Wind tunnel tests of a two-bladed Savonius wind rotor with novel parabolic blades

Abstract

The study presents an experimental research on a vertical-axis Savonius wind rotor featuring optimized parabolic blades. This parabolic blade is developed by optimizing its sectional cut-angle through a series of numerical simulation. The parabolic-bladed Savonius rotor of various aspect ratios is tested in a low-speed wind tunnel to evaluate its power coefficient (C_P) along with its self-starting capability. For a direct comparison, the tests are also conducted for a rotor with the semicircular blades. The wind tunnel tests demonstrate the peak C_P of the parabolic and conventional semicircular bladed rotors to be 0.165 and 0.138, respectively at a tip-speed ratio of 0.67 and an aspect ratio of 0.9. The wind rotor with the parabolic blades shows an improvement of C_P by 19.56% against its conventional semicircular counterpart. With the inclusion of blockage correction, the test rotors with parabolic and semicircular blades show the C_P of 0.161 and 0.134, respectively.

Keywords

Wind rotor parabolic blades wind tunnel power coefficient tip speed ratio blockage correction

Introduction

Wind power is a vital renewable energy source crucial in addressing the global energy crisis (Akwa et al., 2012b; Alom and Saha, 2019b; Amano, 2017; Sarma et al., 2021). Wind turbines are machines designed to harness wind power and transform it into electrical energy. There are two primary types of wind turbines: horizontal-axis wind turbines (HAWTs) and vertical-axis wind turbines (VAWTs). HAWTs have their rotation axis aligned parallel to the direction of the wind, whereas VAWTs spin perpendicular to the wind flow (Alom and Saha, 2018; Golecha et al., 2012). The HAWTs are typically used in areas with higher energy demands and larger coverage but require a yaw mechanism and are not self-starting, unlike the VAWTs (Ghosh et al., 2009; Gupta and Biswas, 2011; Wong et al., 2017). There are on-shore and off-shore HAWTs designed for land and ocean wind power extraction, respectively. However, the HAWTs require extensive infrastructure for power distribution, and are often expensive. This type of turbines are less suitable for remote areas. During the last decade, the VAWTs such as Savonius and Darrieus rotors have gained immense interest due to their inherent advantages, including wind direction independence, reduced noise, easy installation and maintenance, and potential for domestic energy solutions (Al-Bahadly, 2009; Jain and Saha, 2020; Sarma et al., 2021). The drag-based Savonius rotor is notable for its structural simplicity, low initial torque requirement, and an efficiency of around 30% (Alom and Saha, 2018; Golecha et al., 2012; Mojola, 1985). Savonius rotors offer cost-effective power generation, especially for smaller and variable energy demands as compared to the Darrieus rotors.

Figure 1(a) illustrates a standard Savonius rotor with two blades, demonstrating the torque produced by its advancing and returning blades. The forces (lift and drag) acting on it, along with geometric parameters such as separation gap, overlap distance, and overlap ratio are shown in Figure 1(b).

Figure 1.

A typical Savonius rotor. (a) Front view and (b) Top view.

In recent decades, researchers have focused on enhancing the Savonius wind rotor designs through experimental (Altan and Atılgan, 2008; Ersoy and Yalcindag, 2014; Kamoji et al., 2009; Mahmoud et al., 2012), numerical (Agrawal et al., 2019; Fujisawa, 1992; Jaohindy et al., 2011; Kacprzak et al., 2013; Kalluvila and Sreejith, 2018; Mohan and Saha, 2021), and combined approaches (Alom and Saha, 2018; Mohamed et al., 2011; Mohan et al., 2023; Rahai and Hefazi, 2008; Świrydczuk and Doerffer, 2011; Zhou and Rempfer, 2013). Several studies have also been attempted to arrive at an efficient design using optimization algorithms (Akwa et al., 2012a; Chan et al., 2018; Das et al., 2018; Deb et al., 2002; Mari et al., 2017; Mohan et al., 2021). It is also evident from literatures that the design of newer blades can significantly improves the power coefficient (C_P) of a Savonius rotor. In this context, using the numerical analysis, a novel parabolic blade profile with superior performance has recently been developed (Mohan and Saha, 2023). Now, it has become essential to investigate the parabolic-bladed Savonius rotor experimentally in a wind tunnel to corroborate the findings of the numerical investigation. The ultimate purpose is to develop the prototype design for practical applications.

Research outline

As mentioned in previous research, the parabolic profile with a sectional cut angle (θ) of 32.5° proved promising for Savonius rotor blade design. The comprehensive findings of the numerical investigation were previously documented (Mohan and Saha, 2023). In the current study, wind tunnel experiments are performed on the rotor with parabolic blades to determine its C_P and starting torque. In this connection, several two-bladed rotors with θ ranging from 27.5° to 47.5° have been fabricated and tested. The road map of the study starting from the optimization method to the wind tunnel tests is outlined in Figure 2.

Figure 2.

The outline of the study.

Brief description of the parabolic blade development

The blade profile’s geometry is created using SOLIDWORKS, where the θ is defined by line AB concerning the x-axis on a parabolic curve. Line AB divides the parabola, forming an arc AOB. The point C, where line AB meets the y-axis, serves as a pivotal point for adjusting and optimizing the angle θ, representing AOB as one-half of the blade profile (Mohan and Saha, 2023).

As depicted in Figure 3, the parabolic curve in this study follows the equation x² = 4ay (Mohan and Saha, 2023). The chosen parabola has a focus (F = 0, 0) and a vertex point (O = 0, −2). Although only one parabola is arbitrarily chosen to create the blade profile, there are countless parabolic curves that could be optimized using an optimization algorithm. This research focuses on exploring a novel blade profile by selecting an arbitrary parabola with a specific θ. The standard parabolic equation with a vertex at (0, −2) and a directrix length of (a = 2) is represented by equation (2).

{(x - h)}^{2} = 4 a (y - k)

(1)

Figure 3.

Illustration of the sectional cut angle.

Therefore, the current equation for the parabola can be expressed as:

x^{2} = 8 y + 16

(2)

Additionally, line AB can be represented as:

y = - \tan θ \cdot x + l - 2

(3)

With l = 0.164D and taking into account that points A and B meet the criteria outlined in equations (2) and (3), the arc AOB can be expressed as a function of θ, as stated in equation (4).

x^{2} = 8 y + 16 (\frac{- 8 \tan θ - \sqrt{64 \tan^{2} θ + 1049.6}}{2} < x < \frac{- 8 \tan θ + \sqrt{64 \tan^{2} θ + 1049.6}}{2})

(4)

Geometric details of the tested blades

The top views of the tested blades with their geometric details are shown in Figure 4. The overlap distance (e) between the semicircular and parabolic blades is consistently maintained at 15% of the blade chord length, as previously described (Kalluvila and Sreejith, 2018; Mohan et al., 2021). In each scenario, the overall diameter (D) of the two-bladed rotor is fixed at 230 mm (Roy and Saha, 2015). Additionally, the blades are affixed to a central shaft with a diameter of 12 mm.

Figure 4.

Specifications of the blade profiles under examination. (a) Semicircular and (b) Parabolic.

Experimental setup

The newly designed rotors with parabolic blades were tested in a low-speed wind tunnel of the open test section type as shown in Figure 5. This wind tunnel developed by Grinspan et al. (2003, 2004) has been widely utilized by researchers in subsequent studies (Patel et al., 2024; Roy and Saha, 2015; Saha et al., 2008; Saha and Rajkumar, 2006). The tunnel comprises (a) a fan at the beginning to initiate airflow, (b) an inlet section directing the incoming air, (c) a diffuser section to decelerate and stabilize the airflow, (d) a settling chamber equipped with coarse and fine screens as well as a honeycomb structure to create a smooth flow, (e) a nozzle accelerating the airflow, and (f) an open test section housing the tested object and various instruments. The airflow in the tunnel is generated by an axial fan powered by a 0.5 HP motor. A voltage regulator controls the fan, allowing adjustment of the airspeed within the range of 0–10 m/s. The open test section is located at the wind tunnel nozzle’s exit, which has a square cross-section of 500 mm × 500 mm. The turbine models are positioned 250 mm away from the wind tunnel exit (Alom and Saha, 2018; Rajkumar and Saha, 2006; Roy and Saha, 2015).

Figure 5.

Schematic diagram of the wind tunnel.

The test section is constructed using mild steel angles measuring 50 mm × 50 mm × 4 mm, while the peripheral components of the wind tunnel are made from galvanized iron (GI) sheet with a thickness of 1.6 mm. Inside the test section, there are two bearing houses placed at different heights to allow sufficient room for the rotation of the turbine blade. These bearing houses contain an aluminum shaft with a diameter of 12 mm and are equipped with two nylon material bushes. The turbine is attached to the shaft using nuts and bolts, positioned at the shaft’s center, allowing it to rotate in tandem with the turbine blades. Additionally, the test section features a mass balance holder to which two spring mass balances are affixed. The difference in the readings of these mass balances provides an accurate measurement of the load applied to the turbine.

Fabrication of the turbine blades

The rotors consisting of parabolic (θ = 32.5°) and semicircular blades used in this study are manufactured using 0.5 mm thick (GI sheets). In each case, the AR of the blades is varied from 0.6 to 1.1. The material used for the fabrication of the blade is strong enough to withstand the wind flow ranging from 0 to 10 m/s. The various blades manufactured are shown in Figure 6.

Figure 6.

Fabricated blades of the test rotors. (a) Parabolic blades and (b) semicircular blades.

Measurement procedure

The wind speed is measured using a digital anemometer (Figure 7), that operates within a range of 0–20 m/s and provides an accuracy of ±2%. This device detects the wind velocity by recognizing changes in a fluid’s physical properties or the fluid’s impact on a mechanical device submerged in it.

Figure 7.

The digital anemometer.

The voltmeter is supplied with input voltage ranging from 150 to 220 V, and the corresponding speed is measured using a digital anemometer (Table 1). It is important to note that the wind speed remains relatively consistent within the 250 × 250 mm² area around the center. However, there is an increase in speed toward the corners, attributed to the influence of the nozzle section. Hence, considering this variation, the average wind speed is calculated from multiple positions across the test section to get the area weighted average velocity. This is to maintain the flow uniformity across the turbine model. The turbulence intensity at the upstream and at the downstream of the rotor is estimated to be 1% (Alom and Saha, 2019; Grinspan et al., 2004; Patel et al., 2024; Saha and Rajkumar, 2006).

Table 1.

Wind speed measured at various voltage inputs.

Fan input voltage (volts)	Wind speed (m/s)
150	3.5
160	4.3
170	5.4
180	6.2
190	7.1
200	7.5
210	8
220	8.5

The torque measurement is accomplished by imposing a load on the rotor through spring balances. A spool is connected to the rotor’s shaft, and a rope passes around it, connecting to two mass balances as shown in Figure 8. The rotational speed of the shaft is controlled by applying load through the spring balances to achieve the desired speed. As the shaft starts rotating, one part of the spring balance becomes tight while the other remains slack as depicted in Figure 9. The disparity in their readings indicates the operational load on the shaft. To measure the rotor’s rotational speed, a digital tachometer as shown in Figure 10 with a range of 0–50,000 rpm and an accuracy of ±1.0% is employed.

Figure 8.

The torque measuring unit.

Figure 9.

Tight and slack sides of the rope.

Figure 10.

The tachometer.

To attain the desired rotational speed, the load on the shaft is adjusted, and measurements from the mass balance are recorded (M_t and M_s). The output torque (T_o) is then calculated as follows:

T_{o} = (M t - M s) \times g \times R p

(5)

where M_t and M_s are mass on tight and slack sides, g is the gravitational acceleration and R_p is the radius of the pulley.

The total input torque (T_i) to the system is calculated as:

T_{i} = 0 . (5) {ρ A V}^{2} L

(6)

Here, ρ represents the air density, A denotes the frontal area (calculated as D × H), V stands for the inlet air velocity, and R represents the radius of the turbine blade. Using the aforementioned equations, the torque coefficient (C_T) is calculated as:

C_{T} = \frac{T o}{T i} = ((M_{t} - M_{s}) \times g \times R_{p}) / 0.5 {ρ A V}^{2} L

(7)

The power coefficient (C_P) is then calculated by using equation (8):

C_{P} = C_{T} \times T S R

(8)

Error analysis

In a given experiment, it is not possible to get the exact value of the readings every time. The readings keep on changing when they are taken repetitively. Thus, the mean value is calculated to get the final result. It is therefore necessary to make an error analysis in such a way that the fluctuations can be understood to get the accuracy of the experimental results. For this, the standard deviation as given by an expression (Holman, 2004; Roy and Saha, 2015) is used.

The uncertainties in the experiment can be estimated using the sequential perturbation technique (Kline, 1985; Moffat, 1982), revealing values of 4.5%, 4.8%, and 2.9% for C_P, C_T, and T, respectively.

σ = \sqrt \frac{1}{J} \sum_{i = 1}^{J} (x_{i} - m)^{2} \times 100 %

(9)

In the given equations, σ represents the standard deviation, J indicates the number of data points, m represents the mean value, and x denotes the measured value. Several data points are gathered for a particular load and shaft speed. The error analysis was conducted for both the parabolic-bladed and semicircular-bladed rotors at an inlet air speed of 7 m/s. According to the analysis, the percentage deviation for the parabolic-bladed rotor was determined to be 4.5% (Figure 11), whereas for the semicircular-bladed rotor, it was approximately 4% (Figure 12).

Figure 11.

Standard deviation of C_T at various TSRs.

Figure 12.

Standard deviation of C_P at various TSRs.

Results and discussion

This section deals with the effect of AR, dynamic and static performance analysis, and the blockage effect.

Effect of aspect ratio (AR)

The aspect ratio (AR = H/D) is an important geometric parameter of a Savonius rotor. The literature reveals that with an increase in AR the moment and the inertia of the rotor get decreased, but angular acceleration increases. A higher AR rotor blade is desired at higher wind speeds. Thus, the variation of AR (0.6–1.1) study is done in this section to get the optimum AR in terms of C_P_max the wind tunnel experiment shows that the parabolic blade outperformed the conventional semicircular blade throughout the range of AR (Figure 13). Moreover, the C_P goes on decreasing while moving from AR = 0.9. Thus, the optimum AR = 0.9 is chosen for further progression of the present study. Table 2 represents a brief comparison of present AR study and the AR from the literatures.

Figure 13.

Changes in C_P concerning different AR.

Table 2.

Comparison of present optimum AR with the published work.

Investigators	V (m/s)	AR	C_P _max
Grinspan et al. (2004)	6–11	1.83	0.12
Kamoji et al. (2009)	6–7	0.88	0.21
Alom and Saha (2018)	6.2	0.7	0.19
Present study (2024)	5–8	0.9	0.16

Dynamic performance analysis

The dynamic performance assessment involves evaluating the C_T and C_P of the parabolic-bladed rotor. For a direct comparison, the dynamic performance of the semicircular-bladed rotor has also been assessed. Wind tunnel tests were conducted at an air speed of 7 m/s. Figure 14 illustrates how C_T and C_P vary with TSR for the tested rotors.

Figure 14.

Performance coefficients obtained by wind tunnel experiment. (a) C_T versus TSR and (b) C_P versus TSR.

The parabolic-bladed rotor (AR = 0.9) achieves a maximum power coefficient (C_P_max) of 0.165 at TSR = 0.7, while the semicircular-bladed rotor at the same AR exhibits a C_P_max of 0.138 at TSR = 0.69. This indicates a notable 19.56% performance improvement of the parabolic-bladed rotor over its semicircular counterpart. This enhancement is attributed to the accelerated flow in the overlap region, generating an additional force on the concave side of the returning blade.

It is evident that the C_T value decreases with increasing TSR due to gradual loads on the turbine shaft reducing rotational speed. Conversely, the C_P rises with higher TSR values and reaches a peak beyond which it decreases. The superior performance of the parabolic-bladed rotor is due to its straight blade trailing edge and a higher radius of curvature at the leading edge compared to the semicircular-bladed rotor. This results in higher pressure drag. The parabolic-bladed rotor having a straight trailing edge on the returning blade guides the flow whereby the rotor’s moment increases. Additionally, the straight leading edge delays the flow separation, enhancing the pressure recovery. This reduces the negative torque, and increases the rotor C_P.

Figures 15 to 20 illustrate the variations in C_T and C_P for both rotors at different air speeds (V = 5, 6, and 8 m/s). In all the cases, the parabolic-bladed rotor outperforms its semicircular counterpart. Table 3 compares the C_P_max values of the tested rotors. From the data, it is seen that the parabolic-bladed rotor consistently achieves the C_P_max values in the range of TSR = 0.68−0.73, whereas the semicircular-bladed rotor the C_P_max falls in the range of 0.67–0.74. Table 3 demonstrates the impact of air speed (V) on the dynamic performance of the newly developed parabolic-bladed rotor.

Figure 15.

Fluctuation of C_T with TSR at V = 5 m/s.

Figure 16.

Fluctuation of C_P with TSR at V = 5 m/s.

Figure 17.

Fluctuation of C_T with TSR at V = 6 m/s.

Figure 18.

Fluctuation of C_P with TSR at V = 6 m/s.

Figure 19.

Fluctuation of C_T with TSR at V = 8 m/s.

Figure 20.

Fluctuation of C_P with TSR at V = 8 m/s.

Table 3.

Maximum power coefficients corresponding to TSR.

Rotor blades	V = 5 m/s		V = 6 m/s		V = 7 m/s		V = 8 m/s
Rotor blades	C_P _max	TSR	C_P _max	TSR	C_P _max	TSR	C_P _max	TSR
Parabolic	0.139	0.73	0.154	0.68	0.165	0.70	0.152	0.71
Semicircular	0.108	0.70	0.133	0.67	0.138	0.69	0.127	0.74

Static performance analysis

The static torque (C_Ts) is a measure of the rotor’s self-starting capability. Figure 21 displays the variation of C_Ts at different angles of attack (α). The α represents the angle between the chord of the advancing blade and the wind flow direction (Figure 1). The starting capabilities of both the parabolic and semicircular-bladed rotors were assessed at V = 7 m/s. The parabolic design exhibited superior C_Ts across the entire range of α. For the semicircular-bladed rotor, lower C_Ts were observed between α = 125°−180° and α = 290°−350° due to negative pressure on the returning blade, hindering its self-starting. However, the self-rotation occurred between α = 30°−60° and 210°−240°, representing its optimal starting range. At α = 30° and 160°, the semicircular-bladed rotor exhibited C_Ts of 0.27 and −0.16, respectively. In contrast, the parabolic-bladed rotor displayed higher C_Ts within the α range, demonstrating its enhanced self-starting ability. At α = 220° and 162°, the parabolic-bladed rotor achieved maximum and minimum C_Ts of 0.35 and −0.133, respectively, indicating a 29.6% increase in its maximum C_Ts compared to the semicircular design.

Figure 21.

Fluctuation of static C_Ts at various α.

Blockage effect

In experimental studies, accounting for the blockage effect is vital, as emphasized in previous researches (Abraham et al., 2012; Plourde et al., 2012). The blockage correction factor (f) relies on the type of wind tunnel test section and the blockage ratio (BR). The BR indicates the ratio of turbine blade area to test section area. Traditionally, the blockage correction has extensively been investigated for closed test sections (Akwa et al., 2012a; Biswas et al., 2007; Chen and Liou, 2011). However, the relationships established for the closed test sections do not apply to those of open test sections (Roy and Saha, 2015). To bridge this gap, Roy and Saha (2014) introduced a new relationship for the blockage correction specifically tailored to wind tunnel experiments of Savonius rotors in open test sections. This f is crucial for adjusting the measured parameters such as wind velocity (V), applied mechanical load (F) on the turbine, and turbine rotational speed (N). These variables are expressed by the following equations (Alom and Saha, 2018; Roy and Saha, 2014).

V^{*} = V (1 - \frac{1}{5} f)

(10)

F^{*} = F (1 - f)

(11)

N^{*} = N (1 - f)

(12)

In these equations, V*, F*, and N* denote the blockage-corrected values. The f is determined by using TSR and BR. By applying these equations, a suitable f ranging from 4% to 9% was applied, corresponding to various TSR and BR values of 21.16% (Roy and Saha, 2014). After applying the blockage correction, the C_P_max values for the parabolic- and semicircular-bladed rotors were determined to be 0.161 and 0.134, respectively (Figures 22 and 23).

Figure 22.

Blockage corrected C_T with TSR.

Figure 23.

Blockage corrected C_P with TSR.

Concluding remarks

The performance analysis of a newly developed parabolic-bladed rotor was conducted focusing on its C_P_max at various AR, TSR, and V. To have a direct comparison, a semicircular-bladed rotor was also tested under identical condition. It was observed that specifically at AR = 0.9, TSR of 0.67, and V = 7 m/s, the parabolic-bladed rotor exhibited a C_P_max of 0.165, while the semicircular-bladed rotor showed a C_P_max of 0.138. This indicates a 19.56% improvement in C_P for the parabolic-bladed rotor over the semicircular counterpart.

Additionally, the study delved into the static torque performance of the parabolic-bladed rotor. The parabolic-bladed rotor exhibited higher C_Ts values and superior self-starting capabilities, ranging from 0.35 to −0.133, at α = 220° and 162°. The semicircular-bladed rotor, on the other hand, displayed C_Ts values ranging from 0.27 to −0.16. Thus, the parabolic-bladed rotor demonstrated a 29.6% enhancement in C_Ts values.

With the blockage correction, the parabolic-bladed rotor achieved a C_P of 0.161, surpassing the semicircular-bladed rotor’s C_P of 0.134. The physical attributes of the newly developed parabolic-bladed rotor featuring a straight trailing edge and a higher radius of curvature at the leading edge contributes to the increased pressure drag. Notably, this higher pressure drag was more pronounced on the advancing side of the parabolic-bladed rotor compared to the semicircular rotor.

It is worth noting that this study focused on the static and dynamic performances of the newly developed parabolic-blade rotor in a wind tunnel without utilizing the end plates, augmented techniques, or multi-staging. Future research could explore the performance of the parabolic rotor with the incorporation of these advanced approaches.

Footnotes

Appendix

Acknowledgements

During the period of this study, the scholarship extended to the first author by the Indian Institute of Technology Guwahati, India, is gratefully acknowledged. The authors express their sincere thanks to Dr. Nur Alom, Assistant Professor, Department of Mechanical Engineering, National Institute of Technology Meghalaya, Shillong, India, for providing some technical suggestions.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Ujjwal K. Saha

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