5.2.1. Non-Parametric Studies on Turbines (Blades)
An experimental study was conducted by Dhakal et al. [
47] to determine how the number and radius of turbine blades affect the performance of GWVHT systems in both cylindrical and conical basins. They discovered that the most effective position for the turbine was at the bottom of the basin, where the velocity head increased with depth. They also found that fewer blades resulted in increased efficiency, as larger numbers caused significant vortex distortion. Additionally, increasing blade radius decreased efficiency due to friction at the basin’s inner surface. Using a conical basin enhanced vortex formation, leading to a maximum efficiency of 29.63% being achieved in the experiments. To increase power extraction from GWVHT systems, Gautam et al. [
81] suggested adding a boost turbine in series with the main turbine, placed near the discharge hole in a conical basin. Due to the basin’s shape, the boost turbine was smaller than the main turbine. They conducted numerical and experimental studies to determine how different booster turbine parameters, such as inlet and outlet blade angles, impact angle, taper angle, number of blades, and turbine height, affected the system’s performance. Their numerical simulations were performed using the ANSYS Fluent 16.2 package. The main turbine had five blades (their shape was not specified), while two of the boost turbines had three curved blades and the other one had six curved blades. They found that under the optimal conditions, the addition of a boost turbine can increase the system’s efficiency by 6%. This study was continued by Dhakal et al. [
54], who carried out a very similar numerical and experimental study. In this case, the main turbine studied had five curved blades while the boost turbine had five blades with four different shapes and sizes. They found that, overall, the GWVHT system with the best boost turbine produced an increase of 3.84 W in power output, which corresponds to an increase of 20.4%, compared to the system using only the main turbine. Yadav et al. [
75] also studied the effect of adding a boost turbine to a GWVHT system with a conical basin through three-dimensional numerical simulations using the ANSYS 2020 R2 package. Both the main turbine and the boost turbine had four curved blades and the same shape, with the boost turbine placed below the main turbine along the same shaft. Their research focused on the effect of the gap between the main and booster turbines in order to obtain the optimal gap. They found that the optimal power output could be achieved if the distance of the main turbine’s bottom position was fixed at 16.72% of the distance between the top of the conical basin and the top position of the booster turbine.
Sharif et al. [
56] carried out a numerical and experimental study on the performance of a GWVHT system with a conical basin. Their numerical simulations were performed using the ANSYS CFX package. The turbine they investigated had five curved blades, and the dimensions of the turbine were 0.2 m in diameter, 0.067 m in height, and 0.03 m in hub diameter. The curved blades with an angle of 167
were placed at 65–75% of the height of the conical basin from the top position. Their results showed that with the flow rate of 2 L/s, the power output and the efficiency were in the ranges of 3.89–6.17 W and 33.19–52.64%, respectively.
In a study by Warjito et al. [
68], the impact of turbine blade shape on a GWVHT system with a conical basin was analyzed using the Ansys Fluent 18.1 package and two turbulence models:
and SST
. The researchers assessed three types of turbines, each with six blades: vertically flat, tilted flat, and curved. The results showed that tilted flat blades had the highest performance, with a maximum efficiency of 36%. This was 3% and 6% better than the vertically flat and curved blade designs, respectively. The researchers attributed this to the more stable pressure distribution area and the better vortex flow formation of the tilted flat blades compared to the other two designs.
Kueh et al. [
83] tested two different turbines in a cylindrical basin. The first turbine had four flat, vertical blades that were 0.45 m wide and 0.5 m long, while the second turbine also had four vertical blades, but each blade consisted of a flat section that was 0.45 m wide and 0.4 m long and a curved section that was 0.45 m wide and 0.1 m long at the bottom of the blade. The researchers discovered that the turbine with flat blades generated power outputs between 0.0 and 16.42 W and had an efficiency range of 0.0–22.2% at flow rates between 11.19 and 15.47 L/s. Meanwhile, the turbine with curved blades generated power outputs between 0.0 and 14.17 W and had an efficiency range of 0.0–21.6% at flow rates between 10.68 and 13.48 L/s.
The influence of turbine blade length and number of blades on the performance of GWVHTs in a cylindrical basin was experimentally investigated by Rahman et al. [
130]. Four turbines were tested, with two having three vertically flat blades and the other two having six vertically flat blades. Two different blade lengths were used, and vortex profiles were obtained for each turbine configuration. The study found that the maximum vortex tangential velocity occurred at a head of 0.12 m. The highest efficiency of 43% was achieved with a three-blade turbine and a discharge diameter of 0.027 m. Interestingly, the study also found that the highest rotational velocity did not necessarily result in the highest efficiency, which aligns with the conclusions drawn by Dhakal et al. [
47].
Wichian et al. [
129] conducted a numerical and experimental study to investigate the effect of the baffle blades in a GWVHT system with a cylindrical basin. The baffle blades were specially designed, with semi-curved metal plates with different widths added horizontally at the bottom and the top of the vertical curved blades. The baffle plates generally have the same or similar shape as the curved blades and were used to direct or restrain flow. For the experimental study, two turbines with and without baffles having five curved blades were used in the cylindrical basin, which is 1 m in diameter and 1 m in height, and operated at flow rates from over 0.04 m
/s to 0.06 m
/s. For the numerical study, five models of the five-blade turbines with ratios of the area of the baffle plate to the total area of the blade of 0% (no baffle), 25%, 50%, 75%, and 100%, respectively, were numerically simulated with a CFD package with the
turbulence model (but no specific package was specified). The results showed that the model with the ratio of 50% produced the maximum efficiency and the largest torque, with increases of 4.12% and 10.25%, respectively, and the larger baffle plates at the 75% and 100% ratios created greater inertia and thus reduced the torque and efficiency significantly.
Nishi and Inagaki [
50] conducted a numerical and experimental study on the performance of a GWVHT system with a cylindrical basin and a turbine with 20 curved blades. They carried out the numerical simulation using the ANSYS CFX 15.0 package, coupled with the Volume of Fluid (VOF) method to deal with the air–water interface dynamics. The SST turbulence model was selected. Based on the comparison of the results obtained numerically and experimentally in terms of the produced torque, power output, and efficiency, they concluded that after considering the free surface using the VOF method, the experimental results agreed well with the numerical results. They also showed that when the rotational speed increased at the turbine inlet, the forward flow area enlarged, but when the air area decreased, the backward flow area also enlarged. Nishi et al. [
40] continued this study and studied the effect of flow rates on the performance of the GWVHT system through experiments and a free surface flow analysis. With their analysis results, they proposed a loss analysis method and quantitatively assessed the hydraulic loss. They noted that the effective head and the turbine efficiency increased as the flow rate increased; thus, the power output increased at a rate larger than the increase rate of the flow rate. The results further showed that the tank loss and tank outlet loss were the most dominant of all losses, followed by the friction loss inside the tank, while the turbine loss and friction loss in the turbine were small. In addition, Nishi et al. [
59] conducted a detailed numerical study to analyse the behaviour of the vortex structure with respect to the flow in the rotary and stationary regions in a GWVHT system and the effect of the blade directions on vorticity and its related flow path between the blades. The loss of the vorticity path was noted. To understand the loss, the loss coefficients of the rotational and stationary regions were defined and analysed. They found that the vortex structure was relatively small in the optimised turbine due to the swirling flow, and the loss due to the tip leakage vortex and the vortex near the turbine outlet hub were suppressed. Ruiz Sánchez [
7] also revealed some loss generation mechanisms by determining that the sources of loss were due to the increase in the flow rate, which increased the turbine head and efficiency linearly, thus affecting the turbine output, as the water zone expanded at the blade inlet.
The optimal number of blades in a vortex-type turbine depends on the strength of the formed vortices and several other factors, especially the friction losses. Ruiz Sánchez et al. [
63] studied two turbines of a GWVHT system numerically based on their generation of torque with H-Darrius and flat blades in a cylindrical basin. Using Ansys 2019 R3, the models were configured at constant operating conditions. They found that the torques were 0.76 N and 0.16 N for the turbines with the flat blades and the H-Darrius blades, respectively, indicating that the flat blades were more favourable compared to the H-Darrius blades in this case. Wardhana et al. [
131] conducted a detailed study on GWVHT systems using propeller-type impellers having various blade cords, shapes, lengths, and numbers of blades. The result showed that the turbine with three twisted blades was the most efficient, with an efficiency of 54.4%. It was also shown that the number of blades was inversely proportional to the efficiency. They also studied the effect of enhancing the vortex strength using water nozzles on five different types of conical basins. The result showed that the turbine with fix nozzles of 0.050 m in diameter, separated 0.15 m from the upper surface, produced a power efficiency of 54.42%. The results agreed with those of Dhakal et al. [
22], who found an efficiency of 54.41%. The nozzles strengthened the vortex formation and increased the efficiency.
5.2.2. Parametric Studies on Turbines (Blades)
Handoko et al. [
102] experimentally investigated the effect of the arc angle of the curved turbine blade in a GWVHT system with a conical basin. The turbine has five curved blades with the dimensions of 0.08 m and 0.16 m for the blade width and length and 0.1 m and 0.012 m for the diameters of the hub and the shaft, respectively. The blades are inclined by 60
. Three blade arc angles (75
, 90
, and 105
) were studied. The experimental results showed that, overall, the blade arc angle of 90
produced the largest power output.
A parametric study was conducted experimentally by Power et al. [
49] to examine the GWVHT performance in terms of various geometries and turbine parameters. The experiment consisted of a cylindrical basin of 0.7 m in height, 0.5 m in diameter, and a central outlet hole of 0.025 m in diameter. The turbines used in the experiments had two and four vertically flat blades with two lengths (0.25 m and 0.5 m) and four widths (0.075 m, 0.1 m, 0.15 m, and 0.2 m). Their experimental results showed that the size and number of the blades have a similar effect on performance, with their increase resulting in lower vortex heights but larger power outputs and higher efficiencies. Thus, further optimisation studies should focus on the use of larger blades and more blades.
Ullah et al. [
43] analytically and experimentally investigated the performance of a multi-stage GWVHT system with a conical basin. There were three turbines in series, but each of them generated power independently through a telescopic shaft arrangement. The blades of each turbine were curved. The effects of key parameters, including the rotor ratio, the offset distance between neighbouring turbines, and the intra-staging and inter-staging of two-stage and three-stage GWVHT systems, were studied. They found that in a multi-stage GWVHT system, the profile of the blades of the upstream turbines produced minimal vortex distortion, indicating that the power generation capacities of the downstream turbines are ultimately increase, as the performance of the latter turbines strongly depends on the head utilization capacity of the former turbine. They also found that turbines with tilted blades were best suited to the position near the basin’s bottom, whereas the cross-flow blades should be at the top position. Furthermore, their results showed that the rotor ratio of the neighbouring turbines should be selected in such a way that the two turbines have the same rotor-to-basin diameter ratio with the optimal offset distance. They concluded that multi-stage GWVHT systems, which combine the effect of solid-body rotation and a free vortex, present a significant improvement in the overall performance compared to that of single-stage GWVHT systems. Ullah et al. [
36] further expanded this study by carrying out more experiments with some other configurations of the multi-stage GWVHT systems. However, this study essentially did not provide more new information, but it did recommend that further mathematical performance prediction models and flow visualisation techniques should be developed and used to explore the intrinsic physics involved in multi-stage GWVHT systems to obtain a deeper understanding of the systems to achieve optimisation.
Haghighi et al. [
39] developed a hydrodynamic design method and carried out numerical simulations of a GWVHT system. Their design procedure was developed based on classical free vortex theory, which determined the hydrodynamic features at the turbine blades’ radial sections and formed the selected hydrofoils with appropriate stagger angles and chord lengths in each section. They then carried out a steady-state, homogeneous, two-phase numerical analysis using the ANSYS CFX 15.0 package and incorporating the SST turbulence model to obtain the turbulence structures and validated their numerical results with experimental data. They used the simplified Rayleigh–Plesset equation to determine the bubble growth rate in the homogeneous two-phase model to explore the cavitation phenomenon in different states of turbine blade opening angles and rotational speeds. The maximum efficiencies for most of the turbine positions are more than 80%. They suggested that future research should focus on seeking an appropriate method for the transient simulation of a GWVHT system in an open channel and optimising different parts of the system.
Bajracharya et al. [
57] carried out a comprehensive parametric study numerically and experimentally on the effects of turbine blade geometry on GWVHT systems with a conical basin. They identified seven geometrical parameters for the turbine design and investigated their effects on system efficiency. These parameters are blade height, blade angle in the vertical and horizontal planes, impact angle, taper angle, cut, and the number of blades. Their three-dimensional numerical simulations were performed using the ANSYS Fluent package with the SST
turbulence model with curvature correction, as this turbulence model performs well for flows involving adverse pressure gradients and rotating and separating flows, which are exactly what are involved in GWVHT systems. Their experiments were conducted in the GWVHT system with similar basins, channels, shafts, hubs, and dimensions to those in [
22] and with the gross head of 0.27 m and the flow rate of 0.0065 m
/s kept unchanged throughout all cases studied. They studied 22 turbines with different combinations of blades with the variations in the seven parameters. Based on their detailed results and analysis, they recommended the following values for the turbine blades’ geometrical parameters for the optimisation of the turbine design in GWVHT systems with a conical basin: a turbine height to basin height ratio of 0.31–0.32; a taper angle conforming to the basin cone angle and impact angle of 20
; the blades should be curved when viewed from the top only, with a blade angle in the range of 50–60
; and a cut ratio smaller than 15%. They also recommended that further studies based on vortex flow theory and multiphase numerical simulations should be carried out to improve understanding of the performance of GWVHT systems and further optimise the turbine designs.
In addition to their study on optimising the design of dome-shaped (concave) basins, Esa et al. [
79] also investigated six different turbines. Two turbines had four flat blades with 30
and 90
drums attached, two turbines had four curved blades with 30
and 90
drums attached, and two turbines had curved blades with small 30
and 90
mountings attached. They found that the larger blades reduced the turbine’s rotational speed, thus reducing efficiency, and increasing the weight of vertically installed blades also reduced the overall system performance. They found that the optimised location for placing the turbine was close to the discharge hole at the basin’s bottom.
Saleem et al. [
92] conducted an experimental study on the effects of several key parameters, including flow rate, vortex height, hub diameter, blade position, notch angle, and blade shape, in a GWVHT system with a cylindrical basin. The turbine had four blades, which have three different shapes: a curved one with a radius of curvature of 0.05 m, another curved one with a radius of curvature of 0.1 m, and a flat one. Several inclinations of these blades were studied. They found that the maximum power output could be generated when the vortex height was large and the blades were placed close to the basin’s bottom; the power output increased approximately linearly with the radius of curvature for various vortex heights when the chord length of the blades was kept constant; inclined blades generally enhanced the performance; the diameter of the hub on which the blades were fixed affected the vortex significantly, with a smaller hub having less effect, whereas a hub with a diameter larger than the air core’s diameter disturbs the vortex shape, so it is better to use the least possible hub diameter; and an optimised ratio of the width to the height of the blades existed for certain basin designs and flow rates, but more work needs to be conducted on this. Saleem et al. [
42] expanded this work by carried out further experiments to present a much more detailed performance evaluation of the GWVHT system with a cylindrical basin with the help of mathematical considerations and expressions. The experimental results further confirmed that the vortex height and a good vortex shape with a fully developed air core were key parameters dictating the system performance. They concluded that the performance could be enhanced between the minimum and maximum load conditions by using the minimum possible notch angle and hub diameter, which creates the least disturbance in and minimum distortion of the vortex formed, and by using inclined blades with zero curvature (i.e., flat blades) fixed near the bottom of the basin.
In a study by Irwansyah et al. [
61], both analytical and numerical methods were used to compare curved and flat turbine blades for a GWVHT system with a conical basin. The blade geometry and performance were determined using analytical methods, while the internal flow in the turbine was analysed using the ANSYS Fluent 18.1 package with the SST
turbulence model. Both turbines had five blades, and the results showed that there was no significant difference in efficiency between the flat and curved blade turbines, with both achieving around 63% efficiency. However, by placing the blades in the optimal position (about one-third of the basin height from the bottom), the efficiency could be increased up to 84%. This is because, at this position, the kinetic energy converged the best, indicating that blade location is more important than the type of blade used.
In addition to the study on the effect of adding a small draft tub eto the conical basin, Kim et al. [
62] also used the ANSYS CFX 17.2 package to investigate the effect of the number of blades on the performance of a GWVHT system with a conical basin using four turbines which have 5, 6, 8, and 10 vertically twisted blades. For each blade, the twist angle was 30
between the top and bottom blade profile, where the twist was gradually increased from the top to the bottom of the blade. They noted that the eight-blade turbine performed the best, with an efficiency of 57%, so for the eight-blade turbines, the exposure area to the vortex is optimal while maintaining a stable air core propagation. Turbines with fewer blades caused water to splash due to the impact of a massive water mass against a single blade, whereas turbines with a larger number of blades easily blocked the outflow of water and therefore propagated back pressure.
Sritram and Suntivarakorn [
45] investigated the performance of GWVHT systems with both crossflow turbines and propeller turbines using experiments and the response surface methodology (RSM) method. The RSM method has been widely used in many laboratory experiments to determine the correlation between independent and dependent factors by forming equations to numerically simulate the experiment, and additionally, it is able to provide better levels and degrees of independent factors with satisfactory accuracy. A cylindrical basin with a diameter of 1 m and a height of 0.5 m was used in the experiments. The discharge hole at the basin’s bottom was 0.2 m in diameter. The water flow rates for the experiments were in the range of 0.2–0.6 m
/s. Two types of turbines were tested: one is the propeller turbine and the other is the crossflow turbine. For the first one, 12 propeller turbines with five curved blades each were produced and tested, which have three different heights (0.2 m, 0.3 m, and 0.4 m). For each height, there were four different turbines with the diameters of 0.4 m, 0.5 m, 0.6 m, and 0.7 m, respectively. For the second turbine, eight crossflow turbines at the height of 0.3 m were produced and tested, with four of them having 24 blades with the diameters of 0.4 m, 0.5 m, 0.6 m, and 0.7 m and four of them having 12 blades, 18 blades, 30 blades, and 36 blades at the same diameter of 0.4 m. Curved blades were used in all these crossflow turbines as well. The authors’ major conclusion is that the crossflow turbine could perform better, generating more power output than the propeller turbine. More specifically, they found that at the same flow rate of 0.02 m
/s, the 5-blade propeller turbine with a 0.4 m height and a 0.7 m diameter achieved 13.92% efficiency, while the 18-blade crossflow turbine with a 0.3 m height and a 0.4 m diameter achieved 23.01% efficiency at the same water flow rate. Based on the experimental results, they obtained an efficiency equation using the RSM method in terms of the flow rate, blade height, and turbine diameter. They also concluded that a turbine with five blades was the most appropriate to use and that the right distance between the blades of the turbine could maximize the exertion of the water flow rate. The RSM method was also used by Faraji et al. [
72] in their study on the effects of speed, hub–blade angle, number of blades, and turbine profile in a GWVHT system with a cylindrical basin. Their numerical, analytical, and experimental study involved both flat blades and curved blades, and they obtained the relations for the efficiencies for both types of blades in terms of the turbine speed, hub–blade angle, and the number of blades.
Edirisinghe et al. [
38] expanded their earlier work [
108] to numerically carry out a parametric study on the effects of different configurations of turbine blades in a GWVHT system with a conical basin using the ANSYS CFX 17.2 package. The configuration parameters representing the turbine blades are the blade inclination, turbine height, vertical twisting, and horizontal curving. They studied five different turbine models; the first (basic) model consists of five flat blades with 0.5 m in diameter and 0.5 m in height; the second one is a modification of the basic model with the blades inclined to the basin at a conical angle of 41
with the same turbine height at 0.5 m; the third one is another modification of the basic model with the turbine height changed but at the same conical shape; and the fourth and fifth models are modified versions with the turbine blades modified with vertical twisting and horizontal curving, respectively, where the vertical twist angle was determined using the relative angle between the top and bottom blade profile, while the twist length was determined by the vertical twisting length. The numerical simulations were carried out using the SST-CC (SST with circular correction) turbulence models and the VOF method. They analysed the relationship between the flow behaviour and the system performance in detail for each case in terms of the air–water interface, pressure, and velocity fields. They noted that increasing the air core would result in maintaining low pressure behind the blades, thus increasing power output. They also found that the twisted vertical turbine, which has full exposure to a wide area at the vortex area, did not propagate a significant air core, and only when the air core outlet drain was increased was the air core allowed to propagate easily while maintaining the low-pressure region behind the blades, thus increasing pressure difference for power generation. They concluded that the blade inclination, similar to the conical basin inclination, produced improved performance, and the bottom-most position inside the vortex basin was the optimal position of the basic turbine model as the vortex strength was high at the discharge hole. The horizontally curved blades produced a slightly higher efficiency than the vertically twisted blades. However, when the discharge hole size increased, the latter had better performance, at the 55.3% efficiency while maintaining a stable air core. This is a very comprehensive study of the vortex dynamics in a GWVHT system with different turbine configurations, which provided very detailed information about the characteristics of the vortex dynamics, making a significant contribution to the understanding of the complex vortex dynamics. It represents one of several pioneering studies on vortex dynamics and the latest development of high-quality studies on GWVHT systems as well as the appropriate use of advanced numerical simulation tools (such as [
36,
37,
39,
40,
41,
42,
43,
44,
66,
71,
132]). It should be recommended as an exemplar for future studies on GWVHT systems.
Aziz et al. [
69] conducted a numerical study using SolidWorks on the GWVHT with a conical basin with the turbines of different numbers of flat blades at both vertical and horizontal orientations. The selected numbers of the blades are 8, 12, and 18, and the blades were tilted at 25
, 45
, 75
, 90
, and 120
, respectively. The results showed that comparable tangential forces were able to be extracted. In terms of the turbine orientation, the vertical turbine produced better performance, as reviewed by Timilsina et al. [
5]. The study also found that increasing blades resulted in the reduction in the tangential force due to the small gaps in between the blades, so there was no sufficient contact with water.
As mentioned earlier, Vinayakumar et al. [
77] used the finite element method to carry out a series of numerical simulations to perform a parametric study on several key parameters of a GWVHT system for optimisation, which include the height of the cylindrical basin, the number of curved blades, the length of the blades, and the tilt angle of the blades. In addition to the results about the optimal basin height, which is 0.3 m, they also obtained the optimal blade length, number of blades, and tilt angle of the blades through a parametric study by varying these parameters.
In a study by Zamora-Juárez et al. [
78], the vortex formation and its interaction with turbine blades were analysed using both analytical and numerical methods. The aim was to determine the most efficient geometric configuration for a turbine. The numerical model was based on a two-phase flow system. The results indicated that a turbine with a radius coefficient of 0.8 and eight blades had the best performance, achieving an efficiency of up to 64.23%. The study also found that a blade submergence between 90% and 95% resulted in a braking effect on the rear surfaces of the blades, leading to reduced efficiency.
Velásquez García et al. [
112] numerically studied the optimal position of the turbine in a GWVHT system with a spiral inlet channel and a conical basin. There were four curved blades in the turbine, and the numerical simulations were performed by changing their positions in the basin. Three positions (at 0.4H, 0.5H, and 0.6H, where H is the height of the basin) were studied. They found that the maximum efficiency (44.15%) was achieved when the turbine was located at 0.6H. But they stated that the optimal model needed experimental verification and recommended that further studies be carried out to establish the optimal turbine design for GWVHT systems in terms of all parameters representing the turbine.
As mentioned above, the thesis work by Khan [
114] also included the study of the effect of the turbine blades, in addition to their detailed parametric study and optimisation in terms of the geometries of the inlet channel and the basin. They considered four different blade shapes: inverted conical blades, crossflow blades, curved flat blades, and twisted blades. They found that the turbine with the crossflow blades was the most efficient, with a maximum efficiency of 68.84% achieved under the operating conditions considered.