The effect of blade turning angle on rotation improvement of a small horizontal axis wind turbine

Abstract

Optimization of wind turbine aerodynamic performances implies solving the problem in the domains such as airfoil selection, blade rotation angle, chord optimization, number of blades, appropriate tip speed ratio, etc. The current paper studies the effect of blade rotation angle $(β = 5, 7, 10 °)$ on power coefficient $(C_{P})$ , torque $(T)$ and mechanical power $(P_{M})$ in a small horizontal axis wind turbine (HAWT). The analysis involves two models of blades (V and) of the airfoil class SD 7003. The first part of the paper employs numerical analysis, that is, Ansys CFX and Ansys Fluent software packages, to define wind turbine characteristics. The obtained results indicate that as the rotation angle $(β)$ increases the $C_{P}$ increases within an appropriate range of tip speed ratio $(λ)$ change. The second part describes experimental investigation conducted on considered HAWT to define the values of $T$ and $P_{M}$ for studied blade rotation angles and comparison with the values obtained from Ansys. Existing differences in values are a consequence of the design of the HAWT, that is, the influence of the mass moment of inertia of the rotor and generator as well as the placement of the generator. Experimental setup and methodology allow for investigating the effect of different blade models, rotor and generator structure on wind turbine torque and mechanical power output characteristic.

Keywords

Wind turbine blades performance

Literature review

Installing large-scale wind turbines is, among other things, associated with investments related to large capital costs as well as the possibility of connecting to the electricity grid. Recently, small wind turbines have appeared as an alternative, especially considering rural areas off the grid and that the average wind speed at heights of about $10 m$ above the ground rarely exceeds $\frac{6 m}{\sec}$ , which is far below the optimal wind speeds of large wind turbines. Efficient small wind turbines should therefore be specifically designed for wind speeds at small heights and small Reynolds numbers.

One possible solution trend for lower-cost renewable energy production is the development and implementation of compact, small-scale wind turbines. But because of factors—high-intensity turbulence, low wind speed and decreased flexibility to changes in wind direction, and perception of possibly high aerodynamic noise levels from the turbines—the usage of small wind turbines in densely populated suburban areas is still relatively limited. Today, there are several research orientations in the field of small wind turbines (SWTs), from the use of contemporary software packages, model wind tunnel testing and laboratory testing, and all this to find the best solution for optimization and performance improvement for small wind turbines. A lot of investigative work has been performed on SWTs, and some of the most representative studies are listed below.

Schmitz theory is used by Al-Abadi et al.¹ in their work to produce a preliminary blade design. The forces, torque, and power extracted by the turbine are computed using the Blade Element - Momentum (BEM) theory. Only the chord and pitch angle distribution are included in the shape optimization because the airfoil form (NREL S809) stays the same. Wind speeds and rotational speeds are limited to those that can be achieved in the wind tunnel and by the generator. Following the identification of the ideal blade shape with the highest $C_{P}$ within the specified parameter range, the turbine $C_{P}$ is assessed at wind speeds that deviate from the ideal operating state.

Akbari et al.² conducted a multi-objective optimization study to analyze the performance of 10 low Reynolds number airfoils, BW-3, E387, FX 63-137, S822, S834, SD7062, SG6040, SG6043, SG6051, and USNPS4, in a 1 kW wind turbine with regard to the power coefficient and the startup time. The power coefficient and startup time were calculated using the blade element momentum technique, and the optimization was completed using the differential evolution algorithm. The BEM model and computational fluid dynamics (CFD) are the most often used models for forecasting HAWT and VAWT performances. While the lift-to-drag force operating on the turbine blade can be directly calculated with CFD, the BEM model is the outcome of an integral analysis of the wind turbine.

In order to examine its impact on the power coefficient $C_{P}$ , rotor shaft torque, power extracted by the wind turbine, and rotor speed of the wind turbine, Kumar and Baredar³ performed numerical simulations on a HAWT model with various solidities. For two to six blades, a tiny HAWT model’s solidity was investigated. A computational approach for the best aerodynamic blade design is presented by Chaudhary et al.⁴BEM theory was applied to the analysis of the wind turbine rotor. According to the modeling results, the turbine rotates with a smoothly increasing torque for the first 10 s before gaining a constant torque and angular velocity, which is positive because it means that the mechanical vibrations of the system are reduced.

Khan et al.⁵ describes the initial behavior of small horizontal axis wind turbines with low Reynolds numbers and high angles of attack.

The effects of having three or five blades on the dynamic torque, acceleration, and power output of a small horizontal-axis wind turbine are experimentally investigated by Porto et al.⁶ The technique utilized to compute the aerodynamic torque produced by the blades during their acceleration stage is presented by the authors.

Sahu and Rathore⁷ investigated how low wind conditions affected the torque calculations on 1.5 MW horizontal axes. ANSYS 15.0 was used to apply the interaction analysis method for this fluid structure investigation. The wind’s effect on loading is computed throughout the blade using the Fluent module.

With a fixed pitch blade Darrieus type VAWT, Loya et al.⁸ used numerical simulation to study the torque dependency on airfoil geometry.

The impact of offsetting pitching angles and blade counts on the effectiveness of wind-induced rotations VAWT was investigated by Sun et al.⁹

The suitability of the CFD model for exploratory analysis was demonstrated by Nguyen et al.,¹⁰ who also discovered an optimized design that adopted a pitch angle of +20 instead of the zero-referenced pitch angle and provided a 2.3% higher power coefficient.

Wang et al.¹¹ analyze SWTs for the Internet of Things (IoT) applications providing an extensive overview of their development, including wind energy rectifiers, power generation mechanisms and IoT applications.

An overview of current developments in modeling and regulating wind power producing systems was given by Young-duan Song et al.¹² Their main goals were to maximize power capture, protect the system with safety systems, and minimize load impacts in order to optimize wind turbine operating throughout three essential modes. The success of this strategy, however, was largely dependent on precise understanding of machine parameters, such as rotor and stator resistances and inductances. Direct torque control (DTC) is an alternative technique for managing machine torque and flux. The authors’ goals were to provide an update on the most recent advancements in sophisticated wind turbine control and to stimulate additional study in the area.

Pitch angle control is a method suggested by Sreenivas et al.¹³ and Antonysamy and Joo¹⁴ for regulating wind turbine torque in response to varying wind conditions.

Yilmaz¹⁵ used a custom blade element momentum method that accounted for the effect of aerodynamic coefficients on Reynolds number and showed good agreement with experimental findings.

VAWT design and optimization process was proposed by Kumar et al.,¹⁶ Huang et al.,¹⁷ and Farhoody et al.,¹⁸ using CFD simulations and BEM calculations. Svorcan et al.¹⁹ achieved optimization by combining the created neural networks with the genetic algorithm.

Pitch angle’s impact on HAWT operating performances was investigated by Sudhamshu et al.²⁰ using the commercial CFD code Fluent; Roul and Kumar,²¹ using the commercial software Ansys 15; and Jeong et al.,²² using BEM in conjunction with the ABAQUS standard program.

Using numerical simulation of HAWT with untwisted blades, Thumthae and Chitsomboon²³ and Wibowo et al.²⁴ identified the ideal angle of attack that produces the maximum output power.

Cai et al.²⁵ analize the impact of blade rotation on the aerodynamic force of the tower for a range of wind speeds and yaw angles.

From the listed references, it is also apparent that apart from numerical simulation, optimization of the wind turbine design process requires experimental investigation including the wind tunnel.

This paper investigates the effect of blade rotation angle in a small wind turbine HAWT on the torque and mechanical power. Two models of wind turbine blades are analyzed. The first part of the paper employs numerical analysis, that is, Ansys CFX and Ansys Fluent software packages, in order to determine the wind turbine aerodynamic characteristics. In the second part, experimental measurements of the torque are performed at appropriate number of generator revolutions with and without loading, and comparison is done with the results obtained from numerical analysis. Box Wilson’s plan of experiments is used for the experimental part.²⁶

Even in situations when these parameters are entirely unknown, Movahhed Neya et al.²⁷ suggest a disturbance observer-based controller designed to maximize power extraction from a wind turbine system. In order to estimate nonlinear terms resulting from unknown model parameters and an unknown control coefficient, the controller integrates a disturbance observer. It accomplishes this by estimating the nonlinear disturbances only from tracking error feedback. Unlike other research, the authors of this work make the assumption that the parameters of the drive-train model and the aerodynamic model are both completely unknown.

Numerical analysis

Evaluation of aerodynamic performances was carried out using software packages Ansys CFX and Ansys Fluent. Both CFX and Fluent employ the finite volume method to solve the equations that describe fluid flow. Variable values such as mass, energy or moment are calculated in control volumes that make up the computational grid.

In the case of the finite volume method for discretization, CFX uses the vertex-centered method,²⁸ whereas CFD uses the cell-centered method.²⁹ Outputs from the computations may include generated aerodynamic forces, torque, power, pressure distributions along the blades, wakes detaching from blade tips, etc.

The analysis included two blade models of the manufacturer ‘Marsrock’: V-Blades length 65 cm and M-Blades length 58 cm, airfoil class SD 7003, Figure 1. These blades were taken for testing, because they are made exclusively for wind turbines of small dimensions, and as such they have a special airfoil (SD 7003) and twist angle.

Figure 1.

Physical (a) and CAD model (b) of a blade.

The two blades are additionally compared by contrasting their basic geometric features (relative chord and twist angle) at three characteristic cross-sections (corresponding to 25%, 50%, and 75% blade span/length), and these values are listed in Table 1.

Table 1.

Values of chord and twist angles along the blades.

%	c/R		$θ$ (°)
	V	M	V	M
25	0.1538	0.1388	9.27	9.54
50	0.1067	0.0948	15.22	14.39
75	0.0743	0.0632	16.92	14.64

It can be observed that apart from having higher solidity, blade V is also slightly more curved, and their effect on wind turbine output characteristics will be shown by numerical analysis and experimental investigations.

Numerical analysis employed CFX and Fluent, transport equations, that is, the system of equations with the $SST k - ω$ turbulence model. The $SST k - ω$ turbulence model was used because it exhibits small dependence on the manner of grid structuring in the walls zone. The hybrid grid proved to be somewhat better in terms of defining the wind turbine performances.

Figures 2 to 5 show change of the power coefficient $C_{P}$ in wind turbine with blades V and M at appropriate turning pitch angle $(β)$ .

Figure 2.

Change of power coefficient ( $C_{P}$ ) in the function of the tip speed ratio (λ) for blade V pitch angles.

Figure 3.

Change of power coefficient ( $C_{P}$ ) in the function of the number of revolutions (n) for blade V pitch angles.

Figure 4.

Change of power coefficient ( $C_{P}$ ) in the function of the tip speed ratio (λ) for blade M pitch angles.

Figure 5.

Change of power coefficient ( $C_{P}$ ) in the function of the number of revolutions (n) for blade M pitch angles.

Wind turbine mechanical power can be determined via the momentum that causes rotary motion and angular velocities:

P [W] = T [N m] \cdot ω [r a d / s]

(1)

For a specified wind speed of $\frac{10 m}{s}$ , using software package Ansys CFX allows to define the momentum values for the appropriate number of revolutions (n) and considered blades turning angles $(β)$ , the values are given in Tables 2 and 3.

Table 2.

Values of the moment with blades V as a function of (n) and β.

V	T (Nm)
n $(RPM)$	$β = 0 °$	$β = 5 °$	$β = 7 °$	$β = 10 °$
100	0.4288	0.7579	0.8815	1.0798
200	0.6100	1.0406	1.1907	1.4124
300	0.8042	1.4189	1.6361	1.9751
400	1.1134	2.0138	2.3380	2.8234
500	1.5958	2.7635	3.0854	3.1355
600	2.2078	3.3947	3.5419	3.8547

Table 3.

Values of the moment with blades M as a function of (n) and (β).

M	T (Nm)
n $(RPM)$	$β = 0 °$	$β = 5 °$	$β = 7 °$	$β = 10 °$
100	0.4012	0.5636	0.6177	0.8156
250	0.5814	0.7922	0.7393	0.9424
400	0.9804	1.1609	1.0200	0.9780
500	1.2273	1.1649	0.9828	0.5948

Using equation (1) the wind turbine mechanical power was determined and diagrams of change are shown in Figures 6 and 7.

Figure 6.

Change of the wind turbine mechanical power ( $P_{M}$ ) in the function of the number of revolutions (n) for V blade.

Figure 7.

Change of the wind turbine mechanical power ( $P_{M}$ ) in the function of the number of revolutions (n) for M blade.

Experimental setup

Experimental part of the investigation involved torque measurements on a HAWT model with considered blades at appropriate angle $(β)$ values, and numbers of revolutions of the generator shaft $(n)$ . Figure 8 shows the wind turbine model with the accompanying measuring equipment.

Figure 8.

HAWT model (a) and schematic representation of measuring equipment (b).

A wind turbine consists of the electric motor, two couplings, torque sensor, three-phase a synchronous generator, frequency regulator, laser tachometer for RPM, and voltage measuring device. A synchronous generator with permanent magnets (model Logihitech, 48 V) of 300 W nominal power and max operating number of revolutions $n = 600 RPM$ was used. A generator is of disk structure with the rotor formed by surface mounted NdFeB magnets and the stator is formed by a lamellar magnetic core around which toroidal windings are arranged to obtain a three-phase voltage. The torque was measured using a rotating dynamometer - Torque sensor (model WTQ-1050E 5 Nm). Simulation of the wind turbine work was performed using a three-phase asynchronous motor with one pair of poles (model Y2-90L-4, power 1.5 KW and maximum $n = 1400 RPM$ ) and a frequency regulator (model EDS800-4T0022, power 2.2 kW, inverter 380 V) which has the role of regulating the output voltage signal whose frequency is proportional to the angular velocity of the motor shaft controlled by LabVIEW software. Power control of the inverter can be performed using a potentiometer, by means of a voltage input and by means of a digital PWM signal (12–24 V). Considering that the so-called slip effect occurs in electric motors, a real number of revolutions was measured with a laser non-contact tachometer (model DT-2234C, range $2 - 2000 RPM$ ). Generator loading was carried out using thermogenic resistors, of the 48 V/100 W characteristics, connected in a triangle and connected to the generator, and for measuring the voltage and Measuring the torque, apart from a dynamometer, employed a measuring amplifier KWS 3082-A, from the company HBM (Hottinger Baldwin Meβtechnik) with the modules: measuring amplifier 5 kHz KWS 82, analog indicator AE 02 A and automatic balancing device TA3544. The output voltage analog signal from KWS goes to the input module NI 9215 (with a programmable voltage range ±10 V, a 16 bit resolution and maximum sampling rate 100 $\frac{k S}{s}$ ) of a converter NI CompactDAQ USB cDAQ-9174 for A/D conversion. Data acquisition: testing, measuring, control and analysis was performed using program package LabView. On the rotor head the possibility is provided for blades turning by the appropriate angle $(β)$ .

Measurement results

In the first part of testing, the generator was not loaded with a resistor, except for the internal resistance of the generator of 3.9 Ω. Figures 9 and 10 show measurement results for the torque on the generator shaft in the function of a specified number of revolutions $(n)$ at appropriate blades V and M turning angle.

Figure 9.

Change of the torque in the function of the number of revolutions for appropriate blade V pitch angles.

Figure 10.

Change of the torque in the function of the number of revolutions for appropriate blade M pitch angles.

In the second part, the generator was loaded with three resistors connected in a triangle with a 22.9 Ω resistance. The measured resistance of the load resistors in the wind tunnel is 22.7 Ω, while the calculated value is 23.03 Ω. The difference comes from the positive temperature coefficient of the resistors used. The value of 22.9 Ω was adopted for the calculation due to the expected temperature of the resistor during the dissipation of the power obtained from the generator. Tables 4 and 5 present the results of torque measurements, and Tables 6 and 7 appropriate values of the mechanical power.

Table 4.

Torque moment at 22.9 Ω for blade V.

n (RPM)	Torque moment $T (Nm)$
	Pitch angle $β (°)$ for blade V
	0	5	7	10
23	0.266	0.268	0.279	0.281
50	0.520	0.532	0.539	0.550
66	0.633	0.664	0.696	0.722
100	0.985	1.007	1.018	1.033
129	1.240	1.257	1.309	1.347
150	1.458	1.464	1.495	1.540
192	1.880	1.944	2.023	2.056

Table 5.

Generator power at 22.9 Ω for blade V.

n (RPM)	Generator power $P_{M} (W)$
	Pitch angle $β (°)$ for blade V
	0	5	7	10
23	0.641	0.646	0.671	0.677
50	2.725	2.788	2.823	2.881
66	4.377	4.586	4.809	4.987
100	10.313	10.546	10.665	10.820
129	16.749	16.987	17.688	18.203
150	22.897	22.999	23.483	24.185
192	37.793	39.093	40.668	41.337

Table 6.

Torque moment at 22.9 Ω for blade M.

n (RPM)	Torque moment $T (Nm)$
	Pitch angle $β (°)$ for blade M
	0	5	7	10
27	0.288	0.289	0.303	0.305
50	0.514	0.521	0.525	0.536
64	0.640	0.651	0.681	0.702
100	0.950	0.974	0.987	1.007
154	1.555	1.578	1.585	1.624

Table 7.

Generator power at 22.9 Ω for blade M.

n (RPM)	Generator power $P_{M} (W)$
	Pitch angle $β (°)$ for blade M
	0	5	7	10
27	0.815	0.817	0.857	0.862
50	2.690	2.730	2.751	2.804
64	4.287	4.366	4.562	4.702
100	9.953	10.200	10.341	10.541
154	25.074	25.448	25.559	26.195

Figures 11 and 12 display diagrams of change in the mechanical power on the generator with blades (V and M) in the function of $(β)$ and $(n)$ .

Figure 11.

Change of mechanical power on the generator with blade (V) in the function of ( $β$ ) and (n) for 22.9 Ω.

Figure 12.

Change of mechanical power on the generator with blade (M) in the function of ( $β$ ) and (n) for 22.9 Ω.

In order to determine the character of change in the torque and mechanical power, regression analysis was performed using DataFit software package and polynomial regression model $Y = a + b \cdot X_{1} + c \cdot X_{2} + d \cdot {X_{1}}^{2} + e \cdot {X_{2}}^{2} + f \cdot X_{1} \cdot X_{2} + g \cdot {X_{1}}^{3} + h \cdot {X_{2}}^{3} + i \cdot X_{1} \cdot {X_{2}}^{2} + j \cdot {X_{1}}^{2} \cdot X_{2}$ , where $Y$ are output power values $P_{M}$ on the generator, and $X_{1} and X_{2}$ are values of the number of revolutions $n$ and rotation angle $β$ . The model consists of linear, quadratic, cubic, and mixed-interaction terms, making it very flexible for modeling complex relationships between variables. Values of the terms for both variables are given in Table 8.

Table 8.

The parameters of the polynomial regression model.

Blade	a	b	c	d	e	f	g	h	i	j
V	−0.721	0.04	−0.206	0.0005	0.0717	−0.002	0.000001	−0.004	0.000078	0.000015
M	−0.738	0.04	0.006	0.0002	−0.003	0.0001	0.000003	0.00005	0.000068	0.0000001

It can be seen from the Table 8 that coefficients $d, g, h, i and j$ have very low levels so that they can be neglected. Based on obtained coefficients, the models of change in blades mechanical power are given in the form:

\begin{matrix} {(P_{M})}_{V} = - 0.721 + 0.04 \cdot X_{1} - 0.206 \cdot X_{2} \\ + 0.0717 \cdot X_{2}^{2} - 0.002 \cdot X_{1} \cdot X_{2} \end{matrix}

\begin{matrix} {(P_{M})}_{M} = - 0.738 + 0.04 \cdot X_{1} + 0.006 \cdot X_{2} \\ - 0.003 \cdot X_{2}^{2} + 0.0001 \cdot X_{1} \cdot X_{2} \end{matrix}

Figures 13 and 14 show the character of change in the mechanical power and it is evident from them that change is not linear.

Figure 13.

Diagram of change in $P_{M}$ as a function of n and β obtained by regression analysis for blade V.

Figure 14.

Diagram of change in $P_{M}$ as a function of n and β obtained by regression analysis for blade M.

Based on the values from the table, it can be concluded that the character of the influence of the pitch angle on the mechanical power is not linear.

Discussion

Based on numerical analysis and diagrams in Figures 2 to 5, it is evident that at blade rotation angle (V) by $β = 5, 7 and 10 °$ and $λ = 1 - 5$ , a higher value of the coefficient $C_{P}$ is achieved relative to the angle $β = 0 °$ , whereas with $λ > 5$ increase the $C_{P}$ decreases, that is, better result is shown by blades without rotation.

Analogously, when observing the number of revolutions on the rotor (generator), the results indicate that at the change of $β = 5, 7 and 10 °$ and the range of $n = 50 - 750 RPM$ higher $C_{P} = 0.35 - 0.45$ is achieved compared to the blade with $β = 0 °$ . At the condition $β = 0 °$ and n $= 1250 RPM$ , maximum value of $C_{P} = 0.51$ is obtained.

Turning the blade (M) by $β = 5 and 7 °$ and at $λ < 2.5$ , higher $C_{P}$ coefficient is achieved compared to the blade without turning. By increasing $λ > 2.5$ , the blade with $β = 0 °$ yields higher $C_{P}$ value compared to the blades with turning. Converted to the number of revolutions, for the values $n < 400 RPM$ the $C_{P}$ coefficient is increased with blades turning, whereas for the values $n > 400 RPM$ the $C_{P}$ coefficient is higher at $β = 0 °$ .

Data shows that blade V geometry is more favorable compared to blade M because higher $C_{P}$ value is achieved, and thereby higher output power on the wind turbine. Namely, for $λ = 2$ in blade V the coefficient $C_{P}$ is $(β = 0 ° - 10 °) = 0.04 - 0.08$ and in blade the $C_{P}$ is $(β = 0 ° - 10 °) = 0.036 - 0.052$ . Considering the number of revolutions (Figures 3 and 5), for $n = 400 RPM$ blade V has the coefficient $C_{P} (β = 0 ° - 10 °) = 0.07 - 0.13$ and blade M has the $C_{P} (β = 0 ° - 10 °) = 0.055 - 0.07$ . Blade V geometry has better aerodynamic lift/resistance ratio.

At the number of revolutions $n = 750 RPM$ and blade turning angle (V) β = 5,7 and 10°, mechanical power (Figures 6 and 7) ranges over the interval $P_{M} = 270 - 340$ W, and at $β = 0 °$ and $n = 1250 RPM$ it reaches the value of $P_{M} = 390$ W. In the rotor with a blade, the angle $β = 5 and 7 °$ up to the number of revolutions $n = 400 RPM$ exhibits the effect on mechanical power that ranges between $P_{M} = 38 - 50$ W and is higher compared to $β = 0 °$ , while with further increase in the number of revolutions the blade with yields higher $P_{M}$ value.

Experimental data indicates that the effect of blade rotation angle $(β)$ has identical character in both blade V and blade M, that is, as angle $β$ increases the torque increases too at the same number of generator revolutions without loading (Figures 9 and 10). In blade M, at the angle $β = 7 ° and 10 °$ practically there is not change in the torque. Higher torque at the same number of revolutions is shown by the rotor with blade V compared to the blade M, which is logical. It is noticeable from the figure that to start the generator rotor the torque of approx. $T = 0.05 Nm$ is required for overcoming the mass moment of inertia of the rotor, generator and friction in bearings. This implies the differences in characteristics obtained in Ansys CFX and Ansys Fluent and distinction in experimental values due to the presence of mass moments of inertia on HAWT, which Ansys does not take into consideration.

Comparing the values obtained for the torque in Ansys (Tables 2 and 3) and experimental investigation on the unloaded generator (Figures 9 and 10) at the same number of revolutions, the difference is observed as a result of the influence of the mentioned mass moment of inertia. Namely, in blade (V) for the considered rotation angles $(β)$ and the range of the number of generator revolutions $n = 200 - 500 RPM$ , experimental data points to the necessity of increasing the moment, which is obtained from numerical analysis by $1.76$ times so as to obtain the number of generator revolutions $n = 500 RPM$ (Table 2, $β = 10 °, T = 3.1355 Nm;$ Figure 9, $T = 1.773 Nm$ ). As regards the number of revolutions $n = 200 RPM$ (Table 2, $β = 7 °, T = 1.1907 Nm$ ; Figure 9, $T = 0.2 Nm$ ), the increase is higher due to the initiation and overcoming of friction in bearing.

Considering the generator loading, this implies that it is connected to a consumer that has the appropriate resistance. It is commonly known that the accomplishment of the appropriate number of revolutions on the loaded generator requires a higher torque compared to the case of unloaded generator. Higher blade torque needs greater lift/resistance force, whereby the flow mechanism changes as a result of blades deformation due to increase in mentioned forces.

The impact of blade rotation angle (V) from $β = 0 °$ to $β = 10 °$ , at generator loading of 22.9 Ω, leads to mechanical power increase in the 5.6 – 13% range, Table 4. For blade variant the increase is 4.2 – 9.7%, for the considered range of $n = 27 - 154 RPM$ , Table 6.

Generator loading has impact on the moment, and thereby on the mechanical power, because the accomplishment of the same number of rotations requires higher torque in loaded than in unloaded generator. It is known that the wind turbine power P is directly coupled with the wind available power $(P_{W})$ and the coefficient of power $C_{P} (β, λ)$ , that is, $P = P_{W} \cdot C_{P} (β, λ)$ . Accordingly, it can be concluded that at the generator loading the coefficient $C_{P} (β, λ)$ changes, and the causes can be the phenomena such as blade deformation, flow mechanism, etc.

Based on diagrams in Figures 9 and 11, it can be concluded that at a given number of generator rotations the torque increases as the resistance increases (the needed mechanical and therefore electrical power). Namely, with resistance decrease from 22.9 Ω–3.9 Ω on a wind turbine with angle $β = 0 °$ mechanical power is decreased in blade V by 3.88 times at the number of revolutions $n = 23 RPM$ and 11.3 times at $n = 129 RPM$ , respectively. With the turning blade increase from $β = 0 °$ to $β = 10 °$ and loading reduction to 3.9 Ω, the mechanical power is reduced by 4 times at $n = 23 RPM$ and 6.25 times at n $= 129 RPM$ , respectively.

In wind turbine with the blade (Figures 10 and 12) with angle $β = 0 °$ , with resistance decrease from 22.9 Ω–3.9 Ω mechanical power decreases by 2.45 times at the number of revolutions $n = 27 RPM$ . When the number of revolutions is increased to n $= 105 RPM$ , the mechanical power is decreased by approx 5.3 times. Increase in blade turning angle from $β = 0 °$ to $β = 10 °$ and loading reduction to 3.9 Ω results in mechanical energy decrease by 3.94 times at $n = 27 RPM$ and 5.77 times at n $= 105 RPM$ , respectively.

Conclusion

A blade with its geometry, material and manufacturing technology has a significant effect on the wind turbine work behavior and therefore on its output characteristics. The analysis of used blades and their performances was carried out applying software packages Ansys CFX and Ansys Fluent. Numerical analysis confirmed that as the blade (V) turning angle $β = 5, 7, 10 °$ and $λ = 1 - 5$ increases, higher $C_{P}$ coefficient value is accomplished compared to $β = 0 °$ . In blade (M) the effect of blade turning from $β = 0 °$ to $β = 10 °$ leads to the coefficient increase in the range up to $λ < 2.5$ and above that value $C_{P}$ is decreased.

Analysis indicates that the blade V geometry is more favorable compared to blade M, because a higher value of the $C_{P}$ coefficient is achieved, and thereby a higher torque and output power on the wind turbine. This confirms that the blade V geometry has better aerodynamic lift/resistance ratio than blade M.

Experimental setup and methodology enable examining the influence of different blade models on wind turbine output characteristics and comparison with the values obtained from numerical analysis. Comparing the values obtained for torque from Ansys and experimental investigation on the unloaded generator at the same number of revolutions, the difference is observed that developed as a result of the influence of the mass moment of inertia of the rotor, generator and friction present in bearing.

Methodology also allows for measuring the torque and mechanical power at loading (connecting) the generator to a consumer. Thus, at loading of 22.9 Ω, the results show that with increase of rotation angle the moment and mechanical power increase in blades V and M.

Footnotes

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) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research work was supported by the Ministry of Science, Technological Development and Innovation of the Republic of Serbia through contract No. 451-03-65/2024-03/200105 from 5 February 2024.

Ethical approval

Ethical approval is not applicable to this study as it did not involve human or animal subjects.

ORCID iD

Dragoljub Tanovic

Data availability statement

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

References

Al-Abadi

Ertunç

Beyer

, et al. Torque-matched aerodynamic shape optimization of HAWT rotor. J Phys Conf Ser 2014; 555: 012003.

Akbari

Naghashzadegan

Kouhikamali

, et al. Multi-objective optimization and optimal airfoil blade selection for a small horizontal-axis wind turbine (HAWT) for application in regions with various wind potential. Machines 2022; 10(8): 687.

Kumar

Baredar

. Solidity study and its effects on the performance of a small scale horizontal axis wind turbine. In: Mishra

(ed.) Impending power demand and innovative energy paths. Kanchipuram, India: Excellent Publishing House, 2014, pp. 290–297.

Chaudhary

Mondal

Tripathy

, et al. Modeling and optimal design of small HAWT blades for analyzing the starting torque behavior. In: Eighteenth national power systems conference (NPSC), 2014. DOI: 10.1109/NPSC.2014.7103886.

Khan

Shah

Khan

, et al. Observation of the starting and low speed behavior of small horizontal axis wind turbine. J Wind Energy 2014; 2014: 1–8.

Porto

Fortulan

Porto

AJV

. Wind tunnel measurements of a multibladed horizontal-axis small wind turbine. J Aerosp Technol Manag 2021; 13: 1–12. DOI: 10.1590/jatm.v13.1231

Sahu

Rathore

RK.

Determination of torque produced by horizontal axis wind turbine blade using FSI analysis for low wind speed regime. IJISET - Int J Innov Sci Eng Technol 2015; 2(5): 1069–1073.

Loya

Khan

MZU

Bhutta

, et al. Dependency of torque on aerofoilcamber variation in vertical axis wind turbine. World J Mech 2016; 06(11): 472–486.

Sun

Zhu

, et al. Rotation improvement of vertical axis wind turbine by offsetting pitching angles and changing blade numbers. Energy 2021; 215(B): 119177.

10.

Nguyen

Balduzzi

Goude

Effect of pitch angle on power and hydrodynamics of a vertical axis turbine. Ocean Eng 2021; 238: 109335.

11.

Wang

Xiong

Zhang

, et al. Small wind turbines and their potential for internet of things applications. iScience 2023; 26(9): 1–37. DOI: https://doi:10.1016/j.isci.2023.107674

12.

Song

Y-D

Liu

, et al. An overview of renewable wind energy conversion system modeling and control. Meas Control 2010; 43(7): 203–208.

13.

Sreenivas

Srinivasa Murthy

Vijaya Kumar

, et al. Design and analysis of new pitch angle controller for enhancing the performance of wind turbine coupled with PMSG. Mater Today Proc 2022; 52: 1456–1460.

14.

Antonysamy

Joo

YH.

Power maximization and regulation of the super-large wind turbine system using generalized predictive approach-based torque and pitch control. Int J Electr Power Energy Syst 2023; 154: 109416.

15.

Yilmaz

Low-speed, low induction multi-blade rotor for energy efficient small wind turbines. Energy 2023; 282(1): 128607.

16.

Kumar

Paraschivoiu

Low Reynolds number vertical axis wind turbine for Mars. Wind Eng 2010; 34(4): 461–476.

17.

Huang

Nong

, et al. Research and optimization of a built-in entity vertical axis wind turbine by variable pitch strategy. J Build Eng 2023; 68: 105810.

18.

Farhoody

Shafaghat

Alizadeh Kharkeshi

An experimental study to investigate the effect of pitch angle and wave characteristics on the performance of a horizontal axis tidal turbine. Appl Ocean Res 2023; 138: 103646.

19.

Svorcan

Peković

Simonović

, et al. Design of optimal flow concentrator for vertical-axis wind turbines using computational fluid dynamics, artificial neural networks and genetic algorithm. Adv Mech Eng 2021; 13(3): 1–13.

20.

Sudhamshu

Pandey

Sunil

, et al. Numerical study of effect of pitch angle on performance characteristics of a HAWT. Eng Sci Technol Int J 2010; 19(1): 632–641. DOI: https://doi.org/10.1016/j.jestch.2015.09.010

21.

Roul

Kumar

Effect of blade pitch angle on the aerodynamic characteristics of a twisted blade horizontal axis wind turbine based on numerical simulations. Int J Power Electron Drive Syst 2021; 12(1): 511–519.

22.

Jeong

Cha

Kim

, et al. Numerical investigation of optimal yaw misalignment and collective pitch angle for load imbalance reduction of rigid and flexible HAWT blades under sheared inflow. Energy 2015; 84: 518–532.

23.

Thumthae

Chitsomboon

Optimal angle of attack for untwisted blade wind turbine. Renew Energy 2009; 34(5): 1279–1284.

24.

Wibowo

Rudiyanto

Pambudi

, et al. Experimental study on pitch angle effects on the performance of Sg-6043 horizontal wind turbine. In: 9th International conference on physics and its applications, journal of physics: conference series, 2019. DOI: 10.1088/1742-6596/1153/1/012140.

25.

Cai

Zhao

, et al. Effects of yawed inflow and blade-tower interaction on the aerodynamic and wake characteristics of a horizontal-axis wind turbine. Energy 2023; 264(1): 126246.

26.

Montgomery

Design and analysis of experiments. Tempe, Arizona: Arizona State University, John Wiley & Sons, Inc, 2013.

27.

Movahhed Neya

Saberi

Rezaie

. Design of an adaptive controller to capture maximum power from a variable speed wind turbine system without any prior knowledge of system parameters. Trans Inst Meas Contr 2022; 44(3): 609–619.

28.

Kalinowska

Mrokowska

Rowinski

. Recent trends in environmental hydraulics. Warsaw, Poland: Springer, 2020.

29.

Berggren

Ekström

Nordström

A discontinuous Galerkin extension of the vertex-centered edge-based finite volume method. Commun Comput Phys 2009; 5(2–4): 456–468.