tip, and negligible differences are observed in the mean velocity across the boundary layer. This is reflected in a difference of less than 0.3 dB along the entire frequency range of the far-field noise of the segment, as shown in Figure 14(b).

The contour of the wall-pressure spectrum along the blade for the reference [Figure 15(a)] and RVG [Figure 15(b)] cases are plotted. The figures clearly show the shift of the energy content toward higher frequencies along the blade. RVGs significantly increase the wall-pressure spectrum in the frequency range of 0.1–3 kHz for R_a ≥ 0.7, whereas the reduction in the low-frequency range is not clearly visible. This would be reflected in the far-field noise produced by the entire blade, discussed in the next section. Figure 16(a) shows the velocity profile on the suction case for the reference case and with RVGs at several positions along the rotor radius. Small variations in the velocity profiles between the reference rotor and flow-controlled rotor are observed on the suction side. Additionally, at R_a /R = 0.3 which is further upstream of the rods, their impact on the boundary layer should be negligible contrary to what is observed in the figure. The effect of the RVGs located on the suction side on the boundary layer on the pressure side is minimal [Figure 16(b)]; therefore, the contribution of the pressure side to the total noise of the wind turbine is similar for the reference and RVG cases.

The far-field trailing-edge noise spectrum averaged over a full blade rotation for the reference and the flow-controlled case for different locations – M1 [Figure 17(a)], M2 [Figure 17(b)], M3 [Figure 17(c)] is presented. The results align with the near-field observations discussed previously. The implementation of the RVGs leads to a reduction in the far-field noise in the 30 Hz to 200 Hz frequency range and an increase of the noise between 0.3 Hz to 3000 Hz. The increase becomes more pronounced when the A-weighting filter is applied [Figure 17(d)]. Among the analyzed segments, Segment 5 (R_a /R = 0.78) contributes the most to the increase of the total far-field noise due to the largest effect of the RVG. Figure 13(b) shows that there is a huge reduction of the far-field noise of this segment in the 10–300 Hz; however, this reduction is not clearly reflected in the total far-field noise of the entire wind turbine. This discrepancy arises due to higher noise contributions from other sections of the blade, which counterbalance the reduction in this specific segment. Conversely, in the frequency range where Segment 5 exhibits increased noise levels, the RVGs do not significantly affect the far-field noise from other blade sections. As a result, the increase in noise from this segment is reflected in the total noise of the wind turbine.

The maximum increase in the far-field noise by the RVGs exceeds 10 dB, occurring at the in-plane M1 microphone location at f =1 kHz. Conversely, for the same microphone, the greatest reduction induced by the rods is more than 12 dB at f = 150 Hz. The variation in noise levels across different locations is attributed to the directivity of the trailing-edge noise regarding the observer location. Therefore, to further investigate the impact of RVGs on the far-field noise, an additional analysis on the directivity of wind turbine noise with/without RVGs is conducted.

Figure 18 presents the A-weighted OASPL values recorded at several locations around the wind turbine, positioned along a radius of 12.2 m. For reference, 0 is aligned with the Z_WT axis in the downstream location. Microphone 1 is situated at an angle of 90^o, and Microphone 2 would be located at 180^o. The implementation of RVGs leads to an increase in OASPL values by approximately 2 dB at most locations. However, in the plane of the wind turbine rotor, there is an increase of 9 dB. Although this is consistent with the analysis in the previous sections, it is important to note that the trailing-edge noise models used are designed for cases with sufficiently large separation zones, and in the current analysis we have separation zones very close to the trailing edge. Thus the models overpredict the wall-pressure spectrum.

The analysis of rotational noise for the NREL Phase VI wind turbine rotor, using the FW–H solver in both the time and frequency domains, along with the effect of the RVGs, has been presented. It should be emphasized that the vortex generators are implemented only on the outboard part of the blade, covering just 3.7% of the span. RVGs lead to the local reduction of boundary layer separation (as presented in (Suarez et al., 2018a)), but no significant effect on the sound pressure levels emitted by the rotor with/without the RVGs is observed. The relative difference in the OASPL emitted by the rotor blades is negligible for this specific configuration, with Δ < 0.1 dB. Therefore, the vortex generators (rods) do not have any significant acoustic impact on the NREL Phase VI rotor blades equipped with 10 RVGs in terms of rotational noise, while they enhance aerodynamic performance by reducing separation. These results align with a study by Ye et al. (2020), which examined vane-type vortex generators on the NREL wind turbine.

The effect of the streamwise vortices generated by RVGs on separated boundary layer and trailing-edge noise is evaluated using Amiet-Schlinker theory for rotatory noise sources and Amiet’s theory for 2D airfoils. In the case of the investigated wind turbine conditions, one can notice a shift of the hump toward higher frequencies caused by delayed (reduced) boundary layer separation. This leads to the higher total noise of the wind turbine in a wider frequency range. This increase is observed in the frequency range where human hearing is more sensitive. The total noise of the wind turbine due to the implementation of the RVGs is higher by ∼2 dB for off-plane locations. It is important to note that this acoustic impact can be altered if the RVGs completely reduce the boundary layer separation zone. This can be achieved by the improved effectiveness of RVGs, or vortex generators in general, leading to the creation of stronger streamwise vortices interacting with a separated boundary layer. Additionally, it is important to note that these findings are based on steady-state flow data (RANS), which does not fully capture all flow characteristics. Moreover, the trailing-edge noise models used in this study are designed for cases with sufficiently large separation zones, whereas the current analysis involves separation zones located very close to the trailing edge. As a result, these models tend to overpredict the wall-pressure spectrum. Furthermore, a difference in velocity profiles at the inboard regions of the blade was observed between the reference rotor and the flow-controlled rotor, prompting future investigation. Since this region is far upstream of the rods, their influence is expected to be minimal. In future work, scale-resolved simulations will be conducted to provide deeper insights into complex flow structures, thereby improving the accuracy of the acoustic analysis.

This research, specifically, the work conducted by the author Thanushree Suresh was supported by the National Science Centre, Poland’s funding scheme Preludium under project No. 2022/45/N/ST8/01425, and the work conducted by the author Laura Botero Bolivar, by the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreements No. 860101 – zEPHYR.