Computational aeroacoustic study of small three and four blade helical vertical axis wind turbines in turbulent flow

Abstract

Aeroacoustic analysis of a small vertical-axis Darrieus wind turbine suitable for urban area applications is performed using numerical simulation and acoustic analogy. The analysis is performed for two helical wind turbine models with three- and four-blade configurations and under different operating conditions. Numerical simulations are performed using the unsteady Reynolds averaged Navier-Stokes method, along with the Ffowcs-Williams and Hawkings aeroacoustic analogy. Validation of the performance of the computational model against experimental data demonstrates its ability to accurately predict the aerodynamic and aeroacoustic behavior of the turbine. The influence of the number of turbine blades and their distance from the center of the turbine on the generated noise is analyzed. The analysis is further focused on the highest power coefficient, obtained at the tip speed ratio of 1.8, and the sound pressure level (SPL) curves recorded by the receivers are analyzed. Predictions show that while the four-blade turbine has a higher SPL than the three-blade one at a downstream position of about four turbine diameters, the situation is reversed at farther downstream positions. The aeroacoustic findings of this research have direct implications for the proper installation of small vertical-axis Darrieus wind turbines in urban areas, where wind turbine generated noise is important.

Keywords

Darrieus vertical-axis wind turbine aerodynamic noise numerical simulation aeroacoustic analogy

Introduction

The global swift escalation in energy demand has led to unavoidable circumstances for the requirement of increased access to energy sources in developing countries.¹ Depletion of fossil fuel resources, besides their environmental impact, has urged the usage of renewable energy sources.² Wind power is notably one of the most important sustainable energy resources, offering both a reliable and steady energy source.³ Based on the axis of rotation, wind turbines are categorized into horizontal axis wind turbines (HAWTs) and vertical axis wind turbines (VAWTs). Each of these possesses benefits in comparison to one another. The inherent yawing mechanism of VAWTs makes them well-suited for effectively capturing wind energy in urban areas with variable wind direction and intensity.⁴ VAWTs, based on whether they utilize lift or drag for rotation, are further categorized into Darrieus and Savonius turbines. The former is the more prevalent choice for wind energy generation due to higher efficiency, better performance in a range of wind conditions, and easier scaling-up capability for large-scale commercial wind energy projects.⁵ Furthermore, VAWTs often operate at the Reynolds number range $(1 \sim 5) \times 1 0^{5}$ ,⁶ referred to as the low Reynolds number range.⁷ This makes them suitable for urban applications, where the presence of tall buildings reduces wind speed and consequently decreases the Reynolds number. The growth of VAWT usage in urban areas motivates the study of their emitted noise.

The noise due to small VAWTs installed close to residential areas causes more disturbance over time for the residents compared with the noise large VAWTs installed outside urban areas. Small VAWTs have different disturbance criteria compared to typical large-scale wind turbines.⁸ They can create various noise nuisances, including buzzing and whistling, which span a broad spectrum of acoustic frequencies.^9,10 For instance, a staggered configuration of multiple turbines can increase the overall noise emission.¹¹ As a result, there are serious adverse consequences of modest wind turbine noise on both people and animals, including sleep disturbances, mental health issues, and reduced quality of life for people, along with behavioral changes, communication disruptions, and habitat displacement for animals.¹² When small VAWTs are installed together in large numbers in an urban environment, the noise generated by them can have a significant impact on urban noise emissions.¹³ This highlights the importance of noise analysis for VAWTs, which is the subject of the current study. It has to be pointed out that there are two sources of wind turbine noise: aerodynamic noise and mechanical noise. The former is the main topic of this work.

Darrieus turbines have airfoil-shaped blade sections. Hence, their performance is sensitive to the wind direction, which constantly changes with blade rotation. Consequently, turbine rotation induces variations in the boundary layer condition and dynamic stall, particularly at low rotational velocity.¹⁴ Additionally, the turbulence intensity induced by the VAWT has a considerable effect on the downstream flow. The vorticity generated in the upstream areas of the rotor interacts with the turbine shaft while passing through the turbine.¹⁵ Therefore, the interaction between the free-stream flow and the turbulence caused by the VAWT is inevitable. The noise characteristics of the VAWTs are influenced by these interactions, which are significantly different on the windward side. The windward side experiences higher turbulence intensity due to the direct impact of the incoming wind on the turbine blades, which can lead to increased noise levels. Specifically, turbulence intensity can exceed 2 $%$ for over 90 $%$ of the airfoil span on the windward side, indicating a strong interaction between the free jet and the airfoil.¹⁶

Due to the increase in the number of urban wind turbines, there is an increasing interest in research on the noise generated by VAWTs.¹⁷ The analysis conducted by Chong et al. (2013)¹⁸ indicates a notable correlation between the unsteadiness of the boundary layer on the pressure surface and the tonal noise of an airfoil at different Reynolds numbers and angles of attack. Later, Pröbsting et al. (2015)¹⁹ described the tonal noise regimes and how the Reynolds number and the surrounding space affect the noise of VAWTs. In an experimental test conducted by Ottermo et al. (2017),²⁰ it was found that the noise of VAWTs is usually generated within a specific range of azimuthal angles. Additionally, the majority of recent studies have focused on VAWT noise using numerical modeling methods, although these methods face significant difficulties when trying to produce accurate results at low tip speed ratios (TSRs) and complex wake interactions, for instance, Rezaeiha et al. (2018).²¹ Dessoky et al. (2019)²² observed that at low TSRs, the leading edge of the airfoil is the primary region in noise production due to the larger angle of attack and the corresponding change in inflow velocity.

Large-eddy simulation (LES)^8,23 and unsteady Reynolds averaged Navier-Stokes (URANS)^24,25 are typically employed to study flow around VAWTs using computational fluid dynamics (CFD). Investigations performed by Raciti Castelli et al. (2011)²⁶ employed RANS equations for aerodynamic analysis of the flow around a Darrieus wind turbine rotor. Mohamed (2014)²⁷ used URANS and Ffocws-Williams and Hawkings (FW-H) acoustic analogy to study the impact of airfoil shape, rotor solidity, and tip-speed ratio (TSR) on the noise generated by VAWTs. Their findings demonstrated that increased TSR and rotor solidity cause VAWTs to produce loud noise. Balduzzi et al. (2016)²⁸ provides a comprehensive review of two-dimensional simulation studies, summarizes the typical numerical configurations used in RANS investigations of Darrieus rotors, and offers recommendations for appropriate simulation setup. The size of the wind turbine simulation and the available processing resources are the two key factors that influence the CFD modeling approach selection.²⁹ Rezaeiha et al. (2019)³⁰ showed that SST turbulence models, such as the SST $k - ω$ model, can achieve predictions with a fair agreement with experiment results. Consequently, the SST-based models have been ascertained to be the most precise among the various turbulence models evaluated for URANS simulations of VAWTs.

The FW-H equation is derived from Lighthill’s acoustic analogy. Lighthill demonstrated that within the jet stream, the primary factor contributing to aerodynamic noise is the turbulent velocity, which can be characterized as a quadrupole noise source.^31,32 In order to evaluate the impact of a stationary solid body in the turbulent flow, Curle (1955)³³ expanded the acoustic analogy of Lighthill. A dipole noise source term can be used to describe the additional noise components brought on by pressure variations on the surface of a solid body. Ffowcs Williams and Hawkings investigated the aerodynamic noise generated by a moving object in a fluid flow, leading to the development of the FW-H equations.³⁴

The noise reduction of small VAWTs may perhaps result in easier acceptance of them in urban areas. Recently, plenty of studies have been performed focusing on the noise of different types of VAWTs. For instance, the study of Su et al. (2019)³⁵ employs the Improved Delayed Detached Eddy Simulation (IDDES) technique and FW-H acoustic analogy to predict far-field noise from a VAWT, revealing that thickness and loading noises are the dominant sources, particularly as TSR and turbulence intensity increase. Aihara et al. (2021)³⁶ uses LES to predict the aeroacoustic noise of a 12 kW straight-bladed VAWT, confirming that loading noise, rather than thickness noise, becomes the primary contributor at higher TSRs, with results aligning well with experimental data. Yue (2023)³⁷ investigates the aerodynamic noise of H-Darrieus VAWTs and finds that TSR and wind speed significantly affect sound pressure levels, while the addition of vanes at the blade tips helps reduce the noise by weakening tip vortex interactions. Wang and Ferng (2024)³⁸ simulates the noise and torque of a 5 kW VAWT and demonstrates that mesh selection and turbulence model significantly impact predictions, with deflectors proving most effective for noise reduction in small-scale VAWTs. Pearson (2014)³⁹ investigates noise sources in VAWTs, identifying blade wake interaction and dynamic stall as the primary contributors, while boundary layer trips significantly reduce laminar tonal noise, offering an effective solution for quieter rotor designs. Furthermore, Venkatraman et al. (2023)⁴⁰ employs a ray-based method in another study of noise propagation from Darrieus VAWTs in urban environments, illustrating that rooftop installations can mitigate noise exposure and provide valuable insights for turbine certification in such settings. However, currently, aeroacoustics studies on helical VAWTs are very limited in the existing literature. Weber et al. (2016)⁴¹ presents two different numerical schemes of noise prediction for a small, three-blade helical VAWT. Venkatraman et al. (2023)⁴² examines the aerodynamic and aeroacoustic behavior of three-blade helical Darrieus turbines, showing that as the helix angle increases, the tonal peaks at the blade passing frequencies (BPFs) decrease due to enhanced flow mixing and three-dimensional flow. To our knowledge, no noise study on four-blade helical VAWT exists in the literature. Thus, the primary goal of the present study is to perform a numerical investigation of the aeroacoustics of a four-blade helical VAWT and additionally compare that to the three-blade VAWT results.

The present study aims to predict and compare the aerodynamic noise generated by the movement of three-blade and four-blade Darrieus-type VAWTs. To achieve this, a numerical simulation approach is employed using the URANS method with the SST $k - ω$ turbulence model. The selection of the URANS approach has at least two folds: first is the balance of accuracy and computational efficiency, and second is the widespread success of this approach in similar studies.^27,43,44 The far-field noise is then calculated using the FW-H acoustic analogy. The aerodynamic noise of both the three- and four-blade turbines is analyzed at various downstream distances. Notably, it is observed that at distances less than four times the turbine diameter, the four-blade turbine generates higher noise levels than the three-blade turbine. However, at downstream distances greater than approximately seven times the turbine diameter, the noise levels produced by both turbines become comparable.

The rest of this article is organized as follows. The geometry and mesh of three- and four-blade VAWTs are introduced in the following section. Afterwards, governing equations and numerical methods are explained and then, the aeroacoustic validation is reported in the succeeding section. Thereafter, the aerodynamic and aeroacoustic results are described in the next section, and finally, the conclusion and summary are included in the last section.

Geometry and mesh

The geometries of the three- and four-blade turbines investigated in the present study are shown in Figure 1(a) and (b), respectively. Initially, the camber line of the airfoil is defined using coordinates derived from the NACA four-digit series formula. Subsequently, two symmetrical points along the trailing edge are joined by a line to form a blunt trailing edge. The region enclosed by the airfoil’s curve is then extruded to a height of 60 cm and given a helix angle of 60°. Finally, a circular pattern is applied to produce the subsequent blades, aiming to create three- and four-blade models.

Figure 1.

The three-dimensional geometry of (a) three-blade and (b) four-blade helical wind turbines.

Figure 2 shows a two-dimensional schematic illustration of the computational domain from the top view. The upstream and the downstream dimensions are chosen as 15R and 40R, respectively, where R is the turbine radius. The computational geometry is chosen large enough to minimize the effect of the inlet and outlet boundaries on the results. Furthermore, a domain width of 20R has been chosen for symmetry boundaries.

Figure 2.

The two-dimensional schematic illustration of the computational domain showing its dimension in a top view.

The computational domain contains two separate mesh domains. The rotating domain, where the turbine blades are located, with rotation about the turbine axis, and the stationary domain that surrounds the rotating part. The boundary conditions consist of an inlet, outlet, and symmetry on the stationary domain. A velocity inlet boundary condition is applied at the inlet to define the incoming turbulent flow, representing the freestream velocity that the turbine encounters in its environment. A pressure outlet boundary condition is used at the outlet to allow the flow to exit naturally, ensuring the pressure gradient aligns with the surrounding atmosphere and preventing backflow. To reduce computational costs, a symmetry boundary condition is applied to the lateral boundaries instead of a wall boundary. Finally, an interface boundary condition is implemented to couple the rotating and stationary regions of the simulation, enabling proper flow exchange and ensuring accurate transfer of information, such as pressure, velocity, and turbulence, between the two domains. These two regions are generated separately and then connected with interfaces via the corresponding faces.

The geometric parameters of the three- and four-blade wind turbines are presented in Table 1. Both the three- and four-blade turbines have a similar blade height of 60 cm, and the turbine radius is 28 cm. The blades have a cross-sectional profile in the shape of NACA0018, with a chord length of 10 cm. The helix angle is chosen to be 60°, which was observed to be an appropriate helix angle in small helical Darrieus VAWT.⁴⁵ It is important to note that establishing a suitable mesh size and quality at various locations, together with the geometry, strongly affects the numerical simulation results. The size of the mesh is carefully determined in regions where significant flow variations exist, such as in the near-wall regions. Due to the intricate geometry in the present study, a pyramidal triangular mesh has been employed. In the process of discretizing the entire solution domain, the octree mesh generation method has been utilized. Tetrahedral cells have been used for meshing the computational domain. The middle cross-section plane of the total domain volume mesh of three- and four-blade turbines are shown in Figure 3(a) and 4(a), respectively. Figure 3(b) and 4(b) show the rotating region mesh in red color. Figure 3(c) and 4(c) show the volume mesh around one of the airfoil sections. To see the mesh structure in the near-wall region on the leading edge, Figure 3(d) and 4(d) are shown. To verify the independence of the simulation outcomes from the mesh, the power coefficient is evaluated at different grid resolutions. The power coefficient is defined as the ratio of the power generated by the turbine to the total power available from the wind flow. Table 2 provides details on the number of mesh cells for the coarse, medium, and fine mesh, corresponding to cases G1, G2, and G3, along with the number of components for each case. It is observed that the mean power coefficients for cases G2 and G3 are similar and only differ slightly. As a result, the mesh for case G2 has been utilized for the simulations in the present study. To enhance the mesh quality, mesh refinement techniques are employed in regions of the turbine blade geometry with significant curvature. The height of the first prism layer is adjusted to ensure that

y^{+}

values in the near-wall regions are less than 5. The height of the first computational cell on a turbine blade surface was determined using several parameters: maximum relative velocity, density, dynamic viscosity, characteristic length, and nominal

y^{+}

. Using these parameters, the first cell height on the blade surface was calculated to be 0.1 mm, with a cell growth rate of 1.2 and 11 layers. In Figure 5, the distribution contour of the

y^{+}

on the blade surface of the four-blade turbine at TSR = 1.8 is illustrated. The range of

y^{+}

values is between 0 and 5.

Table 2.

Number of cells for each case decomposed into different regions.

Case	G1	G2	G3
Stationary domain	1,076,828	1,026,072	1,270,283
Rotating domain	2,332,193	3,084,889	6,063,122
Total domain	3,409,021	4,110,961	7,333,405
Power coefficient	0.0551	0.0441	0.0458
Error (%)	–	20.033	3.865

Figure 3.

Top view of the computational mesh of the three-blade VAWT in the middle horizontal plane (a), the rotating region (b), near the airfoil (c) and the airfoil leading edge area (d).

Figure 4.

Top view of the computational mesh of the four-blade VAWT in the middle horizontal plane (a), the rotating region (b), near the airfoil (c) and the airfoil leading edge area (d).

Table 1.

Geometry characteristics of the three- and four-blade turbines.

Parameter	Value
Blade number	3 $/$ 4
Blade height	60 cm
Blade chord length	10 cm
Turbine radius	28 cm
Helix angle	60°
Airfoil	NACA0018

Figure 5.

The $y^{+}$ contour plot on the blade surface of the four-blade turbine at TSR = 1.8.

Governing equations and numerical method

The continuity and URANS equations are presented in equations (1) and (2), respectively, where $U_{i}$ is the mean velocity, $P$ is the mean pressure, $ρ$ is the fluid density, $ν$ is the kinematic viscosity and $u_{i}^{'}$ is the velocity fluctuation, in the $i^{t h}$ direction.

\frac{\partial U_{i}}{\partial x_{i}} = 0,

(1)

\frac{\partial U_{i}}{\partial t} + U_{j} \frac{\partial U_{i}}{\partial x_{j}} = - \frac{1}{ρ} \frac{\partial P}{\partial x_{i}} + ν \frac{\partial^{2} U_{i}}{\partial x_{j} \partial x_{j}} - \frac{\partial}{\partial x_{j}} ⟨ u_{i}^{'} u_{j}^{'} ⟩,

(2)

where summation convention over the repeated indices is employed. In the

k - ω

model, the following modeled transfer equations for turbulent kinetic energy

(k)

and specific turbulence dissipation rate

(ω \propto ϵ / k)

are written as follows:

\frac{\partial (ρ k)}{\partial t} + \frac{\partial (ρ k U_{j})}{\partial x_{j}} = \frac{1}{\partial x_{j}} [(μ + \frac{μ_{t}}{σ_{k}}) \frac{\partial k}{\partial x_{j}}] + P_{k} - β^{*} ω k,

(3)

\frac{\partial (ρ ω)}{\partial t} + \frac{\partial (ρ ω U_{j})}{\partial x_{j}} = \frac{1}{\partial x_{j}} [(μ + \frac{μ_{t}}{σ_{ω}}) \frac{\partial ω}{\partial x_{j}}] + \frac{ω}{k} (c_{ω 1} P_{k} - c_{ω 2} ρ k ω) .

(4)

The model coefficients in equations (3) and (4) are prescribed in appropriate references.⁴⁶

In order to predict the radiated noise from the output data of the computational field of the fluid flow and model aerodynamic noise sources, the FW-H equation is used. The FW-H equation is essentially an inhomogeneous wave equation that can be derived by using the continuity and Navier-Stokes equations. This analogy includes all sound sources, such as monopole, dipole, and quadrupole. The three terms on the right-hand side of equation (5) indicate quadruple, dipole, and monopole sources of sound. The FW-H equation can be written as:

\begin{aligned} \frac{1}{a_{0}^{2}} \frac{\partial^{2} p^{'}}{\partial t^{2}} - \nabla^{2} p^{'} = \frac{\partial^{2}}{\partial x_{j} \partial x_{j}} {T_{i j} H (f)} \\ - \frac{\partial}{\partial x_{i}} {[P_{i j} n_{j} + ρ u_{i} (u_{n} - v_{n})] δ (f)} \\ + \frac{\partial}{\partial t} {[ρ_{0} v_{n} + ρ (u_{n} - v_{n})]} δ (f)\} \end{aligned}

(5)

where

u_{i}

and

u_{n}

are the fluid velocity components in the

x_{i}

direction and normal to the surface

f = 0

, respectively. Here,

v_{i}

and

v_{n}

represent the surface velocity components in

x_{i}

direction and normal to the surface, respectively, and

δ (f)

and

H (f)

are the Dirac delta and Heaviside functions. In addition,

p^{'}

is the sound pressure at the far field, i.e.,

p^{'} = p - p_{0}

. The value about

f = 0

leads to a permeable surface. Additionally,

n_{i}

is the unit normal vector pointing toward the exterior region

f > 0

, and

a_{0}

is the far-field sound speed. Here,

T_{i j}

is the Lighthill stress tensor, and

P_{i j}

is the compressive stress tensor; see Lakzayi et al. (2024).⁴⁷ In order to calculate the Lighthill and the compressive stress tensor, equations (6) and (7) have been used, respectively. The free-stream quantities are denoted by the subscript 0.

T_{i j} = ρ u_{i} u_{j} + P_{i j} - a_{0}^{2} (ρ - ρ_{0}) δ_{i j}

(6)

P_{i j} = p δ_{i j} - μ [\frac{\partial u_{i}}{\partial x_{j}} + \frac{\partial u_{j}}{\partial x_{i}} - \frac{2}{3} \frac{\partial u_{k}}{\partial x_{k}} δ_{i j}]

(7)

The first term on the right-hand side of equation (5) represents quadrupole sources, which are caused by unsteady shear stresses. These sources lie outside the surface of the body and have a very small impact on sound generation during each cycle, so they can be ignored.

The wave equation (5) can be integrated analytically under the assumptions of the free-space flow and the absence of obstacles between the sound sources and the receivers. The complete solution consists of surface and volume integrals. The surface integrals represent the contributions from monopole and dipole acoustic sources and partially from quadrupole sources, whereas the volume integrals represent quadrupole or volume sources in the region outside the source surface. The contribution of the volume integrals becomes small when the flow is subsonic and the source surface encloses the source region. In the present simulations, the volume integrals are neglected. Thus, we have:

p^{'} (\vec{x}, t) = p_{T}^{'} (\vec{x}, t) + p_{L}^{'} (\vec{x}, t)

(8)

where

\begin{aligned} p_{T}^{'} (\vec{x}, t) = \frac{1}{4 π} \int_{f = 0} [\frac{ρ (\dot{U_{n}} + U_{\dot{n}})}{r {(1 - M_{r})}^{2}}] d S \\ + \frac{1}{4 π} \int_{f = 0} [\frac{ρ_{0} U_{n} {r \dot{M_{r}} + a_{0} (M_{r} - M^{2})}}{r^{2} {(1 - M_{r})}^{3}}] d S \end{aligned}

(9)

\begin{aligned} p_{L}^{'} (\vec{x}, t) = \frac{1}{4 π a_{0}} \int_{f = 0} [\frac{\dot{L_{r}}}{r {(1 - M_{r})}^{2}}] d S \\ + \frac{1}{4 π} \int_{f = 0} [\frac{L_{r} - L_{M}}{r {(1 - M_{r})}^{2}}] d S \\ + \frac{1}{4 π a_{0}} \int_{f = 0} [\frac{L_{r} {r \dot{M_{r}} + a_{0} (M_{r} - M^{2})}}{r^{2} {(1 - M_{r})}^{3}}] d S \end{aligned}

(10)

to calculate U and L, equations (11) and (12) are given below.

U_{i} = v_{i} + \frac{ρ}{ρ_{0}} (u_{i} - v_{i})

(11)

L_{i} = P_{i j} {\hat{n}}_{j} + ρ u_{i} (u_{n} - v_{n})

(12)

Here, $p_{T}^{'} (\vec{x}, t)$ and $p_{L}^{'} (\vec{x}, t)$ in equation (8) are often referred to as thickness and loading terms, respectively. The various subscripted quantities appearing in equations (9) and (10) are the inner products of a vector and a unit vector implied by the subscript. For instance, $L_{r} = \vec{L} . \hat{\vec{r}} = L_{i} r_{i}$ and $U_{n} = \vec{U} . \vec{n} = U_{i} n_{i}$ , where $\vec{r}$ and $\vec{n}$ denote the unit vectors in the radiation and wall-normal directions, respectively. The Mach number vector $M_{i}$ in equations (9) and (10) relate to the motion of the integration surface, $M_{i} = v_{i} / a_{0}$ . The $L_{M}$ quantity is the scalar product $L_{i} M_{i}$ . Here, the dot over a variable denotes the source-time differentiation of that variable.

The numerical approach employed for solving the three-dimensional equations is based on the finite volume method. Given that the flow is incompressible, a pressure-based solver is utilized. The solution method used is the SIMPLE algorithm, and spatial discretization of variables is conducted using a second-order upwind scheme.

The SIMPLE algorithm has been chosen in this study to solve the URANS equations. This method enforces mass conservation and determines the pressure field by linking velocity and pressure corrections. The SIMPLE algorithm provides stable convergence and efficiently manages the interaction between the velocity and pressure fields. The simulations were conducted using commercial software based on the finite volume method with a solid surface formulation of the Ffowcs Williams–Hawkings (FW-H) analogy for aerodynamic noise prediction. A moving mesh technique captured the blade motion, with noise data sampled at $500 H z$ , to ensure adequate frequency resolution. The convergence residual threshold of simulations is set to $1 0^{- 5}$ . The physical simulation time in the first interval is 0.57 seconds, which corresponds to 7 full rotations of the turbine. The solution time then continues for an additional 0.7 s, making the total physical time of the simulation 1.2 s. In the second interval, during which the aeroacoustic results are recorded, the turbine completes another eight full rotations. The time steps for the first and second intervals are chosen to be 0.0001 and 0.001 seconds, respectively. The inlet boundary condition is specified as a uniform constant velocity inlet, while the outlet is defined as a pressure outlet.

As explained by Mohamed (2016)⁴³ and Glegg and Devenport (2017),⁴⁸ the main source of tonal noise, particularly at low blade speeds, is Loading Noise (LN), which occurs due to unsteady aerodynamic forces acting on the blades as they move through the air. These forces create pressure changes that result in sound, with the blade passing frequency (BPF) being a key frequency for the tonal peaks. When the blades experience changes in airflow, such as turbulence or uneven flow, the angle of attack varies, leading to fluctuations in blade loading that boost the tonal noise. Our findings show that these unsteady loading effects are responsible for the prominent tonal peaks in our spectra.

Aeroacoustic validation

Previous studies on the noise generated by Darrieus VAWTs have mainly concentrated on H-type turbines, with a limited focus on helical-type turbines. To validate the present study, it was important to ensure the geometry detail of VAWT matched a reference, but no single study provided both the acoustic and aerodynamic data needed. As a result, two different references are used for validation in each field. Aeroacoustic validation is conducted in two distinct phases.

The first phase involves validating the acoustic results against experimental data presented in the study by Weber et al. (2015).⁴⁹ The turbine geometry used in Weber et al. (2015)⁴⁹ is an H-Darrieus type, with a height and diameter of 0.2 m and an airfoil chord length of 0.05 m. For the validation process, the turbine is precisely modeled according to these dimensions. The free-stream flow velocity is set to 21.28 m/s, and the receiver’s location is indicated by a cross in Figure 2, with a distance of 1 m from the turbine. The turbine operates at a rotational speed of 800 r/min. Figure 6 presents the sound pressure level (SPL) recorded by the receiver and compares the numerical results from the present study with the experimental data from Weber et al. (2015).⁴⁹ Both the numerical and experimental SPL graphs exhibit similar peak levels: approximately 76 dB at 40 Hz, 65 dB at 80 Hz, 55 dB at 120 Hz, and 52 dB at 200 Hz. The onset frequency of SPL decay for both datasets is around 257 Hz. Additionally, the percentage of decay in SPL is 31.6 $%$ for the present study and 31.2 $%$ for those of Weber et al. (2015),⁴⁹ indicating a fairly good agreement between the numerical and experimental results.

Figure 6.

The comparison of SPL measured by receivers in the present study against SPL measured by receiver 1 in experimental results of Weber et al. (2015)⁴⁹ with the frequency resolution of about 1.428.

The second phase of aeroacoustic validation involves comparing the aerodynamic numerical results from the present study with both the numerical and experimental data reported in Cheng et al. (2017).⁵⁰ The four-blade turbine used in Cheng et al. (2017)⁵⁰ has the geometric characteristics detailed in Table 1. The criterion used to compare the simulations of the present study with those of Cheng et al. (2017)⁵⁰ is the power coefficient. The power coefficient is defined as the ratio of the power generated by the turbine to the total power available from the wind flow. The power coefficient curve obtained from the numerical results of the present study has been validated against the results obtained from simulating a helical Darrieus VAWT using the three-dimensional URANS approach, as well as the experimental by Cheng et al. (2017).⁵⁰ Figure 7 displays the average power coefficient at various TSRs, derived from the numerical simulations of the present study as well as the numerical and experimental results of Cheng et al. (2017).⁵⁰ The average percentage deviation between the numerical results of the present study and the experimental results of Cheng et al. (2017)⁵⁰ is 28.61 $%$ . That is compared to a 42.69 $%$ deviation for the numerical results and experimental results of Cheng et al. (2017).⁵⁰ This indicates that the numerical results of the present study are even closer to the experimental data than those reported in Cheng et al. (2017).⁵⁰

Figure 7.

The three-dimensional simulation results of the power coefficient of the present study together with Cheng et al. (2017)⁵⁰ experimental and three-dimensional numerical study.

Results and discussions

In this section, the numerical simulation results are presented and discussed. It is important to note that the maximum power coefficient is observed at TSR $\approx$ 1.8. Hence, the aeroacoustic predictions are presented at this TSR in the following sections.

The pressure distribution on the surface of the airfoils varies continuously due to their position relative to the free stream. This variation in pressure distribution is a primary factor driving the rotation of the Darrieus VAWT. Figure 8(a)–(d) illustrate the pressure contours at the mid-section of the turbine’s height for azimuthal angles of 0°, 30°, 60°, and 90°, respectively. It can be observed in these figures that the pressure of the upstream region is about 0.027 $%$ higher than in the downstream region. This pressure differential contributes to the noise generation. Additionally, as the blade rotates from an azimuthal angle of 0° in Figure 8(a) to 90° in Figure 8(d), the pressure at the surface of the airfoil adjacent to the upstream flow increases by about 0.189 $%$ , these variations in pressure in the near-wall region of the blade surface are a significant source of noise. As illustrated in Figure 8(a)–(d), the most significant changes in flow pressure occur near the blade on the upstream side of the flow. Consequently, the blade moving through azimuthal angles from 0° to 180° has the most influence on the turbine noise generation. In Figure 8(c), at the azimuthal angle of 60°, an extremely low-pressure region is observed on the leading edge of the blade, with a pressure value of approximately 100,967.5 Pa. As shown in Figure 8(d), this low-pressure area decreases by 0.43 $%$ relative to the atmospheric pressure moving to the azimuthal angle of 90°.

Figure 8.

Pressure distribution contours at azimuthal angles (a) 0°, (b) 30°, (c) 60°and (d) 90° on blades surface at TSR = 1.8.

Figure 9(a)–(d) illustrates the turbulence kinetic energy (TKE) contours around the blades at the mid-height section of the turbine for azimuthal angles of 0°, 30°, 60°, and 90°, respectively. The TKE distribution around each blade varies due to the rotation and the position of the blades. Figure 9 show that the interior regions of the turbine and the adjacent areas of the blades move in the flow direction and consistently exhibit higher TKE compared to other areas. Comparison of Figure 9(a) and (b) with Figure 9(c) and (d) reveals a reduction in TKE values near the trailing edge of the blades in the downstream portion, particularly for blades moving against and perpendicular to the flow direction. Additionally, Figure 9(a)–(d) indicates that in the downstream region, sections of the blade moving in the same direction as the free flow have higher TKE compared to sections moving in the opposite direction. Figure 10 shows the locations of the nine receivers positioned at various distances from the wind turbine relative to the turbine rotor diameter, i.e., d. Receiver 1 is placed at the center of the turbine. Receivers 2 through 6 are linearly arranged in downstream at distances of d, 2d, 4d, 6d, and 8d from the turbine center, respectively. Receivers 7 through 9 are positioned in a circular format at azimuthal angles of 0°, 90°, and 180°, respectively.

Figure 9.

Turbulent kinetic energy at azimuthal angles (a) 0°, (b) 30°, (c) 60°, (d) 90°, at TSR = 1.8.

Figure 10.

Top view schematic of 9 receivers at different downstream positions.

Comparison of SPL spectra of the turbines at similar BPF

Figure 11(a)–(i) presents the SPL, measured in logarithmic scale of frequency, emitted from the blades at TSR $\approx$ 1.8. These measurements are recorded by receivers 1 through 9. Figure 11 illustrates the difference in SPLs between the three-blade and four-blade turbines. Note that the acoustic performance of the three-blade and four-blade turbines is compared while maintaining similar blade passing frequencies (BPF) for both cases. According to the equation relating BPF and the tip-speed ratio (TSR), the rotational speeds differ between the two setups. This alignment ensures that the primary acoustic peaks occur at the same BPF. As a result, the rotational speed is set to $540$ RPM for the three-blade helical turbine and $410$ RPM for the four-blade helical turbine. It can be observed that the difference in SPLs between the two turbine models decreases with increasing distance from the turbine center. This is, however, somewhat of an expected result, and it can be explained as follows. As the distance from the wind turbine increases, the impact of the number of blades is much less perceived. Additionally, the noise spectra of both turbines follow the same trend as the distance increases, and the number of identical frequencies with tonal peaks is enhanced. This indicates that the acoustic behavior of both turbine models becomes similar at greater distances from the turbine center. Thus, when the decisions regarding the wind turbine installation in the urban area are considered, regarding noise generation, the effect of the number of blades is only important at some particular downstream distance.

Figure 11.

The SPL spectra, measured by receivers 1 to 9, are shown in panels (a) to (i), respectively, at equal and constant BPF (BPF $\approx 27$ Hz) for the three- and four-blade turbines.

Analyzing the trend in the SPL graphs from receivers 1 to 6, it is evident that the pressure level spectra of both turbines follow the same path with increasing distance from the turbine. Specifically, up to receiver 4 (i.e., to the downstream distance of about 4 turbine diameter from the turbine center, the SPL spectrum of the four-blade model is higher than that of the three-blade one. Beyond this point, however, the trend reverses, and the SPL of the three-blade model exceeds that of the four-blade one.

Analysis of the variance and standard deviation of SPLs recorded by receivers 1 to 6 for both turbine models reveals that noise fluctuations increase with increasing distance in the downstream direction. Specifically, the standard deviation of pressure level fluctuations for the three-blade turbine increased from 9.6 to 17, while it increased from 9.4 to 49 for the four-blade turbine. This indicates that noise oscillations are more pronounced in the four-blade turbine as compared to the three-blade one. This noise oscillation may have some environmental impacts, which need to be taken into account.

To better understand the effect of distance from the turbine center on the noise emitted by the three-blade and four-blade models, Figure 12(a) and (b) present the SPL graphs recorded by receivers 1 to 6 for each turbine. The graphs show that both the spectrum and peak of the SPL decrease with increasing distance from the turbine. Additionally, the rate of decrease slows as the distance from the turbine increases, as evidenced by the convergence of the SPL spectra. The data on the three-blade turbine, Figure 12(a), and that of the four-blade turbine, Figure 12(b), show interesting trends in the SPL at different frequencies as a function of the STL range. Then, in the three-blade turbine, according to Figure 12(a), at lower frequencies,i.e., 27 Hz, it is found that the SPL reported by receiver 1 has a very high value of about 73 dB. Progressing toward receiver 6, the value tops at about 54 dB. When the frequency is increased to around 100 Hz, the SPL values decrease incredibly to where the SPL reported by receiver 1 is at approximately 41 dB, and SPL 6 reaches even lower, to 4 dB. When the frequency is higher, the resultant loss in sound transmission is more effective. According to Figure 12(b), the four-blade turbine data shows higher initial values of SPL at 28 Hz. SPL reported by receiver one reaches as high as 89.57 dB, much higher compared to that of the three-blade turbine in the same frequency.

Figure 12.

The SPL spectra measured by receivers 1–6 are shown in (a) and (b) for three-blade and four-blade turbines, respectively.

Additionally, to compare the effect of placement angle around the turbine at the same distance, Figure 13(a) and (b) display the SPL graphs recorded by receivers 1, 2, 7, 8, and 9 for the three- and four-blade models, respectively. Figure 13 (a) shows that at the low frequency of 28 Hz, the SPL at receiver 1 is 72.99 dB and at Receivers 2 and 9 is 67.65 dB and 48.51 dB, respectively. While increasing the frequency to 100 Hz, the SPL decreases to 42.80 dB at receiver 1 and further decreases to 18.56 dB at receiver 9. Figure 13(b) indicates that directivity for the four-blade turbine increases the SPL data in a considerably higher sound level situation, especially in the low-frequency part. The key observations include that SPL values reach 89.57 dB at Receiver 1 and 81.60 dB at receiver 9 at 28 Hz, while even frequencies up to 55 Hz still show quite a high value for SPL, being 70.41 dB at Receiver 1 and 68.24 dB at receiver 9. This means that the four-blade turbine produces considerably more noise than the three-blade turbine over a wide frequency range, most notably in the lower frequencies. However, this dissipation rate of the noise across the receivers is less than the dissipation rate for the three-blade configuration, which indicates that the noise profile is sustained for a longer time. In general, the four-blade turbine has higher values of SPL for all receivers and frequencies than the three-blade turbine. In general, an increased number of blades produces a greater amount of aerodynamic noise due to additional vortex shedding and interaction with the surrounding flow.

Figure 13.

The SPL spectra, measured by receivers 1–2 and 7–9 shown in (a) and (b) for three-blade and four-blade turbines, respectively.

Comparison of SPL spectra of the turbines at similar rotation speed

Figure 14 illustrates a comparison of SPL spectra for the three- and four-blade turbines at similar rotation speeds $736$ RPM, and $T S R = 1.8$ . Analysis of the SPL trends from receivers 1 to 6 shows that the SPL spectra for both turbines follow a similar pattern as the distance from the turbine increases. Specifically, up to receiver 4, which is approximately four turbine diameters downstream from the turbine center, the SPL spectrum of the four-blade model is higher than that of the three-blade model. However, beyond this point, the trend shifts, with the SPL of the three-blade turbine surpassing that of the four-blade one. This trend for the SPL spectra is observed both when the rotational speed of the two turbines is the same and when the BPF of the two turbines is similar. The peaks in the SPL spectra corresponding to the first BPFs are less accentuated at further distances.

Figure 14.

The SPL spectra, measured by receivers 1 to 9, are shown in panels (a) to (i), respectively, for the three- and four-blade turbines at equal and constant rotation rates $736$ RPM.

In addition, the peaks attributed to other harmonics of the BPFs are less clear. For instance, in Figure 14(b), for receiver 2 positioned at a downstream distance of about one turbine diameter, the first and next three harmonics clearly stand out. However, in Figure 14(d), which belongs to receiver 4, positioned at a downstream distance of about four turbine diameters, only the first two peaks are prominent. At distances farther than about four turbine diameters, both the three- and four-blade turbines demonstrate similar sound emissions. This outcome is consistently observed both when the BPFs are kept similar for the turbines, see Figure 11, and when the rotating speeds are kept similar for the two turbines.

Conclusions and outlooks

The research carried out is a detailed investigation of the aero-acoustical features developed by small Vertical Axis Wind Turbines (VAWTS) within actual urban contexts, highlighting the influence produced by the number of blades and geometry on noise generation. Advanced URANS simulations are combined with the Ffowcs-Williams and Hawking’s acoustic analogy to compare the acoustic performance of three- and four-blade Darrieus turbines. The investigation is performed both at a constant rotation rate and constant blade-passing frequency. The results show that the number of blades is an important parameter in determining the noise emission from these turbines. Within the shorter distances from the turbines, the four-blade turbine was found to have higher SPLs, while the three-blade turbine gave higher values within the longer distances. This is argued owing to the difference in vortex shedding from these two turbine configurations. It also emerged that the pressure distribution and contours of TKE are closely related to noise emission, with the highest noise fluctuations found in regions of steep and high turbulence. This in itself calls for the critical role of blade design and aerodynamic optimization in controlling the acoustic output of VAWTs. The SPL spectrum for both models decreases in general, along with a decrease in slope in the intensity decrease, as shown from results based on SPL graphs recorded by receivers at increasing distances from the central part of the turbine. Moreover, the difference between the SPL spectra of the two turbines reduces, and these are observed to be closer to each other in their spectra and peak levels every time the distance is increased. Besides, the magnitude of fluctuations in the SPL spectrum is increased. With a brief overview of the graph showing the trend in the SPL, one can have an idea that up to a distance of four turbine diameters from the turbine center, the SPL spectrum for the four-blade model is higher than that of the three-blade one. Beyond this point, though, the trend continues in reverse, and the SPL of the three-blade model surpasses that of the four-blade model. This trend was observed in both cases, i.e., at a constant blade-passing frequency and constant rotation rate. Another observation is that the oscillations for the four-blade turbine are greater than those of the three-blade one. This work gives useful insight into the necessity for the proper optimization of VAWTs installed in urban noise-sensitive areas, considering the acoustic performance, especially related to a different number of blades. Finally, the increased noise variability in the four-blade turbine implies a potentially negative environmental impact, which should be carefully weighed against the suitability of the locations for VAWT installations in heavy settlement areas. This work encourages new studies of the design of new blades, considering both aerodynamic efficiency and noise reduction, to meet the correct performance and public acceptance of VAWTs in urban contexts. Future research should then involve mechanical noise sources to offer a complete understanding of the total acoustic footprint of VAWTs.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Zeinab Pouransari

References

Makhdoum

Pouransari

. Analytical study of Iran nonrenewable energy resources using hubbert theory. ACS Omega 2022; 7(2): 1772–1784.

Kumar

Raahemifar

Fung

. A critical review of vertical axis wind turbines for urban applications. Renew Sustain Energy Rev 2018; 89: 281–291.

Pouransari

Behzad

. Numerical investigation of the aerodynamic performance of a hybrid darrieus-savonius wind turbine. Wind Eng 2024; 48(1): 3–14.

Ghasemian

Ashrafi

Sedaghat

. A review on computational fluid dynamic simulation techniques for Darrieus vertical axis wind turbines. Energy Convers Manag 2017; 149: 87–100.

Wardhana

Fridayana

. Aerodynamic performance analysis of vertical axis wind turbine (VAWT) darrieus type H-rotor using computational fluid dynamics (CFD) approach. In: Proceedings of the 3rd international conference on marine technology. SCITEPRESS - Science and Technology Publications, 2020, pp. 5–11.

Ingram

Dominy

. A review of h-darrieus wind turbine aerodynamic research. Proc IME C J Mech Eng Sci 2019; 233(23–24): 7590–7616.

Thomson

Luedemann

Piper

, et al. Potential effects of offshore wind farm noise on fish. Bioacoustics 2008; 17: 221–223.

Venkatraman

Bresciani

Maillard

et al.

Darrieus wind turbine noise propagation in urban environments using ray tracing

2023. DOI: 10.2514/6.2023-3646.

Taylor

Eastwick

Lawrence

, et al. Noise levels and noise perception from small and micro wind turbines. Renew Energy 2013; 55: 120–127.

10.

Waye

Öhrström

. PSYCHO-ACOUSTIC characters of relevance for annoyance of wind turbine noise. J Sound Vib 2002; 250: 65–73.

11.

Tsai

Hsu

Chen

, et al. Developing the full-field wind generator integrated with the vertical twin rotors. Int J Electr Power Energy Syst 2018; 103: 395–403.

12.

Schmidt

Klokker

. Health effects related to wind turbine noise exposure: a systematic review. PLoS One 2014; 9(12): 1–28.

13.

Anup

Whale

Urmee

. Urban wind conditions and small wind turbines in the built environment: a review. Renew Energy 2019; 131: 268–283.

14.

Buchner

Soria

Honnery

, et al. Dynamic stall in vertical axis wind turbines: scaling and topological considerations. J Fluid Mech 2018; 841: 746–766.

15.

Zajamsek

Yauwenas

Doolan

, et al. Experimental and numerical investigation of blade–tower interaction noise. J Sound Vib 2019; 443: 362–375.

16.

Laratro

Arjomandi

Cazzolato

, et al. Self-noise and directivity of simple airfoils during stall: an experimental comparison. Appl Acoust 2017; 127: 133–146.

17.

Yang

, et al. Experimental investigation of solidity and other characteristics on dual vertical axis wind turbines in an urban environment. Energy Convers Manag 2021; 229: 113689.

18.

Chong

Joseph

Kingan

. An investigation of airfoil tonal noise at different Reynolds numbers and angles of attack. Appl Acoust 2013; 74: 38–48.

19.

Pröbsting

Scarano

Morris

. Regimes of tonal noise on an airfoil at moderate reynolds number. J Fluid Mech 2015; 780: 407–438.

20.

Ottermo

Möllerström

Nordborg

, et al. Location of aerodynamic noise sources from a 200 kW vertical-axis wind turbine. J Sound Vib 2017; 400: 154–166.

21.

Rezaeiha

Montazeri

Blocken

. Towards accurate CFD simulations of vertical axis wind turbines at different tip speed ratios and solidities: guidelines for azimuthal increment, domain size and convergence. Energy Convers Manag 2018; 156: 301–316.

22.

Dessoky

Lutz

Bangga

, et al. Computational studies on Darrieus VAWT noise mechanisms employing a high order DDES model. Renew Energy 2019; 143: 404–425.

23.

Uchida

Ohya

. Micro-siting technique for wind turbine generators by using large-eddy simulation. J Wind Eng Ind Aerod 2008; 96: 2121–2138.

24.

Siddiqui

Durrani

Akhtar

. Quantification of the effects of geometric approximations on the performance of a vertical axis wind turbine. Renew Energy 2015; 74: 661–670.

25.

Siddiqui

Durrani

Akhtar

. Numerical study to quantify the effects of struts and central hub on the performance of a three-dimensional vertical Axis wind turbine using sliding mesh. In: Volume 2: reliability, availability and maintainability (RAM); plant systems, structures, components and materials issues; simple and combined cycles; advanced energy systems and renewables (wind, solar and geothermal); energy water nexus; thermal hydraul. American Society of Mechanical Engineers, 2014. https://appliedmechanics.asmedigitalcollection.asme.org/POWER/proceeding-sabstract/POWER2013/56062/V002T09A020/282168.

26.

Raciti Castelli

Englaro

Benini

. The Darrieus wind turbine: proposal for a new performance prediction model based on CFD. Energy 2011; 36: 4919–4934.

27.

Mohamed

. Aero-acoustics noise evaluation of H-rotor Darrieus wind turbines. Energy 2014; 65: 596–604.

28.

Balduzzi

Bianchini

Maleci

, et al. Critical issues in the CFD simulation of Darrieus wind turbines. Renew Energy 2016; 85: 419–435.

29.

Siddiqui

Khalid

Zahoor

, et al. A numerical investigation to analyze effect of turbulence and ground clearance on the performance of a roof top vertical–axis wind turbine. Renew Energy 2021; 164: 978–989.

30.

Rezaeiha

Montazeri

Blocken

. On the accuracy of turbulence models for CFD simulations of vertical axis wind turbines. Energy 2019; 180: 838–857.

31.

Lighthill

. On sound generated aerodynamically I. General theory. Proc R Soc Lond A Math Phys Sci 1952; 211: 564–587.

32.

Lighthill

. Mathematical methods in compressible flow theory. Commun Pure Appl Math 1954; 7: 1–10.

33.

Curle

. The influence of solid boundaries upon aerodynamic sound. Proc R Soc Lond A Math Phys Sci 1955; 231: 505–514.

34.

Williams

JEF

Hawkings

. Sound generation by turbulence and surfaces in arbitrary motion. Phil Trans Roy Soc Lond Math Phys Sci 1969; 264: 321–342.

35.

Lei

Zhou

, et al. Aerodynamic noise assessment for a vertical axis wind turbine using improved delayed detached eddy simulation. Renew Energy 2019; 141: 559–569.

36.

Aihara

Bolin

Goude

, et al. Aeroacoustic noise prediction of a vertical axis wind turbine using large eddy simulation. Int J Aeroacoustics 2021; 20(8): 959–978.

37.

Yue

. Aerodynamic noise prediction and reduction of h-darrieus vertical axis wind turbine. Aust J Mech Eng 2023; 21(3): 1093–1102.

38.

Wang

Ferng

. Numerical model for noise reduction of small vertical-axis wind turbines. Wind Energ Sci 2024; 9(3): 651–664.

39.

Pearson

Vertical axis wind turbine acoustics. PhD Thesis, University of Cambridge Press, United Kingdom, 2014. DOI: 10.17863/CAM.14070.

40.

Venkatraman

Bresciani

Maillard

, et al. Darrieus wind turbine noise propagation in urban environments using ray tracing. In: AIAA AVIATION 2023 forum, San Diego, CA, 12–16 June 2023, p. 3646.

41.

Weber

Tautz

Becker

, et al. Computational aeroacoustic simulations of small vertical axis wind turbine. In: INTER-NOISE and NOISE-CON congress and conference proceedings. Institute of Noise Control Engineering, pp. 4254–4262.

42.

Venkatraman

Moreau

Christophe

et al. Numerical investigation of aerodynamics and aeroacoustics of helical darrieus wind turbines. In AIAA AVIATION 2023 forum, San Diego, CA, 12–16 June 2023. p. 3641.

43.

Mohamed

. Reduction of the generated aero-acoustics noise of a vertical axis wind turbine using cfd (computational fluid dynamics) techniques. Energy 2016; 96: 531–544.

44.

Yue

. Aerodynamic noise prediction and reduction of h-darrieus vertical axis wind turbine. Aust J Mech Eng 2023; 21(3): 1093–1102.

45.

Divakaran

Ramesh

Mohammad

, et al. Effect of helix angle on the performance of helical vertical axis wind turbine. Energies 2021; 14(2): 393.

46.

Wilcox

Turbulence modeling for CFD, La Canada, California: DCW Industries, 1998.

47.

Lakzayi

Pouransari

KargarAbjahan

. Numerical and experimental investigation of aerodynamic noise from a cooling fan in a turbulent flow. Int J Aeroacoustics 2024; 23(1–2): 38–59.

48.

Glegg

Devenport

. Aeroacoustics of low Mach number flows: fundamentals, analysis, and measurement. India: Academic Press, Elsevier, 2017.

49.

Weber

Becker

Scheit

, et al. Aeroacoustics of darrieus wind turbine. Int J Aeroacoustics 2015; 14(5–6): 883–902.

50.

Cheng

Liu

, et al. Aerodynamic analysis of a helical vertical Axis wind turbine. Energies 2017; 10: 575.