Revista Facultad de Ingeniería, Universidad de Antioquia, No.111, pp. 21-30, Apr-Jun 2024
CFD modeling and modal analysis for research
of energy harvesters by wind loads
Modelación CFD y análisis modal para investigación de cosechadoras de energía por cargas
de viento
Carlos Montes-Rodríguez1*Miguel Herrera-Suárez2
1Departamento de Nivelación Académica, Instituto de Admisión y Nivelación, Universidad Técnica de Manabí. Avenida
Urbina y Portoviejo. C. P. 130105. Portoviejo, Ecuador.
2Departamento de Mecánica, Facultad de Ciencias Matemáticas, Físicas y Químicas, Universidad Técnica de Manabí.
Avenida Urbina y Portoviejo. C. P. 130105. Portoviejo, Ecuador.
CITE THIS ARTICLE AS:
C. Montes-Rodríguez and M.
Herrera-Suárez.”CFD
modeling and modal analysis
for research of energy
harvesters by wind loads”,
Revista Facultad de Ingeniería
Universidad de Antioquia, no.
111, pp. 21-30, Apr-Jun 2024.
[Online]. Available: https:
//www.doi.org/10.17533/
udea.redin.20221096
ARTICLE INFO:
Received: July 12, 2021
Accepted: October 11, 2022
Available online: October 11,
2022
KEYWORDS:
Simulation models; CFD
simulation; wind power;
vibration
Modelo de simulación;
simulación CFD; energía
eólica; vibración
ABSTRACT: This work aims at coupling computational fluid dynamics (CFD) and modal
analysis (FEM) to simulate energy harvesting of wind loads to produce electrical
energy by piezoelectric effect. To complement this objective, CFD-FEM simulation was
performed by means of SolidWorks® 2021 add-ins, starting from the generation of the
virtual model, computational domain definition, and imposition of wind loads, boundary
conditions, and model discretization, by means of a mesh comprising a total of 84
709 nodes and 50 157 high order quadratic elements of 1 mm size and finally a mesh
calibration was performed. The results showed that the section near the clamping base
concentrated the highest pressures, regardless of the simulated velocity (3 to 21 m/s).
The maximum velocity caused a pressure over the impact zone of 101 716 Pa, a relative
pressure of 391.75 Pa, and shear stress of 4.78 Pa. The natural frequencies of vibration
using the CFD output, range from 69 to 99 Hz. The direction of wind action is defined as
the direction of piezoelectric placement, specifically near the base where the maximum
effective voltage output (6.79 V) is obtained which, with an external resistance of 10 and
20 MΩ, produces an electrical power of 4.62 and 2.31 μW, respectively.
RESUMEN: Este trabajo tiene como objetivo el acoplamiento de la dinámica de fluidos
computacional (CFD) y análisis modal (FEM) para simular la cosecha de energía
de cargas de viento para producir energía eléctrica por efecto piezoeléctrico. Para
complementar dicho objetivo, se realizó la simulación mediante CFD-FEM con los
complementos de SolidWorks® 2021, que partió de la generación del modelo virtual,
definición del dominio computacional e imposición de cargas de vientos, condiciones
de frontera, y discretización del modelo, mediante un mallado que comprendió un total
de 84 709 nodos y 50 157 elementos cuadráticos de alto orden de 1 mm de tamaño y
finalmente se realizó una calibración de malla. Los resultados mostraron que la sección
cercana a la base de sujeción se concentran las mayores presiones, independientemente
de la velocidad simulada (3 a 21 m/s). La velocidad máxima provoco una presión sobre la
zona de impacto de 101 716 Pa, una presión relativa de 391.75 Pa y un esfuerzo cortante
de 4.78 Pa. Las frecuencias naturales de vibración utilizando la salida CFD, oscilan de
69 a 99 Hz. La dirección de acción del viento se define como la dirección de colocación
del piezoeléctrico, específicamente cerca de la base donde se obtiene la máxima salida
de voltaje eficaz (6.79 V) que con una resistencia externa de 10 y 20 MΩ, produce una
potencia eléctrica de 4.62 y 2.31 μW, respectivamente.
1. Introduction As stated by the International Energy Agency [1], energetic
consumption has increased considerably in the last
decades, and significant increases are estimated for the
next years. Nonrenewable resources are the main source
of energy generation in countries that do not have the
necessary technologies to take advantage of other less
polluting energy sources.
21
* Corresponding author: Carlos Montes-Rodríguez
E-mail: carlos.montes@utm.edu.ec
ISSN 0120-6230
e-ISSN 2422-2844
DOI: 10.17533/udea.redin.20221096 21
CFD modeling and modal analysis for research
of energy harvesters by wind loads
Modelación CFD y análisis modal para investigación de cosechadoras de energía por cargas
de viento
Carlos Montes-Rodríguez1*Miguel Herrera-Suárez2
1Departamento de Nivelación Académica, Instituto de Admisión y Nivelación, Universidad Técnica de Manabí. Avenida
Urbina y Portoviejo. C. P. 130105. Portoviejo, Ecuador.
2Departamento de Mecánica, Facultad de Ciencias Matemáticas, Físicas y Químicas, Universidad Técnica de Manabí.
Avenida Urbina y Portoviejo. C. P. 130105. Portoviejo, Ecuador.
CITE THIS ARTICLE AS:
C. Montes-Rodríguez and M.
Herrera-Suárez.”CFD
modeling and modal analysis
for research of energy
harvesters by wind loads”,
Revista Facultad de Ingeniería
Universidad de Antioquia, no.
111, pp. 21-30, Apr-Jun 2024.
[Online]. Available: https:
//www.doi.org/10.17533/
udea.redin.20221096
ARTICLE INFO:
Received: July 12, 2021
Accepted: October 11, 2022
Available online: October 11,
2022
KEYWORDS:
Simulation models; CFD
simulation; wind power;
vibration
Modelo de simulación;
simulación CFD; energía
eólica; vibración
ABSTRACT: This work aims at coupling computational fluid dynamics (CFD) and modal
analysis (FEM) to simulate energy harvesting of wind loads to produce electrical
energy by piezoelectric effect. To complement this objective, CFD-FEM simulation was
performed by means of SolidWorks® 2021 add-ins, starting from the generation of the
virtual model, computational domain definition, and imposition of wind loads, boundary
conditions, and model discretization, by means of a mesh comprising a total of 84
709 nodes and 50 157 high order quadratic elements of 1 mm size and finally a mesh
calibration was performed. The results showed that the section near the clamping base
concentrated the highest pressures, regardless of the simulated velocity (3 to 21 m/s).
The maximum velocity caused a pressure over the impact zone of 101 716 Pa, a relative
pressure of 391.75 Pa, and shear stress of 4.78 Pa. The natural frequencies of vibration
using the CFD output, range from 69 to 99 Hz. The direction of wind action is defined as
the direction of piezoelectric placement, specifically near the base where the maximum
effective voltage output (6.79 V) is obtained which, with an external resistance of 10 and
20 MΩ, produces an electrical power of 4.62 and 2.31 μW, respectively.
RESUMEN: Este trabajo tiene como objetivo el acoplamiento de la dinámica de fluidos
computacional (CFD) y análisis modal (FEM) para simular la cosecha de energía
de cargas de viento para producir energía eléctrica por efecto piezoeléctrico. Para
complementar dicho objetivo, se realizó la simulación mediante CFD-FEM con los
complementos de SolidWorks® 2021, que partió de la generación del modelo virtual,
definición del dominio computacional e imposición de cargas de vientos, condiciones
de frontera, y discretización del modelo, mediante un mallado que comprendió un total
de 84 709 nodos y 50 157 elementos cuadráticos de alto orden de 1 mm de tamaño y
finalmente se realizó una calibración de malla. Los resultados mostraron que la sección
cercana a la base de sujeción se concentran las mayores presiones, independientemente
de la velocidad simulada (3 a 21 m/s). La velocidad máxima provoco una presión sobre la
zona de impacto de 101 716 Pa, una presión relativa de 391.75 Pa y un esfuerzo cortante
de 4.78 Pa. Las frecuencias naturales de vibración utilizando la salida CFD, oscilan de
69 a 99 Hz. La dirección de acción del viento se define como la dirección de colocación
del piezoeléctrico, específicamente cerca de la base donde se obtiene la máxima salida
de voltaje eficaz (6.79 V) que con una resistencia externa de 10 y 20 MΩ, produce una
potencia eléctrica de 4.62 y 2.31 μW, respectivamente.
1. Introduction As stated by the International Energy Agency [1], energetic
consumption has increased considerably in the last
decades, and significant increases are estimated for the
next years. Nonrenewable resources are the main source
of energy generation in countries that do not have the
necessary technologies to take advantage of other less
polluting energy sources.
21
* Corresponding author: Carlos Montes-Rodríguez
E-mail: carlos.montes@utm.edu.ec
ISSN 0120-6230
e-ISSN 2422-2844
DOI: 10.17533/udea.redin.20221096 21
C. Montes-Rodríguez et al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 111, pp. 21-30, 2024
This reality encourages the development of clean
and accessible technologies to use renewable energy
sources [2–5]. Harvesting energy from vibrations is
an alternative to taking advantage of non-conventional
energy sources, which have been gaining space in
the last decades. Vibrations as a source of energy
can be harnessed by conversion mechanisms such
as electromagnetic, electrostatic, and piezoelectric
transduction [6–9]. Piezoelectric transduction is
consolidating as one of the most promising methods
in electric energy micro-generation, due to its high power
density; moreover, it does not show any electromagnetic
interference [10, 11].
The studies on piezoelectric materials have allowed
the production of composite materials with excellent
properties, focused on obtaining the maximum equipment
or systems performance, which has led these materials
to have a great variety of applications in different fields of
science [12–14].
Wind’s kinetic energy is able to produce induced vibrations
of vortex, slipstream, flapping, and gallop types [15]. In
the scientific advances in the use of aero-elastic vibrations
and the development of several prototypes, the L-type
[16], circular cylinders [17], and triangular leaf shape [18]
stand out. The connection in parallel of several harvesting
models [19] has also been experienced, among others.
There exists a remarkable variety of harvesting devices
models that use basic geometric forms (square, circular,
triangular) as surfaces of interaction or of kinetic energy
capture, but the use of geometries of certain complexity
in panels focused on rising the energy or vibrations
harvesting can have a positive effect on the power output;
this fact increases performance and reduces in a certain
way, the economic costs of production. The selection of
profiles is made using criteria such as design simplicity,
economic factors, time for manufacturing, size, and
maximum stresses, or pressures, among others.
The high variability of the vibration frequencies can
affect the harvesters’ performance; therefore the study of
these scenarios is of fundamental importance in order to
estimate the average electric energy production [19].
Technologies and devices of micro-consumption that
operate in daily activities, point to the development of
energy harvesters, considering these as one of the main
sources of energy for future smart cities, where the use of
endogen resources is a fundamental aspect.
The advances in computational tools for design assisted
by computers, allow studying physical processes of high
complexity. An example of this fact is computational fluid
dynamics (CFD), which is capable of analyzing with high
precision, the effects of a fluid on an element considered
as a frontier or obstacle in the computational domain,
independently of its geometry [20–23].
Along with these computational advances, the
development reached by numerical methods has allowed
the coupling of fluid problems (CFD) with modal analysis
(FEM), making possible the identification of zones of
higher stresses due to fluid pressure. It also allows the
analysis of frequencies in order to investigate the effects
of the different vibration modes of a particular element or
system.
Most of the CFD models developed on energy harvesters
use different flow velocities, being frequent some values
within the range of 1.8 to 23 m/s. The geometrical
characteristics of the models are different between
authors; still, the obtained power outputs varying from
0.001 mW to 4 mW can be related, which are dependent
on the flow velocity, the transduction method, and the
geometrical parameters used [24, 25]. CFD results are
often not used as a basis for further studies with other
techniques such as modal analysis; consequently, in
general, the displacements and oscillation frequency of
the harvesters are the result of experimental validations
[26, 27].
Based on the above-mentioned background, this work
aims to the simulation of the mechanical response of a
model of energy harvester by wind loads, using the method
of computational fluid dynamics (CFD) coupled with the
modal analysis (FEM).
2. Materials and methods
2.1 Description of the phenomenon to be
modeled
To take advantage of aero-elastic energy vibrations from
a uniform, horizontal air flux, a mathematical model
CFD/FEM is developed for a prototype of an energy
harvester from the vibrations generated by wind loads.
The harvester’s organ response in function of the
different vibrational modes (modal analysis) in FEM is
simulated. Subsequently, an analysis of the virtual model
mechanical response is developed to define its resistance
to loads or fluid pressure CFD and, at the same time, to
identify zones of maximum stress concentrations, strains
and displacements where the piezoelectric material could
be placed and generate an output voltage and usable
power for the energy supply of devices or sensors.
22
This reality encourages the development of clean
and accessible technologies to use renewable energy
sources [2–5]. Harvesting energy from vibrations is
an alternative to taking advantage of non-conventional
energy sources, which have been gaining space in
the last decades. Vibrations as a source of energy
can be harnessed by conversion mechanisms such
as electromagnetic, electrostatic, and piezoelectric
transduction [6–9]. Piezoelectric transduction is
consolidating as one of the most promising methods
in electric energy micro-generation, due to its high power
density; moreover, it does not show any electromagnetic
interference [10, 11].
The studies on piezoelectric materials have allowed
the production of composite materials with excellent
properties, focused on obtaining the maximum equipment
or systems performance, which has led these materials
to have a great variety of applications in different fields of
science [12–14].
Wind’s kinetic energy is able to produce induced vibrations
of vortex, slipstream, flapping, and gallop types [15]. In
the scientific advances in the use of aero-elastic vibrations
and the development of several prototypes, the L-type
[16], circular cylinders [17], and triangular leaf shape [18]
stand out. The connection in parallel of several harvesting
models [19] has also been experienced, among others.
There exists a remarkable variety of harvesting devices
models that use basic geometric forms (square, circular,
triangular) as surfaces of interaction or of kinetic energy
capture, but the use of geometries of certain complexity
in panels focused on rising the energy or vibrations
harvesting can have a positive effect on the power output;
this fact increases performance and reduces in a certain
way, the economic costs of production. The selection of
profiles is made using criteria such as design simplicity,
economic factors, time for manufacturing, size, and
maximum stresses, or pressures, among others.
The high variability of the vibration frequencies can
affect the harvesters’ performance; therefore the study of
these scenarios is of fundamental importance in order to
estimate the average electric energy production [19].
Technologies and devices of micro-consumption that
operate in daily activities, point to the development of
energy harvesters, considering these as one of the main
sources of energy for future smart cities, where the use of
endogen resources is a fundamental aspect.
The advances in computational tools for design assisted
by computers, allow studying physical processes of high
complexity. An example of this fact is computational fluid
dynamics (CFD), which is capable of analyzing with high
precision, the effects of a fluid on an element considered
as a frontier or obstacle in the computational domain,
independently of its geometry [20–23].
Along with these computational advances, the
development reached by numerical methods has allowed
the coupling of fluid problems (CFD) with modal analysis
(FEM), making possible the identification of zones of
higher stresses due to fluid pressure. It also allows the
analysis of frequencies in order to investigate the effects
of the different vibration modes of a particular element or
system.
Most of the CFD models developed on energy harvesters
use different flow velocities, being frequent some values
within the range of 1.8 to 23 m/s. The geometrical
characteristics of the models are different between
authors; still, the obtained power outputs varying from
0.001 mW to 4 mW can be related, which are dependent
on the flow velocity, the transduction method, and the
geometrical parameters used [24, 25]. CFD results are
often not used as a basis for further studies with other
techniques such as modal analysis; consequently, in
general, the displacements and oscillation frequency of
the harvesters are the result of experimental validations
[26, 27].
Based on the above-mentioned background, this work
aims to the simulation of the mechanical response of a
model of energy harvester by wind loads, using the method
of computational fluid dynamics (CFD) coupled with the
modal analysis (FEM).
2. Materials and methods
2.1 Description of the phenomenon to be
modeled
To take advantage of aero-elastic energy vibrations from
a uniform, horizontal air flux, a mathematical model
CFD/FEM is developed for a prototype of an energy
harvester from the vibrations generated by wind loads.
The harvester’s organ response in function of the
different vibrational modes (modal analysis) in FEM is
simulated. Subsequently, an analysis of the virtual model
mechanical response is developed to define its resistance
to loads or fluid pressure CFD and, at the same time, to
identify zones of maximum stress concentrations, strains
and displacements where the piezoelectric material could
be placed and generate an output voltage and usable
power for the energy supply of devices or sensors.
22
C. Montes-Rodríguez et al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 111, pp. 21-30, 2024
2.2 Virtual model of the harvester organ
The object of study is a piezoelectric energy harvester,
consisting of a panel in the form of a wave (wave-shaped by
the wind in a fluid) and a rectangular piezoelectric patch.
The patch resides on the panel’s internal surface (Figure
1). The organ’s virtual model was generated using the
SolidWorks® 2020 software, by some utilities, including
sketch, equidistance, and solid operations.
2.3 Definition of the harvester material
properties
Typically, in a real scenario, the energy harvesters are in
corrosive and abrasive environments, a fact that conditions
the selection of materials for their construction, besides
the economic cost that the material can represent when
having better mechanical properties to give a longer
service life. Table 1 shows the materials’ physical and
mechanical properties required by the models for the
simulation of the harvester prototype functioning and
operation.
The piezoelectric material voltage output is conditioned
by its properties and the applied force, in piezoelectric
materials of a disk with diameters higher than their
thickness, in a proportion of 5:1 [28]. The theoretical or
calculated output voltage can be obtained by means of
Equations 1 and 2
VP D = 4t
πd2 g33F (1)
VP D = 0.00382F (2)
Where t is the thickness, m; d is the diameter, m; g33 is the
piezoelectric voltage constant, V m/N ; F is the force on N;
VP D is the output peak voltage in V.
Figure 1 Harvester Virtual Model
Equation (2) expresses the voltage as a function of the
applied force. With the calculation of VP D, we proceed to
calculate the efficient voltage, as shown in Equation 3.
VEf = VP D
√2 (3)
Table 1 Physical and mechanical properties of the semi-curved
panel and piezoelectric material
Parts Properties Value
Semi-curved
Elastic module, (MPa) 200 000
panel
Poisson Coefficient 0.35
Copper
Density, (kg/m3) 8 900
Tensile or traction limit, (MPa) 413
Elastic limit, (MPa) 172
Thickness, (mm) 0.2
Piezoelectric EDensity, (kg/m3) 0.0078
material Piezoelectric voltage, (Vm/N) 0.0027
PZT NCE51 Diameter, (mm) 30
Thickness, (mm) 1
Where VEf is the efficient or effective voltage in V.
Finally, it is possible to know the electric power from the
fundamental equations in Ohm’s Law.
2.4 Model in CFD for the simulation of the
effects of wind loads
The simulation made by CFD will allow investigating
the factors influencing the energy harvest produced by
the wind loads, such as the wind velocity variation, the
aerodynamic pressure, shear force, turbulence, and
environmental conditions. The CFD model was developed
in the SolidWorks® software using the complement Flow
Simulation.
Figure 2 Panel-fluid study configuration, CFD study
A study of external type fluid is defined, where the
computational domain is adjusted to the panel’s geometry;
the interactions between the structure and the fluid
(velocity variations), and the surface objectives for the
study of the stresses are established (Figure 2). The
computational domain considers that the laminar type
fluid with kinetic energy moves at a constant velocity in
the direction –z, with an ambient temperature of 298 K
and a pressure of 101.325 kPa, which is within the average
ranges for the city of Portoviejo, Ecuador, a zone where
the study is performed [29–31].
23
2.2 Virtual model of the harvester organ
The object of study is a piezoelectric energy harvester,
consisting of a panel in the form of a wave (wave-shaped by
the wind in a fluid) and a rectangular piezoelectric patch.
The patch resides on the panel’s internal surface (Figure
1). The organ’s virtual model was generated using the
SolidWorks® 2020 software, by some utilities, including
sketch, equidistance, and solid operations.
2.3 Definition of the harvester material
properties
Typically, in a real scenario, the energy harvesters are in
corrosive and abrasive environments, a fact that conditions
the selection of materials for their construction, besides
the economic cost that the material can represent when
having better mechanical properties to give a longer
service life. Table 1 shows the materials’ physical and
mechanical properties required by the models for the
simulation of the harvester prototype functioning and
operation.
The piezoelectric material voltage output is conditioned
by its properties and the applied force, in piezoelectric
materials of a disk with diameters higher than their
thickness, in a proportion of 5:1 [28]. The theoretical or
calculated output voltage can be obtained by means of
Equations 1 and 2
VP D = 4t
πd2 g33F (1)
VP D = 0.00382F (2)
Where t is the thickness, m; d is the diameter, m; g33 is the
piezoelectric voltage constant, V m/N ; F is the force on N;
VP D is the output peak voltage in V.
Figure 1 Harvester Virtual Model
Equation (2) expresses the voltage as a function of the
applied force. With the calculation of VP D, we proceed to
calculate the efficient voltage, as shown in Equation 3.
VEf = VP D
√2 (3)
Table 1 Physical and mechanical properties of the semi-curved
panel and piezoelectric material
Parts Properties Value
Semi-curved
Elastic module, (MPa) 200 000
panel
Poisson Coefficient 0.35
Copper
Density, (kg/m3) 8 900
Tensile or traction limit, (MPa) 413
Elastic limit, (MPa) 172
Thickness, (mm) 0.2
Piezoelectric EDensity, (kg/m3) 0.0078
material Piezoelectric voltage, (Vm/N) 0.0027
PZT NCE51 Diameter, (mm) 30
Thickness, (mm) 1
Where VEf is the efficient or effective voltage in V.
Finally, it is possible to know the electric power from the
fundamental equations in Ohm’s Law.
2.4 Model in CFD for the simulation of the
effects of wind loads
The simulation made by CFD will allow investigating
the factors influencing the energy harvest produced by
the wind loads, such as the wind velocity variation, the
aerodynamic pressure, shear force, turbulence, and
environmental conditions. The CFD model was developed
in the SolidWorks® software using the complement Flow
Simulation.
Figure 2 Panel-fluid study configuration, CFD study
A study of external type fluid is defined, where the
computational domain is adjusted to the panel’s geometry;
the interactions between the structure and the fluid
(velocity variations), and the surface objectives for the
study of the stresses are established (Figure 2). The
computational domain considers that the laminar type
fluid with kinetic energy moves at a constant velocity in
the direction –z, with an ambient temperature of 298 K
and a pressure of 101.325 kPa, which is within the average
ranges for the city of Portoviejo, Ecuador, a zone where
the study is performed [29–31].
23
C. Montes-Rodríguez et al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 111, pp. 21-30, 2024
Concerning the wind velocity, a variation range of 3
to 21 m/s was established to represent this variable’s
variations in the different zones of the Republic of Ecuador
[30, 32, 33].
Model’s discretization
The model’s discretization is made by the Cartesian
mesh method of the Solid Works Flow Simulation, which
gives great advantages in generating the mesh algorithm
considering the original CAD model data (virtual model).
The method generates three types of cells that represent
the solids, the fluid, and partial cells that represent
the intersection with the immersed solid. These cells
are rectangular divisions (cuboids) of the computational
domain. For the meshing, a manual configuration was
used for both the virtual model and the fluid, with an
advanced channel refinement; the minimum size of space
was 1 mm and a radius factor of 4, resulting in a total of
243 607 cells for the fluid, 15 542 cells of the solid and
20 641 cells in contact with the solid. Figure 3 shows the
mesh calibration process, and a number of elements are
chosen within the range of 17 200 to 21 200, because the
results are independent of the mesh.
Figure 3 Mesh calibration
2.5 Coupling of modal analysis by the finite
elements method (FEM)
In order to determine the harvesting response in the
different vibration modes of the harvester work organ,
a modal analysis was developed in which there were
also determined the model’s natural frequencies and
the contributions of the organ mass, in each one of the
coordinate axes, where the deformation mode can define
the most adequate scenario for the energy capture from
the wind loads. From the interaction structure-fluid
results, the four lower modal forms were analyzed.
The computational tool allows the coupling of the
results of a model CFD with a modal analysis in FEM to
link aerodynamic pressure loads. The general procedure
for performing a CFD/FEM study in SolidWorks®, is shown
in Figure 4.
2.6 Harvester’s physical integrity
determination
With the fluid pressure and shear stress calculations
in three dimensions (CFD), we proceed to study the
mechanical response of the harvester panel’s material,
produced by the action of the mechanical stress simulated
by the SolidWorks Simulation software component. By
means of this method application, the harvester’s physical
integrity against the different pressure magnitudes is
evaluated. For the frequency studies, the lower ends of the
panel are fixed (Figure 5), allowing the panel to oscillate
in the function of the applied loads. Finally, the model
discretization was developed, starting from a mesh based
on a curvature composed of quadratic elements of a high
order, which generates a total of 84 709 nodes and 50 175
elements.
3. Results and discussion
3.1 Results of the organ-fluid interaction
(CFD
The harvester organ’s geometry allows the opposition to
the kinetic energy transmitted by the wind load, generating
pressure on the panel’s surface in the central zone, that
reaches a maximum of 101 716 Pa and of 101 336 Pa, for
the wind velocities of 21 and 4 m/s respectively, in the zone
of direct impact with the wind (Figure 6a).
The wind velocity experiences a small drop of 2 m/s
on the surface of the direct impact of the wind on the
panel, but in the superior part of the structure (vortex),
a small velocity increment is observed (23.48 m/s), while
that for the velocity of 4 m/s, it is of 5.859 m/s. Both
increments are a result of the fluid accumulation and the
low resistance that the organ’s geometry generates in the
zone. (Figure 6b).
The relative pressure shows negative values of -244.62
Pa in the panel’s superior zone; that is, a small vacuum
is generated, which initiates vorticity; also, in the impact
zone, we observe how the pressure rises to 391.75 Pa.
This trend is similar to the velocity of 4 m/s, having values
of -10.87 Pa in the vortex zone and 11.51 Pa in the impact
zone (Figure 6c). Negative values indicate that there is a
deflection causing traction, resulting in an expansion of
the material, while positive values represent compression
24
Concerning the wind velocity, a variation range of 3
to 21 m/s was established to represent this variable’s
variations in the different zones of the Republic of Ecuador
[30, 32, 33].
Model’s discretization
The model’s discretization is made by the Cartesian
mesh method of the Solid Works Flow Simulation, which
gives great advantages in generating the mesh algorithm
considering the original CAD model data (virtual model).
The method generates three types of cells that represent
the solids, the fluid, and partial cells that represent
the intersection with the immersed solid. These cells
are rectangular divisions (cuboids) of the computational
domain. For the meshing, a manual configuration was
used for both the virtual model and the fluid, with an
advanced channel refinement; the minimum size of space
was 1 mm and a radius factor of 4, resulting in a total of
243 607 cells for the fluid, 15 542 cells of the solid and
20 641 cells in contact with the solid. Figure 3 shows the
mesh calibration process, and a number of elements are
chosen within the range of 17 200 to 21 200, because the
results are independent of the mesh.
Figure 3 Mesh calibration
2.5 Coupling of modal analysis by the finite
elements method (FEM)
In order to determine the harvesting response in the
different vibration modes of the harvester work organ,
a modal analysis was developed in which there were
also determined the model’s natural frequencies and
the contributions of the organ mass, in each one of the
coordinate axes, where the deformation mode can define
the most adequate scenario for the energy capture from
the wind loads. From the interaction structure-fluid
results, the four lower modal forms were analyzed.
The computational tool allows the coupling of the
results of a model CFD with a modal analysis in FEM to
link aerodynamic pressure loads. The general procedure
for performing a CFD/FEM study in SolidWorks®, is shown
in Figure 4.
2.6 Harvester’s physical integrity
determination
With the fluid pressure and shear stress calculations
in three dimensions (CFD), we proceed to study the
mechanical response of the harvester panel’s material,
produced by the action of the mechanical stress simulated
by the SolidWorks Simulation software component. By
means of this method application, the harvester’s physical
integrity against the different pressure magnitudes is
evaluated. For the frequency studies, the lower ends of the
panel are fixed (Figure 5), allowing the panel to oscillate
in the function of the applied loads. Finally, the model
discretization was developed, starting from a mesh based
on a curvature composed of quadratic elements of a high
order, which generates a total of 84 709 nodes and 50 175
elements.
3. Results and discussion
3.1 Results of the organ-fluid interaction
(CFD
The harvester organ’s geometry allows the opposition to
the kinetic energy transmitted by the wind load, generating
pressure on the panel’s surface in the central zone, that
reaches a maximum of 101 716 Pa and of 101 336 Pa, for
the wind velocities of 21 and 4 m/s respectively, in the zone
of direct impact with the wind (Figure 6a).
The wind velocity experiences a small drop of 2 m/s
on the surface of the direct impact of the wind on the
panel, but in the superior part of the structure (vortex),
a small velocity increment is observed (23.48 m/s), while
that for the velocity of 4 m/s, it is of 5.859 m/s. Both
increments are a result of the fluid accumulation and the
low resistance that the organ’s geometry generates in the
zone. (Figure 6b).
The relative pressure shows negative values of -244.62
Pa in the panel’s superior zone; that is, a small vacuum
is generated, which initiates vorticity; also, in the impact
zone, we observe how the pressure rises to 391.75 Pa.
This trend is similar to the velocity of 4 m/s, having values
of -10.87 Pa in the vortex zone and 11.51 Pa in the impact
zone (Figure 6c). Negative values indicate that there is a
deflection causing traction, resulting in an expansion of
the material, while positive values represent compression
24
C. Montes-Rodríguez et al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 111, pp. 21-30, 2024
Figure 4 Schematic of the general process for linking pressures from CFD to FEM
Figure 5 Frequency analysis configuration
or contraction caused by the wind load. On the other hand,
the shear stress of the fluid action on the surface is in
the range of 2.44 to 4.87 Pa for the maximum velocity,
while for the minimum velocity, the stress is 1.55 Pa (Fig
6d). The friction coefficient decreases as the velocity
increases, in this way, for the maximum velocity, the
friction coefficient is 2.26 for the maximum velocity, and at
4 m/s, the coefficient is 6.47.
Additionally, pressure, shear stress, and relative pressure
variables are dependent on the velocity variation; the
higher the magnitude of velocity, the higher the resultant
of the other variables.
Since the harvesters left and right surfaces have different
geometries, the pressures and the other variables can vary
depending on the section with which the fluid interacts.
The analysis of the relations between dynamic pressure
and wind velocity, considering the direction from which
the wind blows, allowed obtaining the models that relate
both variables (Figure 7). These models evidence the
existence of a third- order polynomic relation in all the
analyzed cases, showing that, as the fluid velocity raises,
the dynamic pressure exerted by the fluid increases in
a non-linear way. In cases 1 and 3, it is observed that
for velocities higher than 12 m/s, the non-linear relation
between both variables is accentuated.
The correlation coefficient reached high values of R2 =
0.9926, 0.989, and 0.9874, and the errors of 0.051, 0.029
and 0.034, respectively for each one of the cases. The
maximum pressures were obtained when the wind’s
direction acts in the negative direction of the z-axis. The
simulation shows that the panel geometry can accumulate
a higher aerodynamic pressure with respect to the curved
panel [34].
In Figures 6b and 6c, it can be clearly appreciated
how the capture geometry (panel) opposes the laminar
flux and modifies its displacement that, in principle, is
made in an ordered way with a homogeneous velocity
between fluid layers. The interaction produces a decrease
in the pressure on the panel backside, modifying the
fluid’s direction and velocity, forming a forced vortex
in a clockwise direction. The variations and location of
pressures show significant relations with other models of
harvesters that also take advantage of the wind loads to
oscillate [17, 22, 35]. This vortex concentration (turbulent
flows) after the geometry, and allows us to say that, part
of the air’s kinetic energy is transformed into aerodynamic
pressure; that is, the flux changes to turbulent below the
panel maximum height.
The resulting pressure of the interaction between the fluid
and the harvester organ produces small displacements in
the geometry, that compress and extend certain zones of
the panel, producing vibrations that can be used later.
25
Figure 4 Schematic of the general process for linking pressures from CFD to FEM
Figure 5 Frequency analysis configuration
or contraction caused by the wind load. On the other hand,
the shear stress of the fluid action on the surface is in
the range of 2.44 to 4.87 Pa for the maximum velocity,
while for the minimum velocity, the stress is 1.55 Pa (Fig
6d). The friction coefficient decreases as the velocity
increases, in this way, for the maximum velocity, the
friction coefficient is 2.26 for the maximum velocity, and at
4 m/s, the coefficient is 6.47.
Additionally, pressure, shear stress, and relative pressure
variables are dependent on the velocity variation; the
higher the magnitude of velocity, the higher the resultant
of the other variables.
Since the harvesters left and right surfaces have different
geometries, the pressures and the other variables can vary
depending on the section with which the fluid interacts.
The analysis of the relations between dynamic pressure
and wind velocity, considering the direction from which
the wind blows, allowed obtaining the models that relate
both variables (Figure 7). These models evidence the
existence of a third- order polynomic relation in all the
analyzed cases, showing that, as the fluid velocity raises,
the dynamic pressure exerted by the fluid increases in
a non-linear way. In cases 1 and 3, it is observed that
for velocities higher than 12 m/s, the non-linear relation
between both variables is accentuated.
The correlation coefficient reached high values of R2 =
0.9926, 0.989, and 0.9874, and the errors of 0.051, 0.029
and 0.034, respectively for each one of the cases. The
maximum pressures were obtained when the wind’s
direction acts in the negative direction of the z-axis. The
simulation shows that the panel geometry can accumulate
a higher aerodynamic pressure with respect to the curved
panel [34].
In Figures 6b and 6c, it can be clearly appreciated
how the capture geometry (panel) opposes the laminar
flux and modifies its displacement that, in principle, is
made in an ordered way with a homogeneous velocity
between fluid layers. The interaction produces a decrease
in the pressure on the panel backside, modifying the
fluid’s direction and velocity, forming a forced vortex
in a clockwise direction. The variations and location of
pressures show significant relations with other models of
harvesters that also take advantage of the wind loads to
oscillate [17, 22, 35]. This vortex concentration (turbulent
flows) after the geometry, and allows us to say that, part
of the air’s kinetic energy is transformed into aerodynamic
pressure; that is, the flux changes to turbulent below the
panel maximum height.
The resulting pressure of the interaction between the fluid
and the harvester organ produces small displacements in
the geometry, that compress and extend certain zones of
the panel, producing vibrations that can be used later.
25
C. Montes-Rodríguez et al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 111, pp. 21-30, 2024
(a) (b)
(c) (d)
Figure 6 CFD simulation results, velocity of 21 m/s. (a) aerodynamic pressure, (b) velocity, (c) relative pressure, and (d) shear stress
Figure 7 Aerodynamic pressure variation against wind loads.
(Case 1) negative fluid direction for the z- axis. (Case 2) positive
fluid direction for the y-axis and (Case 3) curved panel model
3.2 Modal analysis FEM results
Results show the natural frequencies, periods, and
amplitudes of the vibrations when the harvester organ
is impacted by the wind load (Table 2). The three first
resonance modes have low natural frequencies compared
to the fourth mode, whose oscillation period is shorter.
With respect to the oscillations’ amplitudes, it can
be observed that the second modal form, has major
displacements (Figure 8).
To get the most out of displacements, it is necessary
to identify the higher amplitudes in the axis “y” and “z”,
because this, starting from the wind pressures, generates
flection and torsion stress that the piezoelectric material
can transform into electric output. In accordance with this
fact, the more feasible vibration modes in low frequency
are the first, the second, and the third modal forms, while
the fourth modal form can also be used, but has a higher
frequency.
Some design considerations for these harvesters
recommend avoiding excessive torsional stresses,
which could produce significant deformations, and the
frequency of excitation in the harvester should be close
to or coincide with the natural frequency in order to
reach the resonance state that generates an increase in
the amplitude of the oscillation and the electric generation.
The natural frequency values are higher than the ones
found by [34]; however, because the model is in a dynamic
environment, it was considered to link the pressures
generated by the fluid, which, in a certain way, induce
displacements, deformations, and tensions that modify
the modality characteristics, increasing them.
The appropriate zones to place the piezoelectric
transductor material are those where the vibration
amplitudes are higher; that is, in the zones where the
maximum amplitudes are reached. It must be remarked
that for each one of the natural frequencies, the location
of the zoneswhere the maximum amplitudes are reached,
changes.
Figure 9 shows the percentage of cumulative mass
participation (CEMPF) for the different frequency modes.
For the x-axis, the three last modal forms have the same
CEMPF of 23.5%. With respect to the y-axis, the CEMPF
values for the four modal forms are 42%, 65%, 72%, and
77%, respectively. In the z-axis, the higher participation
percentages are obtained for the frequency modes; the
third and fourth modal forms stand out, where the CEMPF
26
(a) (b)
(c) (d)
Figure 6 CFD simulation results, velocity of 21 m/s. (a) aerodynamic pressure, (b) velocity, (c) relative pressure, and (d) shear stress
Figure 7 Aerodynamic pressure variation against wind loads.
(Case 1) negative fluid direction for the z- axis. (Case 2) positive
fluid direction for the y-axis and (Case 3) curved panel model
3.2 Modal analysis FEM results
Results show the natural frequencies, periods, and
amplitudes of the vibrations when the harvester organ
is impacted by the wind load (Table 2). The three first
resonance modes have low natural frequencies compared
to the fourth mode, whose oscillation period is shorter.
With respect to the oscillations’ amplitudes, it can
be observed that the second modal form, has major
displacements (Figure 8).
To get the most out of displacements, it is necessary
to identify the higher amplitudes in the axis “y” and “z”,
because this, starting from the wind pressures, generates
flection and torsion stress that the piezoelectric material
can transform into electric output. In accordance with this
fact, the more feasible vibration modes in low frequency
are the first, the second, and the third modal forms, while
the fourth modal form can also be used, but has a higher
frequency.
Some design considerations for these harvesters
recommend avoiding excessive torsional stresses,
which could produce significant deformations, and the
frequency of excitation in the harvester should be close
to or coincide with the natural frequency in order to
reach the resonance state that generates an increase in
the amplitude of the oscillation and the electric generation.
The natural frequency values are higher than the ones
found by [34]; however, because the model is in a dynamic
environment, it was considered to link the pressures
generated by the fluid, which, in a certain way, induce
displacements, deformations, and tensions that modify
the modality characteristics, increasing them.
The appropriate zones to place the piezoelectric
transductor material are those where the vibration
amplitudes are higher; that is, in the zones where the
maximum amplitudes are reached. It must be remarked
that for each one of the natural frequencies, the location
of the zoneswhere the maximum amplitudes are reached,
changes.
Figure 9 shows the percentage of cumulative mass
participation (CEMPF) for the different frequency modes.
For the x-axis, the three last modal forms have the same
CEMPF of 23.5%. With respect to the y-axis, the CEMPF
values for the four modal forms are 42%, 65%, 72%, and
77%, respectively. In the z-axis, the higher participation
percentages are obtained for the frequency modes; the
third and fourth modal forms stand out, where the CEMPF
26
C. Montes-Rodríguez et al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 111, pp. 21-30, 2024
(a) (b)
(c) (d)
Figure 8 Vibration modes with an overlap of the model on the deformation, (a) first, (b) second, (c) third, and (d) fourth
Table 2 Frequency modes parameters
Frequency Natural Period (s) Amplitude (mm)
mode frequency (Hz) x-axis y-axis z-axis Resultant)
1 69.013 0.01449 0.0037 0.915 1.178 15.51
2 88.872 0.011252 13.28 13.01 12.31 19.41
3 99.482 0.010052 0.022 1.487 13.40 14.42
4 253.54 0.0039441 0.021 11.52 12.22 14.11
Figure 9 Mass participation factor associated with the
excitation frequencies and possible piezoelectric material
location for first (a), second(b), and third (c) modal forms with
respect to the z-axis
is 124% and 130%, respectively. This result shows that
the piezoelectric material location must be done along the
z-axis or the harvester organ’s longitudinal axis, in the
zones where the major displacements are observed.
3.3 Results of the structural integrity check of
the element or organ
The stress distributions (Figure 10a) show that the
maximum von Mises stresses are located in the central
zone of the panel, where the wind load impacts directly,
as well as in the model’s posterior support. These
displacements are in the range of 0.015 to 0.018 mm
(Figure 10b). The maximum displacements are able to
produce significant flection stress on the piezoelectric
material, if its location is near the model’s center.
The unitary deformations in the structure allowed showing
that the deformations caused by the wind load are in the
range of 0.000000941 a 0.00000219 (Figure 11a), so the
panel’s structural integrity is not compromised. These
deformations are located directly in the zone of wind
impacts with the panel’s surface, which corroborates or
indicates the zone where the piezoelectric material should
be placed.
A security factor distribution analysis shows that it
reached values Fs = 44, which evidences that the
harvester resists the loads as well as the deformations
that arise from wind loads, without affecting its structural
27
(a) (b)
(c) (d)
Figure 8 Vibration modes with an overlap of the model on the deformation, (a) first, (b) second, (c) third, and (d) fourth
Table 2 Frequency modes parameters
Frequency Natural Period (s) Amplitude (mm)
mode frequency (Hz) x-axis y-axis z-axis Resultant)
1 69.013 0.01449 0.0037 0.915 1.178 15.51
2 88.872 0.011252 13.28 13.01 12.31 19.41
3 99.482 0.010052 0.022 1.487 13.40 14.42
4 253.54 0.0039441 0.021 11.52 12.22 14.11
Figure 9 Mass participation factor associated with the
excitation frequencies and possible piezoelectric material
location for first (a), second(b), and third (c) modal forms with
respect to the z-axis
is 124% and 130%, respectively. This result shows that
the piezoelectric material location must be done along the
z-axis or the harvester organ’s longitudinal axis, in the
zones where the major displacements are observed.
3.3 Results of the structural integrity check of
the element or organ
The stress distributions (Figure 10a) show that the
maximum von Mises stresses are located in the central
zone of the panel, where the wind load impacts directly,
as well as in the model’s posterior support. These
displacements are in the range of 0.015 to 0.018 mm
(Figure 10b). The maximum displacements are able to
produce significant flection stress on the piezoelectric
material, if its location is near the model’s center.
The unitary deformations in the structure allowed showing
that the deformations caused by the wind load are in the
range of 0.000000941 a 0.00000219 (Figure 11a), so the
panel’s structural integrity is not compromised. These
deformations are located directly in the zone of wind
impacts with the panel’s surface, which corroborates or
indicates the zone where the piezoelectric material should
be placed.
A security factor distribution analysis shows that it
reached values Fs = 44, which evidences that the
harvester resists the loads as well as the deformations
that arise from wind loads, without affecting its structural
27
C. Montes-Rodríguez et al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 111, pp. 21-30, 2024
(a) (b)
Figure 10 (a) von Mises stresses distribution and (b) displacement, air flux z-axis negative direction
(a) (b)
Figure 11 ((a) von Mises stresses distribution and (b) displacement, air flux z-axis negative direction
integrity. Despite the harvester having these resistance
reserves, we decided to maintain the panel’s dimensions
because of the significant contributions to the three-axis
displacement that a higher mass generates, besides
giving a significant wind impact area.
3.4 Mechanical stress transduction
In figure 12, it can be observed that, as the wind load
applied on the panel increases, the peak voltage and
the efficient voltage of the PZT NCE51 increase linearly,
showing a directly proportional relation. For the case of
power, a non-linear relation between applied force and
efficient voltage is shown, evidencing that as the load
rises, the power increases in a polynomic manner, as a
result of the vibrations generated in the harvester’s panel.
The correlation coefficient reached values of R2 = 1
for the analyzed cases. It is evident that the location of
the piezoelectric material in a different section, of higher
stresses, produces higher values of voltage output and
power. The use of piezoelectric PZT exhibits higher output
power and efficiency, as mentioned by several authors
[34, 36].
4. Conclusions
The coupling of the results of CFD simulation with the
computational simulation by FEM, allowed simulating the
Figure 12 Relation between voltage, electric power, and force
wind pressure effects on the harvester’s work organ, as
also to know the vibration modes most favorable for the
electricity generation, in a range of wind velocities of 3 to
21 m/s.
The CFD simulation results allowed identifying the
zones where the pressures concentrate, which vary from
-0.244 to 0.391 kPa, as a product of the load impact
imposed by the action of the wind on the panel’s surface,
as well as to determine the maximum deformations.
Maximum deformations in the three analyzed axes
are originated in the second mode of vibration, which
makes it the most adequate for electricity generation in
the simulated operating conditions.
28
(a) (b)
Figure 10 (a) von Mises stresses distribution and (b) displacement, air flux z-axis negative direction
(a) (b)
Figure 11 ((a) von Mises stresses distribution and (b) displacement, air flux z-axis negative direction
integrity. Despite the harvester having these resistance
reserves, we decided to maintain the panel’s dimensions
because of the significant contributions to the three-axis
displacement that a higher mass generates, besides
giving a significant wind impact area.
3.4 Mechanical stress transduction
In figure 12, it can be observed that, as the wind load
applied on the panel increases, the peak voltage and
the efficient voltage of the PZT NCE51 increase linearly,
showing a directly proportional relation. For the case of
power, a non-linear relation between applied force and
efficient voltage is shown, evidencing that as the load
rises, the power increases in a polynomic manner, as a
result of the vibrations generated in the harvester’s panel.
The correlation coefficient reached values of R2 = 1
for the analyzed cases. It is evident that the location of
the piezoelectric material in a different section, of higher
stresses, produces higher values of voltage output and
power. The use of piezoelectric PZT exhibits higher output
power and efficiency, as mentioned by several authors
[34, 36].
4. Conclusions
The coupling of the results of CFD simulation with the
computational simulation by FEM, allowed simulating the
Figure 12 Relation between voltage, electric power, and force
wind pressure effects on the harvester’s work organ, as
also to know the vibration modes most favorable for the
electricity generation, in a range of wind velocities of 3 to
21 m/s.
The CFD simulation results allowed identifying the
zones where the pressures concentrate, which vary from
-0.244 to 0.391 kPa, as a product of the load impact
imposed by the action of the wind on the panel’s surface,
as well as to determine the maximum deformations.
Maximum deformations in the three analyzed axes
are originated in the second mode of vibration, which
makes it the most adequate for electricity generation in
the simulated operating conditions.
28
C. Montes-Rodríguez et al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 111, pp. 21-30, 2024
The piezoelectric material must be placed in the direction
of wind action, because this is the direction where the
panel suffers the maximum deformations.
The harvester is able to preserve its structural integrity
during its operation in the simulated wind load regime.
5. Declaration of competing interest
We declare that we have no significant competing interests,
including financial or non-financial, professional, or
personal interests interfering with the full and objective
presentation of the work described in this manuscript.
6. Acknowledments
The authors wish to thank the Postgraduate Institute of
the Technical University of Manabí, Ecuador (Instituto de
Posgrado de la Universidad Técnica de Manabí, Ecuador)
for the support required for the development of this
research work, within the framework of the Master’s
Program of Research in Mechanics, Mention: Energy
Efficiency.
7. Funding
The authors of the paper declare that they are the
only source of funding for the research described in the
presented work.
8. Author contributions
Carlos Montes Rodríguez developed the methodology,
simulations, data analysis and initial writing of the article
and Miguel Herrera Suárez contributed to the writing of the
article, formal analysis and project management.
9. Data availability statement
The authors confirm that the data supporting the findings
of this study are available within the article [and/or] its
supplementary materials.
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29
The piezoelectric material must be placed in the direction
of wind action, because this is the direction where the
panel suffers the maximum deformations.
The harvester is able to preserve its structural integrity
during its operation in the simulated wind load regime.
5. Declaration of competing interest
We declare that we have no significant competing interests,
including financial or non-financial, professional, or
personal interests interfering with the full and objective
presentation of the work described in this manuscript.
6. Acknowledments
The authors wish to thank the Postgraduate Institute of
the Technical University of Manabí, Ecuador (Instituto de
Posgrado de la Universidad Técnica de Manabí, Ecuador)
for the support required for the development of this
research work, within the framework of the Master’s
Program of Research in Mechanics, Mention: Energy
Efficiency.
7. Funding
The authors of the paper declare that they are the
only source of funding for the research described in the
presented work.
8. Author contributions
Carlos Montes Rodríguez developed the methodology,
simulations, data analysis and initial writing of the article
and Miguel Herrera Suárez contributed to the writing of the
article, formal analysis and project management.
9. Data availability statement
The authors confirm that the data supporting the findings
of this study are available within the article [and/or] its
supplementary materials.
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enconman.2020.112503
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from fluid flow using piezoelectrics: A critical review,” Renewable
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1016/j.renene.2019.05.078
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harvesting using piezoelectric macro fiber composites based on
flutter mode,” Microelectronic Engineering, vol. 231, Jul. 15, 2020.
[Online]. Available: https://doi.org/10.1016/j.mee.2020.111333
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piezoelectric beam energy harvesting,” International Journal of
Mechanical Sciences, vol. 175, Jun. 01, 2020. [Online]. Available:
https://doi.org/10.1016/j.ijmecsci.2020.105532
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integration of the wind-induced flutter energy harvester (wifeh)
into the built environment: Experimental and numerical analysis,”
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https://doi.org/10.1016/j.apenergy.2017.06.041
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computational fluid dynamic simulation techniques for darrieus
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vol. 149, Oct. 01, 2017. [Online]. Available: https://doi.org/10.1016/j.
enconman.2017.07.016
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flapping foil-based energy harvester by a rotating foil,” Computers
& Fluids, vol. 160, Jan. 04, 2018. [Online]. Available: https:
//doi.org/10.1016/j.compfluid.2017.10.024
[23] J. Vives, M. Massanés, J. J. de Felipe, and L. Sanmiquel,
“Computational fluid dynamics (cfd) study to optimize the auxiliary
ventilation system in an underground mine,” Dyna, vol. 89, no. 221,
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v89n221.100297
[24] C. Montes-Rodríguez, J. A. Pérez-Rodríguez, and
M. Herrera-Suárez, “Análisis del estado actual de la cosecha
de energía por medio de vibraciones producidas por cargas de
viento,” Dominio de las ciencias, vol. 7, no. 4, 2021. [Online].
Available: http://dx.doi.org/10.23857/dc.v7i4.2436
[25] M. Rajarathinam and S. F. Ali, “Energy generation in a hybrid
harvester under harmonic excitation,” Energy Conversion and
Management, vol. 155, Jan. 01, 2018. [Online]. Available: https:
//doi.org/10.1016/j.enconman.2017.10.054
[26] V. Jamadar, P. Pingle, and S. Kanase, “Possibility of harvesting
vibration energy from power producing devices: A review,”
in International Conference on Automatic Control and Dynamic
Optimization Techniques (ICACDOT), Pune, India, 2016, pp. 496––503.
[27] B. Maamer, A. Boughamoura, A. M. F. El-Bab, L. A.
Francis, and F. Tounsi, “A review on design improvements
and techniques for mechanical energy harvesting using
piezoelectric and electromagnetic schemes,” Energy Conversion
and Management, vol. 199, Nov. 01, 2019. [Online]. Available:
https://doi.org/10.1016/j.enconman.2019.111973
[28] A. Martín-Malmcrona, “Aplicaciones del efecto piezoeléctrico para
la generación de energía,” B. A. thesis, Universidad Carlos III de
Madrid, Madrid, Spain, 2018.
[29] E. Morán-Tejeda, J. Bazo, J. I. López-Moreno, E. Aguilar,
C. Azorín-Molina, and et al., “Climate trends and variability
in ecuador (1966–2011),” International Journal of Climatology,
vol. 36, no. 11, Jan. 15, 2016. [Online]. Available: https:
//doi.org/10.1002/joc.4597
[30] E. C. Vega and J. C. Jara, “Estimation of crop reference
evapotranspiration for two locations (coastal and andean region) of
ecuador,” Engenharia Agrícola, vol. 29, no. 03, Sep. 2009. [Online].
Available: https://doi.org/10.1590/S0100-69162009000300006
[31] S. Vicente-Cerrano, E. Aguilar, R. Martínez, N. Martín-Hernández,
C. Azorín-Molina, and et al., “The complex influence of enso
on droughts in ecuador,” Climate Dynamics volume, vol. 48,
Mar. 26, 2017. [Online]. Available: https://doi.org/10.1007/
s00382-016-3082-y
[32] A. C. Nuñez-Basantes and E. Higueras-García, “Altitude, climate
variables and people’s length of stay in ecuador squares,”
Brazilian magazine of urban management, vol. 10, no. 2, May-Aug.
2018. [Online]. Available: https://doi.org/10.1590/2175-3369.010.
002.AO11
[33] D. Jijón, J. Constante, G. Villacreses, and T. Guerrero, “Modelling
of performance of 2 mw wind turbines in ecuador: Electric-wind,”
Energía, no. 15, Jul. 18, 1996. [Online]. Available: https://tinyurl.
com/4mb2ycxc
[34] X. Shan, H. T., D. Chen, and T. Xie, “A curved panel energy harvester
for aeroelastic vibration,” Applied Energy, vol. 249, Sep. 01, 2019.
[Online]. Available: https://doi.org/10.1016/j.apenergy.2019.04.153
[35] A. Abdelkefi, “Aeroelastic energy harvesting: A review,” International
Journal of Engineering Science, vol. 100, Mar. 2016. [Online].
Available: https://doi.org/10.1016/j.ijengsci.2015.10.006
[36] S. Sojan and R. Kulkarni, “A comprehensive review of energy
harvesting techniques and its potential applications,” International
Journal of Computer Applications, vol. 139, no. 3, Apr. 2016. [Online].
Available: https://tinyurl.com/2ebx3vvw
30