Experimental Assessment of Hydrodynamic Behavior in a Gravitational Vortex Turbine with Different Inlet Channel and Discharge Basin Configurations

Abstract

Gravitational vortex turbines can provide a sustainable and efficient solution for generating renewable energy from small watercourses, minimizing environmental impact, and contributing to the decentralization of energy production. Their design allows for high energy efficiency even under low flow conditions, thus benefiting rural communities and reducing their dependence on fossil fuels. This paper presents an experimental assessment of the hydrodynamic behavior of gravitational vortex turbines by examining various geometric configurations. The combinations of two types of inlet channels (spiral and tangential) and two types of discharge basins (conical and cylindrical) were investigated. Additionally, different geometries and placements of the runners were evaluated to determine their influence on the efficiency and performance of the turbine. The results indicate that the highest efficiency of 60.85% was achieved with a configuration that included a spiral inlet channel, cylindrical discharge, and a runner placement of 50%.

1. Introduction

Diversification of the energy matrix is an imperative global priority, aimed at reducing dependence on conventional energy sources, such as fossil fuels, which significantly contribute to pollution and climate change. In this context, unconventional energy sources such as small-scale hydropower, solar photovoltaic energy, and wind energy, play a crucial role [1,2,3]. These technologies not only harness renewable and abundant resources but also produce lower greenhouse gas emissions during operation. Small-scale hydropower, in particular, can be integrated into existing infrastructure without the need for large reservoirs, thereby minimizing disruptions to aquatic ecosystems. Solar and wind energy, on the other hand, can generate decentralized electricity, thus reducing transmission losses and enhancing the resilience of the electrical grid. The complementarity between these systems allows for more stable and sustainable generation by offsetting the individual variability of each source. For instance, while solar and wind energy can be intermittent, combining them with small-scale hydropower can help maintain a more consistent energy supply [4,5,6,7].

Among various generation technologies, run-of-river hydropower plants stand out for their lower environmental impact than large hydroelectric facilities [5,7]. Although large plants are efficient in energy production, they have significant disadvantages, such as the displacement of communities in reservoir-influenced zones, alteration of river sediment flows, and greenhouse gas emissions resulting from the decomposition of vegetation in water bodies. In contrast, run-of-river plants exploit the natural flow of rivers without the need for large reservoirs, significantly reducing disruptions to aquatic and terrestrial ecosystems. Additionally, they offer several advantages, including a smaller ecological footprint and lower construction and operational costs. These plants are also ideal for distributed generation in energy communities with water resources, promoting energy autonomy and local resilience. However, they face challenges related to generation capacity because of their greater dependence on river flow variability [7]. Despite these limitations, run-of-river plants represent a viable and sustainable alternative that contributes to the diversification of the energy matrix while reducing environmental impact [5,8].

Run-of-river power plants can use conventional turbines such as Pelton, Michell-Banki, and Turgo [5,9]. However, it is crucial to explore the use of innovative turbines beyond conventional designs. An emerging technology in this field is the gravitational vortex hydrokinetic turbine (GWVHT), which promises higher efficiency and adaptability to various geometric and flow conditions. Nevertheless, this technology necessitates thorough studies to evaluate its performance and optimize its design. GWVHTs are hydroelectric devices that harness the potential energy of low-height water to generate electricity. These systems consist of an inlet channel that directs water into a basin, typically conical or cylindrical, with an opening at the bottom through which the water outlets. The falling water creates a vortex, and it is this spiraling motion that drives the blades of a turbine located at the center of the basin, which is connected to an electric generator [10,11,12].

The efficiency of GWVHTs largely depends on the hydraulic turbine, and numerous studies have focused on optimizing their design to enhance performance [13,14]. In their initial research conducted in 2013, Marius et al. [15] experimented with various hydroelectric turbines placed at different heights within a conical reservoir and concluded that optimal performance was achieved when the turbine was positioned at the outlet of the reservoir, although the blade profile was not considered. Sritram et al. [16] demonstrated that aluminum turbines outperformed steel turbines in terms of energy conversion across different loads and flow rates. Power et al. [17] investigated nine configurations of vertical-axis turbines with varying blade sizes, finding efficiency ranges of 15.1% to 25.36%, influenced by basin geometry, flow volume, turbine position, and blade shape. Nishi and Inagaki [18] proposed a centrifugal water vortex turbine, achieving an approximate efficiency of 35.4%. Moreover, Bajracharya et al. [19] developed two turbines with different blade angles, yielding efficiencies of 29.02% and 48.57%, respectively. Significant developments include the design by Franz Z. Zotloterer, who presented a robust stainless steel turbine with chromium content, achieving up to 80% efficiency with a height range of 0.7 to 3 m and a power output of 0.2 to 500 kW and was designed to be safe for fish due to its low speed [20]. Turbulent, a Belgian company, manufactures gravitational vortex hydropower turbines (GVHTs) featuring submerged units built to operate continuously in challenging environments. These turbines are designed with fish-friendly blades optimized for efficiency. Their models can generate between 5 to 70 kW of power, operate at heights from 1 to 4.4 m, and handle water flow rates ranging from 0.7 to 4 m³/s. Research conducted at Khon Kaen University in Thailand indicated that a turbine with five blades produced the highest torque and was the most efficient [21,22]. Additionally, adding deflectors to cover 50% of the blade tips increased the torque by an average of 10.25% compared to a similar runner without deflectors [23].

Gravitational vortex hydrokinetic turbines (GWVHTs) represent a promising renewable energy technology, and ongoing research has focused on enhancing turbine efficiency [24]. To improve the performance of gravitational vortex turbines, it is crucial to consider several design-related aspects of basins, as basin shape and basin dimensions significantly influence vortex formation and stability. The design of the turbine blades is also important because the shape, size, number, and orientation of the blades are key determinants of energy conversion efficiency. Additionally, the turbine’s location within the basin affects its performance. The use of new materials and advanced manufacturing techniques can also enhance turbine durability and efficiency. Ongoing research in this field is essential for developing more efficient and long-lasting turbines. Numerical simulations and experimental studies are particularly valuable in this context because they enhance our understanding of vortex behavior and its interaction with turbine blades. These studies help identify the most efficient configurations and optimize the turbine design. For instance, conducting multi-phase flow analysis and turbulence modeling is vital for a comprehensive understanding of vortex dynamics and energy transfer. Advanced simulation models that consider air and water flows as two-phase systems and include appropriate turbulence models. In this regard, the literature review suggests that to improve the efficiency of gravitational vortex turbines, interdisciplinary research is required, covering the optimal basin and blade design, turbine placement, and material selection, all supported by rigorous numerical simulations and experiments [12,13].

To support the advancement of gravitational vortex turbines, this study aims to experimentally evaluate their performance across different geometric configurations. The configurations include all possible combinations of two types of inlet channels, namely, spiral and tangential, as well as two types of discharge basins, conical and cylindrical. Furthermore, the geometry of the two types of runners was considered, along with their placement and performance in these geometric configurations.

2. Materials and Methods

The main components of a gravitational vortex hydrokinetic turbine (GWVHT) are the discharge basin, the multi-blade turbine, and the inlet channel. The design of these components plays a crucial role in the overall system performance. The inlet channel regulates the flow of water into the basin, and its design influences both the velocity and distribution of the water flow, affecting vortex formation and turbine performance. The basin itself is the element where the water vortex forms to drive the turbine; its shape, size, and design affect the vortex’s stability and strength.

Table 1. Summary of experimental studies on gravitational vortex turbines.

Reference	Inlet Channel Type	Basin Type	Experimental Installation Characteristics	Relevant Aspects
[25]	Tangential	Conical	Square inlet channel with a 400 mm side and an 1850 mm channel length inclined at 3°. Basin diameter of 800 mm, height of 750 mm, and outlet diameter of 120 mm	Efficiency of 74.35%, runner located at 50% from the top of the basin, with a flow rate of 0.018 m3/s
[26]	Tangential	Cylindrical and conical	The cylindrical and conical basins both had a diameter of 600 mm and a height of 850 mm, with a six-blade runner of 420 mm in diameter.	Maximum efficiency for the conical basin was 36.84% at a runner position of 60.5%, while for the cylindrical basin it was 27.75% at 50%. Output power peaked in both basins when the runner was positioned between 65% and 75% of the basin height from the top.
[27]	Tangential inclined	Conical	The conical basin has a diameter of 600 mm and a height of 850 mm. The hole diameter is mm. At the top of the basin, six injectors of 50 mm diameter and 60° orientation were considered.	The maximum efficiency achieved was 42.47% for a mass flow rate of 15.92 kg/s.
[28]	Tangential	Cylindrical	Three types of blades were examined with curvature radii of 5.08 cm, 10.16 cm, and infinite (flat blades).	Maximum efficiency obtained was 20%.
[29]	Tangential	Conical	The study was conducted with a gross head of 0.27 m and a flow rate of 0.0065 m3/s. The test setup consisted of a conical chamber with a 400 mm top diameter and a 60 mm outlet. Water entered the basin tangentially through a channel with a 13° notch. The runner, with an outer diameter of 40 mm, was placed at 65% of the basin height.	The maximum efficiency achieved was 47.8%.
[30]	Tangential	Conical	The water enters the conical basin through the inlet channel, which consists of an open rectangular cross-section channel. The basin has a height of 610 mm, a top diameter of 400 mm, and a discharge hole diameter of 56 mm.	Maximum efficiency of 54.44% was observed at a height of 0.70 m and flow rates of 0.004 m3/s.
[22]	Tangential	Cylindrical	The test bench with a cylindrical basin has a diameter of 1 m and a height of 0.5 m, with an outlet drain of 0.2 m at the bottom.	At a water flow rate of 0.02 m3/s, the maximum efficiency was 9.09%.
[31]	Tangential	Conical	Water enters the conical basin through an open rectangular inlet channel, which includes a baffle to guide the flow tangentially. The channel is connected to a small round basin, 300 mm high and 600 mm in diameter.	Maximum torque (0.84 N-m) and rotational speed (114 rpm) were achieved with a 5-blade runner, reaching an efficiency of 43% at a height of 0.98 m.
[32]	Tangential	Cylindrical	The runner used in the tests, 3D printed, has a diameter of 200 mm, a height of 300 mm, and a blade twist angle of 60%. The number of blades was set to 5. The cylindrical basin where the runner was installed has a diameter of 0.8 m and an outlet hole of 0.14 m.	The maximum efficiency achieved was 25% for a rotational speed between 90 and 120 rpm.
[33]	spiral	Conical	The runner used in the tests had 4 Savonius-profile blades. A constant inlet flow rate of 4 L/s was maintained for all experiments.	The results indicate that the runner should be installed at 60% of the basin height. Blades inclined in the vertical plane are recommended for energy extraction near the bottom of the cone, while cross-flow blades are more suitable for the rotational flow near the top, in the surface vortex region.
[34]	Tangential	Conical	The basin has an upper diameter of 400 mm, a height of 610 mm, and a 57 mm outlet for stable vortex formation, with a cone angle of 23°. Water enters through a rectangular inlet channel. The runner, positioned between 65% and 75% of the basin height, has a diameter of 200 mm, a height of 70 mm, a hub diameter of 30 mm, and a shaft diameter of 12.5 mm.	The results indicate that a fully developed air core is achieved at a rotational speed of 172 rpm and a vortex height of 0.59 m, representing the ideal operating conditions for maximum efficiency and power output.
[35]	spiral	Conical	A conical vortex basin was designed with a maximum diameter of 625 mm, extended to 875 mm by a spiral design that guided the water flow. The water channel, 325 mm wide, converged towards the spiral inlet with a 9° inclined guide channel. The conical basin’s drainage outlet had a diameter of 150 mm.	Maximum efficiency obtained was 60.5% for a flow rate of 60 m3/h and a head of 0.5 m.
[36]	Tangential	Conical	They tested double-stage vortex turbines (2 turbines installed on the same shaft) using different flow rates and variations in the distance between runners.	The findings indicated that increasing the spacing between the blades led to improved performance at a higher flow rate. Specifically, with a flow rate of 9.5 L/s and a blade separation of 150 mm, the system achieved a total mechanical power of 28.51 W and an efficiency of 28.92%.
[14]	Tangential	Conical	Basin diameter of 500 mm, outlet hole of 80 mm, cone height 577 mm, cone angle 20°, a channel with a square cross-section of side 250 mm, and length 1250 mm. runner with 6 curved blades with a helical angle of 55°, upper and lower diameters of 250 mm and 115 mm, respectively.	Efficiency of 49.5%.
[37]	Tangential	Cylindrical	Runner with 5 blades, external diameter of 300 mm, internal diameter of 20 mm, blade height of 120 mm.	Maximum efficiency was 56.8% with a flow rate of 0.018 m3/s.
[13]	spiral	Conical	Rectangular inlet of height 282.5 mm, width 180.5 mm, and length 759 mm, basin diameter of 500 mm, cone height 786 mm. spiral inlet angle of 92.14°.	Maximum efficiency was 60.77% for a runner position of 55%.
[38]	Tangential	Cylindrical	Rectangular inlet channel of base 150 mm and height of 300 mm. Cylindrical basin with a diameter and height of 500 mm. Basin outlet diameter of 100 mm.	Maximum experimentally obtained efficiency was 58.13% for a flow rate of 6.0 L/s.
[39]	Tangential	Conical	The runner with 5 blades has a height of 240 mm, a blade angle of 60°, a helix angle of 63°, and a conicity angle of 20°. Its upper diameter is 350 mm, while the middle diameter is 262.7 mm.	Maximum efficiency was 28% for a flow rate of 0.00477 m3/s.
[40]	Tangential	Cylindrical	The setup consists of a channel with a rectangular cross-sectional area, a cylinder with a height of 550 mm, and a diameter of 390 mm. The runner’s upper diameter is 0.13 m, the outlet diameter is 0.20 m, with a height of 0.20 m, and 18 blades.	The maximum reported efficiency, for a runner that showed a torque and output power of 0.27 m and 1.49 m, respectively, was 18.98%.
[41]	spiral	Cylindrical	The rectangular inlet channel measures 15 cm wide, 30 cm high, and 145 cm long. The vortex chamber has a spiral shape with an internal diameter of 47 cm, while the external spiral arm connecting to the water channel has a diameter of 58 cm. The experimental setup includes two tanks of 500 and 300 L, respectively. Two runners with four curved blades (straight and inclined) with an external diameter of 250 mm and a height of 150 mm were employed.	Maximum efficiency of 56% for a flow rate of 2.0 m3/min.

presents some experimental studies reported in the literature. Although this is an emerging technology, relatively few experimental studies have been conducted to date.

The overall performance of a gravitational vortex hydrokinetic turbine (GWVHT) is governed by the interaction of all its components. Therefore, systematic and exhaustive parametric studies are required to understand the effects of all relevant parameters that represent the configuration, geometry, and operating conditions, to optimize the design of GWVHT systems [10,11].

In this study, a comprehensive assessment of the performance of the six GWVHT configurations was conducted, as illustrated in Figure 1, Figure 2 and Figure 3. The geometries and dimensions used in the experiments were selected from previously documented studies in the literature [12,14]. Model 1, shown in Figure 1a, features a spiral inlet channel and a cylindrical discharge basin. In contrast, Model 2, presented in Figure 1b, incorporates a tangential inlet channel and a cylindrical discharge basin. Model 3, depicted in Figure 2a, is characterized by a tangential inlet channel and a long conical discharge basin (with a cone height of 786.07 mm). Model 4, represented in Figure 2b, features a tangential inlet channel and a short conical discharge basin (with a cone height of 577.00 mm). Model 5, shown in Figure 3a, consists of a spiral inlet channel and a long conical discharge basin (also with a cone height of 786.07 mm). Finally, Model 6, illustrated in Figure 3b, presents a design with a spiral inlet channel and a short conical discharge basin (with a cone height of 577.00 mm).

These configurations were strategically selected to cover a variety of designs and hydrodynamic conditions that could significantly influence the performance of GWVHTs.

To evaluate the hydrodynamic performance of the six considered models, an efficiency curve was plotted for two distinct runner geometries (Runner 1 and Runner 2). These geometries were selected based on their proven effectiveness in previous research, which ensured a significant and reliable comparison between the models. By plotting these efficiency curves, we can analyze how each GWVHT configuration interacts with the runner in terms of energy capture and conversion efficiency. This analysis allows us to identify potential variations in hydrodynamic performance among the models, as well as to better understand how factors such as the geometry of the inlet channel and discharge basin influence the overall effectiveness of the system.

The runners used in the experimental tests were conceptualized by [13] (Runner 1) and [14] (Runner 2). Figure 4a,b show the studied runners. In an impulse turbine, such as a gravitational vortex turbine, water travels from the inlet to the outlet of the blades; the speed and direction of the water at the outlet change relative to the inlet. This variation in speed and flow direction modifies the water jet’s momentum, which is transferred to the runner. Figure 4c illustrates the velocity triangles of inlet and outlet for an impulse turbine. A thorough comprehension of velocity triangles and flow angles is crucial for designing and optimizing impulse turbines, as these elements dictate how efficiently the runner can convert the water’s kinetic energy into mechanical power. The term $V_b$ refers to the linear velocity of the blades, while V denotes the absolute velocity of the fluid. The relative speed of the jet concerning the blades is given by $V_r$, and $V_f$ represents the flow velocity at the blade’s inlet, which corresponds to the vertical component of V. The horizontal component of V at the blade’s inlet is described by $V_w$, which reflects the rotational velocity. The angle $\theta$ is defined as the one formed between the jet’s relative velocity and the blade’s motion, whereas $\alpha$ indicates the angle at which the jet enters the blades, relative to their movement. The subscript 1 is used to denote these values at the blade’s outlet.

Table 2. Geometric characteristics of gravitational vortex turbine runners.

Symbol	Variable	Runner 1	Runner 2
$\alpha$	Blade inlet angle [°]	16.00	16.00
$\beta$	Blade outlet angle [°]	90.00	90.00
$\theta$	Water inlet angle [°]	40.00	40.00
$\gamma$	Water outlet angle [°]	42.70	42.70
$\lambda$	Blade twist angle [°]	68.80	55
L	runner height [mm]	200	200
$D_s$	Upper diameter [mm]	291	252
$D_i$	Lower diameter [mm]	163	122
Z	Number of blades	6	6

summarizes the inlet and outlet angles of the blades of the two studied runners. The selection of these parameters is critical for optimizing the efficiency of gravitational vortex turbines.

The runners were positioned at three locations within the discharge basin during the experimental tests for each of the geometric configurations (Models 1, 2, 3, 4, 5, and 6). To establish the positions of the runners within the cylinder, three equidistant vertical points were selected, corresponding to 50%, 60%, and 70% of the total height of the discharge basin, as shown in Figure 5.

For the conical discharge basins, positions at 50%, 55%, 60%, and 65% were selected. These points were carefully chosen to ensure uniform distribution along the vertical axis of the basin, allowing assessment of the flow conditions at different locations. Additionally, the midpoint of each runner height was used as a reference to ensure proper placement within the basin, thereby facilitating comparisons between various positions. Both runners were 200 mm in length and were equipped with six blades.

The equations used to calculate the hydraulic power of a hydraulic turbine are also applicable to determining the available power of hydraulic gravitational vortex turbines. The maximum available power ($P_{disp}$) of hydraulic gravitational vortex turbines is given by Equation (1):

$$P_{disp}=\rho gQH$$

(1)

where $\rho$ and g represent the densities of water and gravitational acceleration, which are established at 998.2 kg/m³ and 9.81 m/s², respectively. On the other hand, H is the height difference between the inlet channel and the midpoint of the runner. Q is the flow rate, which varied across three values during the experimental tests (0.0025 m³/s, 0.003 m³/s, and 0.0035 m³/s).

Once each model was configured and installed on a hydraulic test bench, the power generated ($P_{out}$) by the turbine was determined using Equation (2). The experiment was designed to calculate the torque (T) generated by the runner in different configurations at various angular velocities ($\omega$) and flow rates (Q). This approach ultimately enabled the evaluation of the turbine efficiency ($\eta$) using Equation (3).

$$P_{out}=T\omega$$

(2)

$$\eta ={\displaystyle \frac{P_{out}}{P_{disp}}}={\displaystyle \frac{T\omega }{\rho gQH}}$$

(3)

2.1. Experimental Setup

In this research, an experimental setup was employed, consisting of a lower tank with a capacity of 2 m³, a centrifugal pump, and a superior tank of 0.18 m³ that can be connected to the gravitational vortex turbine. This turbine features an inlet channel connected to the superior tank, a basin, and a runner. The lower tank is made of fiberglass and reinforced with an external steel frame, while the superior tank is constructed from 14-gauge steel sheets. The turbine shaft is supported by a structure positioned at the top of the basin. At the end of this shaft, a torque sensor and motor are installed to apply load to the turbine, allowing for the efficiency curve of the gravitational vortex turbine to be measured. The experimental arrangement is illustrated in Figure 6 [14].

2.2. Data Repeatability

To ensure the reliability and statistical robustness of the experimental results, each experimental configuration and flow rate was tested in triplicate. Conducting three repetitions per setup was determined to be sufficient for capturing potential variations across trials while minimizing experimental error. This approach provided a solid dataset with minimized random variation, offering a more accurate basis for analyzing performance trends. Careful control of testing conditions was maintained to uphold consistency across all trials. This included using the same experimental bench, materials, and environmental settings to avoid any discrepancies that could affect the results. By standardizing the setup and procedures, each trial was effectively isolated from external influences, strengthening the repeatability and reliability of the findings. Furthermore, the methodology for each experiment is meticulously documented to facilitate reproducibility. Detailed descriptions of the experimental setup, including the models, equipment specifications, and operational procedures, allow other researchers to replicate the tests under comparable conditions. This transparency in documentation ensures that the experiments can be reliably reproduced in different laboratory settings, offering a pathway for independent validation of the findings and contributing to the overall rigor of the research. Additionally, by standardizing all key variables and ensuring stable flow conditions, the repeatability of these tests extends to similar setups beyond the current laboratory environment. This replicability supports broader generalizability and strengthens the study’s contributions to advancing hydrokinetic turbine research.

3. Results and Discussion

Efficiency curves are essential tools for the design and analysis of hydraulic turbines. These curves illustrate how the turbine efficiency varies with the flow rate and rotational speed. The efficiency curve allows for the identification of the turbine’s optimal operating point, where the efficiency is maximized. The results also indicate the effective operating range of the turbine, which is the range of rotational speeds within which the turbine efficiency remains acceptably high. This information is crucial for determining the turbine’s flexibility and ability to adapt to variations in water flow, which may arise from changes in hydrological conditions or energy demand.

Additionally, these curves are valuable during the design and optimization of turbines because they enable the assessment of expected performance under various operating conditions and assist in selecting the most suitable turbine type for a specific application.

3.1. Model 1

In Figure 7 and Figure 8, the measured efficiency curves are shown for a rotational speed range of 0–150 RPM, specifically for the configuration with a spiral inlet channel. The maximum efficiencies for each configuration (runner, flow rate, and position) are presented in

Table 3. Maximum efficiencies of the turbine with a spiral inlet channel and cylindrical basin.

	Efficiency [%]
	Runner 1			Runner 2
Flow Rate [L/s]	50%	60%	70%	50%	60%	70%
2.5	54.44	30.62	35.53	37.54	15.9	25.22
3.0	60.85	40.94	29.69	52.67	16.26	42.12
3.5	52.25	45.49	25.25	21.11	10.00	42.46

.

From Figure 7 and Figure 8, it can be concluded that Runner 1 exhibits greater efficiency than Runner 2 at all three positions. Both turbines are geometrically identical in terms of the number of blades and height; the key difference lies in their mean diameter (measured at half their height), with Runner 1 having a larger diameter than Runner 2. This geometric feature is crucial because a larger contact area enhances the interaction between the turbine and the flow, thereby increasing the energy extracted from the vortex and, consequently, the overall efficiency of the turbine.

Additionally, it is evident that for both turbines, the highest efficiencies occurred at the 50% position. At this height, the turbine can interact more effectively with the gravitational vortex formed in the basin. Being centrally located in the cylinder allows the turbine to capture the maximum amount of kinetic energy from the vortex more efficiently. As the water flow in the basin rises, it tends to become more stable and uniform. This stability means that the turbine can operate under more predictable and consistent conditions, leading to higher efficiency in the conversion of hydraulic energy into mechanical energy. By being separated from both the bottom and top walls of the basin, the turbine avoids interference from solid surfaces, which could disrupt the flow and reduce the turbine’s efficiency. Conversely, a position too close to the cylinder outlet may interfere with the outgoing flow and reduce the turbine’s efficiency. This could result from the turbulence created by the interaction between the turbine and the outflow, as well as potential blockage effects that might limit the flow’s ability to efficiently outlet the basin.

3.2. Model 2

Figure 9 and Figure 10 present the efficiency curves measured for a rotational speed range of 0–150-RPM for the tangential channel configuration. The maximum efficiencies for each configuration (runner, flow rate, and position) are given in

Table 4. Maximum efficiencies for a turbine with a tangential inlet channel and cylindrical basin.

	Efficiency [%]
	Runner 1			Runner 2
Flow Rate [L/s]	50%	60%	70%	50%	60%	70%
2.5	16.03	13.50	5.55	7.07	5.53	8.28
3.0	25.83	16.08	10.51	18.78	15.06	8.96
3.5	20.24	15.63	14.05	24.19	12.05	15.85

.

The same behavior observed in the efficiency curves for the enveloping channel is also evident in the efficiency curves for the tangential channel, as shown in Figure 9 and Figure 10. The highest efficiency is achieved by Runner 1, positioned at 50% of the basin height. However, compared to the enveloping channel, all efficiencies in the tangential channel are lower, with some configurations reporting efficiencies below 10%.

Although both channel configurations generate an efficient gravitational vortex to drive the turbine, specific characteristics may affect the efficiency of each design. In a tangential inlet channel, water flow is introduced tangentially into the cylindrical basin, resulting in a smaller and more concentrated vortex. In contrast, an enveloping or spiral inlet channel introduces a flow that gradually envelops the basin, potentially generating a larger and more stable vortex. A more uniform and broader distribution of the flow can provide more kinetic energy to the vortex, potentially increasing the turbine efficiency.

How the vortex interacts with the turbine may also differ between the two types of inlet channels. In a tangential inlet channel, the vortex might reach the turbine in a more defined and angular direction, whereas in an enveloping or spiral inlet channel, the vortex may have a smoother, circular trajectory around the turbine. These interactions can affect the turbine’s energy conversion efficiency. Additionally, how the vortex is generated and maintained within the cylindrical basin may vary between the two inlet channel designs. An enveloping or spiral inlet channel can create a more stable and longer-lasting vortex, enabling more efficient energy extraction over time than a vortex generated by a tangential channel.

The experimental data showing higher efficiency for the enveloping inlet channel support these assumptions, indicating that a more uniform flow distribution and smoother interaction with the turbine provide optimal energy generation conditions for a vortex turbine with a cylindrical basin.

3.3. Model 3

Figure 11 and Figure 12 present the efficiency curves measured for a rotational speed range of 0–150 RPM, corresponding to a configuration with a tangential channel and a long conical basin. The maximum efficiencies for each configuration (runner, flow rate, and position) are given in

Table 5. Maximum efficiencies for a turbine with a tangential inlet channel and long conical basin.

	Efficiency
	Runner 1		Runner 2
Flow Rate [L/s]	50%	55%	50%	60%	65%
2.5	18.47	20.12	7.00	8.96	5.30
3.0	30.80	6.57	3.22	8.43	12.62
3.5	23.09	7.18	7.10	13.44	10.98

.

From Table 5, Runner 1 has efficiencies that are higher at lower flow rates, with the highest value observed at 3.0 L/s and 50% rotor position (30.80%). However, for higher flow rates, such as 3.5 L/s, the efficiencies decrease, with a marked reduction at the 55% position. On the other hand, for Runner 2, the efficiency follows a different trend, showing an initial drop at 50% rotor position for a flow rate of 3.0 L/s (3.22%) but a notable increase at 60% rotor position (13.44%) for a flow rate of 3.5 L/s. As the flow rate increases to 3.0 L/s and 3.5 L/s, the efficiencies for Runner 2 show more variation, with an improvement observed at certain positions, such as 65% at 3.0 L/s (12.62%).

3.4. Model 4

Figure 13 and Figure 14 show the efficiency curves measured for a rotational speed range of 0–150 RPM with a tangential channel and short conical basin. The maximum efficiencies of each configuration (runner, flow rate, and position) are presented in

Table 6. Maximum efficiencies of the turbine with a tangential inlet channel and long conical basin.

	Efficiency
	Runner 1		Runner 2
Flow Rate [L/s]	50%	55%	50%	55%	60%	65%
2.5	18.09	35.96	32.03	6.28	13.58	57.16
3.0	18.02	26.36	33.37	12.93	8.30	37.42
3.5	36.65	20.57	35.01	18.4	12.27	44.03

.

The data presented in Table 6 show the maximum efficiencies for a turbine with a tangential inlet channel and a long conical basin at different flow rates and rotor positions. For Runner 1, the efficiency generally increases with the flow rate, with a notable peak at 50% for the flow rate of 3.5 L/s, where the efficiency reaches 36.65%. On the other hand, for Runner 2, the efficiency shows more variation across the different flow rates. The highest efficiency for Runner 2 is observed at the 65% position with a flow rate of 2.5 L/s, where the efficiency is 57.16%. This value is significantly higher compared to the efficiencies at other flow rates for Runner 2, indicating that the 65% position provides the best performance at this flow rate. The efficiencies for Runner 2 decrease as the flow rate increases, with a marked decrease at the 60% position for a flow rate of 3.0 L/s, where the efficiency drops to 8.30%, before rising again at the 65% position for the 3.5 L/s flow rate, where the efficiency reaches 44.03%.

3.5. Model 5

Figure 15 and Figure 16 show the efficiency curves measured for a rotational speed range of 0–150 RPM with a tangential channel and long conical basin. The maximum efficiencies for each configuration (runner, flow rate, and position) are presented in

Table 7. Maximum efficiencies of the turbine with a spiral inlet channel and long conical basin.

	Efficiency
	Runner 1		Runner 2
Flow Rate [L/s]	50%	55%	50%	55%	60%	65%
2.5	29.46	35.81	7.75	30.59	38.55	30.22
3.0	36.47	60.79	14.14	19.76	23.15	12.56
3.5	40.35	41.47	12.73	15.34	18.18	14.88

.

The data presented in Table 7 show the maximum efficiencies for a turbine with a spiral inlet channel and a long conical basin, evaluated at different flow rates and rotor positions. For Runner 1, the efficiency increases as the flow rate increases from 2.5 L/s to 3.0 L/s, with a peak at 60.79% at the 55% rotor position for the 3.0 L/s flow rate. However, the efficiency drops slightly at 3.5 L/s, with a value of 41.47% at the 55% rotor position. This indicates that for Runner 1, the best efficiency is obtained at the intermediate flow rate (3.0 L/s), with a higher rotor position (55%). For Runner 2, the efficiency varies significantly across the different flow rates and rotor positions. The highest efficiency for Runner 2 is observed at 60% rotor position for the 2.5 L/s flow rate, reaching 38.55%, which is the highest value for this configuration. However, the efficiency decreases for the 65% rotor position across all flow rates, with the lowest value of 12.56% at the 3.0 L/s flow rate. The spiral inlet configuration shows a performance trend where the efficiency peaks at specific flow rates and rotor positions but decreases at the highest flow rates, especially at higher rotor positions.

3.6. Model 6

Figure 17 and Figure 18 display the efficiency curves measured for a rotational speed range of 0–150 RPM for the configuration with the tangential channel and short conical basin. The maximum efficiencies of each configuration (runner, flow rate, and position) are presented in

Table 8. Maximum efficiencies of the turbine with a spiral channel and a short conical basin.

	Efficiency
	Runner 1		Runner 2
Flow Rate [L/s]	50%	55%	50%	55%	60%	65%
2.5	26.04	26.51	9.24	16.33	23.57	21.18
3.0	41.92	38.19	24.89	38.87	40.67	41.85
3.5	45.05	54.68	24.60	45.55	36.23	38.69

.

The data presented in Table 8 show the maximum efficiencies of a turbine with a spiral channel and a short conical basin, evaluated at various flow rates and rotor positions. For Runner 1, the efficiency increases as the flow rate rises from 2.5 L/s to 3.5 L/s, with the highest efficiency of 54.68% at the 55% rotor position for the 3.5 L/s flow rate. At lower flow rates (2.5 L/s and 3.0 L/s), the efficiencies are relatively similar, with values around 26–41%, indicating that the turbine operates more efficiently at higher flow rates, particularly at 3.5 L/s. For Runner 2, the efficiency trend differs slightly. At 3.5 L/s, the efficiency at the 55% position is the highest at 45.55%. As the flow rate increases to 3.0 L/s, the efficiency rises across most rotor positions. In general, the analysis shows that the turbine with a spiral inlet channel and short conical basin tends to have better performance at higher flow rates (3.5 L/s), with the efficiencies generally peaking at intermediate rotor positions (55%). The performance at the 65% rotor position is less consistent, particularly for Runner 2, where the efficiency drops at the highest flow rate.

3.7. Comparisons with Previous Studies

Based on the efficiency results obtained, a comparison was made with those reported by Velásquez et al. [13] and Betancour et al. [14].

Table 9. Comparison of efficiencies.

		Runner		Inlet Channel		Basin		Flow Rate
	Model	1	2	Spiral	Tangential	Conical	Cylindrical	[L/s]	Position	η (%)
1	1	x		x			x	3.0	50	60.85
2	1		x	x			x	3.0	50	52.67
3	2	x			x		x	3.0	50	25.83
4	2		x		x		x	3.5	50	24.19
5	3	x			x	x		3.0	50	30.80
6	3		x		x	x		3.5	60	13.44
7	4	x			x	x		3.5	50	36.65
8	4		x		x	x		2.5	65	57.16
9	5	x		x		x		3.0	55	60.79
10	5		x	x		x		2.5	60	38.55
11	6	x		x		x		3.5	55	54.68
12	6		x	x		x		3.5	55	45.55
13	-	x		x		x		3.0	55	60.70
14	-		x		x	x		3.125	65	52.20

summarizes the maximum efficiency results for the six models of the current study with both runners (for 12 configurations) and the results from two previous studies.

According to the results in Table 9, the models with Runner 1 consistently showed superior performance compared to those with Runner 2, suggesting that Runner 1 is more efficient. Configuration 1 with a Runner 1 and shrouded channel achieved an efficiency of 60.85% while switching to a Runner 2 reduced the efficiency to 52.67% under the same flow conditions and runner positions. Runner 1, which is larger and has a greater surface area, allows for better use of the available energy in the vortex. Conical basins generally have higher efficiency than cylindrical basins, especially when combined with Runner 1.

A clear efficiency difference can be observed depending on the channel type. Shrouded channels tend to generate higher efficiency. Tangential channels seem to offer lower efficiencies in certain combinations, such as in configuration 3, where efficiency drops to 25.83% with a tangential channel compared to configuration 1, which uses the same basin and runner.

The flow rate also affects efficiency. In configuration 8, a reduced flow rate of 2.5 L/s resulted in an efficiency of 57.16%, suggesting that a more controlled flow can be more efficient in certain setups. The runner’s position relative to the basin (expressed as a percentage of the basin’s height) also influences the efficiency. There is a general trend in which the runner achieves higher efficiency when positioned closer to 50% or 55% of the basin height. A lower flow rate combined with a higher position (as in configuration 8, with a flow rate of 2.5 L/s and a position at 65%) also demonstrates relatively high efficiency (57.16%), indicating that the interaction between these variables is significant. Conversely, with a higher flow rate (3.5 L/s) and a position near 50–55% (configurations 7, 11, and 12), the efficiencies were reasonably high (36.65%, 54.68%, and 45.55%, respectively), though lower than in setups with lower flow rates. Adjusting the flow rate along with the runner position can further enhance the efficiency, with lower flow rates being advantageous in certain configurations.

Regarding previous studies, in a configuration with a conical basin, shrouded inlet channel, and Runner 1, Velásquez et al. [13] achieved a maximum efficiency of 60.77%. In this case, the turbine was positioned at 55% of the cone height (786.00 mm) and tested at a flow rate of 3 L/s. On the other hand, Betancour et al. [14] reported a maximum efficiency of 52.2% in a configuration with a conical basin, tangential inlet channel, and Runner 2. The turbine was positioned at 65% of the cone height (577.00 mm) and tested at a flow rate of 3.125 L/s. With efficiencies of 60.85% and 60.79%, configurations 1 and 9 were the most efficient models, even surpassing the efficiencies reported by Velásquez et al. [13] and Betancour et al. [14]. The difference between these models lies in the runner position and the shift from a cylindrical to a conical basin, demonstrating that the shrouded inlet channel offers better performance than the classic tangential channel configuration.

4. Experimental Images

In the study and optimization of gravitational vortex turbines, visual evidence plays a critical role. In this context, actual photographs of the turbines and their configurations serve as valuable tools for understanding, analyzing, and improving their performances. The following Figures present real images of the turbine in various study configurations. These photographs not only provide an accurate visual representation of a turbine in its operational environment but also reveal important details that may be overlooked in simulations or theoretical models. The ability to examine a turbine in its physical context offers researchers and designers an invaluable perspective, enabling them to identify potential areas for improvement, validate assumptions, and make precise adjustments to the turbine configuration and design.

At the bottom of the runner, as shown in Figure 19 left, a well-defined vortex can be observed. The vortex takes on a funnel-shaped shape, with the narrowest point directed toward the base of the cylindrical basin. In Figure 19 left, the runner is completely stopped, and the vortex is just beginning to form and is not yet fully reaching the runner. In Figure 19 right, the flow appears significantly more turbulent and disorganized, with visible air bubbles surrounding the runner. This suggests that the system may have been operating at a higher speed or that there was greater interaction between the runner and the air trapped in the water, generating turbulence. In Figure 19 right, the runner is actively spinning and is fully submerged in the fluid. The same behavior can be seen in Figure 20, depicting Runner 2.

In the conical basin shown in Figure 21 left, the water is just beginning to fill the channel. This was evident because the water does not yet fully cover the runner, particularly at its top. At this stage, the water flow is not in complete contact with the runner blades, which limits the runner’s ability to generate runner rotation. A clear vortex formation has not yet been observed, as the system has not reached the water level necessary for the expected hydrodynamic effects to develop.

In Figure 21 right, the basin is completely filled with water, fully covering the runner blades. This allows the flow to completely interact with the runner. The vortex is clearly formed, and the circulation of water around the runner is more pronounced, indicating that the flow has reached the optimal speed and volume for generating this hydrodynamic phenomenon. An increased number of bubbles and turbulence in the water is observed, likely due to the complete interaction between the runner and the flow. The runner is fully in contact with the flow, it absorbs kinetic energy from the water more efficiently, effectively generating the vortex.

Figure 22a,b illustrate two types of vortices in a cylindrical basin, formed under different flow inlet conditions. In Figure 22a, the vortex formed in the cylindrical basin with an enveloping inlet is observed. Here, due to the shape of the inlet channel, water is distributed evenly around the basin, resulting in a smoother and more uniform vortex at the top. The base of this vortex is narrower compared to that in Figure 22b, and the water surface in the basin appears to transition more gradually into the vortex. The more homogeneous flow distribution likely allows for better energy kinetic dispersion throughout the basin, leading to a less aggressive but more stable vortex structure.

In Figure 22b, the vortex formed in a cylindrical basin with a tangential inlet is displayed. In this configuration, water enters tangentially along the basin wall, inducing a faster and more concentrated vortex at the center. This type of inlet tends to generate a higher angular velocity within the vortex. The vortex is more pronounced and exhibits a stronger twist along its length, with a more noticeable effect on the water column. Its visibility extends throughout its entirety, indicating a greater rotational speed. The fluid’s energy concentrates at the center of the basin, potentially resulting in a more vigorous and dynamic vortex. While this configuration may yield a higher speed at the center, it also incurs greater energy loss due to friction against the basin walls.

Figure 23a,b illustrate two types of vortices in a conical basin. Figure 23a shows the vortex for the long cone, while Figure 23b shows the vortex for the short cone.

5. Conclusions

The gravitational vortex hydrokinetic turbine (GWVHT) presents a promising solution for harnessing energy from low-head water, adaptable to various geometries and flow conditions. This study investigates the performance of GWVHTs by testing different combinations of inlet channels (spiral and tangential), discharge basins (conical and cylindrical), and the effects of runner geometry and positioning on efficiency.

The experimental investigation into gravitational vortex turbines demonstrates that geometric configurations significantly influence their efficiency. Notably, the combination of a spiral inlet channel, a cylindrical discharge basin, and a runner positioned at 50% of the basin height yielded the highest efficiency of 60.85%. This finding underscores the importance of ensuring a smooth and stable interaction between the water flow and the runner, thereby maximizing the kinetic energy harnessed from the vortex. Furthermore, the runner design plays a crucial role in optimizing turbine performance. Larger runners (e.g., Runner 1) with increased surface area have proven to be more effective in capturing the available flow within the vortex, leading to higher energy extraction compared to smaller runners (e.g., Runner 2). The enhanced performance of Runner 1 is particularly pronounced in configurations employing conical basins, where overall efficiencies are generally superior.

Additionally, the type of inlet channel significantly affects efficiency. Shrouded or spiral channels tend to outperform tangential configurations. Experimental data indicate that the tangential channel produces a smaller, more concentrated vortex, which may not interact as effectively with the turbine. In contrast, the enveloping flow from a spiral channel fosters a broader and more stable vortex, thereby enhancing energy conversion efficiency. The positioning of the runner within the basin is another critical determinant of turbine efficiency. Runners positioned at 50% or 55% of the basin height consistently exhibit superior performance, as this central placement facilitates optimal interaction with the vortex. Conversely, positioning the runner too close to the basin’s bottom or outlet can diminish efficiency due to potential flow disturbances and increased turbulence.

Finally, the relationship between flow rate and runner position reveals the complexity of optimizing turbine performance. In specific setups, lower flow rates combined with higher runner placements can improve efficiency, highlighting the necessity for precise control of flow dynamics in gravitational vortex turbine systems. Understanding the interplay between these variables is essential for maximizing energy extraction potential across various geometric configurations.

Building on these conclusions, future research on gravitational vortex turbines (GWVHTs) should concentrate on optimizing runner geometry and material selection to further enhance efficiency. Given that Runner 1, with its larger surface area, demonstrated superior performance, exploring alternative runner designs that optimize the turbine’s interaction with the vortex is warranted. Investigating advanced materials, such as composites or lightweight metals, could improve turbine durability while reducing operational costs. Moreover, examining various blade shapes and their effects on energy conversion under diverse flow conditions would be a valuable area of exploration, as the current results indicate that blade geometry significantly influences overall turbine efficiency.

Another promising avenue for future research involves integrating GWVHTs into hybrid renewable energy systems that combine small-scale hydropower with solar or wind energy. This approach could mitigate the intermittency associated with renewable energy sources, providing a more stable and reliable energy supply for rural or off-grid communities. Additionally, further experimental investigations and real-world validations would enhance the understanding of vortex behavior and interactions between the turbine and flow dynamics. This would enable researchers to optimize turbine design and placement for maximum efficiency across a variety of environmental conditions.