391
Indonesian Journal of Science & Technology 11.
391-410 Indonesian Journal of Science & Technology Journal homepage: http://ejournal.
edu/index.
php/ijost/ Parametric Rotor Innovation for Gravitational Vortex Turbines: Advancing Clean Energy through Integrated Computational Fluid Dynamics (CFD)Simulation and Experimentation to Support the Sustainable Development Goals (SDG.
Pyrez-Rodriguez Andrys Juliyn1,*.
Juan D.
Pyrez2.
Flyrez-Arango Santiago2.
Jorge Andrys Sierra Del Rio2 Universidad Catylica de Oriente.
Rionegro.
Colombia.
Instituto Tecnolygico Metropolitano.
Medellyn.
Colombia.
* Correspondence: E-mail: ajperez@uco.
ABSTRACT
This study aims to optimize the rotor design of gravitational vortex turbines through an integrated approach combining parametric modeling, computational fluid dynamics (CFD), and experimental validation.
The rotor geometry was formulated using velocity triangle theory and refined using a CFD-based evaluation of flow behavior across multiple turbulence models.
To ensure accurate comparisons, experimental tests were conducted under controlled flow conditions, and mechanical losses due to bearing friction were measured and accounted for.
The simulation results demonstrated strong agreement with empirical data, validating the effectiveness of the proposed design.
enhancing energy conversion efficiency while minimizing environmental impact, this research supports the development of decentralized, renewable microhydropower systems.
The findings contribute to the advancement of Sustainable Development Goals (SDG.
A 2026 Tim Pengembang Jurnal UPI
ARTICLE INFO
Article History:
Submitted/Received 05 Jun 2025
First Revised 02 Jul 2025
Accepted 04 Sep 2025
First Available Online 06 Sep 2025
Publication Date 01 Dec 2026
____________________
Keyword:
Computational fluid dynamics.
Gravitational vortex turbine.
Hydropower.
Renewable energy.
Rotor optimization.
Julian et al.
Parametric Rotor Innovation for Gravitational Vortex Turbines: Advancing CleanA | 392
INTRODUCTION
The global population and economic growth have intensified attention toward renewable energy sources, particularly highlighting hydropower as a key resource aligned with the United NationsAo Sustainable Development Goals (SDG.
ee https://unstats.
org/sdgs/report/2023/The-Sustainable-Development-Goals-Report2023_Spanish.
However, current efforts remain insufficient to meet the 2030 targets, revealing an urgent need to implement innovative renewable technologies with reduced environmental and social impacts.
Although hydropower is a renewable source that avoids combustion processes, traditional implementation through large-scale hydroelectric projects results in significant alterations to surrounding terrestrial and aquatic ecosystems .
, as well as social issues related to forced displacement and community conflicts caused by flooding .
In response to these challenges, there is a growing interest in small-scale hydropower technologies that allow for efficient, renewable, and socially inclusive energy generation with minimal impacts .
In this context, the gravitational vortex turbine (GVT), developed in 2004, has gained attention due to its constructive simplicity, low economic and environmental cost, and capability for small-scale energy generation .
ico-generatio.
ee Zotlyterer patent in 2004 regarding Hydroelectric power plant (Patent No.
WO2004061295A.
The GVT harnesses the motion of a gravity-induced vortex in a rotation chamber to drive a rotor at its core, while also allowing the free passage of aquatic species without compromising their survival.
Additionally, its construction can be carried out using accessible materials with low environmental impact .
GVT efficiency shows high sensitivity to changes in its geometric parameters, with different performances observed depending on the specific rotor configuration implemented .
Several studies have explored innovative geometric alternatives, including straight and curved blades, multiple rotors, and optimized configurations to harness vertical flows, highlighting a theoretical gap regarding vortex behavior in the presence of a rotor .
To properly analyze the behavior of these gravity-induced vortical flows in GVTs, numerical methods such as computational fluid dynamics (CFD) and advanced experimental techniques like Particle Image Velocimetry (PIV) are commonly employed .
However, few studies have integrated both methodologies to optimize rotor design based on a detailed analysis of the velocity triangle applied to swirling flows, a methodology that has proven effective in other types of hydraulic turbines .
In this research, a specific geometry of a GVT is analyzed, based on a conical chamber designed to induce and stabilize a gravitational vortex (Figure .
This configuration includes a rectangular inlet channel, a main conical tank, and a lower discharge orifice that ensures stable vortex formation.
The dimensions and specific geometric parameters used are summarized in Table 1.
The selection of this GVT geometry was based on various numerical and experimental studies available in the literature.
These studies have demonstrated that a conical tank geometry optimizes turbine performance by improving the tangential velocity of the flow .
,17,.
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Main geometric parameters for the turbine.
Parameter yayca yayca yaycaycc yayc yaycuycyc ycOyca yu yaycaycc Description Height of the inlet channel Length of the inlet channel Height of the discharge chamber Height of the rotor Outlet diameter Width of the inlet channel Wraparound angle Upper chamber diameter Value Units Figure 1.
Main geometric parameters for the turbine.
METHODS
Rotor Design and Parametric Modeling For the development of this study, a rotor design is proposed based on the fourth hydrorotor .
This design is modifiable and allows the resizing of geometric parameters such as height, top and bottom radii, twist angle, and concavity.
To this end, a parametric mathematical function was developed to describe the radius of a blade, using the next two principles to ensure that the rotor remains similar to its original model:
ycc2 ycs .
The variation of Z is not constant with the variation of yuE .
ccyuE2 O .
The twist angle of each blade equals 2A radians divided by the number of blades 2yuU .
u = ycu ).
The parametric design used for this study is presented in Equations .
, and .
= hr Oo2 Oo2 Oo.
Oe ) ea Oe Oo ea ) Oo2 = OeOo2 .
Oe Oo.
Oe 2 ) ea Oo2 ea ) r.
Oo2.
up Oerdown ) .
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Parametric Rotor Innovation for Gravitational Vortex Turbines: Advancing CleanA | 394 where z is the height parameter.
A is the sweep angle in cylindrical coordinates, r is the variable rotor radius, t is the parameter ranging from 0 to Ooya, and a is the parameter controlling the curvature of the blade.
The parameter hr is defined as 25 cm to maximize the use of the available 3D printing volume.
The rotor selected for this study, shown in Figure 2, features a specific 4-blade configuration and an incidence angle (A) of -3 degrees.
This design aims to maximize the torque generated by the rotor and consequently improve the overall hydraulic efficiency of the system.
The specific blade geometry was defined using the aforementioned parametric equations, enabling precise control of blade curvature via a Figure 2.
Design of the parametric runner.
For this analysis, the top surface .
is assumed to be the inlet to the control For this study, efficiency is calculated using Equation .
, and for its maximization, it is necessary to maximize the torque generated in the rotor, which can be calculated using the angular momentum equation presented in Equation .
yuayui yuC = ycEyciyayu yua = O yc y ycO Oo .
cO Oo ycuC)yuyccya .
where yuC corresponds to the efficiency, yua represents total torque, yui represents angular velocity, ycE corresponds to the total flow rate, yci is the acceleration of gravity, ya is the total head, and yu corresponds to the density of the water.
yee represents the vector from the rotor C is the normal axis to each point in the analyzed surface.
yc is the velocity vector of the flow.
yea vector perpendicular to the analyzed surface.
and A is the area of each surface.
The control surface selected for this analysis is shown in Figure 3.
Volume, and the inner surface .
as the outlet.
The lateral surface .
, which coincides with the chamber wall, does not contribute to torque generation in the rotor or domain (Figure .
With the domain established.
Equation .
can be represented arithmetically as shown in Equation .
yua=O 2yuU yc1 2yuU yc2 C )yuyccycyccyuE Oe O O yc Oo yee y ycO1 Oo .
cO1 Oo yea C )yuUyccycyccyuE O yc Oo yee y ycO2 Oo .
cO2 Oo yea 2yuU yc O yc 2 ycO1 2 cos.
uEyuE1 ) cos.
uEyc1 ) yuUyccycyccyuE Oe O 2yuycO1 2 yc13 yuU 2yuycO3 2 yc33 yuU yc O yc 2 ycO32 cos.
uEyuE3 ) cos.
uEyc3 ) yuUyccycyccyuE cos.
uEyc1 ) cos.
uEyuE1 ) Oe cos.
uEyc3 ) cos.
uEyuE3 ) .
where cos.
uEyc ) is the directional cosine of the velocity vector angle along the rotor axis and cos.
uEyuE ) is the tangential directional cosine.
The total velocity of the water at the top of the rotor can be calculated using TorricelliAos equation, shown in Equation .
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Volume 11 Issue 3.
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Main components of the GVT for the control volume details.
ycO = Oo2yciEa Therefore.
Equation .
can be rewritten as shown in Equation .
4yciyuUyuU yua = 3 (Ea1 yc1 3 cos.
uEyc1 ) cos.
uEyuE1 ) Oe Ea3 yc3 3 cos.
uEyc3 ) cos.
uEyuE3 )) .
For this study, radial velocity is considered negligible in relation to tangential and axial velocities, so the directional cosines at the inlet are calculated using Equations .
ycOyc cos.
uEyc ) = = sin.
uEyuE ) .
OoycOyc 2 ycOyuE 2 cos.
uEyuE ) = ycOyuE OoycOyc 2 ycOyuE 2 = sin.
uEyc ) .
where VZ and VA are the axial and tangential velocities, respectively.
Since the analysis is performed under steady-state conditions, the average axial velocity can be calculated using the continuity principle and assuming constant density, while the tangential velocity is determined from the circulation .
obtained through CFD simulations using the expression proposed for vortex characterization .
, as shown in Equation .
ycOyuE = 2yuU yc 2 2yc2 yco where rm is the radius at which the vortex reaches its maximum velocity, assumed to be 0.
according to literature .
On the other hand, the terms associated with the lower surface .
utlet surface .
can be controlled via the velocity triangles of the rotor shown in Figure 4.
This figure shows both the general 3D representation and the planar projection of the velocity triangles at the rotor inlet and outlet to facilitate analysis.
This figure presents the velocity triangles at three key positions in the GVT rotor: the inlet (Figure 4.
), the internal blade passage (Figure 4.
), and the outlet (Figure 4.
At the inlet, the absolute velocity of the flow (V.
, the blade velocity (U.
, and the relative velocity (W.
define the angle of incidence and the energy input into the rotor.
Within the blade passage (Figure 4.
), the direction and magnitude of these velocity components change as energy is transferred from the fluid to the At the outlet (Figure 4.
), the remaining absolute (V.
and relative (W.
velocities, along with blade velocity (U.
, determine how much energy has been effectively converted into torque and how much is lost with the exiting flow.
Understanding these velocity relationships is crucial for optimizing rotor design and accurately calculating hydraulic efficiency based on momentum theory.
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Parametric Rotor Innovation for Gravitational Vortex Turbines: Advancing CleanA | 396 Angle A1 corresponds to the angle of AA.
Substituting Equations .
, .
, and .
into Equation .
, and considering the velocity triangles, yields a hydraulic efficiency formulation for the machine, expressed in Equation .
yuC= 4.
cO1 Ea1ya1 sin yu1 cos yu1 OeycO3 Ea3ya3 sin yu3 cos yu3 ) .
3ycEEa The relationships derived from the velocity triangles are presented in Table 2, and the correlation is in Equation .
Figure 4.
Velocity triangles at the inlet .
, inside the blade passage .
, and outlet .
of the GVT rotor.
Table 2.
Summary of velocity and flow equations.
Equation Velocity relationship Velocity components Flow rate equation Velocity magnitude Angular velocity = Expression ycO Oo cos yu ycO Oo cos yu = ycO ycO Oo sin yu = ycO Oo sin yu ycE = yaycO Oo sin yu ycO 2 = ycO 2 ycO 2 Oe 2ycOycO Oo cos yu ycO = yuiyc 4C(Oeh3.
os 3 cot 3 sin 3 ) cos 3 h1.
os 1 cot 1 sin 1 ) cos 1 ) Eq.
No.
where ycn defines which height is used and can take the values of 1 or 3, referring to the distance from the free water surface at the chamber inlet to positions 1 or 3 as shown in Figure 4.
The constant ya is introduced to account for system losses.
To reduce Equation .
to independent terms only, it is necessary to express yu1 and yu3 in terms of yu1 and yu3 .
This is done using Equations .
, which were calculated using the partial derivative of the parametric equation used for the description of the rotor.
ca, yu ) = tan ca, yu ) = tan Oe1 Oe1 (Ea Oo Oe2 1 2yceyca 1 2yceyca 1 2yceyca 2 Oo (Ea Oo 1 yc 1 Oo Oe1 2 1 2yceyca Oo From the last mathematical formulation, an estimate for efficiency can be obtained by predicting the directional components of the water at the inlet of the rotor.
This prediction can be developed using CFD simulation.
Notwithstanding, unlike other turbines, the GVT DOI: https://doi.
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A1.
Through CFD simulation, it is possible to predict the physical variables involved in the rotational flow within the chamber using finite element analysis and numerical approximations of the timeaveraged NavierAeStokes equations (RANS) .
The tangential velocity of water inside the turbine is approximated by calculating the circulation .
over the upper surface shown in Figure 3 using Equation .
, developed in previous works .
e = Oyui E Oo yccycI Mesh Generation.
Solver Configuration To conduct a detailed numerical study, nine CFD simulations were carried out in ANSYS CFX, aiming to compare three different turbulence models .
-Au.
SST, and BSL) using the GCI methodology .
The goal is to select the model that best fits the experimental conditions of the study.
Both the geometry and the interfaces that define the basic simulation parameters (Figure .
were kept constant, regardless of the turbulence model simulated .
Two servers from the Instituto Tecnolygico Metropolitano (ITM) were used for this their technical specifications are shown in Table 3.
Figure 5.
Domains for the CFD simulation of the GVT.
Table 3.
Comparison of Computational Resources for CFD Simulations.
Specification Server 1: CLUSTER Server 2: NEFTIS CPU / Processor Brand and Model Intel Xeon E5-2690 Intel Xeon Silver 4216 Number of Cores Clock Speed (GH.
Number of Threads RAM / Memory Total RAM Capacity (GB) RAM Speed (MH.
DDR3 1333
DDR4 1200
Operating System
OS Name and Version
Windows 10
Windows 10
CFD Software / Version
Software Name
ANSYS CFX
ANSYS CFX
Exact Version
ANSYS R2 2022
ANSYS R1 2024
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Parametric Rotor Innovation for Gravitational Vortex Turbines: Advancing CleanA | 398 The mesh used for the CFD simulations was generated using the ANSYS Meshing module, employing tetrahedral elements (Figure .
To ensure the quality and reliability of the numerical results, different quality metrics were evaluated for the generated elements.
Table 4 presents the average values obtained for these metrics across the nine case studies .
Table 4.
Mesh quality metrics for different levels of refinement.
Mesh Level Fine Medium Coarse Min Orthogonal Quality Avg Orthogonal Quality Max Avg Skewness Skewness Max Aspect Ratio Avg Aspect Ratio Figure 6.
Mesh on the control volume.
The parameters used for configuring the CFD simulations in ANSYS CFX are summarized in Table 5.
These parameters were carefully selected to accurately reflect the experimental conditions described in the previous section, thus ensuring proper numerical convergence in all analyzed cases.
Additionally, the results obtained with the three evaluated turbulence models will be contrasted using the mesh independence methodology (GCI), ensuring the quality and reliability of the numerical study conducted .
Table 5.
Parameters used in the CFD simulation configuration.
Parameter Inlet velocity .
Angular velocity .
Reference pressure .
Outlet pressures .
Time step Density (A) .
g/m.
Gravitational acceleration .
/s.
Average Courant number Surface tension [N/.
Rotor interface type Pitch angle Value Frozen Rotor Experimental Methodology Experimental setup and parameters For the development of the experimental tests, a setup was assembled in the GEA laboratory using available components (Figure .
The system is primarily composed of an inlet channel and a discharge chamber made of transparent acrylic to allow visualization of vortex formation, specific sensors for accurate measurement of flow rate (SITRANS F M MAG DOI: https://doi.
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, and a specially designed runner manufactured through 3D printing .
It is worth noting that the rotor was printed using a Creality Ki printer with PLA filament, 1.
75 mm in diameter, 0.
2 mm layer height, and 100% infill.
The printing parameters included an extruder temperature of 220 AC and a bed temperature of 45 AC, ensuring the dimensional accuracy and surface quality required for the experimental tests.
During the tests, a constant water flow rate of 2.
5 and 3 L/s was maintained.
The rotorAos dynamic variables, including speed and torque, were recorded over 30 seconds after the flow reached a steady state (Figure .
The key components of the experimental setup are summarized in detail in Table 6 .
Figure 7.
Elements of the experimental setup.
Figure 8.
Experimental facilities.
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Parametric Rotor Innovation for Gravitational Vortex Turbines: Advancing CleanA | 400 Once the experimental setup was defined and validated, a comparison with the numerical study was carried out.
The specific methodology and characteristics for this analysis and its results will be detailed in the following section.
Table 6.
Components of the Measurement and Control System and Hydraulic Elements.
Element
Measurement and Control System
Sub-Element
Flow Sensor
Torque Sensor
CPU and Software Dimensions Inlet Channel and Inlet
Tank
Water Reserve Tank
Pump
Description SITRANS F M MAG 5100W
FUTEK USB 520/530
SENSIT software Structures for controlled water routing, made of 5 mm-thick transparent acrylic Height: 250 mm Width: 250 mm Length: 1250 Capacity of 2 m3 IHM 30A-15W Ae IE2, controlled with a variable frequency drive Calculation of bearing losses Due to the conditions of the experimental setup, specifically the state of the bearings coupled to the rotor shaft, it is necessary to consider friction losses when comparing the experimental results with the numerical data .
To quantify these losses, the experimental setup shown in Figure 9 was used.
In these tests, a constant speed of 100 RPM was maintained, equivalent to the simulation speed, and the rotor deceleration was recorded after interrupting the airflow.
Thanks to the torque sensor, it was possible to determine the angular acceleration from the variation in angular velocity over time .
Figure 9.
Experimental setup for determining bearing losses.
(A) Physical assembly used for testing, and (B) Schematic diagram of the measurement system.
The angular acceleration is obtained from Equation .
iyui iyc DOI: https://doi.
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ycoya2 ycoycI 2 The friction torque is calculated by multiplying this moment of inertia by the absolute value of the angular acceleration (Equation .
ycNyaycycnyca = ya .
u | .
Finally, the power lost due to friction at 100 RPM is determined by Equation .
ycEyaycycnyca = ycNyaycycnyca yui100 Table 7 summarizes all the experimental parameters needed to quantify friction losses in the rotor shaft bearings .
This corrected torque value will be used for comparison between experimental and numerical results.
It is emphasized that, due to the state of the bearings, this value is essential for accurately describing the experimental results, as friction losses in the bearings account for approximately 11 % of the measured net torque.
In this way, a corrected experimental torque of 0.
664 Nm is obtained, which is essential for accurately accounting for the losses induced by the condition of the bearings.
This corrected torque value will be used for comparison between experimental and numerical results.
It is emphasized that, due to the state of the bearings, this value is essential for accurately describing the experimental results, as friction losses in the bearings account for approximately 11% of the measured net torque.
In this way, a corrected experimental torque of 0.
664 Nm is obtained, which is essential for accurately accounting for the losses induced by the condition of the bearings.
Table 7.
Experimental parameters and calculated values to quantify friction losses.
Parameter Rotor shaft mass Moment of inertia Symbol yco ya Value 042yce Oe 02 Average angular acceleration Friction torque Power loss Net experimental torque Corrected experimental torque yu ycNyaycycnyca ycEyaycycnyca ycNyaycuycyycA ycNyaycuycyya Oe1.
Units ycoyci
ycAyco
ycAyco
ycAyco
RESULTS AND DISCUSSION
This section presents both the numerical analyses and the efficiency evaluation.
First, the numerical results obtained from simulations using three turbulence models .
-Au.
SST, and BSL) are detailed, with emphasis on the prediction of rotor torque.
this is achieved through the evaluation of convergence using the Richardson extrapolation method and the calculation of the GCI .
This analysis allows the identification of differences in stability and result dispersion among the various models.
On the other hand, the efficiency of the turbine is addressed through a direct comparison between numerical and experimental values, describing the methods used to calculate the available power and the shaft power .
, which are essential to determine the systemAos performance, reaching a maximum experimental value close to 50.
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Parametric Rotor Innovation for Gravitational Vortex Turbines: Advancing CleanA | 402 Numerical and GCI results Once the configuration parameters for the numerical simulations were defined, the cases were executed for the three turbulence models considered .
AcA.
SST, and BSL).
The results obtained for rotor torque in the time interval between 34 and 37 seconds are summarized in Table 8 and illustrated in Figure 10.
In the finest mesh, composed of 9,974,357 elements, the BSL model yields the highest torque value at 0.
73 Nm, while the kAcA model records the lowest value of 0.
613 Nm.
The SST model presents intermediate values with 0.
661 Nm.
This trend remains consistent across the different mesh configurations evaluated, considering in all cases a constant inlet velocity of 0.
0539 m/s.
Table 8.
Torque results for different mesh configurations and turbulence models.
Elements 9,974,357 3,610,398 1,295,088 KOeyuI
SST
BSL
The analysis using the Richardson extrapolation method enables the evaluation of numerical convergence and stability for each model in torque prediction, based on the calculation of the Grid Convergence Index (GCI) for fine and coarse meshes.
In the case of the kAcA model, very close values are observed, with a GCI of 7.
341% in the fine mesh and 7.
in the coarse mesh, indicating stable and consistent convergence.
In contrast, the SST model exhibits significantly higher indices, with 38.
124% for the fine mesh and 39.
873% for the coarse mesh, suggesting greater result dispersion.
The BSL model presents the highest GCI values, reaching 48.
493% on the fine mesh and 57.
097% on the coarse mesh (Figure .
, indicating strong mesh dependence and potential convergence issues by this criterion .
However, when considering only the minimum relative error within the experimental uncertainty range, the BSL model shows the best performance, with an error of just 4.
followed by the SST model at 9.
1%, and the kAcA model at 11.
These results suggest that, under ideal conditions within the uncertainty band, the BSL model approximates the corrected experimental torque value of 0.
6025 Nm more closely than the others.
Nonetheless, this agreement does not guarantee the modelAos reliability, as its high GCI indicates a strong sensitivity to mesh resolution, raising concerns about the robustness and generalizability of its predictions under varying simulation conditions (Figure .
Therefore, these findings underscore the importance of jointly considering both convergence indicators and direct comparison with experimental data.
A seemingly accurate prediction may be misleading if it is not supported by a numerically stable and meshindependent solution .
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Numerical results by model.
Figure 11.
Richardson extrapolation method and Grid Convergence Index.
Figure 12.
The average value of the numerical results of each model is relative to the experimental value.
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Parametric Rotor Innovation for Gravitational Vortex Turbines: Advancing CleanA | 404 Experimental Results Table 9 summarizes the main findings from four experimental tests .
wo performed at a flow rate of 2.
5 L/s and two at 3.
0 L/.
Each row presents the maximum power measured during the experiment, the angular speed at which the maximum torque was observed, and the best efficiency predicted by the correlation equations derived from the experimental These correlation equations obtained by fitting the relationship among torque, power, angular speed, and flow rate are valid exclusively for the tested conditions.
Their purpose is to relate the useful power (PU) and the hydraulic power (PH).
Thus, the efficiency can be predicted within the measured operating range (Equation .
ycEycO = ycNyui where A is the angular speed of the rotor and T is the torque (Equation .
ycEya = yuUyciyaycN ycE where the total head is HT = 0.
488 m, and all other relevant hydraulic and operational parameters such as fluid properties, flow conditions, and rotor speed are summarized in Table The flow rate (Q) is derived from the inlet velocity and cross-sectional area, as detailed A representative form of the power speed correlation used in these tests, for instance, can be written as Equation .
yua = yca yyayeE where A is the torque, and A is the angular speed.
By substituting A into (Equation .
ycE = yuiyua We obtained Equation .
yca ycE.
= .
ca yca ) .
yui This expression shows how the power output depends on the rotorAos angular speed.
The constants a, b, and c were determined from experimental data and are valid only within the specific range of flow rates .
5 - 3.
0 L/.
and the geometrical parameters tested.
The values obtained from the best-performing case are: a = 0.
6927, b = -0.
6465, and c = -2.
Test 3 in Table 9 exhibits the best performance among the four tests, reaching the highest measured power of 13.
262 W at a flow rate of 3.
0 L/s.
Moreover, for an angular velocity of 11 rpm, the measured torque in this test was 0.
6025 Nm, with an associated uncertainty of A0.
0829 Nm.
This torque value should be taken as the representative experimental result under these operating conditions.
Table 9.
Test results of experiments.
Flow rate (L/.
Maximum Measured Power (W) Angular speed of max.
Best Efficiency .
Torque Torque at 11 rpm at max.
(N.
(N.
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Figure 13 shows the efficiency percentage (A) for the turbine design.
The efficiency is calculated using Equation .
yc yuC = ycyc 100% .
yc where P0 is the shaft power and PH is the available power.
With these parameters, the overall performance of the turbine is estimated, whose maximum measured value is approximately In contrast, the numerical simulations carried out showed efficiencies ranging around similar values .
-52%, depending on the turbulence model and mesh refinemen.
Although the BSL model presented a relatively high Grid Convergence Index (GCI), it ended up providing torque and efficiency results closer to the experimental data than other models .
, k-A.
This behavior can be attributed to the BSL model's better capability to represent the fluid dynamic behavior occurring in the vortex chamber, even when the dispersion according to the GCI is greater.
The main discrepancies between numerical and experimental values can be explained by various causes, such as vortex and free surface flow, experimental limitations, or assumptions in the simulation setup.
Nevertheless, the fact that the BSL model better reproduces the results, despite its higher GCI, highlights the relevance of comparing the physical accuracy of simulations with experimental data, in addition to analyzing mesh In other words, a favorable GCI does not necessarily guarantee the most accurate prediction, especially in flows with high circulation.
Discussion and Future Work The GVT is reaffirmed in this study as a promising technology for small-scale renewable energy generation, particularly in geographically remote or underserved areas where conventional electrification infrastructure is limited or economically unfeasible .
Its design simplicity, low ecological footprint, and adaptability make it well-suited for decentralized energy applications.
Within this context, optimizing hydrokinetic turbine components is essential for maximizing energy conversion efficiency from natural water This research confirms that rotor geometry, specifically when derived from parametric curves and adjusted to circulation characteristics, plays a decisive role in determining overall turbine performance .
The proposed rotor configuration demonstrated improved hydraulic efficiency in both numerical simulations and physical testing, with performance results aligning well between experimental measurements and CFD predictions .
This alignment reinforces the effectiveness of integrating computational modeling with empirical validation.
Moreover, the analysis revealed that physical constraints in the test setup .
specially bearing frictio.
had a notable impact on performance, highlighting the importance of mechanical design considerations in real-world implementations.
From a broader perspective, these findings directly contribute to the United Nations SDGs.
The advancement of clean and affordable energy technologies aligns with SDG 7, while the application of computational and experimental innovation supports SDG 9.
Furthermore, by promoting the use of localized, non-polluting energy systems that reduce dependency on fossil fuels, this work contributes meaningfully to SDG 13 on climate action.
Indeed, this study adds new information regarding support for sustainable energy and SDGs as reported elsewhere .
Future work should focus on holistic optimization of the entire GVT system.
This includes redesigning additional components such as the inlet channel, the vortex chamber, and the DOI: https://doi.
org/10.
17509/ijost.
p- ISSN 2528-1410 e- ISSN 2527-8045 Julian et al.
Parametric Rotor Innovation for Gravitational Vortex Turbines: Advancing CleanA | 406 outlet to ensure seamless integration with the rotorAos geometric characteristics.
Implementing multi-variable optimization algorithms .
ased on circulation, vorticity, and turbulence modelin.
could enable more precise control of internal flow behavior and further enhance energy recovery.
In addition, real-world deployment studies in off-grid communities could help validate long-term performance, reliability, and social impact, further solidifying the role of GVTs as practical contributors to sustainable energy infrastructure.
Figure 13.
Comparison of experimental efficiency with numerical models.
Conclusion This study proposed and validated a novel rotor design for a GVT using a combined approach of parametric modeling.
CFD, and experimental testing.
The proposed rotor, designed through mathematical parameterization to optimize blade curvature and flow interaction, achieved a maximum experimental efficiency of 50.
6%, which is competitive with or superior to values reported in prior studies.
Numerical simulations using three turbulence models .
-A.
SST, and BSL) were evaluated, with the BSL model demonstrating the closest agreement to experimental results despite exhibiting higher sensitivity to mesh resolution.
These findings highlight the importance of not only ensuring numerical convergence but also validating model predictions against experimental data.
The corrected torque and efficiency values accounted for bearing friction losses, ensuring accurate performance assessment.
Overall, the results confirm that optimized rotor geometry significantly enhances energy conversion in GVT systems.
Future work should focus on the integrated optimization of the rotor, inlet channel, and tank geometry, as well as the application of advanced optimization algorithms based on circulation and vorticity parameters.
This study supports SDGs.
ACKNOWLEDGMENT
We acknowledge the financial support provided by the announcement No.
890 de 2020 AuConvocatoria para el fortalecimiento de CTeI en Instituciones de Educaciyn Superior (IES) Pyblicas 2020Ay (Contract No.
AUTHORSAo NOTE The authors declare that there is no conflict of interest regarding the publication of this The authors confirmed that the paper was free of plagiarism.
DOI: https://doi.
org/10.
17509/ijost.
p- ISSN 2528-1410 e- ISSN 2527-8045 407 | Indonesian Journal of Science & Technology.
Volume 11 Issue 3.
December 2026 Hal 391-410
REFERENCES