Content uploaded by Mesfin Belayneh Ageze
Author content
All content in this area was uploaded by Mesfin Belayneh Ageze on Dec 14, 2024
Content may be subject to copyright.
Available via license: CC BY 4.0
Content may be subject to copyright.
Perspectives of Vertical Axis Wind Turbines in Cluster Configurations
Ryan Randall
1
, Chunmei Chen
1
,
*
,Mesfin Belayneh Ageze
2,3
and Muluken Temesgen Tigabu
4
1
College of Automation, Qingdao University, Qingdao, 266071, China
2
Center for Renewable Energy, Addis Ababa Institute of Technology, Addis Ababa University, Addis Ababa, 1000, Ethiopia
3
BTeQ R&D Labs, Addis Ababa, 1000, Ethiopia
4
Bahir Dar Energy Center, Bahir Dar Institute of Technology, Bahir Dar University, Bahir Dar, 6000, Ethiopia
*Corresponding Author: Chunmei Chen. Email: chunmei.chen@qdu.edu.cn
Received: 06 September 2024 Accepted: 19 November 2024
ABSTRACT
Vertical Axis Wind Turbines (VAWTs) offer several advantages over horizontal axis wind turbines (HAWTs),
including quieter operation, ease of maintenance, and simplified construction. Surprisingly, despite the prevailing
belief that HAWTs outperform VAWTs as individual units, VAWTs demonstrate higher power density when
arranged in clusters. This phenomenon arises from positive wake interactions downstream of VAWTs, potentially
enhancing the overall wind farm performances. In contrast, wake interactions negatively impact HAWT farms,
reducing their efficiency. This paper extensively reviews the potential of VAWT clusters to increase energy output
and reduce wind energy costs. A precise terminology is introduced to clarify ambiguous terms researchers use to
quantify cluster parameters. While examining commonly studied and proposed VAWT cluster configurations,
several aspects are discussed such as aerodynamic interactions, wake characteristics, structural dynamics, and per-
formance metrics. Additionally, the current state-of-the-art and research gaps are critically described. The review
also covers computational modeling, optimization techniques, advanced control strategies, machine learning
applications, economic considerations, and the influence of terrain and application locations.
KEYWORDS
Vertical axis wind turbines (VAWTs); cluster configuration; wind farm; wind energy; performance enhancement
1 Background
During the past decade, a remarkable surge in the adoption of renewable energy sources has been
witnessed. Reference [1] evaluated renewable energy development between 2012 and 2021. The global
consumption of renewable energy rose from 480 to 1945 GW, and wind energy use grew by 562%, from
283 to 845 GW. Generally, wind energy conversion systems are classified based on the axis of rotation of
the rotor, as either horizontal axis wind turbines (HAWTs) or vertical axis wind turbines (VAWTs).
Research into VAWTs cluster aerodynamics is growing, encompassing rotor aerodynamics and inter-
turbine wake interactions. Rotor aerodynamics studies are promisingly undertaken to improve the
aerodynamic performance of VAWTs [2–4]. Several researchers used different strategies to enhance the
overall performance of VAWTs. It has been found that the core of rotor aerodynamics is to have a high-
efficiency turbine at low tip speed ratios and enhanced self-starting capability such as the studies of
Copyright © 2024 The Authors. Published by Tech Science Press.
This work is licensed under a Creative Commons Attribution 4.0 International License, which permits un-
restricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
DOI: 10.32604/fdmp.2024.058169
REVIEW
ech
T
PressScience
Published Online: 12 December 2024
[5–8]. Some of the strategies are presented here, Reference [9] proposed a novel hybrid Darrieus and
modified-Savonius turbine to achieve an efficient turbine through a rotor aerodynamics study. Reference
[10] implemented blade pitch to control the turbine blade which resulted in performance improvements,
Reference [11] studied integrates the aerodynamic characteristics with that of the vibration characteristics
used to investigate performance VAWTs by comparing with HAWTs.
On the other hand, the wake modeling deals with the flow fields downstream, the detailed review of
available wake models is highlighted by [12,13]. The wake effect refers to an aerodynamic phenomenon
produced by each turbine behind its rotor. Reference [12] demonstrate that due to the effect of dynamic
stall, the wake aerodynamics of VAWTs are more complex than HAWTs. Because of the Magnus effect,
which is described by [14], and deep dynamic stalls at windward, the wake of VAWTs demonstrates
strong asymmetry in the horizontal direction. Using wake aerodynamics modeling, several researchers
showed that HAWTs have higher efficiency as compared with VAWTs. However, this argument is valid
when both turbines operate in isolation. It has been reported by several authors that arranging HAWTs in
clusters leads to a decrease in performance, due to the turbulent wakes of adjacent wind turbines. The
main issue with wakes is that it requires a large distance to fully recover, for this reason, it is necessary to
install wind turbines as far as possible from one another. Spacing the turbines apart offers another notable
benefit to reducing the fatigue load due to upstream turbines’turbulence. This results in the use of land
which is most of the time not feasible. To avoid the effect of wakes, HAWTs in a wind farm need to be
placed at least 20 rotor diameters (20D) apart in the downwind direction. Similarly, the study of [15]
presented that for modern wind farms, HAWTs are typically spaced 3 to 5 rotor diameters apart in the
cross-wind direction and 6 to 10 diameters apart in the stream wise direction. This arrangement aims to
minimize aerodynamic interference between adjacent turbines. According to [16] the minimum distance
required for VAWTs to recover the wake is about 6 times the diameter of the turbine. Furthermore,
Reference [17] tests a hypothesis that arranging VAWTs in clustering can provide enhanced performance
as compared with HAWTs. They verified that coupled configurations of counter-rotating VAWTs can
provide improved performance. An appropriate arrangement of turbines in clusters plays a vital role in
decreasing wake. Hence, it is possible to lower wake losses and raise the wind farm energy generation by
considering this impact while placing the turbines.
The present paper explores the perspectives of using VAWTs in cluster configurations. This
comprehensive review contains all aspects of vital information required for the clustering of VAWTs such
as theoretical models, computational and numerical tools, optimization techniques, economic and market
assessments, and other relevant aspects.
1.1 Review Methodology
The objective of the literature review is to determine and map research and project findings related to
VAWTs in cluster configuration. The review aimed to provide insights into future perspectives to increase
their global wind energy share with HAWTs. To examine the perspectives of VAWTs in the cluster
configuration and identify key research gaps, a systematic literature review approach was adopted from
the study of [18]. Synonyms for the following keywords were identified based on themes and
terminology from a preliminary literature review: VAWTs, cluster configuration, and wind farm. The
strings were used to search for titles, abstracts, and keywords of publications in Web of Science and
Scopus. A total of 287 publications were found in the search, but after removing duplicates, 110 relevant
ones were reviewed through abstract reading. Out of those, only 97 were systematically reviewed.
Finally, 94 publications were found to be relevant and included in the final literature review. The review
process of these 94 papers was based on a predefined protocol consisting of four themes: common cluster
2FDMP, 2024
configurations, computational modeling approaches and tools, optimization methods, and market and
economics perspectives. Additionally, the performance comparison with HAWTs in cluster configurations
was also reviewed.
1.1.1 Cluster Configuration vs. Wind Farm
According to a literature survey on the Scopus database, searching for VAWTs and cluster configuration,
and VAWTs and wind farm as separate keyword combinations resulted in a different number of papers. The
search returned 287 papers related to VAWTs and wind farms (see Fig. 1), and 56 papers related to VAWTs
and clusters (see Fig. 2). It’s worth mentioning that, during our search, we noticed that the term “wind farm”
was more commonly used in the Scopus database as compared to the term “cluster”. However, these terms
have been used by several authors to imply and convey similar meanings. In general, Figs. 1 and 2show that
the attention to VAWTs has significantly increased. In this study, a comprehensive review was conducted,
including a total of 94 papers.
1.1.2 Scope of the Review
The present review covered the state of research related to VAWTs cluster configurations and identified
prospective research gaps in this area. It discussed several cluster configurations studied in the literature
(Section 2), reorganized Section 3 into modeling and optimization, and experimental tests and
Figure 1: Number of published papers based on Scopus database with VAWTs and wind farm as search
keywords
Figure 2: Number of published papers based on Scopus database with VAWTs and cluster as search keywords
FDMP, 2024 3
prototyping, presented findings from the experimental work (Section 4), provided insights into the market
and economic aspects (Section 5), and some aspects of terrain and application (Section 6). The paper
concluded by discussing key research gaps that require further investigation in this domain.
1.2 Terminology
To draw clarity among researchers’usage of different terms for VAWTs cluster, the following sections
brieflydefined cluster parameters. Fig. 3 describes the most commonly used terminology used in the study
and optimizations of the VAWTs cluster configurations.
To further elaborate on these terminologies, Table 1 is provided. The description provided in the table
can be referred to better understand the specific meaning and context of these important terminologies.
Figure 3: Cluster configuration terminology
Table 1: Common terminology used in cluster configurations of VAWTs
Terminology Descriptions Reference
Arrangement angles (Oblique angles
or Angular arrangement)
The relative positioning of wind turbines in clusters. It
is the angle between the line connecting the centers of
two turbines and the wind direction
[19–21]
Blade pitch angles (BPA) Angle between the chord line of the blade and the plane
of rotation
[17]
Blockage ratio The ratio of the turbine frontal area to the total frontal
area of the farm. It depicted the flow blocked by the
upstream turbines in a cluster
[22,23]
Characteristic diameter It is the outer diameter of the rotor [24]
Counter-down rotating turbines The turbines are placed in a configuration where they
rotate in opposite directions, along the wind direction
[25]
Counter-up turbines The turbines are placed in a configuration where they
rotate in opposite directions, against the wind direction
[25]
Tip speed ratio The ratio of the blade tip tangential and the free-stream
wind velocity
[24]
Turbine spacing (distance between
turbines)
The distance between individual wind turbines [26,27]
(Continued)
4FDMP, 2024
2 Cluster Configurations
A VAWT can be classified by several factors, including the alignment axis of rotation to the wind flow
direction (cross-flow or vertical), and the blade orientation (straight, helical, curved) [31]. For this review, the
main classification used is according to the type of force acting on the blades, i.e., drag force-based Savonius
and lift force-based Darrieus. These types of turbines are commonly employed in the isolation or clustering
of VAWTs due to their simplicity, fewer moving parts, and scalability when compared to other types of
VAWTs. Recently, several VAWTs cluster configurations have been studied, to enhance the performance
of the farm. Most of them are inspired by common geometry relations and bio-mimicry configurations of
two or three VAWTs. The work of [32] demonstrates the implementation of bio-inspired configurations to
VAWTs, they used Darrieus VAWT and their respective performance. Migrating birds and fishes can
travel farther by positioning themselves at specific coordinates and gaining from the vortices shed by
those ahead of them. Reference [25] reviewed different cluster configurations as the arrays of two and
three VAWTs. They examined various parameters affecting the performance of clusters of VAWTs and
presented a general guideline for selecting suitable values for each parameter in future research. However,
the full implementation and realization of VAWTs in clusters still require substantial research. The
clustering of VAWTs is a promising area, but several important concerns need to be addressed. In the
spirit of this, the present reviews will provide substantial information and address different aspects of
clustering VAWTs to further explore new possibilities. We have performed a thorough review of the
existing clustering configuration suggested and studied by different authors. The findings of the review
are summarized and briefly described in Table 2. The findings of the review are systematically
summarized and briefly described in Table 2. This table provides a comprehensive exploration of various
cluster configurations of VAWTs, detailing their rotational directions, configuration type, and schematics.
Each configuration is presented with detial descriptions. Additionally, the schematics included in Table 2
visually represent the design and arrangement of each cluster, facilitating a better understanding of how
these configurations function in practical applications. This structured overview not only highlights the
diversity of VAWT designs but also underscores the potential advantages and limitations associated with
each configuration, making it a valuable resource for both researchers and practitioners in the field.
Table 1 (continued)
Terminology Descriptions Reference
Wake decay The gradual decrease in wind speed and increase in
turbulence intensity within the wake of a wind turbine
[25,28,29]
Wake recovery It is when the wind speed and turbulence levels within a
turbine’s wake gradually return to the free-stream
conditions as the wake moves downstream
[12,19]
Wake contraction It is the process when the wake of a wind turbine
narrows in diameter downstream, due to the effect of
surrounding air into the wake
[25]
Vortex shedding The periodic formation and detachment of swirling
vortices from the edges of wind turbine blades
[25,30]
Velocity wake The reduction in wind speed downstream of a wind
turbine, caused by the extraction of energy from the
wind by the turbine
[19,25]
FDMP, 2024 5
Table 2: Review various cluster configurations of VAWTs
Ref. Rotational
directions
Number
of
turbines
Configuration type Description Schematics
[25] Co-rotating,
Counter-
rotating
along the
wind
direction,
Counter-
rotating
against the
wind
direction,
Co/counter-
rotating
2 Co-rotating,
Counter-down
rotating, Counter-
up rotating, Two
staggered co-
rotating up,
Tandem, Two
staggered co-
rotating down
The Counter-down configuration
generates more power due to stronger
vortex interaction. While co-rotating
configuration generates more power
than counter-up configuration.
Counter-down configuration is more
efficient for both parallel straight-
blade Darrieus and staggered wind
turbines. For two largely spaced
tandem wind turbines, the counter-
rotating configuration showed better
performance.
[19,33] Co-rotating
wind
turbines,
counter-
rotating, All
co-rotating
wind
turbines
3 Triangular Placing turbines nearby, it’s essential
to consider the flow created between
them and how it interacts with the
wind. However, for wider spacing, the
primary factor is the direction of the
wake deflection behind the upstream
turbines. The induced flow and the
wake deflection direction depend on
the rotation direction of the turbines.
For optimal results, a cluster with
counter-rotating downstream turbines
is best for smaller spacing, while co-
rotating turbines are ideal for larger
spacing.
Wind
turbines
rotate in the
same
direction and
the opposite
direction of
the turbine
[34] Counter-
rotating
4 Four counter-
rotating straight
blade Darrieus
wind turbines
It has been found that using small
values of b(between 0 to 7.5 degrees)
results in better cluster performance.
This is because, for such small values
of b, the impact of the wake coming
from the wind turbines situated
upstream on the ones situated
downstream is minimal.
[35] Counter
rotating
4 × 4, 16
× 16,
and 32 ×
32
Fish schooling Compared to a single wind turbine,
the power output of these
configurations has significantly
increased.
(Continued)
6FDMP, 2024
Table 2 (continued)
Ref. Rotational
directions
Number
of
turbines
Configuration type Description Schematics
[36] Co-rotating 7 Single column
configuration of
straight blade
Darrieus wind
turbines
The column generates 50% to 100%
more power than a single wind
turbine.
[37] Co-rotating 7 × 5 Column
configuration of
straight blade
Darrieus wind
turbines
Downstream turbines are more
efficient than upstream turbines, for
optimal farm layout.
[38] Counter-
rotating
9 9 pairs of counter-
rotating straight
blade Darrieus
turbines
The counter-down outperform the
counter up configuration in power
generation. Furthermore, the average
power coefficient of each line
decreases from Line 1 to 3, while
remaining nearly constant from Line
3to5.
[33] Co-rotating 9 3 triangular shaped
cluster co-rotating
straight blade
Darrieus turbines
The power density of a cluster of
9 turbines is 13 times greater than that
of 9 isolated turbines.
[26] Co-rotating 27 27 pairs of co-
rotating Savonius
wind turbines
The power density of the wind
clusters of 9 and 27 turbines are
7 times greater than 9 isolated
turbines, and 4 times greater than
27 isolated turbines, respectively.
(Continued)
FDMP, 2024 7
Table 2 (continued)
Ref. Rotational
directions
Number
of
turbines
Configuration type Description Schematics
[39] Co-rotating 8 2, 8 and 16 co-
rotating Savonius
wind turbines
Increasing the number of turbines and
reducing the spacing between them
can lead to higher power generation.
For instance, increasing the number of
turbines from 2 to 16 can increase
power output by 19%. For the
8 turbines cluster, the efficiency of
those in the middle of the column is
better with larger turbine spacing,
whereas those at the bottom generate
more power when the spacing is
smaller. The difference in power
generation between top and bottom
wind turbines is due to the direction of
their rotation.
[40] Co-rotating
and counter
Multiple Aligned (see A),
Staggered (see B),
Staggered
triangular clusters
(see C), Staggered
triangular clusters
(see D)
It was discovered that wind farms
with staggered triangular clusters with
an angle less than ,90are more
efficient. This is because the
synergistic interaction between
clusters results in improved power
generation.
[41] Co-rotating
and counter
Multiple Planetary cluster The optimal cluster resulted in an
efficiency increment of 1.01% on the
performance of the “sun”turbine in
the planetary arrangement over the
isolated turbine.
[42] Aligned
collocated
wind plant,
Staggered
collocated
wind plant
Multiple Collocating cluster
of HAWT and
straight VAWT
Aligned VAWTs and HAWTs
upstream resulted in a 3.5% increase
in power. Staggered arrangement
caused a 2.6% decrease. Aligned
configuration produces a similar wake
to a traditional HAWT. A staggered
configuration produces two
interacting wakes that generate a more
confined skewed wake.
[43] Mixed with
HAWT and
windbreaks
Multiple Vertically
staggered cluster
of HAWT and
VAW T
Both windbreaks and VAWTs aid in
the recovery of the upstream wind
turbine wake by facilitating the
mixing of wind flow and reducing
wind shear, thereby increasing the
power output of VSWFs.
8FDMP, 2024
3 Modeling and Optimization
3.1 Computational Modeling Approaches and Tools
One of the important topics in clustering VAWTs is the interaction between each turbine. Usually, this
interaction is the most vital to optimizing and modeling the performance of clustered turbines. The wake
interaction between turbines significantly determines the performance of the farm and the structural loads.
Hence, the state-of-the-art aerodynamics modeling approaches for VAWT cluster configurations are
examined in the following section. Furthermore, the review is extended to understand the structural
dynamics of VAWTs under the influence of farm wake and turbulence.
3.1.1 Aerodynamics Models
To this end understanding the wake of each turbine is vital, which has led researchers to develop various
methodologies for modeling it. There are various methodologies available to model the wake some of them
are (1) analytical models such as the diploe model, top-Hat Wake Model, and actuator model, (2)
computational fluid dynamics (CFD) which includes Reynolds-averaged Navier–Stokes (RANS) and
large-eddy simulation (LES) methods, and (3) field measurements or wind tunnel experiments. The
comparisons of different aerodynamics models are provided in Table 3.
CFD methods involve numerically solving fluid equations (such as Navier-Stokes equations) using
computational methods, which provide a detailed representation of the flow field. The fidelity of CFD
methods for the study of VAWTs are well presented by [51], they investigated seven eddy-viscosity
Table 3: Comparison of aerodynamic and flow characterization modeling tools for VAWTs in cluster
Model name Approach Accuracy Reference
CFD methods:
Reynolds-Averaged Navier-Stokes
(RANS)
Averaging over time to obtain statistical
mean values of variables
Moderate [44]
Large-Eddy Simulation (LES) Directly simulate large-scale turbulent
structures
High [45,46]
Detached-Eddy Simulation (DES) Combine RANS and LES approaches in
different flow regions
High [45]
Unsteady Reynolds-Averaged
Navier-Stokes (URANS)
Solve unsteady RANS equations to capture
time-averaged behavior
Moderate [20]
Analytical methods:
Top-Hat wake model Assume a simplified rectangular wake
profile
Low [28]
Gaussian wake model Model wake using a Gaussian distribution Moderate [47]
Asymmetric Gaussian Wake Model Model asymmetric Gaussian wake with
varying parameters
Moderate [48]
Actuator Line Model (ALM) Represent blade aerodynamics using line
elements
Moderate [49]
Actuator Disk Model (ADM) Account for average velocity deficit caused
by turbine disk
Moderate [50]
Vortex model Represent interconnected vortices in the
wake
High [49]
FDMP, 2024 9
turbulence models to select the best-performing turbulence model. According to their findings, SSTk !is
the recommended model to investigate the aerodynamics of VAWTs.
On the other hand, analytical methods simplify the wake behavior using mathematical formulations
based on empirical correlations. They provide low computational cost insights into wake characteristics
and are commonly used for initial assessments, conceptual designs, and quick estimations of wind farm
performance. The relative performances of these models in terms of VAWTs cluster modeling have not
been extensively explored. However, a brief review of recent computational research using these
individual tools is discussed in the following sections.
One of the simplest analytical wake models used for VAWTs is proposed by [28] as the top-hat Wake
Model. The model assumes the wake downwind of the turbine to have a rectangular form. The rectangular
dimensions defined by Hwand Dw, which are defined by linear relationship as the wake is transported
downstream, and can be expressed as;
Hw¼Hþ2kwzx;Dw¼Dþ2kwy x(1)
where the constants used to define the wake expand in the normal direction at the rate of kwz and in the span-
wise direction at the rate of kwy.
Other wake models are based on continuity equation, conservation of momentum, and energy equation.
Since the flow pattern in wind turbine applications is classified as low Mach flow, roughly 0.1 according to
[52], the incompressible flow model is a good fit.
As the wind passes the turbines, it generates wake phenomena which have a negative effect on HAWTs
farms. However, wake generation has significant importance in VAWTs clusters. To optimize VAWTs cluster
layout, the wake effect must be modeled first. The wake effect is an aerodynamic phenomenon that occurs
when each turbine creates a disturbance in the flow of wind that passes through its rotor. This disturbance
causes the wind speed to decrease in the area behind the turbine, which results in less energy being
extracted by subsequent turbines. By taking the wake effect into account when placing the turbines in the
wind farm, it is possible to minimize wake losses and significantly increase the energy production of the
wind farm. Several attempts have been made to model the flow characteristics of VAWTs in cluster
configurations. The LES study of [45] for three different coupled configurations of VAWT for two values
of tip speed ratio (TSR). Their finding demonstrated that the vortex interaction between coupled VAWTs
wake is weak. However, the blockage effects play a significant role in creating a higher momentum flux
downstream. This effect is more pronounced at higher TSRs, indicating turbines in staggered wind farm
layout along the wind direction, can increase the momentum flux of downstream turbines. The
aerodynamics study of VAWTs using CFD provides a powerful tool to study and visualize the details of
complex wakes. There are three main modeling approaches these are RANS, LES, and DES. Hence,
these aerodynamics models are used for the flow characteristics of VAWTs in clusters to provide clear
insight for enhanced farm performance. The CFD investigation [53] using RANS kmodel for cross-
flow wind turbine for two type cluster configurations (1) aligned and (2) staggered configuration. Besides
configurations, they also varied the distance between the turbine into three categories 0.5D, 1D, and 1.5D
(D is the diameter of the turbine), and investigated the optimal distance between turbines within
configurations. Their findings indicated that the optimal arrangement is staggered, and the closest distance
between turbines can be 0.5D. In the wake zone, it is evident that the wind speed decreases, while the
turbulence intensity increases, resulting in a high wind speed shear before downstream turbines. Hence,
one of the advantages of a staggered layout is helps to reduce wake losses. The study of [54], used 2D
CFD-simulation aiming to improve the power output from two different VAWTs in tandem arrangement.
The simulation investigated the improvements by varying the array layout, rotational direction, and
spacing. The authors provide a broader insight how the rotation orientation of the turbines as co and
counter-rotating, the effect of turbine spacing, and the cluster layout. Their results indicated that pairs of
VAWTs generated 15% more power than isolated turbines, and increasing the number of turbines
10 FDMP, 2024
increased the overall efficiency. The hypothesis suggested for better performance of VAWTs clustering is the
wake interaction. The detailed wake characterization done by [45] coupled configurations using LES. They
found that the inter-turbine vortex interaction between wakes of coupled VAWTs is weak, resulting
improving performance compared to isolated turbines.
One of the common computational tools used in VAWTs cluster modeling is LES, for example [45] has
done LES of three different cluster configurations of VAWT at two TSRs. The mutual vortex interaction
between wakes of coupled VAWTs is determined to be weak. However, the blockage effects play a
significant role in achieving an increased momentum flux of downstream turbines. This effect is more
pronounced at higher TSRs, indicating that arranging staggered clusters can increase the momentum flux
of downstream turbines.
The study of [43] on vertical staggered wind farms (VSWFs). The study found that both windbreak and
VAWTs contribute to enhancing wake recovery of upstream wind turbines, leading to increased power output
as shown in Figs. 4 and 5. The power generation rate of VSWFs increases with turbine spacing, and VSWF
with VAWTs generates more power output than a windbreak. The height of the VAWTs significantly affects
the power output, and the optimal configuration should not have an overlapping area or gap between the
projection area of HAWT’s and VAWT’srotors, i.e., blockage effect.
The study of [55] employed 2D URANS simulations to identify an optimal arrangement based on average
turbine efficiency and area utilization efficiency. They have tested various arrangements that have been
demonstrated to provide better performance, such as bioinspired layouts, and new and hybrid designs with
several turbines. The capability of two-dimensional CFD analysis to accurately simulate the impact of the
wake on the performance of different VAWT farms is explored by [44]. They investigated two H-Darieus
turbines using a commercial tool called STAR CCM+. The study demonstrated for the downstream of
turbines that the wakes hold significant importance on the overall performance for a range of turbine
spacing 2.5D to 40D. Using CFD and combining the ALM with LES to accurately investigate the effect of
inter-turbine spacing and turbine rotation on the performance of VAWTs clusters have be studied by [49].
The ALM is one of the reduced-order models, and coupling it with LES makes it an effective tool for
Figure 4: Streamwise velocity contour of aligned HAWTs with VSWF and windbreak for different tilt
angles [43]. Adapted with permission from Reference [43]. Copyright ©2023, Elsevier
FDMP, 2024 11
analyzing wind turbine wakes. As compared with other reduced-order models, such as the ADM or Vortex
Model, ALM is a more accurate model. The basic consideration of ALM model is the lifting surfaces of
the turbine as actuator lines. Each actuator line is divided into several stations, as shown in Fig. 6a,b.The
validation results showed the proposed tool determined wake characteristics properly and are in good
agreement with the references. The study of [49] also investigated the effect of turbine spacing and
rotations of three VAWT clusters. The proposed open-source tool demonstrated a robust framework for
modeling and analyzing VAWTs, to comprehensively understand their performance and characteristics.
In addition to the turbine spacing and rotational direction, other turbine characteristics have a significant
role in the performance of farms. Reference [56] studied the effect of fixed and variable pitch control on the
power coefficient CPand mutual interaction between closely positioned VAWTs using 2D-CFD analysis, to
Figure 5: Streamwise velocity contour of aligned HAWTs and VSWFs with VAWT for different spacing
[43]. Adapted with permission from Reference [43]. Copyright ©2023, Elsevier
Figure 6: Schematics of ALM representation of (a) HAWT and (b) VAWT
12 FDMP, 2024
examine the power coefficient CPfor a range of TSR. The analysis indicates an enhancement in the
performance up to 18%.
A series of CFD simulations, based on the two-dimensional 2D-URANS method, were performed on
four arrangements of VAWTs clusters to achieve optimal power coefficient [20]. The study reveals that
the average power generation is greatly influenced by the constraint effect in the lateral direction and the
blockage effect of upstream turbines, which can be triggered at a specific separation distance. In most
cases, a cluster of 3 VAWTs demonstrates a higher power coefficient compared to a cluster of two
VAWTs. The configuration of three VAWTs—consisting of one upstream turbine and two downstream
turbines—resulted in an average power coefficient improvement of up to 11.1% compared to that of an
isolated turbine [20].
The efficiency of a planetary cluster design was studied using CFD simulations with a transient k-omega
(SST) turbulence model. The use of “planet”turbines enhanced the efficiency of the central “sun”turbine by
extracting power from the free stream. It has also witnessed an increase of 1.01% in the efficiency of the
“sun”turbine of the planetary arrangement over isolated turbine [41].
Computational studies are further demanded to analyze tilted VAWTs for emerging applications such as
high-rise buildings and floating wind turbines. It requires numerical validation of an existing experimental
and computational work of VAWT in upright and tilted conditions. The correct parametric study for
selecting the appropriate turbulence model and optimal computational parameters for solving the URANS
equations, under constant TSR and tilted turbine conditions was demostarted by [22]. Their results
indicated that SST k-omega captured the wake vortices better and closer to the experimental value than
RNG k-epsilon model. Furthermore, based on the SST k-omega simulation, the wake of the tilted axis
turbine proceeds downstream in a tilted manner. As a result, the wake stream shifts downward, and
VAWT in tilted conditions produces higher torque downwind compared to the upright turbines.
The combined effects of different cluster parameters should also be investigated to provide
comprehensive insight into VAWTs cluster development. According to the study of [57], the numerical
simulation of twenty-two test scenarios on Savonius turbines in aligned, parallel, and oblique
configurations using 0:25D, 0:5D, 1D, 1:5D, and 2D spacing. The power coefficient of backward two
oblique turbines is determined to be twice higher than an isolated rotor. For three Savonius turbines
arranged in optimal spacing, the average power output of the farm increased by a factor of 3. From this
analysis, Reference [57] concluded that the average power output of a large number of Savonius turbine
clusters will be proportional to the number of three turbine clusters.
The study of [19] employed CFD analysis to study the effect of spacing two turbines. Compared to
isolated turbines, there was an improvement of 8.06% at a 2D turbine spacing, while a low improvement
was seen at 12D spacing. The performances of 3 VAWTs in a pyramid- and inverted pyramid-shaped
clustered configurations with varying oblique angles between 15° to 165° at a fixed spacing 2D were also
investigated. For such configurations, the left-side and right-side turbines showed performance increase
proportional to the oblique angle, except at 165°. Meanwhile, the center turbine achieved the highest
performance at an oblique angle of 45°. The maximum cluster performance was achieved in the inline
configuration and perpendicular to the wind direction, resulting 9.78% improvement of the overall
performance over the isolated turbine [19].
The use of the ALM could significantly reduce the computational effort and cost of simulating VAWTs
by modeling turbines as momentum source terms in the NS equations. ALM to investigate the synergy
patterns within a cluster of two and three VAWTs employed by [58]. In conjunction with a URANS
method using the SST k-omega turbulence model, the ALM has shown good computational accuracy in
predicting VAWT synergy. The variation of the power ratio is characterized as a function of the cluster
layout parameters, and the results show good agreement with previous investigations [58].
FDMP, 2024 13
The study of [59] on the unsteady aerodynamics involved in the operation of VAWTs cluster using the
actuator line model. The study involved a wide range of tip speed ratios (TSRs) and considered different inlet
conditions such as uniform flow, logarithmic wind shear, and atmospheric boundary layer (ABL). The study
also explored performance improvements through the deflected wake produced by the pitched struts of the
upstream turbine. Numerical results were compared to experimental measurements, and the study found that
the applied ALM could be considered as a potential tool for VAWTs studies, with relatively low
computational cost showing accuracy and numerical stability. The study by [37] analyzed the flow
structures and energy production of VAWTs arrays. The wake of co and counter-rotating VAWTs shows
similarities with pairs of cylinders, and multiple turbines in a column increase power output due to
regions of excess momentum between them. It also suggests that downstream columns can be more
efficient than the leading column, potentially improving wind farm productivity.
3.1.2 Structural Loads and Dynamics
As VAWTs in cluster configuration are exposed to high turbulence and wake conditions, the structural
reliability of the blades is an important factor affecting their safe operation. The detailed investigation of
critical structural parameters on the aerodynamic performance VAWTs are rovided by [60]. Hence, the
structural safety of the turbines shall be examined for different load cases, mainly ultimate and fatigue
strength due to steady and cyclic loads, and dynamics and flow-induced loads. As downstream turbines
operate under extreme wake conditions, the effects of vortex shedding and flow-induced vibration should
be quantified properly. When the frequency of the external load is close to the natural frequency of the
structure, resonance will occur. Resonance will reduce the fatigue life of the structure and lead to blade
failure. It will have a significant impact on the flutter limit of the blade, causing the VAWT blade to lose
its aeroelastic stability.
Currently, research on the structural dynamics of wind turbine blades primarily focuses on HAWT.
However, there are limited published documents regarding the structural dynamics of VAWT blades. Few
efforts have been made to establish a VAWT dynamics model. For instance, Reference [61] considered
the coupling effects between shaft bending, torsion, tension, rotor tension, and bending modes.
Additionally, Reference [62] compared the connection method between the main shaft and blades of a
5 MW offshore floating VAWT to a cantilever beam model. Nevertheless, a comprehensive examination
and quantification of the overall farm performance, as well as the interaction between structural dynamics
and aerodynamic performance, are necessary to enhance farm output and extend the turbines’s operational
life.
A comprehensive computational analysis to study the wake interaction and the resulting aerodynamic
loads exerted on the turbine blades was presented by [63]. The study investigates alterations in the
normal and tangential aerodynamic loading across the blades of each turbine at various azimuth positions,
see Fig. 7. Moreover, the radial and azimuth fluctuations in the aerodynamic blade loads play a crucial
role in determining the magnitude of the rotor hub moments. These moments become particularly
significant when there is an imbalance between the loads on the left and right sections or the upper and
lower sections of the rotor. Reference [63] also showed for selected cases to indicate the variability of the
loading and thus its fatigue driving potential. The analysis showed that the loading on the blades of the
upstream turbine is highest when they are oriented upwards 90
ðÞ
and lowest when pointing downwards
270
ðÞ. The external loading is also determined to be nearly the same for the two horizontal positions 0
and 180.
The load profiles of the downstream rotor exhibit notable variations depending on the specificflow
conditions. Under full wake operation, the loads amplify as the turbulence level and turbine spacing
increase. The blade loads at different horizontal positions display significant dissimilarities for laminar
ambient flow and closely positioned turbines. Similarly, for laminar ambient flow and large turbine
14 FDMP, 2024
spacing, a horizontal asymmetry is observed in the blade loads of the downstream rotor, see Figs. 8 and 9.
Lateral displacement of the rotors affects the downstream rotor by the influence of the upstream wake.
This leads to a decrease in average blade loading and an increase in standard deviation at a position of 0.
The presence of heightened turbulent mixing, resulting from ambient turbulence, causes an elevation in
average loading on the blade at 0. However, average loads on the blade in other directions experience a
slight decrease as the turbulence level increases. The standard deviation of normal loads on the
downstream turbine blades generally rises with higher ambient turbulence levels. In the scenario of full
wake, there is only a minor difference in standard deviations between laminar inflow and an ambient
turbulence intensity of 0.05. Limited meandering and organized vortex structures are potential explanations
for this observation according to the work of [63].
3.2 Optimizations
Based on numerical modeling reviewed in the previous section, the performance of the VAWTs cluster is
determined by several design variables, namely, rotational direction, turbine spacing, oblique angle, farm
layout/pattern, wind direction, turbine types, number of turbines, tip speed ratio, blade pitch angle, flow-
control methods employed, and wind shear profile. The optimal combinations of these variables are
required to develop satisfactory VAWTs cluster configuration. There are two significant considerations for
optimization. Firstly, the availability of limited land area for wind turbine farms necessitates optimizing
the spacing between each turbine. Secondly, the arrangement of the turbines plays a critical role in their
Figure 7: Normal (a) and Tangential (b) loads of the upstream rotor blade for different azimuth positions,
V1=8m/sand[std(V0)/V1=0][63]. Adapted with permission from Reference [63]. Copyright ©2010, Wiley
Figure 8: Downstream rotor blade span-wise normal load for different azimuth positions with the rotors
stream-wise and lateral spacing z¼3:3D and x¼0, respectively, and ambient turbulence intensity 0,
0.05, and 0.1, from left to right, respectively [63]. Adapted with permission from Reference [63].
Copyright ©2010, Wiley
FDMP, 2024 15
performance, leading to the study of wake effects and the optimization of the arrangements of the turbines. To
conduct the optimization study the most frequently used tool is computational study, while few recorders of
using analytical and experimental studies have been found during the literature survey. One of the few
pioneer research performed on full-scale field tests on VAWTs in arrays is the work of [17]. The work
aims to provide a baseline for future research on computational and scale model experiments. During the
field test, they used counter-rotating arrangements of VAWTs, they hypothesized that aerodynamic
interactions between adjacent turbines can benefit the performance when nearby. The field tests used six
10-m tall by 1.2-m diameter VAWTs and were conducted with the turbines positioned within the same
75 m by 75 m tract of land. To optimize the best positions of array arrangement the following three sets
were used in the field tests as shown in Fig. 10.
Fig. 10a confirms that the proximity of the turbines slightly improved their performance relative to the
turbines in isolation, Fig. 10b explored the effect of downwind blockage caused by the two closely spaced
upwind turbines and a significant decrease in the performance of the downwind turbine was observed, and
Fig. 10c demonstrates that increasing the spacing of all turbines in an array to 4D would be significantly
reduced the upstream blockage effects. Based on their results, it is possible to improve power density by
searching for optimal configurations for counter-rotating VAWTs.
Figure 9: Downstream rotor blade span-wise tangential load for different azimuth positions with the rotors
stream-wise and lateral spacing az¼3:3Dand x¼0, respectively, and ambient turbulence intensity 0,
0.05, and 0.1, from left to right, respectively [63]. Adapted with permission from Reference [63]. Copyright
©2010, Wiley
Figure 10: (a) Illustration of two-VAWT configurations. (b) Illustration of three VAWT configurations. (c)
Illustration of six-VAWT configuration
16 FDMP, 2024
A novel optimization methodology for VAWTs design proposed by [64]. The study investigates the self-
starting behavior of adjacent rotors using CFD and a Taguchi-based design of the experiment approach. The
optimized results demonstrated that the self-starting capabilities of each rotor are affected by modifications in
the flow fields. Specifically, when the second rotor was positioned downstream from the center of the first
rotor, it could not self-start due to momentum loss caused by the upstream rotor. However, with an
optimized layout, the study achieved significant improvement in wake recovery downstream of the first
rotor. Additionally, a substantial reduction in the wake extension for the first rotor was observed, which is
beneficial for potential wind farm layouts. A 3D CFD simulations to examine the simultaneous impact of
some layout parameters on the operation of two H-type straight-blade VAWTs was used by [65]. To
discover optimal configurations, three design parameters were used: the direction of the incoming wind,
the vertical distance between the mid-heights of two turbines, and the horizontal distance between the
axes of the two wind turbines. It has been discovered that the paired wind turbines’performance is most
affected by their vertical distance apart, while their power production is most influenced by their
horizontal distance apart. Through their 3D simulation, it was discovered that the most optimal
configuration for the turbines was achieved by placing them in a side-by-side arrangement, all at the same
height. Besides vertical turbines working in air medium, they can also be deployed in tidal environments
in clusters or as an isolated system. The work of [66] provides a useful insight clustering of Vertical
turbines in tidal turbines. A 2D CFD study was employed to investigate the bidirectional Savonius tidal
turbine to optimize the cluster arrangement and enhance the performance by using deflectors. To find the
optimized deflector Kriging method (which is explained in [67]) combined with a genetic algorithm was
used. The optimization study showed that the optimized cluster has a power coefficient improvement of
34.5% compared with the cluster without deflectors.
Determining the optimal spacing between clustered turbines is a critical parameter within the
optimization process. To find optimized spacing, the study of [20] provides useful insight. The study
follows a three-step approach to investigate the optimal spacing and power coefficient of clustered
turbines. Firstly, a 2D CFD analysis is conducted using the URANS model for a single VAWT. Secondly,
simulations are performed for various configurations including a single turbine, a parallel and staggered
2 VAWTs cluster, and a 3 VAWTs cluster facing the incident and leeward wind directions to determine
the ideal spacing that maximizes the power coefficient. Lastly, the study examines the kinematic
parameters of the ambient flow surrounding the turbine clusters to identify the mechanisms influencing
the power coefficient. The findings confirm that, in general, clustered turbines exhibit superior average
performance compared to isolated turbines when aligned with the prevailing wind direction. Specifically,
the 3 VAWTs cluster demonstrates higher efficiency in terms of the average power coefficient compared
to the 2 VAWTs cluster. For the 2 VAWTs cluster, the optimized spacing is determined to be around
1.5 to 1.6 times the turbine diameter, and the staggered arrangement proves to enhance performance due
to the accelerated flow induced by the upstream turbines. Similarly, Reference [68] used the URANS
equation to investigate the interaction between H-rotor Darrieus turbines in staggered wind farms and
standalone clusters. It is found that the mutual interaction becomes negligible at a minimum distance of 13D.
Using analytical tools [69] develops a wake model of straight-bladed VAWTs and applies it to optimize
the cluster configuration of VAWTs coupled with wind tunnel tests. The use of the wind tunnel tests is to
determine the unknown parameters in the wake model. They have proposed a wake model and the
schematic plot of the proposed wake model is shown in Fig. 11.
The model is based on the use of a continuity conservation equation, with a Cartesian coordinate system
where the x-axis is pointing downstream, the y-axis is pointing windward, and the z-axis is aligned with the
tower. A covariance matrix adaption-based evolutionary strategy (CMA-ES) was implemented to optimize
the micro-siting of VAWTs using the wake model. The procedure of the CMA-ES algorithm for micro siting
of VAWTs is shown in Fig. 12.
FDMP, 2024 17
Other analytical models (top-hat model, the Gaussian model wake model, and Gaussian wake) coupled
with experimental studies were used by [70] for layout optimizations. The utilization of wake models has
enabled a comparison between layout solutions employing HAWTs and VAWTs within the same wind
farm site. The findings indicate that in the wind farm layout optimization process, the energy density of
VAWTs can surpass that of HAWTs, resulting in a more efficient utilization of sea areas. This is further
enhanced by incorporating a layout optimization formulation that takes into account the direction of
Figure 11: Schematic of the wake model of the VAWT [69]. Adapted with permission from Reference [69].
Copyright ©2017, Elsevier
Figure 12: The procedure of the CMA-ES algorithm for micro siting
18 FDMP, 2024
rotation specific to VAWTs. By fully exploiting the asymmetric wakes generated by VAWTs, their potential is
maximized within the wind farm layout.
Another benefit that comes from the wake interaction of VAWTs is their ability to improve the overall
performance of HAWTs farms. To demonstrate this, Reference [71] used LES and analytical wake models to
optimize the layout of HAWTs. The proposed strategy is to use small-scale VAWTs in triangular clusters
deployed within a finite-size wind farm consisting of HAWTs. The clustering is shown in Fig. 13.
According to the LES CFD analysis, VAWT wakes are visible far downstream of the farm because the
wake behind VAWTs must expand enough vertically before it can be seen at the hub height of the HAWT.
Because of the relatively wide relative distance between the two columns of VAWTs clusters, it is evident
from Fig. 14 that the wakes of these clusters had almost recovered before the following column. When
compared to the baseline scenario when just the HAWTs are present, they have discovered that the co-
located wind farm’s power output rises by up to 21%.
Furthermore, Reference [40] investigated the interactions of multiple VAWTs in small clusters, and
subsequently used these clusters to design large VAWTs farms. For optimization, they have used the LES
CFD model coupled with the actuator-line model (ALM-LES). They have performed the cluster design
by geometric and shading considerations as shown in Fig. 15. The range of wind directions where two
turbines can directly shadow one other is then enlarged by adding one more turbine. Nevertheless,
depending on the direction of the wind, the third turbine could benefit from the increased wind speed
created between the two upstream turbines, or the two downstream rotors may profit from the upstream
Figure 13: VAWTs clusters between HAWTs [71]. Adapted with permission from Reference [71].
Copyright ©2020, Purpose-Led Pulishig
Figure 14: Stream-wise velocity of VAWTs clustered in HAWTs from LES [71]. Adapted with permission
from Reference [71]. Copyright ©2020, Purpose-Led Pulishig
FDMP, 2024 19
turbine’s transverse flow deflection. By pairing these three turbines, they will be able to produce more power
than from three distant, non-interacting turbines.
To investigate the interactions between VAWTs to increase the wind-farm power density, Reference [40]
have also performed the LES simulations of different cases. To visualize the differences in the flow patterns
in these designs, the average stream-wise velocity component for a few selected configurations is shown in
Fig. 16.
The simulations confirm that VAWTs, when arranged in well-planned clusters, positively impact one
another: in such configurations, the power generation of a single turbine is increased by approximately
Figure 15: Two-, three-, and four turbine vertical-axis wind directions with upstream rotors [40]. Adapted
with permission from Reference [40]. Copyright ©2018, Springer
Figure 16: A 10D horizontal spacing wind farm with stream-wise velocity magnitude, mean flow from left
to right: (a) regular aligned, (b) regular staggered, (c) cluster staggered with 0-degree wind direction, and (d)
cluster staggered with 60-degree wind direction [40]. Adapted with permission from Reference [40].
Copyright ©2018, Springer
20 FDMP, 2024
10%. Furthermore, compared to traditional setups, the cluster designs allow for closer turbine spacing, which
results in almost three times as many turbines for a given land area. Using 2D CFD simulation [33] proposed
an efficient way of clustering Savonius turbines. They have used the same geometric model arranged in three,
nine, and twenty-seven to form a wind farm. They propose that the patterned Savonius VAWT farms, as
shown in Fig. 17.
A similar study was performed for Efficient clusters and patterned farms for Darrieus wind turbines [33].
Their results of the simulation of the multi-turbine clusters are used to develop an efficient triangular shaped
three turbine cluster having an average power coefficient up to 30% higher than an isolated turbine. A CFD
study was performed for double Nautilus VAWT by [72] to optimize different layouts proposed, as shown in
Fig. 18. They generally showed that the enhancement of the wind turbine arrays situation could significantly
increase the average efficiency of the entire wind turbine cluster. The maximum average power coefficient
reached 28.9%. Reference [73] also presents a variable-speed control method that provides an easy strategy
to improve the power output of a cluster of turbines.
3.2.1 Optimal Configurations
Several cluster configurations have been studied for enhanced performance of the VAWTs farm. The
most common optimal configurations are (1) collocated wind plants, (2) planetary clusters, (3) vertically
staggered cluster, and (4) bio-mimicking blusters. Collocated wind plants are one of the promising cluster
configurations is a collocated wind farm, wind farms with VAWTs are often staggered or aligned with the
horizontal axis wind turbines to introduce clusters of VAWTs [42]. Collocated wind plant configuration
encompasses three arrangements: (1) a typical wind farm with just wind turbines oriented horizontally,
(2) an aligned collocated wind plant, and (3) a staggered collocated wind plant. In the collocated wind
plants, clusters of three VAWTs are introduced to the standard wind farm and placed either in alignment
with the horizontal axis wind turbines or staggered between the rows. Planetary cluster: according to [41],
a new planetary cluster of VAWTs that can increase the efficiency and power density of wind farms. To
conduct a parametric study and optimize this setup, the PCD (pitch circle diameter) and oblique angular,
, position of the smaller “planet”turbines were varied about the “sun”turbine. The “planet”turbines
extract power from the free stream, which creates varied wind velocities and improves the efficiency of
the central “sun”turbine. After conducting the study, it was found that the optimal PCD was 5D, and the
best angular position for the “planets”was 30. By comparing the “sun”turbine of the planetary
arrangement to the optimum isolated, there was a percentage increase of 1.01% from 33.04% to 34.05%.
Figure 17: Farm development [26]. Adapted with permission from Reference [26]. Copyright ©2016,
Elsevier
FDMP, 2024 21
Additionally, an average improvement of 4% across the TSR range was discovered. Vertically staggered
cluster: one of the major challenges in wind energy harnessing is to minimize the wake effect to enhance
the power output of wind farms. To address this issue, windbreaks, and VAWTs have been added to
traditional aligned wind farms, resulting in two innovative types of vertically staggered wind farms
(VSWFs). Both windbreaks and VAWTs aid in the recovery of the upstream wind turbine wake by
facilitating the mixing of wind flow and reducing wind shear, thereby increasing the power output of
VSWFs. The power output of VSWFs with VAWTs is significantly higher than that of windbreaks. The
layout optimization and effects of different parameters are discussed in [43]. Bio-mimicking clusters: the
layout of the VAWTs cluster could also be optimized based on bio-inspired concepts. Reference [35]
introduced an innovative VAWTs farm design inspired by the concept of fish schooling. They utilized the
[74] potential flow model to study the wake effects of shed vortices on a school of fish. Inspired by the
propulsion benefits of the reversed Karman vortex street observed in schooling fish, they utilized a
similar configuration and modeling tools to analyze VAWT arrays. This approach produced optimal
configuration results, resulting in a significant improvement in farm performance compared to isolated
VAWTs and higher power density than HAWTs. Other bio-mimicking concepts could be employed to
develop optimal farm layouts.
3.2.2 Application of Machine Learning and AI
In addition to advanced computational approaches, AI could benefit the optimization and enhancement
of VAWTs cluster configurations. In this regard, in [75], a model has been developed that integrates three
ensemble learning algorithms with clustering approaches to model wind power in a wind farm, using
multiple meteorological factors. Ensemble models with clustering outperform models without clustering
by approximately 15%, with the best-performing model using Farthest First clustering and improving by
around 30%. Stacking fuses ensembles with varying clusters, further boosting power modeling
Figure 18: Different array layouts investigated [72]. Adapted with permission from Reference [72].
Copyright ©2023, MDPI
22 FDMP, 2024
performance by about 5%. The proposed modeling framework is efficient, robust, and promising. Reference
[76] suggested a unique method for combining data and knowledge to build the first digital twin of an
offshore and onshore wind farm flow system that is capable of predicting the spatiotemporal wind field in
situ over the whole wind farm. Through the use of physics-informed neural networks, the digital twin is
created by combining the Lidar observations, the Navier-Stokes equations, and the actuator disk
technique of turbine simulation. The architecture allows the merging of flow physics to retrieve
unmeasured wind field information and the smooth integration of Lidar observations and turbine
operating data for real-time flow characterization. As a result, it overcomes the shortcomings of current
supervised machine learning-based wind prediction techniques, which are unable to make such
predictions due to a lack of training objectives. The digital twin accurately mirrors the physical wind
farm, capturing detailed flow features. Case studies have exhibited this. It also has a low prediction error
of 4.7% for flow fields, enabling new research for wind farm life-cycle monitoring, control, and load
assessment. There is a great deal of effect that wake interactions have on a wind farm’s overall
performance. A novel deep learning method, called Bilateral Convolutions Neural Network (BiCNN), is
proposed and then employed to accurately model dynamic wind farm wakes based on flow field data
generated by high-fidelity simulations [77]. As opposed to the current machine-learning-based dynamic
wake models, which depend on dimensionless reduction, the suggested BiCNN is made to directly
process various input kinds via background and foreground paths, thereby eliminating dimensional
reduction errors. Significant findings demonstrate that the created machine learning-based wake model
can accurately forecast wakes in real-time; that is, it can run at the same speed as low-fidelity static wake
models and capture the spatial fluctuations of dynamic wakes in a manner akin to high-fidelity wake
models. Regarding the free-stream wind speed, the derived model’s overall forecast error is 3.7%.
Moreover, the outcomes for a test farm with 25 turbines demonstrate that the created model can forecast
the dynamic wind farm wakes in a matter of seconds [77]. The work of [78] demostrated the application
of machine learning for predictive maintenance of wind turbines and they propsed a revolutionized the
way wind energy systems are maintained.
3.2.3 Control Strategies
The common control principles employed in VAWTs to benefit the cluster performance are Variable
swept area (VSA) as smart rotors [79], rotation direction [49], TSR [80], Variable pitch controller [56],
and through the application of active flow controllers such (i) surface blowing or suction, (ii) VG’s,
surface heating, plasma or (iii) changes in section shape (aileron, smart materials, and micro-tabs) [81–
83]. Furthermore, the application of AI and machine learning as smart controllers will enhance the farm
performance. Reference [79] employed a Fuzzy Logic Controller (FLC) to vary the turbine’s swept area,
which is adjustable for height and width with actuators. The VSA rotors are controlled by an FLC to
maintain a constant power rating at the PMSG. Furthermore, the change in the turbine swept area will
then alter the downstream flow characteristics. In a general sense in existing studies on VAWT arrays,
little attention is paid to the real-time control of individual rotors in VAWT arrays. In arrays, the pitch
control curve for VAWT in different positions should change due to the interaction of adjacent turbines.
References [58,84] explored the dynamic pitch control strategies in double-VAWT arrangements. Pitch
control enables the downstream rotor deviating from the wake (.15) to fully utilize the flow
acceleration adjacent to the upstream VAWT. With upstream pitch control, downstream rotor efficiency
can also be improved see Fig. 19. The primary causes of the changes and improvements in the flow and
the effectiveness of the VAWTs in the configurations are the decrease in the rotor’s blockage effect and
the acceleration of the wake brought on by pitch control.
In addition, other wind farm control principles used in HAWTs farms could be adapted for VAWTs
clusters. For instance, the recently proposed collective wind farm operation and control based on a
FDMP, 2024 23
predictive model by [85], could be employed for VAWTs clusters to collectively control all the turbines
within the farm for a synergized farm operation.
4 Experimental Tests and Prototyping
Alongside analytical and computational studies, experimental tests and validations are essential. To
examine the performance of VAWTs in cluster configurations, few experimental studies have been done.
For example, experimental study of wake evolution under vertical staggered arrangement of wind
turbines of different sizes are presnted by [86] with the experimental setup show in Fig. 20 and the
measuremnts made by [87] showed the wake from lift-driven VAWTs in a wind tunnel and compared the
results for three counter-rotating and isolated versions. They discovered that the wake of a paired VAWT
is greatly influenced by the direction of rotation and that the wake of an isolated VAWT is deflected. The
length, breadth, and replenishment of the wake of a counter-rotating VAWT that has adjacent blades
moving downwind are comparable to those of an isolated VAWT. The wake of a counter-rotating VAWT
with nearby upwind moving blades, however, is very different from the wake of an isolated VAWT in
terms of replenishment and breadth. Paired VAWTs provide distinct benefits for wind farm applications
because of their attractive wake characteristics, particularly for offshore floating wind farms. In another
study, Reference [88] conducted an experimental investigation to explore the interactions between
VAW T ’srotor and wake. By considering various wake deflections, they evaluated the interactions, taking
into account the pitch angles of the upwind VAWT’s blades. Using stereoscopic particle image
velocimetry, they examined wake interactions between two VAWTs in nine different wake deflection and
rotor position combinations. Additionally, force balances were employed to assess the time-average loads
on the VAWTs. The study findings confirmed the effectiveness of wake deflection and quick wake
recovery, ultimately enhancing the available power of the second rotor.
The work of [89] showed a thorough investigation using wind tunnel tests to determine how the
arrangement of the array affects VAWT power performance. When the transverse spacing is 2.4 rotor
diameters, the maximum power coefficient of the turbine pair is 8.2% greater than that of an isolated
turbine. The ideal mode of the transversal arrangement is counter-forward rotation. In the two-turbine and
three-turbine longitudinal layouts, the maximum power coefficient of a downstream turbine is found to be
Figure 19: Wake development of the VAWTs in arrays under different control strategies (1¼2¼2:0Þ:
(a) ¼45(b) .15[84]. Adapted with permission from Reference [84]. Copyright ©2023, Elsevier
24 FDMP, 2024
enhanced by 45% and 61.1%, respectively, in comparison to an isolated turbine. The proposed design
includes trusses and triangles depending on the direction the wind is blowing. The experiment’s outcomes
verified that by fine-tuning the turbines’array arrangement, the average power coefficient may be raised
even higher.
5 Market and Economics
In addition to the aerodynamic performance of VAWTs in a clustered configuration, it is important to
evaluate their financial feasibility under various scenarios. Although the technology for horizontal wind
turbines (HAWTs) is advancing rapidly and driving down costs, it may be possible to further decrease the
cost of offshore floating wind by opting for VAWT technology. VL Offshore has developed a cost-
effective 5 MW floating foundation, known as the Y-Wind semi, for HAWTs [90]. To compare the
Levelized Cost of Energy (LCoE) of the Y-Wind semi with a 5 MW HAWT against the same foundation
with a 5 MW VAWT, a 200 MW wind farm located approximately 10 km offshore the Northeast U.S. at
a water depth of 100 m was considered for bench-marking. The LCoE results indicated that a foundation
for a 5 MW VAWT will be more commercially viable than a comparable foundation for a 5 MW HAWT.
These LCoE values compare favorably to most electricity prices in the Northeast states [90].
The technological advancements have reduced a variety of capital, operational, and financial cost
categories, resulting in a regional diversity in LCOE was examined by [91]. Due to the variable
geospatial features of the farm sites under consideration and the nonlinear dependence on these input
parameters, a specified change in the cost of a single turbine subsystem produces a range of LCOE
outcomes; for instance, a 10.8% improvement in net capacity factor can reduce LCOE by between 6%
and 20% at different sites [91]. Hence, technical innovations can have a significant influence and should
be taken into account both spatially and temporally when funding or prioritizing technology innovation
research to enhance offshore wind technologies. Through the analysis conducted by [92], the impact of
varying spatial characteristics in the U.S. offshore wind resource area on the LCOE and economic
feasibility of offshore wind was quantified. The report takes into consideration current technology,
market, and regulatory conditions and presents a cost-effective option between fixed-bottom and floating
offshore wind technologies for different site conditions while also evaluating the impact of technology
advancement and market maturity. The results of the study suggest that offshore wind can potentially
achieve significant cost reductions and forecasted economic viability in select regions of the United States
within the next 15 years [92].
Figure 20: (A) schematic of the experimental setup; (B) a snapshot of the setup [88]. Adapted with
permission from Reference [88]. Copyright ©2023, Wiley
FDMP, 2024 25
In general, the factors commonly considered in calculating LCoE include Capital Cost, Operating
Lifetime, Capacity Factor, Fixed O&M cost, Variable O&M cost, and Electricity Price [92]. To reduce
LCoEs for Wind Farms, advancements in turbine and blade technologies should continue to increase
power output, improve efficiency, and decrease costs. Additionally, optimizing the spacing of individual
wind farm units could also help reduce LCoE values. Further research may uncover ways to minimize
down turbine wake effects, increase capacity factor, decrease in-field cable lengths, and improve power
output by spacing VAWTs closer together [38,90].
6 Terrain and Application Locations
6.1 Noise Generation
All rotating machines inherently generate a significant amount of sound, which affects the vicinity. The
application of most types of machinery depends on sound pollution. Several studies indicated that VAWT is
more silent than HAWT in comparison. Reference [93] provided LES and aeroacoustic spectra for three
configurations of increasing flow complexity: a nearby farm of four vertical axis turbines (that have the
same characteristics as the isolated turbine), an isolated rotating VAWTs made up of three rotating airfoils
and an isolated NACA0012 airfoil. Only the blade passage frequency and the boundary layer tones can
be distinguished when comparing the spectrum with the isolated turbine. The aeroacoustic footprint of
nearby VAWTs cannot be adequately described by a linear combination of sources from isolated turbines,
as indicated by variations in acoustic amplitudes, tonal frequencies, and sound directives. Rather, farms
should be viewed and investigated as distinct entities. This will benefit VAWTs for application in urban
and rooftop applications and other sound-constrained sites.
6.2 Onshore vs. Offshore
One important new source of clean, renewable energy is onshore wind power. However, onshore wind
does have certain limitations. It is hard to locate wind-generating projects in heavily populated areas like
the Northeast of the United States. Because of this, any onshore wind farms will need to be situated farther
out, which will present more logistical and transmission difficulties, along with increased costs and power
loss. One of the promising solutions is to install floating wind power offshore. Offshore wind offers
proximity to large population centers, a vast and more consistent wind resource, and a scale-up
opportunity. On the other hand, offshore wind suffers from high LCOE and, in particular, high balance
of system (BoS) costs owing to accessibility challenges and limited project experience. Preliminary
studies on offshore VAWTs clusters showed their significant economic feasibility [90,94]. As discussed
in the section (market and economics), the comparison between offshore HAWTs and offshore VAWTs
clusters indicated that VAWT will be more commercially viable than a comparable foundation for a
5MWHAWT[90]. Fig. 21 sumrrized the work of [94], they explored cost trade-offs within the design
space for floating VAWTs between the rotor and platform configurations and corresponding
performances. The benefitofafloating VAWT is envisioned through system-level improvements and
balance of system (BoS) cost reductions, which are addressed in this project through design studies that
feed into an LCOE analysis.
As per [94] the Darrieus rotor is a VAWT rotor configuration proven with field experience and offering
structural advantages and aerodynamic efficiency similar to a HAWT. However, there is still room for
enhancement of the Darrieus rotor when designing VAWTs at large scale and for floating offshore systems.
6.3 Urban Environment
In addition to the low noise generation benefits of VAWTs, their characteristics under wake conditions
make them a promising source of energy in urban areas. Urbanization leads to more high-rise buildings and
raises questions about their impact on wind flow and energy potential. Matching wind turbine performance
with local conditions is essential for efficient power output in buildings and urban areas.
26 FDMP, 2024
According to the study of [95], the wind characteristics and the interference effects around high-rise
buildings based on the level of building exposure to the wind and the position of surrounding buildings.
They also determined the wind energy resource above the roof in terms of the Wind Power Density
(WPD), turbulence intensities, and skew angle. The analysis forecasted high turbulence and skewed flow
in urban areas were found to affect their efficiency and operability, which indicates the suitability of
VAWTs in such conditions.
The study of [96,97] offered viewpoints on the study of wind energy from the construction and urban
aerodynamics standpoint. They reviewed the recent designs of urban/building-based wind energy systems,
such as building integrated VAWTs, power windows, wind-induced vibration-based wind energy
harvesters, double skin, and other creative building facade systems, and wind source exploration. They
also examined factors affecting urban wind flow and the effects they have on urban wind energy
harnessing.
6.4 Comparison with HAWT
In the previous sections, several configuration of the VAWTs cluster were addressed. Their comparative
advantage against HAWTs shall be identified to provide clear insights. Several studies compared the
performance and characteristics of HAWTs and VAWTs in cluster configurations. The common
comparison criteria considered are, LCOE, aerodynamic performance, power density, aerodynamic loads,
complexity, and noise, to mention a few. Table 4 discusses the few types of comparative research
between equivalently rated VAWTs and HAWTs. Table 4 discusses the few comparative types of research
between equivalently rated VAWTs and HAWTs. This table provides findings from multiple case studies,
highlighting the distinct performance characteristics of each turbine type. The analysis reveals that VAWT
clusters exhibit significant advantages over their HAWT counterparts across a wide range of performance
indicators. Based on the case studies reviewed, VAWTs clusters showed a promising advantage over
HAWTs through wide areas of performance indicators.
Figure 21: Estimated life-cycle cost breakdown for an offshore VAWTs [94]. Adapted with permission from
Reference [94]. Copyright ©2016, Purpose-Led Pulishig
FDMP, 2024 27
Table 4: Performance comparison of cluster of HAWTs and VAWTs
Reference HAWTs description VAWTs description Tool used Comparison
criteria
Results
[98]2–6 MW HAWT 3 Bladed Darrieus (H-
type) and Troposkien
type rotor
configuration
CFD Aerodynamic
performance
VAWTs not only have
superior performance but
also feature a simple and
cost-effective design for
manufacturing and
maintenance.
[90] 200 MW Floating HAWT
farms
200 MW Floating VAWT
farms
Analytical LCOE The LCoE values
compare favorably to the
LCoE values for most
electricity prices in the
Northeast states.
[99] 200 kW HAWT 200 kW VAWT CFD Noise The comparison with an
equivalent horizontal axis
wind turbine operating at
optimum tip speed,
indicates a noise emission
at the absolute bottom of
the range.
[55] Three identical in-line
HAWTs using a spacing of
3D
Three identical in-line
VAWTs using a spacing
of 3D
CFD Aerodynamic
performance
For VAWTs clusters, the
Cp are determined to be
0.462, 0.121 and 0.088,
for the leading, second
and third turbine,
respectively.
[54] Vestas V80 turbines with a
rotor diameter of 80 m and
a hub height of 70 m, are
arranged in six columns
and three rows in the
streamwise and lateral
directions, respectively
Collected 200 kW
turbines, which are the
three and straight VAWTs
with a diameter of 26 m,
the blade span of 24 m,
and the height of 40 m, in
triangular clusters in the
free space among
HAWTs
LES and
analytical
model
Power gain The potential power gain
in the wind farm with
both HAWTs and VAWTs
is up to 21% compared to
a baseline case in which
only HAWTs are present.
[100] Large HAWT, the RE-
power 5 MW model,
placed at x = 500 m and
y = 250 m,
Each HAWT is
surrounded by 20 small
VAW T s ( H o r
Giromilltype) with a
capacity of 50 kW and
evenly distributed in a
vertical staggered
arrangement
The HAWT is
parameterized
with the ALM,
while VAWTs
use the ADM l
Power output The VS wind farm
produces up to 32% more
power than the traditional
one, and the power
extracted by the large
turbines alone is
increased by 10%, caused
by faster wake recovery
from enhanced
turbulence due to the
presence of the small
turbines.
28 FDMP, 2024
7 Conclusion and Recommendations
The present paper comprehensively examined the perspectives of VAWTs in cluster configurations. The
review identified several promising VAWTs cluster configurations and explored their relative performances
with different design variations. The performance of VAWTs cluster is significantly affected by several
design variables, namely, rotational direction, turbine spacing, farm layout/pattern, wind direction, turbine
types, number of turbines, tip speed ratio, pitch control, and wind shear profile. Hence, developing an
efficient cluster requires proper modeling and optimization tools, along with high-end experimental tests
and prototyping. This paper demonstrates that the wake interaction downstream of VAWTs in a cluster
has a positive impact, potentially enhancing the overall performance of the wind farm. However,
conversely, the paper also illustrates that the wake interaction has a negative effect on HAWTs farms,
leading to a reduction in their overall performance. The computational requirement of VAWTs cluster is
very high given the wake interaction between turbines is important in quantifying the farm output. In this
regard, CFD-based models, such as LES, RANS, URANS, and DES, and analytical methods, such as the
Top-Hat Wake Model, Gaussian Wake Model, Asymmetric Gaussian Wake Model, Actuator Line Model
(ALM), Actuator Disk Model (ADM) and Vortex Model are explored. We have found that results from
CFD models show more accurate results than the analytical methods. However, the CFD approach
necessitates cutting-edge computational resources to model the wake effect, resulting in significant costs
associated with running all the simulations. The authors contend that to address the limitations of CFD,
the implementation of hybrid models like ALM-LES has proven to be a promising approach for
modeling the wake while maintaining the accuracy of the results. In addition to the aforementioned
computational efforts, there are few findings on AI and advanced control strategies to enhance the
optimization of VAWTs clusters. Finally, the review explored a few case studies done on comparison
between the HAWTs and VAWTs clusters, to provide future perspectives and insights based on different
comparison criteria such as LCOE, aerodynamic performance, Power density, aerodynamic loads,
complexity, Noise, and gain/loss factor. Despite the promising results presented by several researchers,
the following research gaps and areas are identified for future exploration to enhance the deployment of
VAWTs clusters.
1. Advanced computational models and optimization tools:
The CFD study has scope for expansion on bigger infrastructure by adding more turbines;
There is a scarcity of 3D simulations, which should be addressed to enhance the understanding of
VAWT clusters;
To evaluate the impact of atmospheric thermal stability on the performance of co-located wind farms;
To extend the validation of both computational and analytical wake models to different atmospheric
regimes and wind shear characteristics;
To comprehend different wind-farm layouts such as co-locating, vertical staggered, and other
complex cluster configurations;
To enhance the power generation of co-located wind farms by optimizing the design and placement of
clustered VAWTs inside HAWT arrays;
Coupled and multi-physics modeling, such as FSI, is required to quantify the structural loads due to
wake interactions and layout design;
Application of AI and machine learning to optimize cluster layout; and
Application of advanced and innovative control strategies such as combined wind farm operation
using a predictive model.
FDMP, 2024 29
2. Refined economic models: To refine the designs for the major components and their cost estimates, to
quantify LCOE with reasonable uncertainty for a floating VAWT system. The refinements to the
design and cost analysis will include:
For the rotor inclusion of additional costs such as manufacturing;
For the platform and mooring, consider additional floater types and re-visit practical design
requirements such as free-board height;
For the drive train, sizing of both direct drive and geared options will be considered along with
costing;
For operations and maintenance costs, including unique VAWT characteristics such as improved
drive-train accessibility at the water line;
For BoS costs for a floating VAWT system, including important costs such as installation, assembly,
and electrical infrastructure; and
To evaluate how a realistic wind rose affects the LCoE computation in co-located wind farms and
other configurations
3. Promoting the right technology:
Developing comprehensive environmental pollution metrics such as noise metrics and
psychoacoustic annoyance of the VAWTs vs. HAWTs could clarify the merits of VAWTs;
Exploring environmental activism and vertical-axis wind turbine preferences in urban areas and
offshore locations shall be promoted given their inherent merits and suitability;
Experimental and prototyping shall foster the application of VAWTs cluster in the wind energy
industry;
In addition to advanced computational approaches, AI could benefit the optimization and
enhancement of VAWTs cluster configurations;
Exploring more optimal VAWTs cluster layouts and co-locating in existing shall enhance VAWTs
acceptance in the wind industry; and
The application of advanced control strategies shall also improve the performance of VAWTs cluster
configurations.
Acknowledgement: None.
Funding Statement: The authors received no specific funding for this study.
Author Contributions: The authors confirm contribution to the paper as follows: Study Conception and
Design: Ryan Randall, Chunmie Chen, Mesfin Belayneh Ageze, Muluken Temesgen Tigabu; Literature
Collection: Mesfin Belayneh Ageze; Draft Manuscript Preparation: Ryan Randall, Mesfin Belayneh
Ageze, Muluken Temesgen Tigabu; Final Review and Approval, Manuscript Review and Supervision:
Chunmie Chen. All authors reviewed the results and approved the final version of the manuscript.
Availability of Data and Materials: The data presented in this study are available on request from the
corresponding author.
Ethics Approval: Not applicable.
Conflicts of Interest: The authors declare no conflicts of interest to report regarding the present study.
30 FDMP, 2024
References
1. Yolcan OO. World energy outlook and state of renewable energy: 10-year evaluation. Innov Green Dev. 2023;
2(4):100070. doi:10.1016/j.igd.2023.100070.
2. Tanürün HE. Improvement of vertical axis wind turbine performance by using the optimized adaptive flap by the
Taguchi method. Energy Sour Part Recov Util Environ Eff. 2024;46(1):71–90. doi:10.1080/15567036.2023.
2279264.
3. Mohammed AA, Ouakad HM, Sahin AZ, Bahaidarah HMS. Vertical axis wind turbine aerodynamics: summary
and review of momentum models. J Energy Resour Technol. 2019 Feb;141(5):050801. doi:10.1115/1.4042643.
4. Barnes A, Marshall-Cross D, Hughes BR. Towards a standard approach for future Vertical Axis Wind Turbine
aerodynamics research and development. Renew Sustain Energy Rev. 2021;148(4):111221. doi:10.1016/j.rser.
2021.111221.
5. Tigabu MT, Khalid MSU, Wood D, Admasu BT. Some effects of turbine inertia on the starting performance of
vertical-axis hydrokinetic turbine. Ocean Eng. 2022 May;252(3):111143. doi:10.1016/j.oceaneng.2022.111143.
6. Ghafoorian F, Mirmotahari SR, Eydizadeh M, Mehrpooya M. A systematic investigation on the hybrid Darrieus-
Savonius vertical axis wind turbine aerodynamic performance and self-starting capability improvement by
installing a curtain. Energy. 2025 Jan;6(7):100203. doi:10.1016/j.nxener.2024.100203.
7. Yan D, Yang Y, Ge Z. CFD evaluation of the self-starting of a vertical-axis wave turbine and the related flow and
load characteristics. In: ASME 2024 43rd International Conference on Ocean, Offshore and Arctic Engineering,
2024 Aug; Singapore: American Society of Mechanical Engineers Digital Collection. doi:10.1115/
OMAE2024-125892.
8. Mirmotahari SR, Ghafoorian F, Mehrpooya M, Hosseini Rad S, Taraghi M, Moghimi M. A comprehensive
investigation on Darrieus vertical axis wind turbine performance and self-starting capability improvement by
implementing a novel semi-directional airfoil guide vane and rotor solidity. Phys Fluids. 2024 Jun;36(6):
065151. doi:10.1063/5.0208848.
9. Liu K, Yu M, Zhu W. Enhancing wind energy harvesting performance of vertical axis wind turbines with a new
hybrid design: a fluid-structure interaction study. Renew Energy. 2019;140(4):912–27. doi:10.1016/j.renene.
2019.03.120.
10. Wisner KS, Yu M. Vertical-axis turbine performance enhancement with physics-informed blade pitch control.
Basic principles and proof of concept with high-fidelity numerical simulation. J Renew Sustain Energy.
2024 Mar;16(2):023305. doi:10.1063/5.0178535.
11. Tong M, Zhu W, Zhao X, Yu M, Liu K, Li G. Free and forced vibration analysis of H-type and hybrid vertical-axis
wind turbines. Energies. 2020;13(24):6747. doi:10.3390/en13246747.
12. Peng HY, Liu HJ, Yang JH. A review on the wake aerodynamics of H-rotor vertical axis wind turbines. Energy.
2021;232:121003. doi:10.1016/j.energy.2021.121003.
13. Wang L, Dong M, Yang J, Wang L, Chen S, DuićN, et al. Wind turbine wakes modeling and applications: past,
present, and future. Ocean Eng. 2024 Oct;309(8):118508. doi:10.1016/j.oceaneng.2024.118508.
14. Watts RG, Ferrer R. The lateral force on a spinning sphere: aerodynamics of a curveball. Am J Phys. 1987 Jan;
55(1):40–4. doi:10.1119/1.14969.
15. Sorensen B. Renewable energy: physics, engineering, environmental impacts, economics and planning. London:
Academic Press; 2017.
16. Kelley CL, Maniaci DC, Resor BR. Horizontal-axis wind turbine wake sensitivity to different blade load
distributions. In: 33rd Wind Energy Symposium, 2015; Kissimmee, FL, USA. doi:10.2514/6.2015-0490.
17. Dabiri JO. Potential order-of-magnitude enhancement of wind farm power density via counter-rotating vertical-
axis wind turbine arrays. J Renew Sustain Energy. 2011;3(4):043104. doi:10.1063/1.3608170.
18. Lund K, Madsen E. State-of-the-art value chain roadmap for sustainable end-of-life wind turbine blades. Renew
Sustain Energy Rev. 2024;192:114234.
19. Silva JE, Danao LAM. Varying VAWT cluster configuration and the effect on individual rotor and overall cluster
performance. Energies. 2021;14(6):1567. doi:10.3390/en14061567.
FDMP, 2024 31
20. Zheng H-D, Zheng XY, Zhao SX. Arrangement of clustered straight-bladed wind turbines. Energy. 2020;200(3):
117563. doi:10.1016/j.energy.2020.117563.
21. Mohamed OS, Ibrahim A, El Baz AMR. CFD investigation of the multiple rotors Darrieus type turbine
performance. In: ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition, Jun 17–
21, 2019; Phoenix, AZ, USA: American Society of Mechanical Engineers; V009T48A010.
22. Chowdhury AM, Akimoto H, Hara Y. Comparative CFD analysis of vertical axis wind turbine in upright and
tilted configuration. Renew Energy. 2016;85(1):327–37. doi:10.1016/j.renene.2015.06.037.
23. Ross I, Altman A, Bowman D, Mooney T, Bogart D. Aerodynamics of vertical-axis wind turbines: assessment of
accepted wind tunnel blockage practice. In: 48th AIAA Aerospace Sciences Meeting Including the New Horizons
Forum and Aerospace Exposition, 2010; Orlando, FL, USA. doi:10.2514/6.2010-397.
24. Manwell JF, McGowan JG, Rogers AL. Wind energy explained: theory, design and application. John Wiley &
Sons; 2010.
25. Azadani LN. Vertical axis wind turbines in cluster configurations. Ocean Eng. 2023;272(4):113855. doi:10.1016/
j.oceaneng.2023.113855.
26. Shaheen M, Abdallah S. Development of efficient vertical axis wind turbine clustered farms. Renew Sustain
Energy Rev. 2016;63(8):237–44. doi:10.1016/j.rser.2016.05.062.
27. Kinzel M, Mulligan Q, Dabiri JO. Energy exchange in an array of vertical-axis wind turbines. J Turbul. 2012;13:
N38. doi:10.1080/14685248.2012.712698.
28. Abkar M. Theoretical modeling of vertical-axis wind turbine wakes. Energies. 2019;12(1):10. doi:10.3390/
en12010010.
29. Lam HF, Peng HY. Measurements of the wake characteristics of co- and counter-rotating twin H-rotor vertical
axis wind turbines. Energy. 2017;131:13–26. doi:10.1016/j.energy.2017.05.015.
30. Peng HY, Lam HF, Liu HJ. Numerical investigation into the blade and wake aerodynamics of an H-rotor vertical
axis wind turbine. J Renew Sustain Energy. 2018 Sep;10(5):053305. doi:10.1063/1.5040297.
31. Hand B, Kelly G, Cashman A. Aerodynamic design and performance parameters of a lift-type vertical axis wind
turbine: a comprehensive review. Renew Sustain Energy Rev. 2021;139(3):110699. doi:10.1016/j.rser.2020.
110699.
32. Tjiu W, Marnoto T, Mat S, Ruslan MH, Sopian K. Darrieus vertical axis wind turbine for power generation I:
assessment of Darrieus VAWT configurations. Renew Energy. 2015;75:50–67. doi:10.1016/j.renene.2014.09.038.
33. Shaheen M, Abdallah S. Efficient clusters and patterned farms for Darrieus wind turbines. Sustain Energy
Technol Assess. 2017;19(4):125–35. doi:10.1016/j.seta.2017.01.007.
34. Giorgetti S, Pellegrini G, Zanforlin S. CFD Investigation on the aerodynamic interferences between medium-
solidity darrieus vertical axis wind turbines. Energy Proc. 2015;81:227–39. doi:10.1016/j.egypro.2015.12.089.
35. Whittlesey RW, Liska S, Dabiri JO. Fish schooling as a basis for vertical axis wind turbine farm design*.
Bioinspir Biomim. 2010 Aug;5(3):035005. doi:10.1088/1748-3182/5/3/035005.
36. Duraisamy K, Lakshminarayan V. Flow physics and performance of vertical axis wind turbine arrays. In: 32nd
AIAA Applied Aerodynamics Conference, 2014; Atlanta, GA, USA: American Institute of Aeronautics; p. 3139.
37. Bremseth J, Duraisamy K. Computational analysis of vertical axis wind turbine arrays. Theor Comput Fluid Dyn.
2016;30:387–401.
38. Kinzel M, Araya DB, Dabiri JO. Turbulence in vertical axis wind turbine canopies. Phys Fluids. 2015 Nov;
27(11):115102. doi:10.1063/1.4935111.
39. Mereu R, Federici D, Ferrari G, Schito P, Inzoli F. Parametric numerical study of Savonius wind turbine
interaction in a linear array. Renew Energy. 2017;113(9):1320–32. doi:10.1016/j.renene.2017.06.094.
40. Hezaveh SH, Bou-Zeid E, Dabiri J, Kinzel M, Cortina G, Martinelli L. Increasing the power production of
vertical-axis wind-turbine farms using synergistic clustering. Bound-Layer Meteorol. 2018;169:275–96.
41. Durkacz J, Islam S, Chan R, Fong E, Gillies H, Karnik A, et al. CFD modelling and prototype testing of a vertical axis
wind turbines in planetary cluster formation. Energy Rep. 2021;7(2021):119–26. doi:10.1016/j.egyr.2021.06.019.
32 FDMP, 2024
42. Kadum H, Cal RB, Quigley M, Cortina G, Calaf M. Compounded energy gains in collocated wind plants: energy
balance quantification and wake morphology description. Renew Energy. 2020;150:868–77. doi:10.1016/j.
renene.2019.12.077.
43. Chen J, Zhang Y, Xu Z, Li C. Flow characteristics analysis and power comparison for two novel types of
vertically staggered wind farms. Energy. 2023;263(3):126141. doi:10.1016/j.energy.2022.126141.
44. Belabes B, Paraschivoiu M. CFD modeling of vertical-axis wind turbine wake interaction. Trans Can Soc Mech
Eng. 2023;47(4):449–58. doi:10.1139/tcsme-2022-0149.
45. Posa A. Wake characterization of coupled configurations of vertical axis wind turbines using large eddy
simulation. Int J Heat Fluid Flow. 2019;75(4):27–43. doi:10.1016/j.ijheatfluidflow.2018.11.008.
46. Rivera-Arreba I, Li Z, Yang X, Bachynski-PolićEE. Comparison of the dynamic wake meandering model against
large eddy simulation for horizontal and vertical steering of wind turbine wakes. Renew Energy. 2024 Feb;
221(6):119807. doi:10.1016/j.renene.2023.119807.
47. Ouro P, Lazennec M. Theoretical modelling of the three-dimensional wake of vertical axis turbines. Flow. 2021;1:
E3. doi:10.1017/flo.2021.4.
48. Yuan Z, Sheng Q, Sun K, Zang J, Zhang X, Jing F, et al. The array optimization of vertical axis wind turbine based
on a new asymmetric wake model. J Mar Sci Eng. 2021;9(8):820. doi:10.3390/jmse9080820.
49. Dinesh Kumar Reddy G, Verma M, De A.