Revista Facultad de Ingeniería, Universidad de Antioquia, No.111, pp. 55-63, Apr-Jun 2024
Performance of an Archimedes screw turbine
with spiral configuration for hydrokinetic
applications
Funcionamiento de una turbina tipo tornillo de Arquímedes con configuración en espiral para
aplicaciones hidrocinéticas
Ana Isabel Montilla-López1, Laura Isabel Velásquez-García 1, Johan Betancour1, Ainhoa
Rubio-Clemente 1, 2*, Edwin Lenin Chica-Arrieta1
1Grupo de Investigación Energía Alternativa (GEA), Facultad de Ingeniería, Universidad de Antioquia. Calle 70 # 52-21, C.
P. 050010. Medellín, Colombia.
2Escuela Ambiental. Facultad de Ingeniería, Universidad de Antioquia. Calle 70 # 52-21. C. P. 050010. Medellín, Colombia.
CITE THIS ARTICLE AS:
A. I. Montilla-López, L. I.
Velásquez-García, J.
Betancour, A. Rubio-Clemente
and E. L. Chica-Arrieta.
”Performance of an
Archimedes screw turbine
with spiral configuration for
hydrokinetic applications”,
Revista Facultad de Ingeniería
Universidad de Antioquia, no.
111, pp. 55-63, Apr-Jun 2024.
[Online]. Available: https:
//www.doi.org/10.17533/
udea.redin.20221208
ARTICLE INFO:
Received: November 17, 2021
Accepted: December 02, 2022
Available online: December
02, 2022
KEYWORDS:
Computational fluid dynamics;
Archimedes spiral turbine;
6-DOF
Dinámica de fluidos
computacional; Turbina de
Arquímedes en espiral; 6-DOF
ABSTRACT: The performance of an Archimedes spiral turbine (AST) for hydrokinetic
applications was examined using a three-dimensional unsteady numerical model
utilizing the six degrees of freedom (6-DOF) solver that is available in ANSYs Fluent
software. From the computational fluid dynamics (CFD) simulations, the power
coefficient (Cp) curve was estimated. This curve was compared with the curve of an
Archimedes screw hydrokinetic turbine (ASHT) reported in the literature. The ASHT was
found to be more efficient than the AST for electricity generation. The highest value of Cp
for the AST was 0.337, which is a relatively high value in comparison with that of other
types of hydrokinetic turbines. The results calculated from the CFD for the AST were
compared with an experimental study reported for wind applications.
RESUMEN: El rendimiento de una turbina de Arquímedes en espiral (AST, por sus siglas
en inglés) para aplicaciones hidrocinéticas se examinó utilizando un modelo numérico
transitorio tridimensional utilizando un solucionador de seis grados de libertad (6-DOF,
por sus siglas en inglés) disponible en el software ANSYs Fluent. A partir de las
simulaciones de dinámica de fluidos computacional (CFD, por sus siglas en inglés), se
estimó la curva del coeficiente de potencia (Cp). Esta curva se comparó con la curva
de Cp de una turbina hidrocinética tipo tornillo de Arquímedes (ASHT, por sus siglas en
inglés) disponible en la literatura. Se encontró que la ASHT es más eficiente que la AST
para la generación de electricidad. El valor más alto de Cp para la AST fue 0.337, lo
cual es un valor relativamente alto en comparación con el obtenido por otros tipos de
turbinas hidrocinéticas. Los resultados calculados a partir de CFD para la AST fueron
comparados con los obtenidos del estudio experimental reportado para aplicaciones
eólicas
1. Introduction
Today, the world is facing the effects of climate change and
other situations associated with it. That is the reason why
countries are working hard to reduce the consumption of
fossil fuels that generate more greenhouse gas emissions.
By 2019, fossil fuels accounted for more than 80% of the
global energy consumption. From this perspective, a
considerable replacement of these fuels is expected to
have been achieved by the middle of the century. For
this purpose, implementing energy generation processes
from renewable sources has been fostered to promote
this transition to cleaner and more sustainable energies
55
* Corresponding author: Ainhoa Rubio-Clemente
E-mail: ainhoa.rubioc@udea.edu.co
ISSN 0120-6230
e-ISSN 2422-2844
DOI: 10.17533/udea.redin.20221208 55
Performance of an Archimedes screw turbine
with spiral configuration for hydrokinetic
applications
Funcionamiento de una turbina tipo tornillo de Arquímedes con configuración en espiral para
aplicaciones hidrocinéticas
Ana Isabel Montilla-López1, Laura Isabel Velásquez-García 1, Johan Betancour1, Ainhoa
Rubio-Clemente 1, 2*, Edwin Lenin Chica-Arrieta1
1Grupo de Investigación Energía Alternativa (GEA), Facultad de Ingeniería, Universidad de Antioquia. Calle 70 # 52-21, C.
P. 050010. Medellín, Colombia.
2Escuela Ambiental. Facultad de Ingeniería, Universidad de Antioquia. Calle 70 # 52-21. C. P. 050010. Medellín, Colombia.
CITE THIS ARTICLE AS:
A. I. Montilla-López, L. I.
Velásquez-García, J.
Betancour, A. Rubio-Clemente
and E. L. Chica-Arrieta.
”Performance of an
Archimedes screw turbine
with spiral configuration for
hydrokinetic applications”,
Revista Facultad de Ingeniería
Universidad de Antioquia, no.
111, pp. 55-63, Apr-Jun 2024.
[Online]. Available: https:
//www.doi.org/10.17533/
udea.redin.20221208
ARTICLE INFO:
Received: November 17, 2021
Accepted: December 02, 2022
Available online: December
02, 2022
KEYWORDS:
Computational fluid dynamics;
Archimedes spiral turbine;
6-DOF
Dinámica de fluidos
computacional; Turbina de
Arquímedes en espiral; 6-DOF
ABSTRACT: The performance of an Archimedes spiral turbine (AST) for hydrokinetic
applications was examined using a three-dimensional unsteady numerical model
utilizing the six degrees of freedom (6-DOF) solver that is available in ANSYs Fluent
software. From the computational fluid dynamics (CFD) simulations, the power
coefficient (Cp) curve was estimated. This curve was compared with the curve of an
Archimedes screw hydrokinetic turbine (ASHT) reported in the literature. The ASHT was
found to be more efficient than the AST for electricity generation. The highest value of Cp
for the AST was 0.337, which is a relatively high value in comparison with that of other
types of hydrokinetic turbines. The results calculated from the CFD for the AST were
compared with an experimental study reported for wind applications.
RESUMEN: El rendimiento de una turbina de Arquímedes en espiral (AST, por sus siglas
en inglés) para aplicaciones hidrocinéticas se examinó utilizando un modelo numérico
transitorio tridimensional utilizando un solucionador de seis grados de libertad (6-DOF,
por sus siglas en inglés) disponible en el software ANSYs Fluent. A partir de las
simulaciones de dinámica de fluidos computacional (CFD, por sus siglas en inglés), se
estimó la curva del coeficiente de potencia (Cp). Esta curva se comparó con la curva
de Cp de una turbina hidrocinética tipo tornillo de Arquímedes (ASHT, por sus siglas en
inglés) disponible en la literatura. Se encontró que la ASHT es más eficiente que la AST
para la generación de electricidad. El valor más alto de Cp para la AST fue 0.337, lo
cual es un valor relativamente alto en comparación con el obtenido por otros tipos de
turbinas hidrocinéticas. Los resultados calculados a partir de CFD para la AST fueron
comparados con los obtenidos del estudio experimental reportado para aplicaciones
eólicas
1. Introduction
Today, the world is facing the effects of climate change and
other situations associated with it. That is the reason why
countries are working hard to reduce the consumption of
fossil fuels that generate more greenhouse gas emissions.
By 2019, fossil fuels accounted for more than 80% of the
global energy consumption. From this perspective, a
considerable replacement of these fuels is expected to
have been achieved by the middle of the century. For
this purpose, implementing energy generation processes
from renewable sources has been fostered to promote
this transition to cleaner and more sustainable energies
55
* Corresponding author: Ainhoa Rubio-Clemente
E-mail: ainhoa.rubioc@udea.edu.co
ISSN 0120-6230
e-ISSN 2422-2844
DOI: 10.17533/udea.redin.20221208 55
A. I. Montilla-López et al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 111, pp. 55-63, 2024
such as wind, solar, geothermal, and hydroelectric energy,
among others [1].
In this regard, hydroelectric power generation includes
hydroelectric and hydrokinetic turbines, being hydrokinetic
turbines well accepted. These latter allow the use of a
renewable source, like watercourses from rivers, seas,
or artificial channels, to operate and produce energy.
Hydrokinetic turbines take the kinetic energy of those
sources and avoid the use of big-scale constructions,
since they do not need a dam nor high altitude to operate.
In addition, these turbines can capture energy without
causing any significant disruption to the water stream,
which means a low environmental impact. Additionally,
it has been highlighted that these turbines are becoming
very attractive due to their high energy density and the
relatively easy way to be located near remote areas [2].
Two types of hydrokinetic turbines are commonly known.
The former ones are vertical or cross-flow turbines,
where the axis of the rotor is orthogonal to the water
flow and parallel to the water surface. This configuration
allows unidirectional rotation, even though the fluid flow
is bidirectional, and is suitable for operation in shallow
channels with variable water velocities and shallow
streams with limited water flow [1]. However, this kind
of turbine has disadvantages, including low efficiency
and, given its low starting torque, the requirement of
a mechanism to start-up [1–3]. On the other hand,
horizontal or axial flow turbines have their axis parallel
to the direction of the fluid flow. The advantage of
these turbines is their self-starting capability and the
active control by pitching the blades allowing them more
flexibility in over-speed protection [3].
Several horizontal turbines can be the Archimedes
turbines in screw and spiral-shaped. In the literature,
it has been observed that Archimedes screw turbines
present a high efficiency of approximately 85% when
used in micro-hydroelectric power plants like hydraulic
turbines [4]. In recent years, studies based on Archimedes
screw turbines for hydrokinetic applications have been
introduced, carrying out numerical studies to determine
the geometrical parameters and their optimal values
to achieve a more efficient turbine [5]. The turbine
efficiency has also been assessed through experiments
at a laboratory scale for low tip speed ratio (TSR) values
to discern the coefficient of performance of this kind
of turbine aiming at producing the efficiency curve of
the hydrokinetic turbine, both in aligned and inclined
configurations [6].
On the other hand, the spiral turbine has been recently
used to produce energy, taking the wind to be operated,
in order to determine the effect of certain geometric
parameters on the operation and efficiency of this type
of turbine. An investigation has established the turbine
design parameters from angular momentum conservation,
and studied the behavior of the turbine blade [7]. Based
on computational fluid dynamics (CFD) results, this study
concluded that due to the greater pressure difference in
the blade tip, more energy could be extracted from the
outside of the blade.
Despite the characteristics of horizontal-axis hydrokinetic
turbines, they have a disadvantage associated with the
low energy density that can be obtained compared to the
turbines of hydroelectric power plants. For this reason,
carrying out studies to optimize the geometry of these
turbines is of utmost importance to achieve greater
efficiency and, therefore, a higher performance in the
energy production process.
In the field related to turbine simulation, it is possible to
identify in the literature that in turbo-machinery, the six
degrees of freedom (6-DoF) user-defined function (UDF)
method has been commonly used to analyze systems
as cross-flow turbines [8–11], water wheel turbines
[12] and open flume turbines [13]. The 6-DoF approach
has not been thoroughly investigated in hydrokinetic
turbine rotor modeling. From the authors’ knowledge,
only the work carried out by Wang and coworkers was
found to report the 6-DoF model in the CFD simulation
to evaluate the performance of a vertical-axis Darrieus
turbine [14]. Bouvant et al. report an interesting study
on the geometrical optimization of Archimedes screw
hydrokinetic turbine (ASHT) as a hydrokinetic turbine [5].
The authors provided significant improvement on the topic
by comparing the results obtained with those reported in
the literature, especially on the methodology used for the
optimization.
CFD numerical simulations have been improved with
respect to those proposed by Zitti et al. [6], substituting the
constant angular velocity assigned to the turbine with a
specific and more realistic UDF function [6]. Furthermore,
CFD results are extended with the use of response surface
methodology. This leads to the identification of an optimal
configuration compared with other CFD and experimental
tests. For the numerical simulation, Zittiet al. applied the
multiple reference frames (MRF) method in the ANSYS
Fluent software [6].
The MRF method does not consider the inertia of the
rotor, while it is considered by the 6-DoF UDF method that
is utilized in the current research. Under this scenario, the
presented work studies for the first time the hydrodynamic
performance of an Archimedes spiral turbine (AST) for
hydrokinetic applications. In this work, a comparative
study of the hydrodynamic performance of an AST and
56
such as wind, solar, geothermal, and hydroelectric energy,
among others [1].
In this regard, hydroelectric power generation includes
hydroelectric and hydrokinetic turbines, being hydrokinetic
turbines well accepted. These latter allow the use of a
renewable source, like watercourses from rivers, seas,
or artificial channels, to operate and produce energy.
Hydrokinetic turbines take the kinetic energy of those
sources and avoid the use of big-scale constructions,
since they do not need a dam nor high altitude to operate.
In addition, these turbines can capture energy without
causing any significant disruption to the water stream,
which means a low environmental impact. Additionally,
it has been highlighted that these turbines are becoming
very attractive due to their high energy density and the
relatively easy way to be located near remote areas [2].
Two types of hydrokinetic turbines are commonly known.
The former ones are vertical or cross-flow turbines,
where the axis of the rotor is orthogonal to the water
flow and parallel to the water surface. This configuration
allows unidirectional rotation, even though the fluid flow
is bidirectional, and is suitable for operation in shallow
channels with variable water velocities and shallow
streams with limited water flow [1]. However, this kind
of turbine has disadvantages, including low efficiency
and, given its low starting torque, the requirement of
a mechanism to start-up [1–3]. On the other hand,
horizontal or axial flow turbines have their axis parallel
to the direction of the fluid flow. The advantage of
these turbines is their self-starting capability and the
active control by pitching the blades allowing them more
flexibility in over-speed protection [3].
Several horizontal turbines can be the Archimedes
turbines in screw and spiral-shaped. In the literature,
it has been observed that Archimedes screw turbines
present a high efficiency of approximately 85% when
used in micro-hydroelectric power plants like hydraulic
turbines [4]. In recent years, studies based on Archimedes
screw turbines for hydrokinetic applications have been
introduced, carrying out numerical studies to determine
the geometrical parameters and their optimal values
to achieve a more efficient turbine [5]. The turbine
efficiency has also been assessed through experiments
at a laboratory scale for low tip speed ratio (TSR) values
to discern the coefficient of performance of this kind
of turbine aiming at producing the efficiency curve of
the hydrokinetic turbine, both in aligned and inclined
configurations [6].
On the other hand, the spiral turbine has been recently
used to produce energy, taking the wind to be operated,
in order to determine the effect of certain geometric
parameters on the operation and efficiency of this type
of turbine. An investigation has established the turbine
design parameters from angular momentum conservation,
and studied the behavior of the turbine blade [7]. Based
on computational fluid dynamics (CFD) results, this study
concluded that due to the greater pressure difference in
the blade tip, more energy could be extracted from the
outside of the blade.
Despite the characteristics of horizontal-axis hydrokinetic
turbines, they have a disadvantage associated with the
low energy density that can be obtained compared to the
turbines of hydroelectric power plants. For this reason,
carrying out studies to optimize the geometry of these
turbines is of utmost importance to achieve greater
efficiency and, therefore, a higher performance in the
energy production process.
In the field related to turbine simulation, it is possible to
identify in the literature that in turbo-machinery, the six
degrees of freedom (6-DoF) user-defined function (UDF)
method has been commonly used to analyze systems
as cross-flow turbines [8–11], water wheel turbines
[12] and open flume turbines [13]. The 6-DoF approach
has not been thoroughly investigated in hydrokinetic
turbine rotor modeling. From the authors’ knowledge,
only the work carried out by Wang and coworkers was
found to report the 6-DoF model in the CFD simulation
to evaluate the performance of a vertical-axis Darrieus
turbine [14]. Bouvant et al. report an interesting study
on the geometrical optimization of Archimedes screw
hydrokinetic turbine (ASHT) as a hydrokinetic turbine [5].
The authors provided significant improvement on the topic
by comparing the results obtained with those reported in
the literature, especially on the methodology used for the
optimization.
CFD numerical simulations have been improved with
respect to those proposed by Zitti et al. [6], substituting the
constant angular velocity assigned to the turbine with a
specific and more realistic UDF function [6]. Furthermore,
CFD results are extended with the use of response surface
methodology. This leads to the identification of an optimal
configuration compared with other CFD and experimental
tests. For the numerical simulation, Zittiet al. applied the
multiple reference frames (MRF) method in the ANSYS
Fluent software [6].
The MRF method does not consider the inertia of the
rotor, while it is considered by the 6-DoF UDF method that
is utilized in the current research. Under this scenario, the
presented work studies for the first time the hydrodynamic
performance of an Archimedes spiral turbine (AST) for
hydrokinetic applications. In this work, a comparative
study of the hydrodynamic performance of an AST and
56
A. I. Montilla-López et al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 111, pp. 55-63, 2024
an ASHT was carried out. For this purpose, unsteady
CFD simulations with the 6-DOF solver and the k − ω
shear stress transport turbulence model were employed.
From the simulations, the power coefficient (Cp) curve
for the AST was obtained and compared with the Cp
curve of the ASHT that is available in the literature. The
results calculated from the CFD method for the AST were
compared with the experimental study reported for wind
applications.
2. Methods and materials
The AST has a simple design, operates at low noise,
and is environmentally friendly, with low-cost installation
and maintenance associated. Its performance can be
estimated in terms of Cp, which is defined as the ratio
between the utilized power and the available power; i.e.,
the kinetic energy of the water is converted into rotational
kinetic energy.
Cp is calculated from Equation (1) and depends on the TSR
value; therefore, curves were obtained showing the values
of Cp versus (vs.) TSR, being TSR calculated as expressed
in Equation (2).
Cp = T ω
0.5ρAV 3 (1)
T SR = λ = ωR
V (2)
where T is the torque generated by the turbine, ω is the
angular velocity, ρ is the density of the fluid, A is the swept
area of the turbine, V is the fluid velocity and R is the
radius of the peripheral section of the turbine.
AST has been studied by a number of authors for
wind applications. For example, the behavior of the
turbine has been compared for several blade inclination
angles (γ) with respect to the axial axis. γ was fixed at
several values, such as 50°, 55°, 60° and 65° [15]. In this
case, the higher Cp was equal to 0.22 at a TSR of 1.71 with
a γ of 50°. Labib and coworkers concluded that higher
Cp values were found at low TSR. In addition, a study has
been conducted comparing the behavior of two different
AST values [16]. One of the AST had fixed angle blades
(equal to 60°) and the other one had variable angle blades
(equivalent to 30°, 45° and 60°). To study such as behavior,
simulations were made in CFD.
Finally, it was obtained that the maximum Cp (0.226)
for the variable angle rotor was produced at a TSR equal to
1.96; while the maximum Cp reached for the turbine with a
fixed angle equal to 0.207 occurs at a TSR of 1.57, resulting
in a difference of only 9.18% compared to the maximum
Cp of the turbine with a variable angle. Additionally, the
referred authors indicated that the first and third blades of
the turbine develop a key role in the extraction of energy,
which in this case is wind energy [15].
Based on the previous information, some geometric
parameters were established as conditions to be studied
in the performance of an AST for hydrokinetic applications.
Therefore, the spiral screw had three blades that were
separated 120° between them. The turbine was defined
by an outer diameter (De), a pitch (p) and γ equal to 250
mm, 170 mm and 60°, respectively. The geometry of the
AST was similar to that used by Kim et al. [7] and Jang et
al. [17]. Figure 1 shows a schematic representation of the
AST rotor model used in this study.
For the AST study, CFD simulations were implemented,
employing the UDF, with 6-DOF, to model the rotation of
the turbine. This solver uses the numerical integration of
the pressure and the shear stress over the blade surface
in order to compute the hydrodynamic force and moments
acting on the blades. Additionally, the solver also keeps
track of a rotor motion history, and post-processing the
results, the angular velocity of the rotor is calculated
from the force balance on the blade. In Equation (3), the
translational movement for the center of mass of the body
is calculated with respect to the inertial reference frame.
˙−→
V = 1
m
∑ −→
FG (3)
where ˙−→
V ; m and −→
FG refer to the translational motion for
the body, the mass of the body and the vector of forces,
respectively. In turn, Equation (4) was used to compute the
rotation movement of the body, applying body coordinates;
where −→ωB is the vector of ω, L stands for the matrix with
the inertia moments and −→
MB is the moment vector of the
object (ANSYS Inc., 2018a).
˙⃗ω B = L−1 (∑ −→
MB − −→ωB × L⃗ω B
)
(4)
The 6-DoF approach can be used to predict sequentially
the angular positions according to the turbine mass
properties (mass and moment of inertia) in real time.
The 6-DoF method computes the AST angular velocity (ω)
based on forces and moments acting on the rotor.
For the 6-DoF simulation, the AST footprint and the
entire domain were allocated in a way that with the
water coming from -X to +X, the generated momentum
would make the turbine rotates around the +X axis (one
DoF rotation); the inertia tensor for the 6-DoF UDF
configuration was computed with the help of SolidWorks
software. The AST is limited to rotating around the X-axis,
while the other DoF are not available. The specifications
of the AST, which depend on the geometry and material
of the turbine, are shown in Table 1. Small values of
the moment of inertia promote the startup of the AST.
However, excessively small values will impair the stability
57
an ASHT was carried out. For this purpose, unsteady
CFD simulations with the 6-DOF solver and the k − ω
shear stress transport turbulence model were employed.
From the simulations, the power coefficient (Cp) curve
for the AST was obtained and compared with the Cp
curve of the ASHT that is available in the literature. The
results calculated from the CFD method for the AST were
compared with the experimental study reported for wind
applications.
2. Methods and materials
The AST has a simple design, operates at low noise,
and is environmentally friendly, with low-cost installation
and maintenance associated. Its performance can be
estimated in terms of Cp, which is defined as the ratio
between the utilized power and the available power; i.e.,
the kinetic energy of the water is converted into rotational
kinetic energy.
Cp is calculated from Equation (1) and depends on the TSR
value; therefore, curves were obtained showing the values
of Cp versus (vs.) TSR, being TSR calculated as expressed
in Equation (2).
Cp = T ω
0.5ρAV 3 (1)
T SR = λ = ωR
V (2)
where T is the torque generated by the turbine, ω is the
angular velocity, ρ is the density of the fluid, A is the swept
area of the turbine, V is the fluid velocity and R is the
radius of the peripheral section of the turbine.
AST has been studied by a number of authors for
wind applications. For example, the behavior of the
turbine has been compared for several blade inclination
angles (γ) with respect to the axial axis. γ was fixed at
several values, such as 50°, 55°, 60° and 65° [15]. In this
case, the higher Cp was equal to 0.22 at a TSR of 1.71 with
a γ of 50°. Labib and coworkers concluded that higher
Cp values were found at low TSR. In addition, a study has
been conducted comparing the behavior of two different
AST values [16]. One of the AST had fixed angle blades
(equal to 60°) and the other one had variable angle blades
(equivalent to 30°, 45° and 60°). To study such as behavior,
simulations were made in CFD.
Finally, it was obtained that the maximum Cp (0.226)
for the variable angle rotor was produced at a TSR equal to
1.96; while the maximum Cp reached for the turbine with a
fixed angle equal to 0.207 occurs at a TSR of 1.57, resulting
in a difference of only 9.18% compared to the maximum
Cp of the turbine with a variable angle. Additionally, the
referred authors indicated that the first and third blades of
the turbine develop a key role in the extraction of energy,
which in this case is wind energy [15].
Based on the previous information, some geometric
parameters were established as conditions to be studied
in the performance of an AST for hydrokinetic applications.
Therefore, the spiral screw had three blades that were
separated 120° between them. The turbine was defined
by an outer diameter (De), a pitch (p) and γ equal to 250
mm, 170 mm and 60°, respectively. The geometry of the
AST was similar to that used by Kim et al. [7] and Jang et
al. [17]. Figure 1 shows a schematic representation of the
AST rotor model used in this study.
For the AST study, CFD simulations were implemented,
employing the UDF, with 6-DOF, to model the rotation of
the turbine. This solver uses the numerical integration of
the pressure and the shear stress over the blade surface
in order to compute the hydrodynamic force and moments
acting on the blades. Additionally, the solver also keeps
track of a rotor motion history, and post-processing the
results, the angular velocity of the rotor is calculated
from the force balance on the blade. In Equation (3), the
translational movement for the center of mass of the body
is calculated with respect to the inertial reference frame.
˙−→
V = 1
m
∑ −→
FG (3)
where ˙−→
V ; m and −→
FG refer to the translational motion for
the body, the mass of the body and the vector of forces,
respectively. In turn, Equation (4) was used to compute the
rotation movement of the body, applying body coordinates;
where −→ωB is the vector of ω, L stands for the matrix with
the inertia moments and −→
MB is the moment vector of the
object (ANSYS Inc., 2018a).
˙⃗ω B = L−1 (∑ −→
MB − −→ωB × L⃗ω B
)
(4)
The 6-DoF approach can be used to predict sequentially
the angular positions according to the turbine mass
properties (mass and moment of inertia) in real time.
The 6-DoF method computes the AST angular velocity (ω)
based on forces and moments acting on the rotor.
For the 6-DoF simulation, the AST footprint and the
entire domain were allocated in a way that with the
water coming from -X to +X, the generated momentum
would make the turbine rotates around the +X axis (one
DoF rotation); the inertia tensor for the 6-DoF UDF
configuration was computed with the help of SolidWorks
software. The AST is limited to rotating around the X-axis,
while the other DoF are not available. The specifications
of the AST, which depend on the geometry and material
of the turbine, are shown in Table 1. Small values of
the moment of inertia promote the startup of the AST.
However, excessively small values will impair the stability
57
A. I. Montilla-López et al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 111, pp. 55-63, 2024
Figure 1 Geometric parameters of interest for the design of the screw with a spiral configuration
Table 1 Specification of the six degrees of freedom (6-DoF) body
Parameter and units Value
Mass [kg] 2.70921 kg
Moment of inertia [kgm2] 0.00843
Initial [rad/s] 0
Initial center of mass (x,y,z) [m] (21.404, -0.012, -0.005)
of the AST rotor rotation. For determining the moment of
inertia, ABS (acrylonitrile butadiene styrene) was selected,
and the material density was 1070 Kg/m3.
Once the configuration was completed, and the simulation
was run, the 6-DoF model began to accelerate the body
as a result of the interaction between the fluid and the
turbine walls, and the ω rose to a stable and maximum
value. From that point, a pre-load was set to the 6-DoF
UDF and the turbine slowed down until the condition
of 0 rad/s was reached. The preload of this study was
1.355 Nm. The collected data from the imposition of the
pre-load allowed drawing the Cp vs. the TSR curve. As
the simulation has only one rotational DoF, it was not
necessary to employ any of the mesh methods found in
the setup of dynamic mesh options of the Fluent software;
this allows defining the rotation body as a rigid body whose
rotational movement depends on the total momentum
acting over the footprint surface. To ensure the correct
transfer of information between the stationary and the
moving domains, an interface boundary condition was
employed, which also facilitated convergence.
The computational domain illustrated in Figure 2 was
similar to that employed by other studies in schemes
concerning hydrokinetic turbines [5, 6]. The fixed domain
is a parallelepiped, while the rotational domain has a
cylindrical shape. The dimensions of both of them are a
function of De. The internal domain was located at 5 times
De from the domain inlet.
The spiral-shaped turbine was modeled in the SolidWorks
software, and the meshing was performed in the ANSYs
Fluent meshing solver software. On the other hand,
the three-dimensional (3D) unsteady simulation was
carried out in ANSYs Fluent, where 3D Reynolds-averaged
Navier-Stokes equations were solved with the k − ω
SST turbulence model. It is important to note that the
k − ω SST model is commonly utilized for hydrokinetic
turbine modeling since it has been demonstrated to have
better performance for complex flows, including adverse
pressure gradients and flow separations, as occurs in
horizontal-axis hydrokinetic turbines [5]. The time step
used for the simulation was 0.005 s.
In the domain, at the left surface, a constant velocity
inlet equal to 1.2 m/s was applied. This velocity was
considered as it is an average value in some important
rivers in Colombia, such as the Magdalena or Cauca rivers,
which have velocities between 1.1 and 2.5 m/s [18]. In
addition, in the right surface of the domain, a pressure
outlet equal to 0 Pa was used. No-slip boundary conditions
were applied at the surface of the blade. Wall boundary
conditions were established in the other surfaces of
the external domain. To ensure the correct transfer
of information between the stationary and the moving
domains, an interface boundary condition was employed,
which also facilitated convergence.
During the numerical simulation, the quality of the
generated mesh was checked by using the Richardson
extrapolation. For this purpose, three different meshes
58
Figure 1 Geometric parameters of interest for the design of the screw with a spiral configuration
Table 1 Specification of the six degrees of freedom (6-DoF) body
Parameter and units Value
Mass [kg] 2.70921 kg
Moment of inertia [kgm2] 0.00843
Initial [rad/s] 0
Initial center of mass (x,y,z) [m] (21.404, -0.012, -0.005)
of the AST rotor rotation. For determining the moment of
inertia, ABS (acrylonitrile butadiene styrene) was selected,
and the material density was 1070 Kg/m3.
Once the configuration was completed, and the simulation
was run, the 6-DoF model began to accelerate the body
as a result of the interaction between the fluid and the
turbine walls, and the ω rose to a stable and maximum
value. From that point, a pre-load was set to the 6-DoF
UDF and the turbine slowed down until the condition
of 0 rad/s was reached. The preload of this study was
1.355 Nm. The collected data from the imposition of the
pre-load allowed drawing the Cp vs. the TSR curve. As
the simulation has only one rotational DoF, it was not
necessary to employ any of the mesh methods found in
the setup of dynamic mesh options of the Fluent software;
this allows defining the rotation body as a rigid body whose
rotational movement depends on the total momentum
acting over the footprint surface. To ensure the correct
transfer of information between the stationary and the
moving domains, an interface boundary condition was
employed, which also facilitated convergence.
The computational domain illustrated in Figure 2 was
similar to that employed by other studies in schemes
concerning hydrokinetic turbines [5, 6]. The fixed domain
is a parallelepiped, while the rotational domain has a
cylindrical shape. The dimensions of both of them are a
function of De. The internal domain was located at 5 times
De from the domain inlet.
The spiral-shaped turbine was modeled in the SolidWorks
software, and the meshing was performed in the ANSYs
Fluent meshing solver software. On the other hand,
the three-dimensional (3D) unsteady simulation was
carried out in ANSYs Fluent, where 3D Reynolds-averaged
Navier-Stokes equations were solved with the k − ω
SST turbulence model. It is important to note that the
k − ω SST model is commonly utilized for hydrokinetic
turbine modeling since it has been demonstrated to have
better performance for complex flows, including adverse
pressure gradients and flow separations, as occurs in
horizontal-axis hydrokinetic turbines [5]. The time step
used for the simulation was 0.005 s.
In the domain, at the left surface, a constant velocity
inlet equal to 1.2 m/s was applied. This velocity was
considered as it is an average value in some important
rivers in Colombia, such as the Magdalena or Cauca rivers,
which have velocities between 1.1 and 2.5 m/s [18]. In
addition, in the right surface of the domain, a pressure
outlet equal to 0 Pa was used. No-slip boundary conditions
were applied at the surface of the blade. Wall boundary
conditions were established in the other surfaces of
the external domain. To ensure the correct transfer
of information between the stationary and the moving
domains, an interface boundary condition was employed,
which also facilitated convergence.
During the numerical simulation, the quality of the
generated mesh was checked by using the Richardson
extrapolation. For this purpose, three different meshes
58
A. I. Montilla-López et al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 111, pp. 55-63, 2024
Figure 2 omain for the spiral-shaped turbine
were created and named as coarse, medium and fine
mesh. The target parameter for the comparison of
the meshes was the area under the curve formed by
representing Cp vs. TSR. The Richardson extrapolation
is based on Taylor’s series and allowed obtaining an
improved estimate of the numerical result in derivatives,
integrals, or differential equations [19].
The generalized Richardson extrapolation was well
presented by Roache (1994) [20], standing a way
to estimate the error associated with the spatial
discretization in CFD simulations, which is considered
one of the main numerical error sources. An additional
and widely used concept is the grid convergence index
(GCI) calculated between the size of meshes and the
asymptotic range of convergence index (I), which brings
an assessment of the discretization error among meshes.
The values of I should be approximately 1 in order to ensure
that the numerical simulation is within the asymptotic
range [21].
Figure 3 shows the results of the simulations (the
evolution of Cp vs. TSR) carried out during the mesh
independence test. For the number of elements used, the
variation in the results due to the number of elements
in the mesh can be observed to be not significant. In
Figure 4, the asymptotic tendency of the results obtained
with the used meshes is illustrated. This agrees with the
value of I equal to 1.000054, which was obtained for the
asymptotic convergence analysis. The GCImedium-coarse
and GCIfine-medium values were 0.22% and 0.076%,
respectively, showing that the grid independence was
achieved. Thus, the medium mesh was selected for the
simulations. The medium mesh was set at a first layer
thickness of 1.58 × 10−3 m, a value that allowed obtaining
a maximum dimensionless wall distance (y+) of 90.37,
which is found in the range of 30 and 300, making it
possible to use the wall functions approach [22].
Details for the different meshes are presented in Table 2.
Figure 3 Power coefficient (Cp) vs. tip speed ratio (λ) for the
different meshes
Figure 4 Richardson extrapolation for the mesh independence
The meshes exhibited good quality parameters and the
errors between the mesh results were less than 1%, which
is also a good indicator of convergence. A representation
of the medium mesh used in the numerical study is
illustrated in Figure 5.
59
Figure 2 omain for the spiral-shaped turbine
were created and named as coarse, medium and fine
mesh. The target parameter for the comparison of
the meshes was the area under the curve formed by
representing Cp vs. TSR. The Richardson extrapolation
is based on Taylor’s series and allowed obtaining an
improved estimate of the numerical result in derivatives,
integrals, or differential equations [19].
The generalized Richardson extrapolation was well
presented by Roache (1994) [20], standing a way
to estimate the error associated with the spatial
discretization in CFD simulations, which is considered
one of the main numerical error sources. An additional
and widely used concept is the grid convergence index
(GCI) calculated between the size of meshes and the
asymptotic range of convergence index (I), which brings
an assessment of the discretization error among meshes.
The values of I should be approximately 1 in order to ensure
that the numerical simulation is within the asymptotic
range [21].
Figure 3 shows the results of the simulations (the
evolution of Cp vs. TSR) carried out during the mesh
independence test. For the number of elements used, the
variation in the results due to the number of elements
in the mesh can be observed to be not significant. In
Figure 4, the asymptotic tendency of the results obtained
with the used meshes is illustrated. This agrees with the
value of I equal to 1.000054, which was obtained for the
asymptotic convergence analysis. The GCImedium-coarse
and GCIfine-medium values were 0.22% and 0.076%,
respectively, showing that the grid independence was
achieved. Thus, the medium mesh was selected for the
simulations. The medium mesh was set at a first layer
thickness of 1.58 × 10−3 m, a value that allowed obtaining
a maximum dimensionless wall distance (y+) of 90.37,
which is found in the range of 30 and 300, making it
possible to use the wall functions approach [22].
Details for the different meshes are presented in Table 2.
Figure 3 Power coefficient (Cp) vs. tip speed ratio (λ) for the
different meshes
Figure 4 Richardson extrapolation for the mesh independence
The meshes exhibited good quality parameters and the
errors between the mesh results were less than 1%, which
is also a good indicator of convergence. A representation
of the medium mesh used in the numerical study is
illustrated in Figure 5.
59
A. I. Montilla-López et al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 111, pp. 55-63, 2024
Table 2 Mesh independence test
Parameter Mesh
Coarse Medium Fine
Number of nodes 1866583 3907803 6537940
Number of elements 647898 1325345 2096639
Max skewness 0.699 0.699 0.699
Mean aspect ratio 3.156 2.885 2.814
Min orthogonal quality 0.301 0.301 0.301
Both rotational and external domains were meshed
employing poly-hex core mesh elements. The meshes of
the rotational and fixed domains are illustrated in Figure
5.
As in the mesh independence study, the time step
independency was developed by using 6-DoF simulations.
The Richardson extrapolation process was adapted to
analyze the time step influence on the simulation results;
the test was carried out for three different time steps
(0.00025 s, 0.0005 s, and 0.001 s) and in order to find the
convergence time step index (CTI). The term CTI is the
reciprocal of the GCI [23] and in this study, a value of 2% or
less for the CTI was chosen as a criterion of selection for
the definitive time step. The Cp vs. TSR curves for each of
the above-mentioned time steps are represented in Figure
6. Little differences could be observed at the end of the
curves; however, a good general concordance in the data
behavior was also found. CTI12 and CTI23 were 1.69%
and 2.28%, respectively; good results for CTI were noted
in Figure 7, which covers a variation of less than 0.014.
A time step of 0.0005 s was used in all the simulations.
Additionally, when analyzing asymptotic convergence for
the time step, a value of 0.9952 was obtained. This value is
close enough to 1 to consider that the selected time step
is in the asymptotic convergence region.
Although the criterion adopted to terminate the iterative
process was based on the residual of the corresponding
equation (e.g., the equation for the pressure), during the
numerical analysis the convergence of the simulation
was not assessed in terms of the achievement of a
particular level of residual error. Solution-sensitive
target quantities were carefully defined for the integrated
global parameters of interest and an acceptable level of
convergence was selected based on the rate of change
of these values (e.g., Cp). The convergence criterion
was set at 10−4 during all the simulations. For the
CFD simulation, the first-order upwind scheme was
used for the treatment of advective terms and PRESTO
(Pressure Staggering Option) for the spatial discretization
of pressure in the momentum equation. The couple
scheme pressure-velocity was selected as the coupling
algorithm and was adjusted through the PISO (Pressure
Implicit Split Operator) algorithm.
3. Results and discussion
Figure 8 shows the ratio between Cp and TSR for the AST,
which is obtained by the simulation, and the numerical and
experimental results reported for an ASHT by Mael et al.
[5]. This turbine consists of a screw coupled to an electric
generator and a support structure. Comparing the AST
with the ASHT, the Cp value for the former was 0.3369 at a
TSR equal to 1.909. On the other hand, the ASHT achieved
a Cp of 0.5515 at a TSR equal to 1.35 [5]. The maximum Cp
is slightly higher than those with similar AST presented
in the literature for wind applications [15–17], [24–26].It
is evident that the Cp of the AST is lower than that of the
ASHT.
This can be ascribed to the fact that, although a good area
of contact with the fluid is achieved with the spiral turbine,
this is lower than the area provided by the traditional
screw, resulting in a lower amount of energy extracted
from the fluid. Furthermore, it was noticed that ω for the
maximum Cp was 18.39 rad/s. A comparison between the
CFD results of the AST for hydrokinetic applications and
experimental data for wind applications at a flow velocity of
5 m/s was also represented in Figure 4 [16]. The geometry
for the AST, whose experimental results were presented
in Figure 8 [16], was similar to that one evaluated in this
study. In the figure, for wind applications, the Cp values
were lower; however, the trend of the curve was similar.
The AST had a greater Cp at the lower TSR than the
Savonius turbine, which makes the AST suitable [27].
In addition, in Figure 9a, the streamlines and pressure
contours for AST are illustrated. It is observed that the
velocity values in the streamlines are low at the inlet.
This can be explained because the flow is not disturbed
yet, but as it passes through the blades, this velocity
increases, and then decreases at the turbine outlet. The
AST operation depends on the use of both lift and drag
forces. Nevertheless, the force causing the rotation of the
blade dominantly is the drag acting on the three blades
[17]. Figure 9b shows the pressure distribution on the
spiral. When the AST is rotating, there is a pressure
difference between the pressure side and the suction
side. Due to the spiral surface of the blades, the pressure
difference generates torque. In general, the front side of
the blade has a higher pressure while the corresponding
rear side has a lower pressure. Figure 9b also shows that
the location of the stagnation pressure region was near
the leading edge and the helical blade tip. This means that
most of the energy can be extracted near the blade tip like
a three-bladed horizontal-axis hydrokinetic turbine.
According to the results informed for the ASHT [5], the
authors indicated the influence of the helix angle and the
diameter ratio on the Cp, pointing out that a low diameter
ratio (inner diameter/outer diameter; i.e., Di/Do) leads to
60
Table 2 Mesh independence test
Parameter Mesh
Coarse Medium Fine
Number of nodes 1866583 3907803 6537940
Number of elements 647898 1325345 2096639
Max skewness 0.699 0.699 0.699
Mean aspect ratio 3.156 2.885 2.814
Min orthogonal quality 0.301 0.301 0.301
Both rotational and external domains were meshed
employing poly-hex core mesh elements. The meshes of
the rotational and fixed domains are illustrated in Figure
5.
As in the mesh independence study, the time step
independency was developed by using 6-DoF simulations.
The Richardson extrapolation process was adapted to
analyze the time step influence on the simulation results;
the test was carried out for three different time steps
(0.00025 s, 0.0005 s, and 0.001 s) and in order to find the
convergence time step index (CTI). The term CTI is the
reciprocal of the GCI [23] and in this study, a value of 2% or
less for the CTI was chosen as a criterion of selection for
the definitive time step. The Cp vs. TSR curves for each of
the above-mentioned time steps are represented in Figure
6. Little differences could be observed at the end of the
curves; however, a good general concordance in the data
behavior was also found. CTI12 and CTI23 were 1.69%
and 2.28%, respectively; good results for CTI were noted
in Figure 7, which covers a variation of less than 0.014.
A time step of 0.0005 s was used in all the simulations.
Additionally, when analyzing asymptotic convergence for
the time step, a value of 0.9952 was obtained. This value is
close enough to 1 to consider that the selected time step
is in the asymptotic convergence region.
Although the criterion adopted to terminate the iterative
process was based on the residual of the corresponding
equation (e.g., the equation for the pressure), during the
numerical analysis the convergence of the simulation
was not assessed in terms of the achievement of a
particular level of residual error. Solution-sensitive
target quantities were carefully defined for the integrated
global parameters of interest and an acceptable level of
convergence was selected based on the rate of change
of these values (e.g., Cp). The convergence criterion
was set at 10−4 during all the simulations. For the
CFD simulation, the first-order upwind scheme was
used for the treatment of advective terms and PRESTO
(Pressure Staggering Option) for the spatial discretization
of pressure in the momentum equation. The couple
scheme pressure-velocity was selected as the coupling
algorithm and was adjusted through the PISO (Pressure
Implicit Split Operator) algorithm.
3. Results and discussion
Figure 8 shows the ratio between Cp and TSR for the AST,
which is obtained by the simulation, and the numerical and
experimental results reported for an ASHT by Mael et al.
[5]. This turbine consists of a screw coupled to an electric
generator and a support structure. Comparing the AST
with the ASHT, the Cp value for the former was 0.3369 at a
TSR equal to 1.909. On the other hand, the ASHT achieved
a Cp of 0.5515 at a TSR equal to 1.35 [5]. The maximum Cp
is slightly higher than those with similar AST presented
in the literature for wind applications [15–17], [24–26].It
is evident that the Cp of the AST is lower than that of the
ASHT.
This can be ascribed to the fact that, although a good area
of contact with the fluid is achieved with the spiral turbine,
this is lower than the area provided by the traditional
screw, resulting in a lower amount of energy extracted
from the fluid. Furthermore, it was noticed that ω for the
maximum Cp was 18.39 rad/s. A comparison between the
CFD results of the AST for hydrokinetic applications and
experimental data for wind applications at a flow velocity of
5 m/s was also represented in Figure 4 [16]. The geometry
for the AST, whose experimental results were presented
in Figure 8 [16], was similar to that one evaluated in this
study. In the figure, for wind applications, the Cp values
were lower; however, the trend of the curve was similar.
The AST had a greater Cp at the lower TSR than the
Savonius turbine, which makes the AST suitable [27].
In addition, in Figure 9a, the streamlines and pressure
contours for AST are illustrated. It is observed that the
velocity values in the streamlines are low at the inlet.
This can be explained because the flow is not disturbed
yet, but as it passes through the blades, this velocity
increases, and then decreases at the turbine outlet. The
AST operation depends on the use of both lift and drag
forces. Nevertheless, the force causing the rotation of the
blade dominantly is the drag acting on the three blades
[17]. Figure 9b shows the pressure distribution on the
spiral. When the AST is rotating, there is a pressure
difference between the pressure side and the suction
side. Due to the spiral surface of the blades, the pressure
difference generates torque. In general, the front side of
the blade has a higher pressure while the corresponding
rear side has a lower pressure. Figure 9b also shows that
the location of the stagnation pressure region was near
the leading edge and the helical blade tip. This means that
most of the energy can be extracted near the blade tip like
a three-bladed horizontal-axis hydrokinetic turbine.
According to the results informed for the ASHT [5], the
authors indicated the influence of the helix angle and the
diameter ratio on the Cp, pointing out that a low diameter
ratio (inner diameter/outer diameter; i.e., Di/Do) leads to
60
A. I. Montilla-López et al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 111, pp. 55-63, 2024
(a) (b)
Figure 5 Computational domain for simulation. a. Fixed domain mesh and b. Rotational domain mesh
Figure 6 Power coefficient (Cp) vs. tip speed ratio (λ) for the
different time steps
Figure 7 Adapted Richardson extrapolation for the time step
independence
a larger blade area. In this regard, more energy can be
extracted from the fluid. This allows observing that, in
an AST, parameters such as γ have significant influence
on the Cp. Therefore, in order to obtain an AST with the
Figure 8 Comparison of the power coefficient (Cp) as a function
of the TSR for AST and ASHT
design parameters optimized for obtaining the highest
performance, the turbine Cp is required to be improved.
4. Conclusions
In this study, the performance of an Archimedes
spiral turbine (AST) for hydrokinetic applications was
calculated by unsteady computational fluid dynamics (CFD)
simulations. As a result of the numerical simulations, a
maximum Cp of 0.3369 was observed when the tip speed
ratio (TSR) of the rotor was 1.909. In the unsteady state
simulation, when the water flow passed the blade, the
flow needed to accelerate to pass the spiral surface of the
blades.
As the water continuously passed the AST blade, it
created a low-pressure area on the tip of the blade
because the water across this area had a higher velocity.
The maximum pressure differences were observed at the
blade tip, suggesting that the most kinetic energy could
be extracted from the outer part of the blade. In order
61
(a) (b)
Figure 5 Computational domain for simulation. a. Fixed domain mesh and b. Rotational domain mesh
Figure 6 Power coefficient (Cp) vs. tip speed ratio (λ) for the
different time steps
Figure 7 Adapted Richardson extrapolation for the time step
independence
a larger blade area. In this regard, more energy can be
extracted from the fluid. This allows observing that, in
an AST, parameters such as γ have significant influence
on the Cp. Therefore, in order to obtain an AST with the
Figure 8 Comparison of the power coefficient (Cp) as a function
of the TSR for AST and ASHT
design parameters optimized for obtaining the highest
performance, the turbine Cp is required to be improved.
4. Conclusions
In this study, the performance of an Archimedes
spiral turbine (AST) for hydrokinetic applications was
calculated by unsteady computational fluid dynamics (CFD)
simulations. As a result of the numerical simulations, a
maximum Cp of 0.3369 was observed when the tip speed
ratio (TSR) of the rotor was 1.909. In the unsteady state
simulation, when the water flow passed the blade, the
flow needed to accelerate to pass the spiral surface of the
blades.
As the water continuously passed the AST blade, it
created a low-pressure area on the tip of the blade
because the water across this area had a higher velocity.
The maximum pressure differences were observed at the
blade tip, suggesting that the most kinetic energy could
be extracted from the outer part of the blade. In order
61
A. I. Montilla-López et al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 111, pp. 55-63, 2024
(a) (b)
Figure 9 a. Streamline velocity. b. Pressure contour on the spiral turbine
to improve the turbine Cp, further research focused on
optimization techniques is needed to know the influence
of each design parameter on the turbine performance.
It was also observed that the AST, as a hydrokinetic
technology, has a high potential for power generation
in remote areas due to its easy fabrication, installation,
and good performance. However, experimental research
is needed to discern the real behavior of the AST
turbine under working conditions. The results of these
investigations would allow validating the simulation
methods used here and select the most suitable one for
the study of this type of turbine.
5. Declaration of competing interest
The authors declare that they 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. Funding
The authors gratefully acknowledge the financial
support provided by the Colombia Scientific Program
within the framework of the call Ecosistema Científico
(Contract No. FP44842-218-2018).The authors are also
grateful for the financial support of the Tecnológico
de Antioquia-Institución Universitaria, with the research
project entitled ”Design and experimental characterization
of an Archimedes screw type hydrokinetic turbine”, and
to the Universidad de Antioquia through the Sustainability
Strategy 2020-2021. ES84190067.
7. Author contributions
Ana Montilla: Methodology, Software Investigation,
Writing- Original draft preparation. Laura Velásquez:
Conceptualization, Methodology, Software Investigation,
Writing- Original draft preparation. Johan Betancour:
Conceptualization, Methodology, Software Investigation.
Ainhoa Rubio-Clemente: Conceptualization, Methodology,
Supervision, Writing- Original draft preparation, Funding
acquisition, Resources, Project administration. Edwin
Chica: Conceptualization, Methodology, Writing, Funding
acquisition, Resources, Project administration.
8. Data availability statement
The authors confirm that the data supporting the findings
of this study are available within the article or its
supplementary materials.
References
[1] M. S. Güney and K. Kaygusuz, “Hydrokinetic energy conversion
systems: A technology status review,” Renewable and Sustainable
Energy Reviews, vol. 14, no. 9, Dec. 2010. [Online]. Available:
https://doi.org/10.1016/j.rser.2010.06.016
[2] H. J. Vermaak, K. Kusakana, and S. P. Koko, “Status of
micro-hydrokinetic river technology in rural applications: A review
of literature,” Renewable and Sustainable Energy Reviews, vol. 29,
Jan. 2014. [Online]. Available: https://doi.org/10.1016/j.rser.2013.
08.066
[3] M. J. Khan, G. Bhuyan, M. T. Iqbal, and J. E. Quaicoe, “Hydrokinetic
energy conversion systems and assessment of horizontal and
vertical axis turbines for river and tidal applications: A technology
status review,” Applied Energy, vol. 86, no. 10, Oct. 2009. [Online].
Available: https://doi.org/10.1016/j.apenergy.2009.02.017
[4] S. Waters and G. A. Aggidis, “Over 2000 years in review: Revival
of the archimedes screw from pump to turbine,” Renewable and
Sustainable Energy Reviews, vol. 51, Nov. 2015. [Online]. Available:
https://doi.org/10.1016/j.rser.2015.06.028
[5] M. Bouvant, J. Betancour, L. Velásquez, A. Rubio-Clemente,
and E. Chica, “Design optimization of an archimedes screw
turbine for hydrokinetic applications using the response surface
62
(a) (b)
Figure 9 a. Streamline velocity. b. Pressure contour on the spiral turbine
to improve the turbine Cp, further research focused on
optimization techniques is needed to know the influence
of each design parameter on the turbine performance.
It was also observed that the AST, as a hydrokinetic
technology, has a high potential for power generation
in remote areas due to its easy fabrication, installation,
and good performance. However, experimental research
is needed to discern the real behavior of the AST
turbine under working conditions. The results of these
investigations would allow validating the simulation
methods used here and select the most suitable one for
the study of this type of turbine.
5. Declaration of competing interest
The authors declare that they 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. Funding
The authors gratefully acknowledge the financial
support provided by the Colombia Scientific Program
within the framework of the call Ecosistema Científico
(Contract No. FP44842-218-2018).The authors are also
grateful for the financial support of the Tecnológico
de Antioquia-Institución Universitaria, with the research
project entitled ”Design and experimental characterization
of an Archimedes screw type hydrokinetic turbine”, and
to the Universidad de Antioquia through the Sustainability
Strategy 2020-2021. ES84190067.
7. Author contributions
Ana Montilla: Methodology, Software Investigation,
Writing- Original draft preparation. Laura Velásquez:
Conceptualization, Methodology, Software Investigation,
Writing- Original draft preparation. Johan Betancour:
Conceptualization, Methodology, Software Investigation.
Ainhoa Rubio-Clemente: Conceptualization, Methodology,
Supervision, Writing- Original draft preparation, Funding
acquisition, Resources, Project administration. Edwin
Chica: Conceptualization, Methodology, Writing, Funding
acquisition, Resources, Project administration.
8. Data availability statement
The authors confirm that the data supporting the findings
of this study are available within the article or its
supplementary materials.
References
[1] M. S. Güney and K. Kaygusuz, “Hydrokinetic energy conversion
systems: A technology status review,” Renewable and Sustainable
Energy Reviews, vol. 14, no. 9, Dec. 2010. [Online]. Available:
https://doi.org/10.1016/j.rser.2010.06.016
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https://doi.org/10.1016/j.egyr.2019.11.126
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and H. Trahasdani, “Open flume turbine simulation method using
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and M. H. Mohamed, “Experimental and numerical investigations
of the blade design effect on archimedes spiral wind turbine
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https://doi.org/10.1016/j.energy.2021.120051
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hidrológica de 10 puntos de monitoreo del río cauca en su cuenca
baja,” Undergraduate thesis, Universidad Católica de Colombia,
Bogotá, Colombia, 2017.
[19] L. F. Richardson, “The approximate arithmetical solution by finite
differences of physical problems involving differential equations,
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Sep. 01, 1994. [Online]. Available: https://doi.org/10.1115/1.2910291
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of the cavitation resistance of the traditional and high-lift hydrofoils
for hydrokinetic application,” International Journal of Applied Science
and Engineering, vol. 19, no. 2, Jun. 2022. [Online]. Available:
https://doi.org/10.6703/IJASE.202206_19(2).010
[22] F. Nieto, D. Hargreaves, J. S. Owen, and S. Hernández, “On the
applicability of 2d urans and sst k - ω turbulence model to the
fluid-structure interaction of rectangular cylinders,” Engineering
Applications of Computational Fluid Mechanics, vol. 9, no. 1, Jun. 2015.
[Online]. Available: https://doi.org/10.6703/IJASE.202206_19(2).010
[23] A. P. Prakoso, W. Warjito, A. I. Siswantara, B. Budiarso, , and
D. Adanta, “Comparison between 6-dof udf and moving mesh
approaches in cfd methods for predicting cross-flow picohydro
turbine performance,” CFD Letters, vol. 11, no. 6, Jan. 16, 2021.
[Online]. Available: https://akademiabaru.com/submit/index.php/
cfdl/article/view/3174
[24] A. YoosefDoost and W. D. Lubitz, “Archimedes screw turbines:
A sustainable development solution for green and renewable
energy generation—a review of potential and design procedures,”
Sustainability, vol. 12, no. 18, Sep. 08 2020. [Online]. Available:
https://doi.org/10.3390/su12187352
[25] A. Safdari and K. C. Kim, “Aerodynamic and structural evaluation
of horizontal archimedes spiral wind turbine,” Sustainability, vol. 3,
no. 1, Jan. 2015. [Online]. Available: https://doi.org/10.7763/JOCET.
2015.V3.164
[26] H. Kim, K. Kim, and I. Paek, “Power regulation of upstream wind
turbines for power increase in a wind farm,” International Journal
of Precision Engineering and Manufacturing, vol. 17, May 12, 2016.
[Online]. Available: https://doi.org/10.1007/s12541-016-0081-1
[27] M. B. Salleh, N. M. Kamaruddin, and Z. Mohamed-Kassim,
“Savonius hydrokinetic turbines for a sustainable river-based
energy extraction: A review of the technology and potential
applications in malaysia,” Sustainable Energy Technologies and
Assessments, vol. 36, Oct. 10, 2019. [Online]. Available: https:
//doi.org/10.1016/j.seta.2019.100554
63
methodology,” Renewable Energy, vol. 172, Jul. 2021. [Online].
Available: https://doi.org/10.1016/j.renene.2021.03.076
[6] G. Zitti, F. Fattore, A. Brunori, B. Brunori, and M. Brocchini,
“Efficiency evaluation of a ductless archimedes turbine: Laboratory
experiments and numerical simulations,” Renewable Energy, vol.
146, Feb. 2020. [Online]. Available: https://doi.org/10.1016/j.renene.
2019.06.174
[7] K. C. Kim, H. S. Ji, Y. K. Kim, Q. Lu, J. H. Baek, and
R. Mieremet, “Experimental and numerical study of the aerodynamic
characteristics of an archimedes spiral wind turbine blade,”
Energies, vol. 7, no. 12, Nov. 14, 2014. [Online]. Available:
https://doi.org/10.3390/en7127893
[8] D. Adanta, B. Budiarso, W. Warjito, A. I. Siswantara, and A. P.
Prakoso, “Performance comparison of naca 6509 and 6712 on pico
hydro type cross-flow turbine by numerical method,” Journal of
Advanced Research in Fluid Mechanics and Thermal Sciences, vol. 45,
no. 1, May. 2018. [Online]. Available: https://akademiabaru.com/
submit/index.php/arfmts/article/view/2188
[9] D. Adanta, W. Warjito, R. Hindami, A. I. Siswantara, and B. Budiarso,
“Blade depth investigation on cross-flow turbine by numerical
method,” in 4th International Conference on Science and Technology
(ICST), Yogyakarta, Indonesia, 2018. [Online]. Available: https:
//doi.org/10.1109/ICSTC.2018.8528291
[10] A. I. Siswantara, B. Budiarso, A. P. Prakoso, G. G. R. Gunadi,
W. Warjito, and D. Adanta, “Assessment of turbulence model
for cross-flow pico hydro turbine numerical simulation,” CFD
Letters, vol. 10, no. 2, Dec. 2018. [Online]. Available: https:
//akademiabaru.com/submit/index.php/cfdl/article/view/3290
[11] J. Aguilar, L. Velásquez, F. Romero, J. Betancour,
A. Rubio-Clemente, and E. Chica, “Numerical and experimental
study of hydrofoil-flap arrangements for hydrokinetic turbine
applications,” Journal of King Saud University - Engineering
Sciences, vol. 35, no. 8, Aug. 14, 2021. [Online]. Available:
https://doi.org/10.1016/j.jksues.2021.08.002
[12] D. Adanta and W. Warjito, “The effect of channel slope angle on
breastshot waterwheel turbine performance by numerical method,”
in The 6th International Conference on Power and Energy Systems
Engineering (CPESE 2019), Okinawa, Japan, 2019. [Online]. Available:
https://doi.org/10.1016/j.egyr.2019.11.126
[13] D. Adanta, S. B. S. Nasution, Budiarso, W. Warjito, A. I. Siswantara1,
and H. Trahasdani, “Open flume turbine simulation method using
six-degrees of freedom feature,” in AIP Conference Proceedings
2227, Padang, Indonesia, 2020. [Online]. Available: https://doi.org/
10.1063/5.0004389
[14] X. Wang, X. Luo, B. Zhuang, W. Yu, and H. Xu, “6-dof numerical
simulation of the vertical-axis water turbine,” in ASME-JSME-KSME
2011 Joint Fluids Engineering Conference, Hamamatsu, Japan, 2011.
[Online]. Available: https://doi.org/10.1115/AJK2011-22035
[15] A. M. Labib, A. F. A. Gawad, and M. M. Nasseif, “Effect of blade
angle on aerodynamic performance of archimedes spiral wind
turbine,” Journal of Advanced Research in Fluid Mechanics and
Thermal Sciences, vol. 78, no. 1, Nov. 30, 2020. [Online]. Available:
https://doi.org/10.37934/arfmts.78.1.122136
[16] M. A. A. Nawar, H. S. A. Hameed, A. Ramadan, Y. A. Attai,
and M. H. Mohamed, “Experimental and numerical investigations
of the blade design effect on archimedes spiral wind turbine
performance,” Energy, vol. 223, May 15, 2021. [Online]. Available:
https://doi.org/10.1016/j.energy.2021.120051
[17] H. Jang, D. Kim, Y. Hwang, I. Paek, S. Kim, and J. Baek, “Analysis of
archimedes spiral wind turbine performance by simulation and field
test,” Energies, vol. 12, no. 24, Dec. 05, 2019. [Online]. Available:
https://doi.org/10.3390/en12244624
[18] J. A. Galindo-Galindo and J. A. Gómez-Valbuena, “Caracterización
hidrológica de 10 puntos de monitoreo del río cauca en su cuenca
baja,” Undergraduate thesis, Universidad Católica de Colombia,
Bogotá, Colombia, 2017.
[19] L. F. Richardson, “The approximate arithmetical solution by finite
differences of physical problems involving differential equations,
with an application to the stresses in a masonry dam,” The Royal
Society, vol. 210, no. 459-470, Jan. 01, 1911. [Online]. Available:
https://doi.org/10.1098/rsta.1911.0009
[20] P. J. Roache, “Perspective: A method for uniform reporting of grid
refinement studies,” Journal of Fluids Engineering, vol. 116, no. 3,
Sep. 01, 1994. [Online]. Available: https://doi.org/10.1115/1.2910291
[21] J. Gutiérrez, A. Rubio-Clemente, and E. Chica, “Comparative study
of the cavitation resistance of the traditional and high-lift hydrofoils
for hydrokinetic application,” International Journal of Applied Science
and Engineering, vol. 19, no. 2, Jun. 2022. [Online]. Available:
https://doi.org/10.6703/IJASE.202206_19(2).010
[22] F. Nieto, D. Hargreaves, J. S. Owen, and S. Hernández, “On the
applicability of 2d urans and sst k - ω turbulence model to the
fluid-structure interaction of rectangular cylinders,” Engineering
Applications of Computational Fluid Mechanics, vol. 9, no. 1, Jun. 2015.
[Online]. Available: https://doi.org/10.6703/IJASE.202206_19(2).010
[23] A. P. Prakoso, W. Warjito, A. I. Siswantara, B. Budiarso, , and
D. Adanta, “Comparison between 6-dof udf and moving mesh
approaches in cfd methods for predicting cross-flow picohydro
turbine performance,” CFD Letters, vol. 11, no. 6, Jan. 16, 2021.
[Online]. Available: https://akademiabaru.com/submit/index.php/
cfdl/article/view/3174
[24] A. YoosefDoost and W. D. Lubitz, “Archimedes screw turbines:
A sustainable development solution for green and renewable
energy generation—a review of potential and design procedures,”
Sustainability, vol. 12, no. 18, Sep. 08 2020. [Online]. Available:
https://doi.org/10.3390/su12187352
[25] A. Safdari and K. C. Kim, “Aerodynamic and structural evaluation
of horizontal archimedes spiral wind turbine,” Sustainability, vol. 3,
no. 1, Jan. 2015. [Online]. Available: https://doi.org/10.7763/JOCET.
2015.V3.164
[26] H. Kim, K. Kim, and I. Paek, “Power regulation of upstream wind
turbines for power increase in a wind farm,” International Journal
of Precision Engineering and Manufacturing, vol. 17, May 12, 2016.
[Online]. Available: https://doi.org/10.1007/s12541-016-0081-1
[27] M. B. Salleh, N. M. Kamaruddin, and Z. Mohamed-Kassim,
“Savonius hydrokinetic turbines for a sustainable river-based
energy extraction: A review of the technology and potential
applications in malaysia,” Sustainable Energy Technologies and
Assessments, vol. 36, Oct. 10, 2019. [Online]. Available: https:
//doi.org/10.1016/j.seta.2019.100554
63