Experimental and Simulation Investigation of Performance of Scaled Model for a Rotor of a Savonius Wind Turbine

: Renewable energy sources are preferred for many power generation applications. Energy from the wind is one of the fastest-expanding kinds of sustainable energy, and it is essential in preventing potential energy issues in the foreseeable


Introduction
Electricity production from renewable sources has increased in recent years, making it one of the most significant commodities in contemporary civilization and one that has no negative impact on the environment [1].Wind power is widely regarded as one of the most exciting and potentially useful new kinds of energy because of its seemingly limitless potential.Wind turbines have also been used for mechanical needs and energy production because of their widespread availability, low cost, and ease of assembly.Wind turbine rotors typically fall into two categories: horizontal axis wind rotors (HAWRs) and vertical axis wind rotors (VAWRs).These are named based on the orientation of their revolving shafts.HAWRs, well-known for their better power efficiency, have long been relied upon when efficient power is needed.There are several advantages to employing a VAWR (particularly a Savonius model): a higher starting torque, a lower cut-in speed, self-starting operation, and a low noise level [2].
In view of this, the Savonius wind turbine, with its vertical axis, has become a popular choice to produce electricity from wind power in small-scale applications [3].Improvements upstream of the turbine can be achieved by utilizing the wake energy for different boundary conditions [4].Consequently, applying the V-linear layout-arrangement turbine array when considering the wake energy in a large wind farm was found to result in 11%, 5%, 22.89%, and 21% respective increases in total power [5][6][7][8].Moreover, combinations of other Savonius rotors, which rotate in opposite directions, have been found to increase performance by 38%, 80%, and 6.8% [9][10][11] compared to conventional Savonius rotors.The accumulative inner arc results have been determined to be 17.81%, 11.34%, 32.9%, 41%, and 10%, respectively.This shows an improvement over the conventional configuration [12][13][14][15][16], but a two-dimensional (2D) simulation was used to avoid complex geometries.One of the main methods used to improve rotor performance is adding an auxiliary structure, such as a casing, nozzle, deflector, cylindrical cowling, rotor house, omni-directional guide vane, or circular cylinder [17][18][19][20][21][22][23][24][25][26][27].However, these structures might impact other efficiency criteria, such as the overlap ratio and end plates, and require reevaluation following installation.
Three rotor parameters-factor in shape, overlap ratio, and tip speed ratio (TSR)are used as independent variables to create a regression formula and determine the best parameter set for the power coefficients (Cp).This is undertaken using Minitab software during the experiment design [28].Note that the opening the valve on the blades at the best angle has become a good technique and approach, exhibiting a 14% improvement in performance [29].Furthermore, fluid-structure interaction (FSI) modeling has been used in the analysis of the boundaries of a wind turbine's blades and can define the strain (displacement) using an elastic stiffness matrix [30].However, flexible designs rely on wind speed and the TSR, whereas Savonius turbines, which have rigid blades, are not subject to this limitation.Moreover, genetic algorithms (GAs) can be used to discover innovative geometries automatically by using methods that produce random geometries, increasing the Cp and achieving a maximum substantial improvement of up to 33% [31][32][33][34][35][36].Nevertheless, to prove this assumption is correct, this research utilized a technique called digital image processing (DIP) with the assistance of an optimization technique that generated random models.The particle swarm optimization (PSO) algorithm was applied to determine the optimal design parameters in accordance with the response of a surface model developed using the Kriging [37] and Taguchi [38] methods.The difference in Cp change between a single-stage rotor and multiple-stage rotor indicated that the extra segmentation of rotor plates reduced the rotor's effectiveness.It is simple to envisage that the characteristics of a multi-stage rotor directly result from its more challenging production process [39,40].One investigation has been carried out with the Savonius turbine utilizing a configuration of slotted blades on the rotor, which made it possible to draw a conclusion based on the findings and the study that the installation of slotted blades on Savonius wind turbines can increase their overall performance [41].Here, the Cp increased with the TSR, with a maximum value of 2.5% [42].
Many researchers have investigated the crucial optimized geometric parameters that would significantly improve performance.The investigation carried out by M. Niyat Zadeh et al., used COMSOL software to simulate a Savonius-type turbine helical configuration at two different wind speeds (6 and 8 m/s).This was performed by considering the influence of one important parameter on performance: Bach's section effect [43].Mariem Lajnef et al., and A. Damak et al., conducted experimental research using a three-dimensional (3D) printer to model a Savonius rotor of a helical type in a wind tunnel, where the rotor's static and dynamic design factors were studied [44,45].On the other hand, Nur Alom et al., utilized vent augmenter blades to decrease the rotor's drag-negative force using unsteady 3D simulations of the vented elliptical profile rotor.This was done by estimating its drag force (CD) and lift force (CL) [46] after the tests were conducted in a wind tunnel [47].Likewise, S. Meri et al., proposed an elliptical inner wavy blade through unsteady twodimensional (2D) simulations in ANSYS Fluent and experimentally using a wind tunnel.Further results have detected a considerable increase in power relative to the classical Energies 2022, 15, 8808 3 of 23 model [48].Elmekawy et al. [49] performed computational analyses to examine the impact of varying the twisting angle on the blade rotor.W. A. El-Askary et al. [50] suggested a twisted Savonius rotor with a modified profile and a twist angle of 45 degrees was investigated in both experimental and computational research.An investigation has been carried out to identify the ideal overlap ratio of twisted blades and size ratio of endplates, as well as their influence on the aerodynamic performance of a twisted Savonius rotor [51].M. Tahani et al. [52] proposed enhancements that can be summed up as follows: (1) a Savonius rotor twist with an adjustable cutting plane, (2) a plane that has a conical shaft and a twisted Savonius rotor, (3) a Savonius rotor that twists with a conical shaft and a movable cut plane, and (4) a conical shaft and a movable cut plane making up a twisted wind rotor.
Based on the above relevant research analyses, it can be observed that geometric and operating characteristics influence the Savonius wind turbine's performance.Moreover, the installing space, along with wide range of proposed methods and approaches, were shown to affect the efficiency of typical Savonius wind turbines, as summarized in Figure 1.However, one of the critical issues in developing the Savonius wind turbine is that the rotor performance is less efficient than other types of wind turbines, such as the Darrius VAWR and Archimedes wind turbine HAWR.
conducted in a wind tunnel [47].Likewise, S. Meri et al., proposed an elliptical inn blade through unsteady two-dimensional (2D) simulations in ANSYS Flu experimentally using a wind tunnel.Further results have detected a considerable in power relative to the classical model [48].Elmekawy et al. [49] pe computational analyses to examine the impact of varying the twisting angle on t rotor.W. A. El-Askary et al. [50] suggested a twisted Savonius rotor with a m profile and a twist angle of 45 degrees was investigated in both experimen computational research.An investigation has been carried out to identify t overlap ratio of twisted blades and size ratio of endplates, as well as their influenc aerodynamic performance of a twisted Savonius rotor [51].M. Tahani et al. [52] p enhancements that can be summed up as follows: (1) a Savonius rotor twist adjustable cutting plane, (2) a plane that has a conical shaft and a twisted Savoni (3) a Savonius rotor that twists with a conical shaft and a movable cut plane, a conical shaft and a movable cut plane making up a twisted wind rotor.
Based on the above relevant research analyses, it can be observed that geom operating characteristics influence the Savonius wind turbine's performance.M the installing space, along with wide range of proposed methods and approach shown to affect the efficiency of typical Savonius wind turbines, as summarized i 1.However, one of the critical issues in developing the Savonius wind turbine is rotor performance is less efficient than other types of wind turbines, such as the VAWR and Archimedes wind turbine HAWR.In this study, we compared a chosen basic model [48] and an identical scale version of the same basic model to study the effect of the blockage ratio through of 3D simulation and a wind tunnel experiment.Subsequently, we co computational fluid dynamics (CFD) analysis of the proposed new models, wh directed towards developing the effectiveness of Savonius wind turbines in opera minimizing the quantity of negative torque.However, there are no previously r research efforts that address the issues of performance enhancement and modification for the two-blade elliptical Savonius turbine with inner wa configuration proposed in this investigation.The novelty of this work consis adjustment of the wavy area positions along the concave and convex blades further addition of a flow guide channel with different angles to the wavy blade This method does not need a complex fabrication process; therefore, it can red device's production costs and be performed in actual conditions.In this study, we compared a chosen basic model [48] and an identical scaled-down version of the same basic model to study the effect of the blockage ratio through the use of 3D simulation and a wind tunnel experiment.Subsequently, we conducted computational fluid dynamics (CFD) analysis of the proposed new models, which was directed towards developing the effectiveness of Savonius wind turbines in operation and minimizing the quantity of negative torque.However, there are no previously recorded research efforts that address the issues of performance enhancement and profile modification for the two-blade elliptical Savonius turbine with inner wavy area configuration proposed in this investigation.The novelty of this work consists in the adjustment of the wavy area positions along the concave and convex blades and the further addition of a flow guide channel with different angles to the wavy blade profile.This method does not need a complex fabrication process; therefore, it can reduce the device's production costs and be performed in actual conditions.

Performance Estimation Calculations
The power produced by the wind turbine rotor was estimated by multiplying the rotor torque (T) by the rotor angular velocity (ω).One other significant factor definition used was the wind's available energy, which was measured by the coefficient of power (Cp) with respect to the tip speed ratio (TSR).Note that the Betz law provides the upper bound for the efficiency with which wind energy may be converted into usable energy.Accordingly, the C P describes the maximum efficiency with which the kinetic energy of the air flowing from the wind turbine blades can be turned into rotational energy [53].The C P and TSR formula is as follows: Another definition is the that of the torque coefficient (C T ), which defines the ratio of the rotor's actual torque (T) to the theoretical torque (T w ) generated by the wind [54].
where ρ is the density of air, which is equal to 1.165 kg/m 3 at 30 • C; T represents torque (N-m); T w represents the theoretical torque; A represents the swept blade area (m 2 ); R represents the effective radius of the turbine (m); and V∞ is the velocity of incoming air (m/s).The experiment's generated torque was computed as follows [45].
in which the pulley load (F) and pulley radius (r) are used.W is the side tight tension (kg), S is the side slack (kg), rp is the pulley radius (m), and dr is the string nylon diameter (m).

Methods
This work modified (two adjustments were carried out) the original Savonius rotor's dimensions and geometry using three-dimensional (3D) modeling in Solid Works and simulation in Ansys CFX 2020 R2 in tandem with experimental analysis.However, the size of the test section of the aerodynamic lab was restricted, which led to a different range for the blockage ratio (BR) in this investigation.Note that the definition of the BR is the ratio of the rotor's swept area (A = H × D) to the flow cross-section area (At = L × W).The blockage percentage in this study was under 30%, which is acceptable [55].Therefore, no blockage correction measures were used or applied [56].For the comparison of results, the findings were reported against the dataset with the highest power coefficient (Cp) [57].The first adjustment defined a numerical and experimental model.Here, the small model was tested by scaling down the rotor size of the original model based on the scale factor (SF) procedure [58].For this, it was necessary to use enough experimental procedures to measure the output performance of the configured turbine and computational fluid dynamics (CFD) simulations.To preserve the same BR, a 1:1.3 scale model of the original rotor model (S-ORM) was configured and erected in the wind tunnel test section.The second adjustment involved the modification of the blade shape for multiple configurations, resulting in new models with optimal parametric geometry and utilizing ANSYS CFX to investigate the aerodynamic qualities of the modified models.A flowchart detailing the relationship between the experiment and simulation of the processes and the connection with the new modified model is shown in Figure 2.

Establishment of Geometric Model
This work investigated two elliptical blades' inner wavy areas (WAs) in Savonius turbine models.Figure 3 shows the key features and dimensions of the geometry employed.

Establishment of Geometric Model
This work investigated two elliptical blades' inner wavy areas (WAs) in Savonius turbine models.Figure 3 shows the key features and dimensions of the geometry employed.In accordance with the definitions of each term,  is the rotor height,  denotes the diameter rotor,  represents the length of the blade chord,  is the distance between overlaps, and Do expresses the end plate's diameter.The investigation focused on two input parameters of the geometrical numerical model that affected the model's behavior.Firstly, the aspect ratio () was defined as the ratio found by subtracting  from  using Equation ( 5) [59].Second, the overlap ratio () operator connected elements e and d, similarly to Equation (6) [59].Furthermore, the performance of the model was dependent on the frontal swept area of turbine rotor , which was evaluated using Equation ( 7) [45].
The software packages Solid Works and ANSYS CFX were adopted to design the geometry and computational domain in two stages.The proposed rotor's dimensions were derived from the original model in the first stage.In the second stage, the geometry of the original elliptical model (benchmark model), as highlighted earlier, was modified by considering the modification of the wavy area positions and adding a flow-guiding channel (FGC).Furthermore, a comparison between a benchmark Savonius rotor and ten rotor blades is proposed in this study, as shown in Figure 4.A Savonius rotor was installed vertically on the z-axis, with the flow oriented transversely on the y-axis.Subsequently, the number of blades on the rotor was fixed at two; the maximum rotor diameter of Do was 165 mm, while the maximum H was 150 mm.Therefore, D equaled 150 mm of the rotor.In terms of thickness, the rotor blade was assumed to be 3 mm, with an  of 1 (H/D), an  of 0.2, and several stages of 1. Within the scope of this investigation, in order to define an innovative blade geometry in Solid Works software, we considered ten different configuration to enhance the performance of the base profile.First, the rotor models (M1, M2, M3, and M4) defined the change in WA positions, which were named WTE, WCB, FEW, and TQW.Secondly, the rotor models (M5, M6, M7, M8, M9, and M10) involved adding the FGC to the WA in the vertical axis elliptical wind blade profile models, for which the flow-guiding channel (FGC) model with fixed L equaled 0.33d at different angle orientations (Ⴔ).In accordance with the definitions of each term, H is the rotor height, D denotes the diameter rotor, d represents the length of the blade chord, e is the distance between overlaps, and Do expresses the end plate's diameter.The investigation focused on two input parameters of the geometrical numerical model that affected the model's behavior.Firstly, the aspect ratio (AR) was defined as the ratio found by subtracting H from D using Equation ( 5) [59].Second, the overlap ratio (OR) operator connected elements e and d, similarly to Equation (6) [59].Furthermore, the performance of the model was dependent on the frontal swept area of turbine rotor A, which was evaluated using Equation ( 7) [45].
The software packages Solid Works and ANSYS CFX were adopted to design the geometry and computational domain in two stages.The proposed rotor's dimensions were derived from the original model in the first stage.In the second stage, the geometry of the original elliptical model (benchmark model), as highlighted earlier, was modified by considering the modification of the wavy area positions and adding a flow-guiding channel (FGC).Furthermore, a comparison between a benchmark Savonius rotor and ten rotor blades is proposed in this study, as shown in Figure 4.A Savonius rotor was installed vertically on the z-axis, with the flow oriented transversely on the y-axis.Subsequently, the number of blades on the rotor was fixed at two; the maximum rotor diameter of Do was 165 mm, while the maximum H was 150 mm.Therefore, D equaled 150 mm of the rotor.In terms of thickness, the rotor blade was assumed to be 3 mm, with an AR of 1 (H/D), an OR of 0.2, and several stages of 1. Within the scope of this investigation, in order to define an innovative blade geometry in Solid Works software, we considered ten different configuration to enhance the performance of the base profile.First, the rotor models (M1, M2, M3, and M4) defined the change in WA positions, which were named WTE, WCB, FEW, and TQW.Secondly, the rotor models (M5, M6, M7, M8, M9, and M10) involved adding the FGC to the WA in the vertical axis elliptical wind blade profile models, for which the flow-guiding channel (FGC) model with fixed L equaled 0.33d at different angle orientations (  ).

Numerical Model
In the examined cases, this work used ANSYS CFX 2020 R2 transient flows for numerical simulation with the scaled model.The methodology that was applied during the building of the CFX CFD model was formulated based on recommendations from relevant studies [12,51,52,60] and on previous work by the authors [48,57].The Navier-Stokes equations describe the fluid dynamics of a 3D incompressible Newtonian fluid flow.ANSYS CFX was utilized to solve these equations, and the numerical model was rendered accurate to second-order high-resolution time using the finite-volume method (FVM).Based on previous investigations [61], the shear stress transport (SST) model was selected as the turbulence model.When the SST turbulence model was used in a 3D simulation for this study, the results were very close to the experimental measurements from other turbulence models.The results could be used to solve the flow separation problem under different pressure gradients.Figure 5 illustrates the domain in which 3D computation was used in this work.Furthermore, the computational domain was based on the wind tunnel testing dimensions.Two domains were established for the simulation, a rotating domain for the rotor and a stationary domain for wind flow (test section).The boundary settings of the stationary domain were the velocity inlet, outlet pressure, and no-slip wall.Note that the rotary domain had a dimension of 1.1 D, and the diameter size of the rotor was specified as 150 mm.Specifically, the rotor and stationary domains were two distinct parts of the overall computation domain and the frozen rotor model was used to put them in contact.The simulations were run at wind speeds of 6 and 9 m/s, which caused the rotor domain to spin.In addition, an unsteady influence analysis with 40 time steps per revolution rotor was used for all the situations under investigation.The time setup required five hours for four periods, with 40 times steps in each period and six processor cores.The work also implemented the interface model for 3D viscous flutter investigations using the transient rotor stator (TRS 360), which assumes a general connection interface between the revolving and stationary zones.To obtain a decent root mean square (RMS) at each time step, 1 one to three loops of internal iteration with four rotor spins were typically needed.

Numerical Model
In the examined cases, this work used ANSYS CFX 2020 R2 transient flows for numerical simulation with the scaled model.The methodology that was applied during the building of the CFX CFD model was formulated based on recommendations from relevant studies [12,51,52,60] and on previous work by the authors [48,57].The Navier-Stokes equations describe the fluid dynamics of a 3D incompressible Newtonian fluid flow.ANSYS CFX was utilized to solve these equations, and the numerical model was rendered accurate to second-order high-resolution time using the finite-volume method (FVM).Based on previous investigations [61], the shear stress transport (SST) model was selected as the turbulence model.When the SST turbulence model was used in a 3D simulation for this study, the results were very close to the experimental measurements from other turbulence models.The results could be used to solve the flow separation problem under different pressure gradients.Figure 5 illustrates the domain in which 3D computation was used in this work.Furthermore, the computational domain was based on the wind tunnel testing dimensions.Two domains were established for the simulation, a rotating domain for the rotor and a stationary domain for wind flow (test section).The boundary settings of the stationary domain were the velocity inlet, outlet pressure, and no-slip wall.Note that the rotary domain had a dimension of 1.1 D, and the diameter size of the rotor was specified as 150 mm.Specifically, the rotor and stationary domains were two distinct parts of the overall computation domain and the frozen rotor model was used to put them in contact.The simulations were run at wind speeds of 6 and 9 m/s, which caused the rotor domain to spin.In addition, an unsteady influence analysis with 40 time steps per revolution rotor was used for all the situations under investigation.The time setup required five hours for four periods, with 40 times steps in each period and six processor cores.The work also implemented the interface model for 3D viscous flutter investigations using the transient rotor stator (TRS 360), which assumes a general connection interface between the revolving and stationary zones.To obtain a decent root mean square (RMS) at each time step, 1 one to three loops of internal iteration with four rotor spins were typically needed.In this work, we present an unstructured mesh topology and describe how it can be used to efficiently produce a mesh of good quality for both rotating and fixed domains.As illustrated in Table 1, we analyzed grid independence to determine the skewness and orthogonal quality of the mesh.The total number of elements in the rotary and stationary domains was about 4.056 million, since fine grid meshes were chosen in the end, as shown in Table 2. Inflation on the rotor wall and fine meshing using the tetrahedral technique are depicted in detail in Figure 6.We started from five maximal inflation layers at a 1.1 rate of growth in the test simulation, as shown in Table 2.Under all operating conditions, the thickness of the first layer normal to the wall had to be approximately 0.000122 m to obtain y+ < 5 along all walls.When moving from the inner to the outer domain, the number of grid nodes was reduced by making the outermost grids coarser.

Experimental Work
The laboratory was equipped with a subsonic open-type wind tunnel, where a drive section with a circular outlet was used for experimental testing, as demonstrated in Figure 7.By adjusting the damper, the wind blowing rate at the wind tunnel's test zone could be varied between 1 and 32 m/s at the user's discretion.As illustrated in Figure 7, an S-ORM was installed in the test section area.Note that the size of this wind tunnel test piece was 600 mm in length, 305 mm in width, and 305 mm in height.Correspondingly, clear polycarbonate boards 10 mm in thickness were bolted to the inside of the wind tunnel to create a contained testing environment.Subsequently, a 500 g range spring balance (analog weighing) was employed to quantify the dynamic torque produced by the Savonius wind rotor shaft.The rope brake dynamometer used a rope coiled around the rim of the rotating pulley to simulate the friction belt, in which the belt rope was attached to the spring balance (counterweight) [62].However, a digital torque meter placed on the rotor shaft to measure the dynamic torque was not used, which was a limitation of this study.Wind speeds of around 6 and 9 m/s were used in the experiments.When it first started, the turbine model was under no load.The rotating turbine model's speed was slowed by progressively applying a brake load by ratcheting up the tension on the pulley's braking belt.Consequently, forces generated when braking according to the spring weight at different revolutions per minutes (RPMs) were measured and recorded to determine the tip speed ratio (TSR), rotor torque (T), torque coefficient (C T ), and power coefficient (Cp).This procedure was carried out numerous times until the shaft no longer rotated, with each subsequent increment being increased by 1 g.Hence, experiments were conducted repeatedly for each configuration of the turbines to gather datasets.The efficiency of the used to efficiently produce a mesh of good quality for both rotating and fixed domains.As illustrated in Table 1, we analyzed grid independence to determine the skewness and orthogonal quality of the mesh.The total number of elements in the rotary and stationary domains was about 4.056 million, since fine grid meshes were chosen in the end, as shown in Table 2. Inflation on the rotor wall and fine meshing using the tetrahedral technique are depicted in detail in Figure 6.We started from five maximal inflation layers at a 1.1 rate of growth in the test simulation, as shown in Table 2.Under all operating conditions, the thickness of the first layer normal to the wall had to be approximately 0.000122 m to obtain y+ < 5 along all walls.When moving from the inner to the outer domain, the number of grid nodes was reduced by making the outermost grids coarser.Considering the errors throughout the test, the true values for all test outcomes could be determined.The experimental results for this investigation were determined with uncertainties, where conditions of various parameters were considered.Furthermore, the ranges and accuracies of the velocity, turbine speed, and turbine torque were measured and calculated.The measured data provided information about the accuracy of the tachometer (DT-2268), which was ±0.05 for each revolution (RPM).Moreover, the upstream and downstream air velocity of the AF100 open-circuit subsonic wind tunnel was measured using a Pitot static tube.Here, a traversing Pitot tube was adjusted to an accurate measurement.We also calculated uncertainty [63].Furthermore, we performed a regression analysis for the independent variables of turbine torque and the TSR data when carrying out the tests for each regression formula model.Subsequently, their probabilities were assessed, and a confidence interval that covered 95% of the possible outcomes for compliance was generated.Finally, the overall experiment model uncertainty was estimated for each practical replication of the experiment, was and the uncertainties were closely fit and could be accepted.Considering the errors throughout the test, the true values for all test outcomes could be determined.The experimental results for this investigation were determined with uncertainties, where conditions of various parameters were considered.Furthermore, the ranges and accuracies of the velocity, turbine speed, and turbine torque were measured and calculated.The measured data provided information about the accuracy of the tachometer (DT-2268), which was ±0.05 for each revolution (RPM).Moreover, the upstream and downstream air velocity of the AF100 open-circuit subsonic wind tunnel was measured using a Pitot static tube.Here, a traversing Pitot tube was adjusted to an accurate measurement.We also calculated uncertainty [63].Furthermore, we performed a regression analysis for the independent variables of turbine torque and the TSR data when carrying out the tests for each regression formula model.Subsequently, their probabilities were assessed, and a confidence interval that covered 95% of the possible outcomes for compliance was generated.Finally, the overall experiment model uncertainty was estimated for each practical replication of the experiment, was and the uncertainties were closely fit and could be accepted.

Verification of the Accuracy
Initially, to ensure the accuracy of our model, several different ANSYS CFX software simulation scenarios were developed for the elliptical Savonius turbine, and comparisons were made between the test results and the results given in [48].Performance was measured relative to the power coefficient (Cp) at varying turbine tip speed ratios (TSRs).A variety of TSRs, ranging from 0.1 to 1.2, were simulated with a wind speed of 9 m/s.The Cp reached its maximum value when the TSR was 0.7.Previous experimental and numerical results [48] were used to validate the current findings.As shown in Figure 8, ratios ranging from 0.2 to 0.35 and 1.1 to 1.2 were related to the TSR, with an error percentage range of less than 5%.These variation percentages may have been due to, first, the different grid resolutions when comparing the present three-dimensional (3D)

Verification of the Accuracy
Initially, to ensure the accuracy of our model, several different ANSYS CFX software simulation scenarios were developed for the elliptical Savonius turbine, and comparisons were made between the test results and the results given in [48].Performance was measured relative to the power coefficient (Cp) at varying turbine tip speed ratios (TSRs).A variety of TSRs, ranging from 0.1 to 1.2, were simulated with a wind speed of 9 m/s.The Cp reached its maximum value when the TSR was 0.7.Previous experimental and numerical results [48] were used to validate the current findings.As shown in Figure 8, ratios ranging from 0.2 to 0.35 and 1.1 to 1.2 were related to the TSR, with an error percentage range of less than 5%.These variation percentages may have been due to, first, the different grid resolutions when comparing the present three-dimensional (3D) simulation with a two-dimensional (2D) simulation, which has a higher number of grid cells in 3D simulation computations.Second, different methods of analysis-CFX CFD and fluent-were considered.Finally, they may have been due to the different time steps that were adopted in the current simulation and the previous one.However, no statistically significant change (more than 5%) in the average Cp was found in the comparison to the benchmark model.Hence, the maximum overall relative error was less than 9% according to the simulation results obtained from this study; this demonstrates that the numerical method used in this investigation could accurately predict outcomes.and fluent-were considered.Finally, they may have been due to the different tim that were adopted in the current simulation and the previous one.Howev statistically significant change (more than 5%) in the average Cp was found comparison to the benchmark model.Hence, the maximum overall relative error w than 9% according to the simulation results obtained from this study; this demon that the numerical method used in this investigation could accurately predict outc Each time step in the transient simulations was set to twenty iterations, a optimal solution was convergence, which was achieved as a result of va approaching [64,65].Note that all simulations used an absolute convergence crite meet the residual targets of 10 −4 for continuity, velocity components, and tu characteristics calculated in CFX. Figure 9 plots the instantaneous torque variation the accumulated time step for a Savonius turbine at TSR = 0.2 to 1.2, correspondi maximum Cp at TSR of 0.7.In fact, the last two subsequent rotations converged total of four turbine revolutions.Numerical simulations were used to measure th axis torque coefficient (CT) for each angular location.The last two complete revo were averaged to increase the periodicity stability.This average CT was employed estimate of Cp using Equation (3) for all the geometries.Each time step in the transient simulations was set to twenty iterations, and the optimal solution was convergence, which was achieved as a result of variables approaching [64,65].Note that all simulations used an absolute convergence criterion to meet the residual targets of 10 −4 for continuity, velocity components, and turbulent characteristics calculated in CFX. Figure 9 plots the instantaneous torque variation against the accumulated time step for a Savonius turbine at TSR = 0.2 to 1.2, corresponding to a maximum Cp at TSR of 0.7.In fact, the last two subsequent rotations converged after a total of four turbine revolutions.Numerical simulations were used to measure the rotor axis torque coefficient (C T ) for each angular location.The last two complete revolutions were averaged to increase the periodicity stability.This average C T was employed in the estimate of Cp using Equation (3) for all the geometries.statistically significant change (more than 5%) in the average Cp was foun comparison to the benchmark model.Hence, the maximum overall relative erro than 9% according to the simulation results obtained from this study; this dem that the numerical method used in this investigation could accurately predict ou Each time step in the transient simulations was set to twenty iterations optimal solution was convergence, which was achieved as a result of approaching [64,65].Note that all simulations used an absolute convergence cr meet the residual targets of 10 −4 for continuity, velocity components, and characteristics calculated in CFX. Figure 9 plots the instantaneous torque variatio the accumulated time step for a Savonius turbine at TSR = 0.2 to 1.2, correspon maximum Cp at TSR of 0.7.In fact, the last two subsequent rotations converg total of four turbine revolutions.Numerical simulations were used to measure axis torque coefficient (CT) for each angular location.The last two complete re were averaged to increase the periodicity stability.This average CT was employ estimate of Cp using Equation ( 3) for all the geometries.Subsequently, to verify the scale model of the original rotor model (S-ORM) and deduce the link between results, the performance results were compared with the same study's performance results as used previous [48], as shown in Figure 10.Note that the previous results' performance data for wind turbines [48] were scaled to 1:1.3 according to a scale factor (SF) procedure [58].The matched curves, in which the same behavior was presented, showed a maximum power coefficient (Cp max ) variation concerning flow time for a wind speed of 9 m/s at a TSR of 0.7, justifying the scaled-down model.Nevertheless, the performance Cp curve of the S-ORM was extended to a TSR of 1.8, which was greater than the previous research.This means that the present model operated with a wider range of TSRs and turbines at peak efficiency.
Energies 2022, 15, x FOR PEER REVIEW 13 of 23 Subsequently, to verify the scale model of the original rotor model (S-ORM) and deduce the link between results, the performance results were compared with the same study's performance results as used previous [48], as shown in Figure 10.Note that the previous results' performance data for wind turbines [48] were scaled to 1:1.3 according to a scale factor (SF) procedure [58].The matched curves, in which the same behavior was presented, showed a maximum power coefficient (Cpmax) variation concerning flow time for a wind speed of 9 m/s at a TSR of 0.7, justifying the scaled-down model.Nevertheless, the performance Cp curve of the S-ORM was extended to a TSR of 1.8, which was greater than the previous research.This means that the present model operated with a wider range of TSRs and turbines at peak efficiency.

Results and Discussion
Principally, this study aimed to produce an overall scaled model of the performance of the original rotor model (S-ORM) turbine using numerical and experimental validation approaches.The second objective was to deduce the optimum modified blade shape configuration and compare it with the S-ORM rotor based on performance.

S-ORM Validation Study
To validate and approve the computational model of the S-ORM simulation results and validate this study's computational fluid dynamics (CFD) modeling, experimental and simulation tests were utilized for wind velocities of 6 and 9 m/s.This was to determine whether the numerical results were accurate and to determine the best wind velocity.Figures 11 and 12 show the differences in the power coefficient (Cp) and torque coefficient (CT) for some of the interval tip speed ratios (TSRs) used, which ranged from 0.2 to 1.8 at an overlap ratio of 0.2.The numerical results for the wind velocity of 6 m/s matched very well with the numerical results for the wind velocity of 9 m/s.The deviation in Cp and CT compared to the experimental data was attributed to fluctuating experimental conditions, and the torque values may have been a result of experimental uncertainty.The maximum power coefficient (Cpmax) for the S-ORM numerical results was 0.22 at TSR = 0.7, while Cpmax for the S-ORM experimental results was 0.21 at TSR = 0.7.It was possible to verify that the most effective S-ORM design could be achieved from the CFD study.The maximum relative errors in the values of Cp for both the velocities from the simulation results and those from the experimental data for the S-ORM design occurred at TSRs ranging from 0.2 to 0.35 and 1.1 to 1.2, with the experimental data being about 8% lower

Results and Discussion
Principally, this study aimed to produce an overall scaled model of the performance of the original rotor model (S-ORM) turbine using numerical and experimental validation approaches.The second objective was to deduce the optimum modified blade shape configuration and compare it with the S-ORM rotor based on performance.

S-ORM Validation Study
To validate and approve the computational model of the S-ORM simulation results and validate this study's computational fluid dynamics (CFD) modeling, experimental and simulation tests were utilized for wind velocities of 6 and 9 m/s.This was to determine whether the numerical results were accurate and to determine the best wind velocity.Figures 11 and 12 show the differences in the power coefficient (Cp) and torque coefficient (C T ) for some of the interval tip speed ratios (TSRs) used, which ranged from 0.2 to 1.8 at an overlap ratio of 0.2.The numerical results for the wind velocity of 6 m/s matched very well with the numerical results for the wind velocity of 9 m/s.The deviation in Cp and C T compared to the experimental data was attributed to fluctuating experimental conditions, and the torque values may have been a result of experimental uncertainty.The maximum power coefficient (Cp max ) for the S-ORM numerical results was 0.22 at TSR = 0.7, while Cp max for the S-ORM experimental results was 0.21 at TSR = 0.7.It was possible to verify that the most effective S-ORM design could be achieved from the CFD study.The maximum relative errors in the values of Cp for both the velocities from the simulation results and those from the experimental data for the S-ORM design occurred at TSRs ranging from 0.2 to 0.35 and 1.1 to 1.2, with the experimental data being about 8% lower than the simulation results.Hence, this was an acceptable range.Figure 12 illustrates the link between the C T and the TSR.The graph was inversely related to the TSR, as can be observed.Therefore, C T tended to decrease as TSR increased.The average C T increased linearly with an increase in the TSR of approximately 0.7, and the highest average C T values were reached in all instances with a TRS of 0.2.Nonetheless, comparing to the most outstanding Cp values for velocities between 6 m/s and 9 m/s, the model with a velocity of 9 m/s performed slightly better than the model with a velocity of 6 m/s.Thus, the newly proposed models used a velocity of 9 m/s.
Energies 2022, 15, x FOR PEER REVIEW 14 than the simulation results.Hence, this was an acceptable range.Figure 12 illustrate link between the CT and the TSR.The graph was inversely related to the TSR, as c observed.Therefore, CT tended to decrease as TSR increased.The average CT incre linearly with an increase in the TSR of approximately 0.7, and the highest averag values were reached in all instances with a TRS of 0.2.Nonetheless, comparing to the outstanding Cp values for velocities between 6 m/s and 9 m/s, the model with a ve of 9 m/s performed slightly better than the model with a velocity of 6 m/s.Thus, the n proposed models used a velocity of 9 m/s.

Effect of Variations in Blade Configrations on the Turbine Performance
The performance of each profile was evaluated in terms of the achieved fo established TSR value equal to 1. Figure 13 shows the results of the tests for each pr The Cp values obtained for various configurations showed that the wavy area at th and end (WTE), wavy area on the convex blade (WCB), and flow-guiding channel ( models considerably overpredicted the Cp values compared to the others.Furtherm Energies 2022, 15, x FOR PEER REVIEW 14 than the simulation results.Hence, this was an acceptable range.Figure 12 illustrate link between the CT and the TSR.The graph was inversely related to the TSR, as ca observed.Therefore, CT tended to decrease as TSR increased.The average CT incre linearly with an increase in the TSR of approximately 0.7, and the highest averag values were reached in all instances with a TRS of 0.2.Nonetheless, comparing to the outstanding Cp values for velocities between 6 m/s and 9 m/s, the model with a vel of 9 m/s performed slightly better than the model with a velocity of 6 m/s.Thus, the n proposed models used a velocity of 9 m/s.

Effect of Variations in Blade Configrations on the Turbine Performance
The performance of each profile was evaluated in terms of the Cpmax achieved fo established TSR value equal to 1. Figure 13 shows the results of the tests for each pro The Cp values obtained for various configurations showed that the wavy area at th and end (WTE), wavy area on the convex blade (WCB), and flow-guiding channel (F models considerably overpredicted the Cp values compared to the others.Furtherm

Effect of Variations in Blade Configrations on the Turbine Performance
The performance of each profile was evaluated in terms of the Cp max achieved for the established TSR value equal to 1. Figure 13 shows the results of the tests for each profile.
The Cp values obtained for various configurations showed that the wavy area at the tip and end (WTE), wavy area on the convex blade (WCB), and flow-guiding channel (FGC) models considerably overpredicted the Cp values compared to the others.Furthermore, changes in the wavy area (WA) placements resulted in significant turbulence flow.The addition of the FGC was a characteristic affecting the developing flow close to the entrance.This had an effect on the measured values.Section 5.3 discusses the Cp max obtained for the best three blade profiles with the FGC at

Velocity Contours for S-ORM, FGC at Ⴔ = 30°, WTE, and WCB Models
Figure 14 shows the velocity contour, and variations in the flow velocity o blades in the downstream section are shown in Figure 14.The rotor was per rotate for up to four revolutions, and the plots are from once the rotor had com fourth rotation.The velocity of the contour plots' inlet flows matched the b condition initialization.High-speed rotating vortices formed at the tip of the a blade, and wake zones were included downstream of the rotor.The wake zon when there was a sudden change in pressure between the regions upstr downstream of the rotor as a result of the rotor's blockage.As can be seen in F the velocity of the benchmark model varied from 5 to 14.5 m/s for the advanc and 4 to 9 m/s for the returning blade.The velocity of the FGC at Ⴔ = 30° mod from 5 to 15.25 m/s for the advancing blade and from 2.5 to 7 m/s for the returni The velocity of the WTE model varied from 5 to 14.25 m/s for the advancing bla to 8.25 m/s for the returning blade.The velocity of the WCB model varied from m/s for the advancing blade and 1 to 7 m/s for the returning blade.Figure 14 sh the new profile models had smoother velocity variations than the benchmark m new profile models had lower negative and higher positive moments.Thus, th Cp of the new models were increased.

Velocity Contours for S-ORM, FGC at Ⴔ = 30°, WTE, and WCB Models
Figure 14 shows the velocity contour, and variations in the flow velocity of turbine blades in the downstream section are shown in Figure 14.The rotor was permitted to rotate for up to four revolutions, and the plots are from once the rotor had completed its fourth rotation.The velocity of the contour plots' inlet flows matched the boundary condition initialization.High-speed rotating vortices formed at the tip of the advancing blade, and wake zones were included downstream of the rotor.The wake zone started when there was a sudden change in pressure between the regions upstream and downstream of the rotor as a result of the rotor's blockage.As can be seen in Figure 14, the velocity of the benchmark model varied from 5 to 14.5 m/s for the advancing blade and 4 to 9 m/s for the returning blade.The velocity of the FGC at Ⴔ = 30° model ranged from 5 to 15.25 m/s for the advancing blade and from 2.5 to 7 m/s for the returning blade.The velocity of the WTE model varied from 5 to 14.25 m/s for the advancing blade and 3 to 8.25 m/s for the returning blade.The velocity of the WCB model varied from 5 to 14.25 m/s for the advancing blade and 1 to 7 m/s for the returning blade.Figure 14 shows that the new profile models had smoother velocity variations than the benchmark model.The new profile models had lower negative and higher positive moments.Thus, the CT and Cp of the new models were increased.= 30 • , WTE, and WCB Models Figure 14 shows the velocity contour, and variations in the flow velocity of turbine blades in the downstream section are shown in Figure 14.The rotor was permitted to rotate for up to four revolutions, and the plots are from once the rotor had completed its fourth rotation.The velocity of the contour plots' inlet flows matched the boundary condition initialization.High-speed rotating vortices formed at the tip of the advancing blade, and wake zones were included downstream of the rotor.The wake zone started when there was a sudden change in pressure between the regions upstream and downstream of the rotor as a result of the rotor's blockage.As can be seen in Figure 14, the velocity of the benchmark model varied from 5 to 14.5 m/s for the advancing blade and 4 to 9 m/s for the returning blade.The velocity of the FGC at

Velocity Contours for S-ORM, FGC at Ⴔ = 30°, WTE, and WCB Models
Figure 14 shows the velocity contour, and variations in the flow velocity of turbine blades in the downstream section are shown in Figure 14.The rotor was permitted to rotate for up to four revolutions, and the plots are from once the rotor had completed its fourth rotation.The velocity of the contour plots' inlet flows matched the boundary condition initialization.High-speed rotating vortices formed at the tip of the advancing blade, and wake zones were included downstream of the rotor.The wake zone started when there was a sudden change in pressure between the regions upstream and = 30 • , WTE, and WCB Models Figure 15 shows the pressure contours at 9 m/s wind speeds for the benchmark S-ORM model and the best three profile models.Due to flow separation, the pressure downstream of the advancing and returning blades was lower.For the upstream pressure, the drag on the returning blade was observed to be greater.The drag force act on both of the turbine's blades; however, the drag acting on the blade that moves forward drives the turbine, while the drag acting on the blade that is moving backward restricts it.The distribution pressure varied along the models' test sections: for the benchmark model, from 80 to −160 N/m 2 for the advancing blade and −160 to 20 N/m 2 for the returning blade.The pressure magnitude of the FGC at Abstract: Renewable energy sources are preferred for many power generation applications.Energy from the wind is one of the fastest-expanding kinds of sustainable energy, and it is essential in preventing potential energy issues in the foreseeable future.One pertinent issue is the many geometrical alterations that the scientific community has suggested to enhance rotor performance features.Hence, to address the challenge of developing a model that resolves these problems, the purpose of this investigation was to determine how well a scaled-down version of a Savonius turbine performed in terms of power output using a wind tunnel.Subsequently, the effect of the blockage ratio produced in the wind tunnel during the chamber test on the scaled model was evaluated.This study discusses the influences of various modified configurations on the turbine blades' torque and power coefficients (Cp) at various tip speed ratios (TSRs) using threedimensional (3D) unsteady computational fluid dynamics.The findings showed that the scaled model successfully achieved tunnel blockage corrections, and the experimental results obtained can be used in order to estimate how the same turbine would perform in real conditions.Furthermore, numerically, the new models achieved improvements in Cp of 19.5%, 16.8%, and 12.2%, respectively, for the flow-guiding channel (FGC at  The new models had a lower pressure difference for the advancing blade than the benchmark model, and this increased the new blade profiles' Cp and C T relative to the benchmark profile.The pressure contour was lower for the concave parts and higher for the convex parts of almost all profiles; this created negative torque for the returning blade, reducing overall performance.However, this differential in pressure between the concave and convex portions of the newprofile blades was less than that in the benchmark profile.Consequently, the new-profile blades performed better than the benchmark profile.The pressure contour was lower for the concave parts and higher for the convex parts of almost all profiles; this created negative torque for the returning blade, reducing overall performance.However, this differential in pressure between the concave and convex portions of the new-profile blades was less than that in the benchmark profile.Consequently, the new-profile blades performed better than the benchmark profile.= 30 • model had the best performance with 0.263 for the Cp at a TSR of 1, which was a 19.5% improvement over the original model.This comprehensive evaluation of the new and modified wind turbines showed that the former achieved higher performance than the standard S-ORM turbine.

Conclusions
This study investigated the performance of a scaled rotor model of an original m (S-ORM) using three-dimensional (3D) ANSYS CFX and experimental w Furthermore, it examined the possibility of increasing the output power by chan wavy area positions and adding a flow-guiding channel (FGC) model.Note that the in step in validating the original 3D simulation method was to use numerical experimental data from the published literature.A comparison showed that the calcul results agreed well with the experimental ones.The main conclusions can be liste follows: 1.For comparative investigations, the performance of the benchmark S-ORM mod the basic Savonius wind turbine was calculated numerically; 2. The numerical analysis results and the respective values from the S-ORM m utilized in this work were validated using experimental data.In order to evaluat accuracy of the S-ORM numerical approach for the mesh and turbulent m employed in this study, the simulation results were compared with experime

Conclusions
This study investigated the performance of a scaled rotor model of an original model (S-ORM) using three-dimensional (3D) ANSYS CFX and experimental work.Furthermore, it examined the possibility of increasing the output power by changing wavy area positions and adding a flow-guiding channel (FGC) model.Note that the initial step in validating the original 3D simulation method was to use numerical and experimental data from the published literature.A comparison showed that the calculated results agreed well with the experimental ones.The main conclusions can be listed as follows: 1.For comparative investigations, the performance of the benchmark S-ORM model of the basic Savonius wind turbine was calculated numerically; 2. The numerical analysis results and the respective values from the S-ORM model utilized in this work were validated using experimental data.In order to evaluate the accuracy of the S-ORM numerical approach for the mesh and turbulent model employed in this study, the simulation results were compared with experimental data results for the S-ORM model, and the comparison was accepted; 3. The value of Cps was found to increase with further increases in the tip speed ratios

Conclusions
This study investigated the performance of a scaled rotor model of an original model (S-ORM) using three-dimensional (3D) ANSYS CFX and experimental work.Furthermore, it examined the possibility of increasing the output power by changing wavy area positions and adding a flow-guiding channel (FGC) model.Note that the initial step in validating the original 3D simulation method was to use numerical and experimental data from the published literature.A comparison showed that the calculated results agreed well with the experimental ones.The main conclusions can be listed as follows: 1.
For comparative investigations, the performance of the benchmark S-ORM model of the basic Savonius wind turbine was calculated numerically; 2.
The numerical analysis results and the respective values from the S-ORM model utilized in this work were validated using experimental data.In order to evaluate the accuracy of the S-ORM numerical approach for the mesh and turbulent model employed in this study, the simulation results were compared with experimental data results for the S-ORM model, and the comparison was accepted; 3. The value of Cps was found to increase with further increases in the tip speed ratios (TSRs) to 1.8 for all S-ORM configurations; 4.
Through analysis of the power coefficient variations, the best design configurations for the profiled blades were identified; 5.
It was thus calculated that the values of the power coefficient for the best three out of ten configurations, which were the named the flow-guiding channel (FGC) at

Figure 2 .
Figure 2. Flow chart detailing the procedure steps for the experiment and simulation in the study.Figure 2. Flow chart detailing the procedure steps for the experiment and simulation in the study.

Figure 2 .
Figure 2. Flow chart detailing the procedure steps for the experiment and simulation in the study.Figure 2. Flow chart detailing the procedure steps for the experiment and simulation in the study.
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Copyright: © 2022 by the authors.Submitted for possible open access publication under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/license s/by/4.0/).

Figure 4 .
Figure 4. Rotor cross-sections of benchmark model and modified profiles.Figure 4. Rotor cross-sections of benchmark model and modified profiles.

Figure 4 .
Figure 4. Rotor cross-sections of benchmark model and modified profiles.Figure 4. Rotor cross-sections of benchmark model and modified profiles.
turbine's power output was compared with the reference model in terms of Cp and C T .However, qualitative observations using smoke flow visualization at various wind speeds of turbulent flows were not undertaken in the region of the turbine model.

Figure 6 .
Figure 6.The configuration of the meshes on (a) the blades of the turbine, (b) the rotating domain, and (c) the stationary domain.

Figure 6 .
Figure 6.The configuration of the meshes on (a) the blades of the turbine, (b) the rotating domain, and (c) the stationary domain.

Figure 9 .
Figure 9. Torque variation against the accumulated time step.

Figure 9 .
Figure 9. Torque variation against the accumulated time step.

Figure 9 .
Figure 9. Torque variation against the accumulated time step.

Figure 10 .
Figure 10.Variations in the scaled CpS for the S-ORM, along with the original model.

Figure 10 .
Figure 10.Variations in the scaled Cp S for the S-ORM, along with the original model [48].

Figure 11 .
Figure 11.The variations in Cp with TSRs from 0.2 to 1.8.

Figure 12 .
Figure 12.The variations in CT with TSRs from 0.2 to 1.8.

Figure 11 .
Figure 11.The variations in Cp with TSRs from 0.2 to 1.8.

Figure 11 .
Figure 11.The variations in Cp with TSRs from 0.2 to 1.8.

Figure 12 .
Figure 12.The variations in CT with TSRs from 0.2 to 1.8.

Figure 12 .
Figure 12.The variations in C T with TSRs from 0.2 to 1.8.

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Figure 13 .
Figure 13.Cpmax values obtained from analysis of different blade profiles.

Figure 13 .
Figure 13.Cp max values obtained from analysis of different blade profiles.

5. 3 .
Velocity Contours for S-ORM, FGC at Energies 2022, 15, x FOR PEER REVIEW 16 of 24 addition of the FGC was a characteristic affecting the developing flow close to the entrance.This had an effect on the measured values.Section 5.3 discusses the Cpmax obtained for the best three blade profiles with the FGC at Ⴔ = 30°, WTE, and WCB models.

Figure 13 .
Figure 13.Cpmax values obtained from analysis of different blade profiles.
//creativecommons.org/license s/by/4.0/).= 30 • model ranged from 5 to 15.25 m/s for the advancing blade and from 2.5 to 7 m/s for the returning blade.The velocity of the WTE model varied from 5 to 14.25 m/s for the advancing blade and 3 to 8.25 m/s for the returning blade.The velocity of the WCB model varied from 5 to 14.25 m/s for the advancing blade and 1 to 7 m/s for the returning blade.

Figure 14 .
Figure 14.Velocity contours and diagrams for velocity distribution along the test section for TSR 1.

5. 4 .Figure 14 .
Figure15shows the pressure contours at 9 m/s wind speeds for the benchmark S-ORM model and the best three profile models.Due to flow separation, the pressure downstream of the advancing and returning blades was lower.For the upstream pressure,

5. 4 .
Pressure Contours for S-ORM, FGC at Energies 2022, 15, x FOR PEER REVIEW 16 of 24 addition of the FGC was a characteristic affecting the developing flow close to the entrance.This had an effect on the measured values.Section 5.3 discusses the Cpmax obtained for the best three blade profiles with the FGC at Ⴔ = 30°, WTE, and WCB models.

Figure 13 .
Figure 13.Cpmax values obtained from analysis of different blade profiles.

Ⴔ=
30°), wavy area at tip and end (WTE), and wavy area on the convex blade (WCB) models in comparison to the benchmark S-ORM model and under identical wind speed conditions.This Citation: Al-Gburi, K.A.H.; Al-quraishi, B.A.J.; Ismail Alnaimi, F.B.; Tan, E.S.; Al-Safi, A.H.S. Experimental and Simulation Investigation of Performance of a Scaled Model for a Rotor of a Savonius Wind Turbine.Energies 2022, 15, x.https://doi.org/10.3390/xxxxxAcademic Editors: Galih Bangga and Martin Otto Laver Hansen Received: 12 October 2022 Accepted: 18 November 2022 Published: 22 November 2022 Publisher's Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.
//creativecommons.org/license s/by/4.0/).= 300 model varied from 80 to −60 N/m 2 for the advancing blade and −60 to 0 N/m 2 for the returning blade.The pressure magnitude of the WTE model varied from 70 to −150 N/m 2 for the advancing blade and −150 to 10 N/m 2 for the returning blade.The pressure magnitude of the WCB model varied from 70 to −140 N/m 2 for the advancing blade and −140 to −10 N/m 2 for the returning blade.

Energies 2022 ,
15, x FOR PEER REVIEW 17 of 23the drag on the returning blade was observed to be greater.The drag force act on both of the turbine's blades; however, the drag acting on the blade that moves forward drives the turbine, while the drag acting on the blade that is moving backward restricts it.The distribution pressure varied along the models' test sections: for the benchmark model, from 80 to −160 N/m 2 for the advancing blade and −160 to 20 N/m 2 for the returning blade.The pressure magnitude of the FGC at Ⴔ = 300 model varied from 80 to −60 N/m 2 for the advancing blade and −60 to 0 N/m 2 for the returning blade.The pressure magnitude of the WTE model varied from 70 to −150 N/m 2 for the advancing blade and −150 to 10 N/m 2 for the returning blade.The pressure magnitude of the WCB model varied from 70 to −140 N/m 2 for the advancing blade and −140 to −10 N/m 2 for the returning blade.The new models had a lower pressure difference for the advancing blade than the benchmark model, and this increased the new blade profiles' Cp and CT relative to the benchmark profile.

Figure 16 .
Figure 16.Results of the simulation of the variations in the power coefficients of modified mo along with the S-ORM.

Figure 17 .
Figure 17.Results of the simulation of the variations in the torque coefficients of modified mo along with the S-ORM.

Figure 16 . 23 Figure 16 .
Figure 16.Results of the simulation of the variations in the power coefficients of modified models, along with the S-ORM.

Figure 17 .
Figure 17.Results of the simulation of the variations in the torque coefficients of modified models, along with the S-ORM.

Figure 17 .
Figure 17.Results of the simulation of the variations in the torque coefficients of modified models, along with the S-ORM.

Table 1 .
The grid independence statistics for the S-ORM model.

Table 2 .
Justification of the grid independence statistics.

Table 1 .
The grid independence statistics for the S-ORM model.