# Aerodynamic characterization of two tandem wind turbines under yaw
misalignment control using actuator line model

Jie Su
School of Naval Architecture, Ocean and Civil Engineering
Shanghai Jiao Tong University
Shanghai 200240, China
&Yu Tu
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong
University
Shanghai 200240, China
&Limin Kuang
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong
University
Shanghai 200240, China
&Rui Zhang
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong
University
Shanghai 200240, China
&Yixiao Shao
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong
University
Shanghai 200240, China
&Dai Zhou
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong
University
Shanghai 200240, China
<EMAIL_ADDRESS>
&Zhaolong Han
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong
University
Shanghai 200240, China
& Kai Zhang
School of Naval Architecture, Ocean and Civil Engineering
Shanghai Jiao Tong University
Shanghai 200240, China

(February 17,2023)

###### Abstract

The Darrieus vertical axis wind turbines (VAWTs) are one of the mainstream
devices for wind energy utilization in the urban areas. The market’s pursuit
of high wind energy conversion efficiency promotes the research on improving
the wind turbine power coefficient while reducing noise. This paper makes
further investigation on the aerodynamics and aeroacoustics of a small VAWT
with V-shaped blades and trailing-edge serrations. The feasibility of
utilizing the Reynolds-Averaged Navier-Stokes SST $k-\omega$ turbulence model
and the FW-H method is verified against experiments. The studied V-shaped
blades can effectively improve the power performance of VAWT over a wide range
of tip speed ratios under normal wind speed conditions, and the trailing-edge
serrations will also slightly increase the power output of V-bladed VAWT at
the optimal tip speed ratio. The power coefficient of the V-bladed wind
turbine with trailing-edge serrations is about 28.3$\%$ higher than that of
the original turbine. In addition, a dumbbell-shaped noise directivity
distribution was first discovered in the VAWT compared with the traditional
elliptical distribution. The V-bladed VAWT generated less low-frequency noise
and the trailing-edge serrations realized the expected noise reduction effect.
Practically, this study proposes a feasible solution for the design of high-
efficiency and low-noise wind turbines.

_Keywords_ Vertical axis wind turbine $\cdot$ V-shaped blade $\cdot$ Trailing-
edge serrations $\cdot$ Aerodynamic performance $\cdot$ Noise reduction

##  1 Introduction

Due to the severe climate crisis and environmental pollution, reducing carbon
emissions has become the common goal of the government around the world. Wind
energy is considered one of the most important sustainable and green energy
sources and plays an important role in the supplementation of electricity in
urban and residential areas. Due to the density of buildings, complex
topographical conditions and unique wind conditions in urban areas, the small-
scale vertical axis wind turbines (VAWTs) are becoming increasingly popular in
the urban environment Li et al. (2022).

Compared with the horizontal axis wind turbines (HAWTs), the Darrieus VAWTs
are one of the mainstream devices for wind energy utilization in the urban
areas Griffith et al. (2016). However, the relatively lower aerodynamic
efficiency and incomplete corollary equipment impede the rapid development of
VAWTs. Besides, the public still has different attitudes towards wind turbine
noise. Therefore, it is urgent to further study and evaluate the aerodynamic
and aeroacoustic performance of VAWT to overcome its defects.

###  1.1 Improvement of VAWT’s structure

In order to increase the power output and improve the cost performance of
VAWT, in recent years, researchers have made great efforts to improve the
VAWT’s structure, including the structural configuration and the blade
profile.

In the early stage of development of Darrieus VAWT, the subject of study is
generally curve-bladed turbines, namely the $\Phi$-type VAWT. After that, to
reduce manufacturing cost of blade and simplify the support structure, the
straight-bladed (H-type rotor) VAWT was largely developed in the UK Borg et
al. (2014). Due to its simple structure, clear structural force transmission
path, and easy fabrication and installation, this H-type Darrieus VAWT has
been used as a baseline model for numerous experimental and numerical studies.
Besides, to improve the power performance and reduce the power output
fluctuations, the helically twisted configuration inspired by Gorlov
hydrokinetic turbines was introduced in VAWTs. Scheurich and Brown Scheurich
and Brown (2013) investigated the behavior of helical VAWT. The helical
turbine was shown to experience lower power loss when blade curvature and
helical twist were optimized, and it would generate more power output than the
straight-bladed VAWT at constant rotational speed under unsteady wind
conditions. Marten et al. Marten et al. (2019) performed an aero-elastic
simulation for a helical VAWT, and the aerodynamic performance was evaluated
by the lifting line free vortex wake model, which was validated against
experimental data. By eliminating the horizontal struts and supporting arms of
turbine rotor, Xu et al. Xu et al. (2018) conducted an experimental and
numerical investigation on a V-rotor wind turbine which mimics the lower half
of the $\Phi$-type Darrieus VAWT. The results showed that a higher power
coefficient could be obtained by optimizing the pitch angle and opening angle.
On the other hand, based on the H-type VAWT, Arpino et al. Arpino et al.
(2018) investigated a novel VAWT with three couples of blades in Computational
Fluid Dynamics (CFD) simulations. The blade group consisting of one main blade
and one auxiliary blade was reported to make higher power output at low tip
speed ratios compared with that of traditional H-type wind turbine. Liu et al.
Liu et al. (2019) integrated the Savonius wind turbine and H-type Darrieus
wind turbine to improve the self-starting capability of VAWT. In addition,
Kuang et al. Kuang et al. (2022) and Chen et al. Chen et al. (2021) analyzed
the effects of diffuser and deflector on the VAWT. The results showed that the
power efficiency was improved by 20$\%$ and 51$\%$ by utilizing a suitable
deflector and the optimized diffuser, respectively.

As for the modification in blade profile employed in VAWTs, Ismail and
Vijayaraghavan Ismail and Vijayaraghavan (2015) utilized the Shear Stress
Transport (SST) $k-\omega$ model to investigate the effects of inward semi-
circular dimple and Gurney flap on the power performance of a VAWT. It was
found that the average tangential force of the rotor was increased by about
35$\%$ in steady state case and 40$\%$ in oscillating case. Similarly, Zhu et
al. Zhu et al. (2021) evaluated the aerodynamic performance of VAWT with
different Gurney flaps, and the maximum improvement could reach up to about
21$\%$. Besides, Tiranda and Rezaeiha Tirandaz and Rezaeiha (2021) performed
an analysis of airfoil maximum thickness and its position, as well as the
leading-edge radius to identify the optimal blade profile for designing VAWTs
with morphing airfoils. When tip speed ratio reduced from 3 to 2.5, the
optimal maximum thickness increased from 18$\%c$ to 24$\%c$, and its position
shifted from 27.5$\%c$ to 35$\%c$. In addition, Zamani et al. Zamani et al.
(2016) proposed a J-shaped profile based on Du 06-W-200 airfoil to improve the
self-starting of a VAWT, and the performance of turbine was optimized.
According to this idea, Mohamed Mohamed (2019) numerically investigated the
aerodynamic and aeroacoustic performance of J-shaped Darrieus VAWT. However,
the results showed that the studied J-shaped blade has no benefit for wind
turbine power performance and noise reduction.

###  1.2 Influence of noise emitted from wind turbines

Due to the longer development time and a more complete industrial chain, the
large-scale HAWT has played an important role in wind power generation in the
rural and offshore areas. Hence, a large number of public opinion surveys on
wind turbine noise are also focused on such turbine rotor. Although there is
still no critical evidence that wind turbine noise has adverse health effects,
the results from the quantitative, experimental and longitudinal research
consistently suggest that wind turbine noise presents a risk for sleep and
interference with work Poulsen et al. (2019); Karasmanaki (2022). Compared
with the mechanical noise, the aerodynamic noise emitted from wind turbines is
more significant, and it can be paralleled to the ‘swishing’ sound of a
helicopter Karasmanaki (2022). Since the low frequency wind turbine noise
penetrating the building walls is more likely to cause indoor noise annoyance
Hongisto et al. (2017), there are stricter limits and requirements for wind
turbine noise in urban areas. This also explains another reason why small
VAWTs are more popular than HAWTs in urban areas, namely the former’s less
aerodynamic noise Eriksson et al. (2008).

###  1.3 State of research on VAWT noise

Considering that small VAWTs have more attractive features than HAWTs in urban
areas, including lower cost, better adaptability to complex wind environments,
and lower noise, researchers have begun to explore the noise characteristics
of VAWTs and noise reduction methods. For instance, Botha et al. Botha et al.
(2017) investigated the inflow turbulence noise and airfoil self-noise of a
six-bladed 2kW VAWT by using the analytical flow methods and SST $k-\omega$
turbulence model. It was shown that the use of CFD calculations improved the
accuracy of noise prediction. Besides, the inflow-turbulence noise was the
major source, where blade generated turbulence dominated the atmospheric
inflow turbulence. Aihara et al. Aihara et al. (2021) utilized the large eddy
simulation and the Ffowcs Williams and Hawkings’ (FW-H) acoustic analogy to
solve the aerodynamic noise of a H-type VAWT. The results showed that the
loading noise could be considered to be the main noise contributor, and a
higher noise level was found in the downwind region. Besides, Liu et al. Liu
et al. (2022) combined the CFD technology and FW-H method to investigate the
aerodynamic and aeroacoustic performance of straight-bladed wind turbine with
active blowing-suction devices. The results indicated that the jet coefficient
significantly determined the wind turbine performance, and the optimized
active device could reduce the acoustic noise at low frequency. Recently, an
experimental investigation on small VAWT noise in an urban environment was
conducted by Li et al. Li et al. (2022). The low-frequency noise was recorded
and the impacts of wind turbine noise on humans and animals were analyzed.

For the aerodynamic noise reduction techniques, leading edge modification like
tubercles, trailing-edge serrations or sawtooth structure, blade tip shape
optimization, and boundary-layer trips, were introduced to reduce the pressure
field fluctuation and the interaction between atmospheric turbulence and
rotating blades. For the single wind turbine, Oerlemans et al. Oerlemans et
al. (2009) investigated the aeroacoustics of a HAWT with different airfoils
and trailing-edge serrations as shown in Fig. 1. The results showed that
average overall noise reductions of 0.5 and 3.2 dB could be obtained for the
optimized blade and the serrated blade. Maize et al. Maizi et al. (2018)
evaluated the effect of three tip blade configurations on the noise reduction
of NREL Phase VI wind turbine by using CFD and FW-H methods. The shark tip
blade was found to be the best tip configuration for optimal noise emission.
Besides, Wu et al. Wu et al. (2020) proposed an interesting strategy to
minimize the noise of onshore wind farms without sacrificing power production.
A stringent noise control strategy reducing noise by 11$\%$ and a flexible
strategy reducing noise by 5.7$\%$ were reported.

Figure 1: The serrated blade in a horizontal axis wind turbine Oerlemans et
al. (2009).

On the other hand, there are relatively few studies on the application of
these noise reduction techniques on VAWTs. Mohamed Mohamed (2016) attempted to
reduce the noise of a VAWT by using three couples of blades. It was reported
that the 60$\%$ spacing was the best configuration of the double-airfoil for
reducing wind turbine noise, while the power performance was not revealed.
Last year, the stochastic noise from a model-scale VAWT was tested by Graham
and Pearson Graham and Pearson (2022) in a wind tunnel in the UK. It was found
that the surface trips effectively reduced the laminar-instability noise, and
the influence of relative blade speed on noise is greater than the number of
blades.

###  1.4 Motivation and contribution of this work

Through the above literature review, it can be found that considerable
research efforts have been devoted to improving the power output of VAWTs, but
there is still more space for improvement in the wind turbine structure. On
the other hand, while a number of research on wind turbine noise have been
carried out on, there are few studies on the aerodynamic noise of VAWT other
than straight-bladed wind turbine. The directivity and propagation of such
wind turbine noise are not very clear. Besides, the problem of noise pollution
prompts the VAWT to reduce noise while increasing power performance. The
possibility of applying noise reduction techniques on VAWTs remains to be
explored.

Therefore, the present study attempts to make further investigation on the
aerodynamic and aeroacoustic performance of the small VAWT with V-shaped
blades and trailing-edge serrations based on the authors’ previous study Su et
al. (2020). In this study, a series of V-shaped blades were investigated to
evaluate their effect on the aerodynamic and aeroacoustic characteristics of
the VAWT. The unsteady Reynolds-Averaged Navier-Stokes (URANS) SST k-$\omega$
turbulence model was utilized to perform the simulations, and the
computational settings were demonstrated in Section 2. Then a brief
description of FW-H analogy used for acoustic calculation was presented in
Section 3. In Section 4, a series of three-dimensional CFD simulations were
carried out to evaluate the effects of different V-shaped blades on the wind
turbine performance at different tip speed ratios. Besides, the components of
tonal noise were discussed, as well as the results of noise directivity and
propagation. Moreover, the trailing-edge serrations were employed in the VAWT
to evaluate the noise reduction effect. Finally, several conclusions were
summarized in Section 5.

The contributions of this study are summarized as follows:

(i) The present study comprehensively evaluates the effects of a series of
V-shaped blades on the aerodynamic forces of a small VAWT at different tip
speed ratios. The improved blades can effectively increase wind turbine power
output over a fairly wide range of tip speed ratios while only slightly
increasing the thrust loads on the structure.

(ii) This study verifies the elliptical distribution of noise in the VAWT with
straight blades and a dumbbell-shaped noise directivity distribution is
discovered for the first time in VAWT, which was previously only found in
HAWTs. Besides, the V-bladed VAWT generates less low-frequency noise. It can
be explored for optimizing wind farms to minimize noise disturbance to
potential receivers.

(iii) The trailing-edge serrations that can be manufactured separately and
then installed on the wind turbine blade were successfully applied in the
simulation of VAWTs. The expected noise reduction effect was achieved, and
even a small increase in power output was realized. The combination of
V-shaped blades and trailing-edge serrations can be practically applied to the
design of high-efficiency and low-noise wind turbines.

##  2 Methodology

###  2.1 Wind turbine model

The selected VAWT with V-shaped blades was modified from the prototype of the
straight-bladed wind turbine tested by Castelli et al.Castelli et al. (2010).
The airfoil NACA0021 was utilized to produce the wind turbine blades both in
the V-bladed and straight-bladed VAWTs. The geometrical characteristics of the
reference wind turbine, as well as the operating conditions are listed in
Table 1. The schematics of the two types of wind turbines are illustrated in
Fig. 2 (a). In accordance with the previous study Su et al. (2020), the
V-shaped blade was created by moving the position of the blade middle cross
section along the tangential direction of the rotor. The structure of the
V-shaped blade is controlled by the distance between the leading edge of the
modified blade and that of the straight blade, which can be defined as $\Delta
V$. In this study, a series of V-shaped blades would be investigated to
evaluate their aerodynamic performance and noise generation. The more detailed
construction method of the V-shaped blade is presented in Ref.Su et al. (2020)
and for brevity is not repeated here. Besides, for the sake of computational
cost, the shafts and struts are neglected.

Table 1: Geometric properties of the VAWT model. Property | Symbol | Value
---|---|---
Airfoil profile | - | NACA 0021
Blade number | $N$ | 3
Chord length | $c$ | 0.0858 m
Rotor diameter | $D$ | 1.030 m
Span length | $H$ | 1.456 m
Swept area of rotor | $A$ | 1.236 m2
Solidity | $\sigma$ | 0.25
Tip speed ratio | $\lambda$ | 1.5 - 3.3

Figure 2: The sketch map of the V-bladed VAWT: (a) transformation of the wind
turbine model; (b) the structures of V-shaped blade and trailing-edge
serrations.

On the other hand, to further explore the noise reduction effect, the
trailing-edge serrations were applied to the wind turbine blade as shown in
Fig. 2(b). Among the noise reduction techniques mentioned in Introduction, the
trailing-edge serrations were considered one of the relatively practical
methods. Given that the serrated structures can either be processed directly
on the blade, or can be fabricated separately and then installed on the blade,
this structure has great flexibility in processing and installation. It can be
used as an optional component for wind turbine blades as shown in Fig. 1. In
the present study, the trailing-edge serrations were created by directly
processing the trailing edge of the V-shaped blade as illustrated in Fig.
2(b). The serrated structure can be defined by the wavelength $L$ and root-to-
tip amplitude $2h$. In this preliminary study, the serrated structure with
$L/h=0.4$ and $h/c=0.05$ was adopted as suggested by Lyu et al. Lyu et al.
(2016), which was fully distributed along the blade span.

The power coefficient $C_{P}$, torque coefficient $C_{Q}$, and thrust
coefficient $C_{thrust}$ of the wind turbine can be defined as:

$\displaystyle C_{P}=\frac{Q\Omega}{\frac{1}{2}\rho U_{\infty}^{3}A}$ (1)
$\displaystyle C_{Q}=\frac{Q}{\frac{1}{2}\rho U_{\infty}^{2}AR}$ (2)
$\displaystyle C_{thrust}=\frac{F_{thrust}}{\frac{1}{2}\rho U_{\infty}^{2}A}$
(3)

where $Q$, $\Omega$, $A$, $R$, $\rho$, and $U_{\infty}$ are the rotor torque,
angular velocity, swept area of the rotor, rotor radius, air density, and
freestream velocity, respectively.

###  2.2 Computational settings

The computational model and mesh topology are shown in Fig. 3. The size of the
computational model was $20D\times 10D\times 4H$. The distance between the
outlet boundary and the VAWT was set as 15$D$ to ensure the full development
of wind turbine wake. The computational model was divided into a stationary
domain and a rotational domain, where the latter was used to simulate the
rotational motion of the wind turbine by utilizing the sliding mesh technique.
Besides, two refined regions were set up to obtain the accurate flow field and
the pressure fluctuation information which would be used in the acoustic
calculation. The four sides of the computational model were set as slip walls,
while the inlet and the outlet boundary were set as uniform freestream
velocity inlet ($U_{\infty}$=9 m/s) and pressure outlet (0.0 Pa). Moreover,
the density of the air and the turbulence intensity were set as $\rho=1.225$
kg/m3 and 5$\%$ to reproduce the experimental conditions as much as possible.

Figure 3: The three-dimensional computational model and boundary conditions.

In order to facilitate the analysis of the results, four regions are defined
in the model based on the azimuthal range of the blade. The region ranged from
$45^{\circ}<\theta\leq 135^{\circ}$, $135^{\circ}<\theta\leq 225^{\circ}$,
$225^{\circ}<\theta\leq 315^{\circ}$, and $315^{\circ}<\theta\leq 405^{\circ}$
($45^{\circ}$) are defined as the upwind region, leeward region, downwind
region and windward region, respectively. Apart from that, a total of 33
probes for acoustic calculations were set up in the middle plane of the
computational domain as illustrated in Fig.4. The position distribution of the
other 66 probes in the bottom and top planes near the blade tips is the same
as that in the middle plane. The position statistics of the probes are shown
in Appendix A.

Figure 4: The distribution of probes for acoustic calculation.

The numerical settings employed in the present study are based on the
guidelines for high-fidelity simulations of VAWTs Rezaeiha et al. (2018), and
these settings were successfully applied in the previous study Su et al.
(2020). In this study, the software STAR-CCM+ was utilized to simulate the
three-dimensional incompressible unsteady flow around the VAWT. The SST
$k-\omega$ turbulence model was applied in the current CFD simulations. The
SST $k-\omega$ model is feasible to obtain the flow field information around
the wind turbines, and the acoustic calculation based on this model is also
credible Mohamed (2019); Sobhani et al. (2017); Tadamasa and Zangeneh (2011).
The convection terms and the temporal discretization were set as second order.
The SIMPLE algorithm was applied for coupling the pressure-velocity equation.
The time-step size was set as $2^{\circ}$ Su et al. (2019); Lei et al. (2017)
in the first eight revolutions to obtain the instantaneous flow field, and 20
iterations were conducted in each time step to ensure that the residuals are
small enough. After that, the aeroacoustic calculation were performed in
another two revolutions with FW-H method which would be presented latter. In
the acoustics calculation, considering the convective Courant number and the
sensitive frequency band of human hearing, the time-step size was set as
$2\times 10^{-5}$s. The Reynolds number calculated in this study is about $Re$
= 1.1$\times 10^{5}\sim 2.2\times 10^{5}$. All simulations were carried out on
the small-scale Server with two Intel(R) Exon(R) CPUs (E5-2673 v3, 2.40 GHz).
About 168 h were taken to calculate the eight revolutions and about 360 h were
used to accomplish the acoustic calculation.

###  2.3 Validation studies

A set of validation studies have been conducted on the selected VAWT,
including the grid independence analysis and comparison of target functions
$C_{P}$. A good agreement between the present CFD results and the experiments
can be observed as shown in Fig. 5. The results of the medium mesh scheme with
a total of 11.7 million grids are found to be sufficiently independent of mesh
resolution, where the wall function $y^{+}$ was approximately equal to 1
during the calculation. The present study is conducted based on the authors’
previous research, and the more detailed description of the validation tests
can be found in Ref. Su et al. (2020), which will not be repeated here.

Figure 5: Comparison of the current results against experimental and numerical
data Castelli et al. (2010); Sobhani et al. (2017).

In addition, another grid sensitivity analysis of serrated V-bladed VAWT was
carried out. Table 2 shows the aerodynamic performance with different mesh
refinement levels. The results show that the average deviation of torque is
small enough when the mesh is refined from TE Refinement II to TE Refinement
III, resulting in less than 1$\%$ errors in power coefficient. It can be
observed that the results of mesh scheme TE Refinement II are sufficiently
independent of mesh resolution.

Table 2: Mesh topology around the serrated blade at $\lambda=2.6$. Mesh scheme | Minimum Grid Size | Total Number of Grids | $C_{P}$
---|---|---|---
TE Refinement I | 12$\times 10^{-4}$ m | 21.7 million | 0.3612
TE Refinement II | 6$\times 10^{-4}$ m | 35.4 million | 0.3877
TE Refinement III | 3$\times 10^{-4}$ m | 54.8 million | 0.3904

Overall, the present model is proved to successfully replicate the
experimental results, and the simulations can reflect the aerodynamic of real-
life wind turbine in wind tunnel. Therefore, it suggests that the present
numerical model can be applied as a credible approach in following studies.

##  3 Acoustic calculation

In this study, the Ffowcs Williams and Hawkings’ acoustic analogy method is
utilized to predict the wind turbine noise generated from the straight-bladed
and V-bladed VAWTs. To obtain the acoustic pressure fluctuations at each
receiver as described above, the time-accurate solutions of the flow-field
variables around the VAWT are required from the SST $k-\omega$ model Mohamed
(2019); Tadamasa and Zangeneh (2011).

In order to assess the strength of the wind turbine noise and perform a
comprehensive analysis on the directivity of noise propagation, 33 acoustic
receivers were set up in the middle plane to cover the sound wave propagation.
The details about the receivers can be found in Section 2.2.

Besides, to enhance the credibility of calculation results obtained by using
the SST $k-\omega$ model and the FW-H method, taking into account the
incomplete acoustic experimental data of the selected VAWT, another
verification test of sound generated by flow around a circular cylinder is
shown in Appendix B.

##  4 Results and discussions

In this section, a series of V-shaped blades were investigated to evaluate
their impact on the wind turbine aerodynamic performance and acoustic
characteristics. The aerodynamic forces and noise spectrum were analyzed, and
the effect of trailing-edge serrations was evaluated.

###  4.1 Aerodynamic performance assessment

The power coefficient and thrust coefficient are the key parameters to assess
the wind turbine’s energy conversion efficiency and the load characteristics.
Fig. 6 presents the comparison of average power coefficient and thrust
coefficient for the VAWT with different V-shaped blades at the optimal tip
speed ratio $\lambda=2.6$. It can be observed that the modification of the
original straight blade would greatly affect the torque output of the wind
turbine. The power coefficient of the VAWT gradually increases with the value
of $\Delta V$, and the maximum enhancement of $C_{P}$ occurs at $\Delta
V=0.6c$. According to the previous published study, most positive power
outputs are attributed to the middle segments of the blade, while the effect
of V-shaped structure on the blade tip region is relatively small. After that,
increasing the value of $\Delta V$ has a less positive effect on the power
performance of the wind turbine, and even larger $\Delta V$ may lead to
performance degradation. On the other hand, the influence of V-shaped blade on
the thrust coefficient of the wind turbine is relatively small, and the
variation of $C_{thrust}$ is less than 4$\%$ in the studied cases.

Figure 6: Comparison of the VAWT with different V-shaped blades at the optimal
tip speed ratio $\lambda=2.6$: (a) power coefficient; (b) thrust coefficient.

Based on previous results, the modified blade $\Delta V=0.6c$ with the best
performance in power coefficient was selected and studied at different tip
speed ratios. As shown in Fig. 7 (a), it is clear that the V-shaped blade with
$\Delta V=0.6c$ improves the power outputs from moderate to high tip speed
ratios. In the previous study, it has been demonstrated that the V-shaped
blades effectively increase the torque output in a small part of the upwind
region and half of the leeward region ($115^{\circ}<\theta\leq 180^{\circ}$),
where the drag coefficient of blade is significantly reduced and the local
mutation of drag coefficient would be eliminated. Besides, for the whole
rotor, the fluctuation of torque output of the V-bladed VAWT is smaller than
that of baseline turbine (see Fig. 14). The more detailed explanation can be
found in Refs. Su et al. (2020); Zhang et al. (2020). Over all tip speed
ratios, the improved blade increases the maximum power coefficient by
24.1$\%$, while the value of $C_{P}$ is reduced at low tip speed ratios. The
statistical results show that the average power increment for the modified
blade from moderate to high tip speed ratios is 14.63$\%$.

Similarly, the thrust coefficient was investigated under all operating
conditions. It is well known that the thrust coefficient of the wind turbine
increases with the rotational speed. Compared with the variation curve of
thrust coefficient of the straight-bladed VAWT, it can be found that the
V-shaped blades do not alter this trend. However, it is noticed that the
thrust coefficient of the modified wind turbine blade is less than that of the
original one at low tip speed ratios, while the value of $C_{thrust}$ is
higher than the baseline value at high rotational speed. Although the
increment in $C_{thrust}$ is relatively small at high tip speed ratios, in
terms of structural design, more consideration should also be given to the
loads on the wind turbine blades and tower.

Figure 7: Comparison of the power coefficient and thrust coefficient under
different tip speed ratios between V-shaped blade and straight blade: (a)
power coefficient; (b) thrust coefficient.

###  4.2 Acoustic characteristics

In the following sections, only the baseline model and the V-shaped blade
$\Delta V=0.6c$ with the best performance in $C_{P}$ are investigated at
different tip speed ratios for acoustic analysis. To study the acoustic
characteristics of VAWTs, Fig. 8 presents the noise spectra of studied VAWT at
different tip speed ratios. It can be found that the distinguishing tonal
peaks appear at $f$=14.2, 21.0, 21.7, 25.9, and 27.5 Hz corresponding to the
rotational speeds of wind turbine blade. Besides, the higher tip speed ratio
usually induces larger noise level especially at low frequency. This trend is
not changed in the acoustic spectrum of the VAWT with modified blades.

Figure 8: The sound pressure level of the baseline VAWT under different tip
speed ratios.

Figure 9: The 1/3 octave band spectra of the sound pressure level observed at
a radial distance of 8$D$ from the center of rotor in four directions at
$\lambda=2.6$: (a) upwind direction; (b) downwind direction; (c) windward
direction; (d) leeward direction.

It is clear that observing the overlapping parts of different noise spectra in
logarithmic coordinates is difficult, and generally it is not necessary to
carry out specific analysis of each frequency component. Thus, the 1/3 octave
band spectra of sound pressure level were adopted to compare the noise level
between the straight-bladed and V-bladed wind turbines. Fig. 9 illustrates the
spectra of the sound pressure level of straight blade and V-shaped blades
observed at the radial distance of 8$D$ from the center of rotor in four
directions at the optimal operating condition $\lambda=2.6$. It can be found
that the sound pressure level of all studied wind turbine blades is large in
the low-frequency and high-frequency ranges, while the noise level is
relatively small in the medium frequency (200 Hz-900 Hz). Besides, it is
observed that V-shaped blades generally make less noise in low frequency
($f<100$ Hz). Compared with that, the high-frequency noise of the improved
blade is larger than that of baseline model in four directions. On the other
hand, the noise emitted from the baseline model is almost the same in
different directions (the black solid line in Fig. 9). On the contrary, the
high-frequency noise of V-shaped blades is found to be larger in the windward
and leeward directions than that in upwind and downwind directions. This
involves the directivity of the VAWT noise propagation, which would be
elaborated in the next section.

Figure 10: The 1/3 octave band spectra of the sound pressure level observed at
a radial distance of 8$D$ from the center of rotor in the downwind direction
at different tip speed ratios: (a) $\lambda=1.7$; (b) $\lambda=2.52$; (c)
$\lambda=3.1$; (d) $\lambda=3.3$.

For the same reasons as described above, the 1/3 octave band spectra of the
V-shaped blade $\Delta V=0.6c$ and the original blade were investigated at
other tip speed ratios. The comparison of sound pressure level between
straight-bladed wind turbine and V-bladed VAWT at a distance of 8$D$ in the
downwind direction is shown in Fig. 10. The trend that high-frequency noise of
V-shaped blade is larger than that of baseline blade also occurs at other four
tip speed ratios. In the low frequency range, the noise of V-shaped model is
lower. This phenomenon is contrary to the findings on J-shaped blade noise in
Ref. Mohamed (2019), where lower noise levels were in high frequencies and
high sound levels occurred in low frequencies for modified J-shaped wind
turbine. It is known that the low-frequency noise of wind turbines can spread
over long distances and easily permeate the building structures, causing high
annoyance Liebich et al. (2021). From this perspective, it seems that the
V-bladed VAWT that produces lower low-frequency noise performs better for the
human body. Besides, it can be found that as the rotational speed increases,
the low-frequency range of $SPL_{V}<SPL_{Base}$ becomes narrow. In general,
however, the results suggest that the noise emitted from the V-bladed VAWT is
greater. This phenomenon of increasing power while unexpectedly causing
increased noise is similar to that of Wind-Lens turbine Hashem et al. (2017).

###  4.3 Noise directivity

The directivity of the predicted overall SPL (OASPL) of two types of wind
turbines at three sections with different heights at $\lambda=2.6$ is
illustrated in Fig. 11. For the traditional VAWT, it can be observed that the
noise directivity presents a relatively full elliptical distribution
characteristic as presented in Fig. 11 (a). The isopleth range of OASPL is
slightly smaller in the upwind and downwind directions. This pattern is
consistent with the results reported by Aihara et al.Aihara et al. (2021) and
Liu et al. Liu et al. (2022), although the data in the former study were only
based on the frequency bands from 25 to 3100 Hz. Besides, the noise in the
leeward region is found to be larger than that on the windward side, which
coincides with the results of Refs. Aihara et al. (2021); Liu et al. (2022);
Rasekh and Karimian (2021). On the other hand, an interesting finding in this
study is that the V-shaped blades change the distribution pattern of VAWT
noise from elliptical to dumbbell-shaped as shown in Fig. 11 (b). The noise
level in the windward and leeward regions is obviously larger than that in the
upwind and downwind directions. Besides, it can be observed that the noise
level at the middle horizontal section is higher and the radiation range is
wider. It is found that at the same distance from the center of wind turbine,
the noise level at the middle section is about 5 dB higher than that at the
top or bottom section. It suggests that strategically altering the height
position of small VAWTs may cause less noise annoyance for potential receivers
in urban areas. Based on the previous study, the enhancement in power
coefficient was mainly attributed to the middle part of the V-shaped blade,
while more energy was lost in the blade tip region Su et al. (2020). Besides,
a pair of symmetric vertical structures formed near the blade midspan due to
the induced downward velocity Zhang et al. (2020). This uneven distribution of
blade surface loads as well as the pressure fluctuations may partly explain
the larger noise emitted from V-bladed VAWT.

Figure 11: Directivity and distribution pattern of OASPL of two types of wind
turbines at $\lambda=2.6$: (a) straight-bladed VAWT; (b) V-bladed VAWT $\Delta
V=0.6c$.

It is well known that the rotor of the HAWT is a typical dipole sound source.
Thus, the noise directivity of HAWTs usually presents a dumbbell-shaped
distribution as shown in Fig. 12 Kaviani and Nejat (2017), or has a
symmetrical cardioid shape as revealed the BPM method in Refs. Zhu et al.
(2005, 2018); Bresciani et al. (2022). Based on the similarity of distribution
patterns between the V-bladed VAWT and conventional HAWTs, it can be inferred
that the effect of dipole noise, namely the loading noise, becomes larger for
the V-bladed VAWT. Besides, it should be noted that the orientation of
dumbbell-shaped distribution pattern of the V-bladed VAWT is different from
that of the HAWT. With the wind blowing from left to right, as shown in Fig.
11 (b) and Fig. 12, the two ends of the dumbbell pattern of the V-bladed VAWT
are in the windward and leeward regions, while the two ends of the dumbbell
pattern of the HAWT are in the upwind and downwind positions, respectively.
This dumbbell-shaped distribution could be explored for optimizing wind farms
to minimize noise disturbance to potential residents.

Figure 12:  The noise directivity of the HAWT Kaviani and Nejat (2017).

To make further investigation on the physics behind the shift in the noise
directivity patterns, the components of total noise are studied. As is well
known, the tonal noise emitted from VAWTs can be divided into the thickness,
loading, and quadrupole noise, among which the thickness and loading noise are
the dominant noise sources while the quadrupole noise usually has negligible
influence. Therefore, the distribution patterns of thickness and loading noise
of the baseline model and V-bladed turbine were investigated as presented in
Fig. 13. It is clear that the thickness noise, as also called the monopole
noise, is nearly uniform in directivity in all directions. The V-shaped blade
increases the noise level of thickness noise, but the distribution pattern
does not change. On the other hand, in the case of applying V-shaped blades,
the characteristics of the dipole sound source are more pronounced. As shown
in Fig. 13 (d), the dumbbell-shaped distribution is clearer, and the
propagation range of the loading noise is larger.

Figure 13: Comparison of the components of total noise: (a) the thickness
noise of baseline model; (b) the loading noise of baseline model; (c) the
thickness noise of V-bladed VAWT $\Delta V=0.6c$; (d) the loading noise of
V-bladed VAWT $\Delta V=0.6c$.

Moreover, the overall noise level of the studied VAWTs was compared with that
of the HAWTs with similar size as shown in Table 3. Here, the results of the
noise level of HAWTs were published by Ocker and Blumendeller et al. Ocker et
al. (2022). The reason for choosing this set of noise data for HAWTs is that
the sizes of the tested HAWTs are similar to that of the present VAWT, and the
operating conditions are basically the same. Besides, the Strouhal number and
Mach number of the scaled HAWTs in the experiments are comparable to those of
full-size wind turbines, which means that to some extent it can reflect the
acoustic properties of large HAWTs. The comparison of the noise levels between
the studied VAWTs and the HAWTs with similar size is presented in Table 3. It
can be observed that the noise levels of VAWTs are generally lower than those
of HAWTs. Even if the V-shaped structure increase the noise emitted from the
VAWT, its OASPL is still lower than that of HAWT under similar operating
conditions.

Table 3: Comparison of the overall SPL between the studied VAWTs and the HAWTs with similar size. WT | Receiver | Diameter | Blade | OASPL (dB)
---|---|---|---|---
distance |  $U_{\infty}$=5 m/s | 7 m/s | 9 m/s
HAWTOcker et al. (2022) | 1.96 m | 1.5 m | NACA 4412 shape | 101.2 | 107.7 | 111.9
1.29 m | Clark-Y shape | 102.4 | 104.4 | 114.4
1.16 m | Sickle shape | 101.0 | 106.8 | 111.5
VAWT | Receiver | Diameter | Blade | OASPL (dB)
distance | and height |  $U_{\infty}$=9 m/s
2.1 m | 1.05m$\times$ | NACA0021 Straight | 79.6
1.465m | NACA0021 V-shaped | 91.8

###  4.4 Effect of trailing-edge serrations

The previous results indicate that the V-shaped blade could effectively
increase the power output of a VAWT, although its OASPL is higher than that of
the conventional straight-bladed VAWT. It suggests that there is value in
reducing noise of the V-bladed VAWT while increasing power performance as much
as possible. Therefore, this subsection attempts to further explore the noise
reduction effect of trailing-edge serrations on the V-bladed wind turbine.

####  4.4.1 Aerodyamics

The variations of torque coefficient and thrust coefficient for the VAWT with
different modified blades at the optimal tip speed ratio $\lambda=2.6$ are
shown in Fig. 14. Besides, the averaged values of torque coefficient $C_{Q}$,
power coefficient $C_{P}$ and thrust coefficient $C_{thrust}$ are calculated
as listed in Table 4. It can be observed that the output torque coefficient
$C_{Q}$ for the baseline blade fluctuates most violently, where the peak value
of $C_{Q}$ exceeds 0.3 and the lowest value is less than 0. Compared with
that, the peak value of $C_{Q}$ of the V-bladed wind turbine is slightly less
than that of the straight-bladed model, while the lowest $C_{Q}$ is greatly
improved by the V-shaped blades due to its superiority in reducing drag
coefficient. In this way, the V-bladed VAWT can achieve higher power output
with up to 24.11$\%$ increase in $C_{Q}$ and $C_{P}$. After applying the
trailing-edge serrations, the peak value of $C_{Q}$ of the wind turbine rotor
decreases, and the fluctuations are further reduced. The results show that the
averaged torque output of the modified wind turbine blade with trailing-edge
serrations is slightly higher ($3.35\%$) than that of the blade without this
structure. For the thrust coefficient, similarly, the fluctuation of
$C_{thrust}$ for the V-shaped blade with trailing-edge serrations is smallest,
and the averaged $C_{thrust}$ is also higher than that without trailing-edge
serrations.

Figure 14: Comparison of the fluctuations of the torque coefficient and thrust coefficient of the whole rotor with different blades: (a) torque coefficient; (b) thrust coefficient.  Table 4: The averaged torque coefficient $C_{Q}$, power coefficient $C_{P}$ and thrust coefficient $C_{thrust}$ for the VAWT with different modified blades at $\lambda=2.6$. Blade | $C_{Q}$ | $C_{P}$ | Increment ($\%$) | $C_{thrust}$ | Increment ($\%$)
---|---|---|---|---|---
Baseline | 0.1162 | 0.3023 | - | 0.9766 | -
$\Delta V=0.6c$ | 0.1443 | 0.3751 | 24.11 | 0.9809 | 0.44
$\Delta V=0.6c$ -serrated | 0.1491 | 0.3877 | 28.27 | 1.0297 | 5.43

In the previous studies, it was generally considered that utilizing trailing-
edge serrations or sawtooth structures would deteriorate the aerodynamic
performance of the single blade Liu et al. (2017); Llorente and Ragni (2019).
However, it was also reported that this kind of trailing-edge modification
would slightly increase the power performance of wind turbines under certain
conditions Llorente and Ragni (2020); Zhou et al. (2022). The present results
confirm this phenomenon on the VAWT, although it has only been found on HAWTs
before Llorente and Ragni (2020). To explain this difference in the effect of
trailing edge serration structure on blade performance under different
conditions, more research is needed in the future.

####  4.4.2 Aeroacoustics

Fig. 15 presents the comparison of the tonal noise between V-shaped blades and
V-shaped blades with trailing-edge serrations at different heights. The
overall SPL over the entire frequency range was used to depict the
distribution pattern of wind turbine noise. It can be observed that applying
the serrations to the blade trailing edge would reduce the noise emitted from
the wind turbine. The noise reduction mechanism of trailing-edge serration
structure has been extensively studied Azarpeyvand et al. (2013); Gruber
(2012). The previous results suggested that the noise reduction due to
serration structure originated primarily from the interference effects near
the blade trailing edge Gruber (2012). Besides, the use of serrations can lead
to significant reduction of turbulent kinetic energy and Reynolds shear stress
in the near wake region, thereby reducing the turbulence interaction noise Liu
et al. (2016). According to the values marked on the isopleth in Fig. 15, the
OASPL of serrated V-bladed wind turbine is about 5 dB lower than that of the
unmodified V-bladed VAWT at the same distance from the center of wind turbine.
But it is clear that the dumbbell-shaped noise distribution pattern has not
changed. The results indicate that the trailing-edge serrations could reduce
the noise of VAWTs.

Figure 15: Directivity and distribution pattern of OASPL of two types of wind
turbines at $\lambda=2.6$: (a) V-bladed VAWT $\Delta V=0.6c$; (b) V-bladed
VAWT $\Delta V=0.6c$ with trailing-edge serrations.

To better assess the noise level to which human hearing is sensitive, as well
as to quantify the noise reduction effect of wind turbines, the A-weighted
overall SPL based on the frequency bands from 25 to 5000 Hz was calculated.
Fig. 16 shows the A-weighted OASPL of the studied wind turbine with different
blades. It can be found that the noise level decreases with the distance from
the wind turbine center. The A-weighted noise level of V-bladed wind turbine
is larger than that of the straight-bladed turbine. After applying the
trailing-edge serrations, the noise level is reduced by up to 2.8 dBA, and the
average noise reduction is about 2.3 dBA. This effect is similar to that found
in Ref. Oerlemans et al. (2009). Because this section is a preliminary
application study of trailing-edge serrations on the V-bladed VAWT, only one
recommended serration structure was investigated. The optimal trailing-edge
serrations for the VAWT with V-shaped blades will be studied in the future
work. In summary, the power and thrust coefficients of the studied V-bladed
VAWT with trailing-edge serrations are about 28.3$\%$ and 5.4$\%$ higher than
those of the baseline turbine. Although the A-weighted noise level of the
former is higher than that of the original wind turbine, its noise level is
still much lower than that of the HAWT.

Figure 16: The recorded A-weighted OASPL at different distances for the
studied wind turbine with different blades.

##  5 Conclusion and outlook

The present study investigated the aerodynamic performance and aeroacoustic
characteristics of a small VAWT with V-shaped blades under different
rotational speeds. The CFD model combined with FW-H method was utilized to
evaluate the effects of different V-shaped blades on the aerodynamic forces
and the wind turbine noise level. In addition, as one of the noise reduction
techniques, the trailing-edge serration structure was applied to the wind
turbine blades to assess the noise reduction effect. The main conclusions are
summarized as follows:

1\. At the optimal tip speed ratio $\lambda=2.6$ of the VAWT, the V-shaped
blade $\Delta V=0.6c$ achieved the highest enhancement in power output
compared with the other blade models. This type of V-shaped blade could
effectively improve the power performance of VAWT over a wide range of tip
speed ratios. The maximum increase in power coefficient can reach about
24.1$\%$, while the average power increment for the improved blade is about
14.6$\%$ from moderate to high tip speed ratios.

2\. Under all operating conditions, the V-shaped blades only slightly change
the thrust coefficient of the VAWT. Specifically, the V-bladed wind turbine
generates lower thrust coefficient at low rotational speeds, and produces
larger value of $C_{thrust}$ at high tip speed ratios. The increase in
$C_{thrust}$ on the structure is less than 4$\%$.

3\. The trailing-edge serrations slightly increase the rotor torque output and
thrust of V-bladed VAWT. The power and thrust coefficients of the V-bladed
wind turbine with trailing-edge serrations are about 28.3$\%$ and 5.4$\%$
higher than those of the baseline turbine at the optimal tip speed ratio.

4\. In the acoustic spectrum analysis, the V-bladed VAWT generates less low-
frequency noise compared with that of the original model in the four noise
propagation directions under different tip speed ratios, which is better for
the human body. As the rotational speed increases, the low-frequency range of
$SPL_{V}<SPL_{Base}$ became narrow.

5\. The noise directivity of the straight-bladed VAWT presented a relatively
full elliptical distribution characteristic, while a dumbbell-shaped noise
directivity distribution was discovered for the studied V-bladed wind turbine,
which can be utilized to reduce noise disturbance in wind farm layout.

6\. The trailing-edge serrations realized the expected noise reduction effect,
and the average noise reduction was about 2.3 dBA. Although the A-weighted
noise level of the former is higher than that of the original wind turbine,
its noise level is still much lower than that of the HAWT.

In the practical engineering applications, the cost and difficulty of making
V-shaped blades could be reduced by utilizing the existing manufacturing
process of straight blades. The trailing-edge serrations can be made
separately and installed on the blade as an optional part to meet the
requirements of different work scenarios.

In summary, the results of this work add new knowledge to the design of VAWTs
with high power output and low noise annoyance. However, there are still some
limitations in this study. In the future, research should focus on the
structural response of V-bladed wind turbine, the parameter optimization of
trailing edge serrations and their distribution along the blade span. Besides,
the mechanism that the trailing edge serrations can improve the power output
under certain conditions is also worth exploring

## Acknowledgments

The authors gratefully acknowledge the financial support by the Innovation
Program of Shanghai Municipal Education Commission (No.
2019-01-07-00-02-E00066), the National Natural Science Foundation of China
(Nos. 42076210, 52122110, 52088102, 12202271) , and Oceanic Interdisciplinary
Program of Shanghai Jiao Tong University (Nos. SL2020PT201, SL2021PT302).

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