Theoretical and computational investigations of the optimal tip-speed ratio of horizontal-axis wind turbines

This paper considers the effect of wake expansion on the finite blade functions in blade element/momentum theory for horizontal-axis wind turbines. For any velocity component, the function is the ratio of the streamtube average to that at the blade elements. In most cases, the functions are set by the trailing vorticity only and Prandtl’s tip loss factor can be a reasonable approximation to the axial and circumferential functions at sufficiently high tip speed ratio. Nevertheless, important cases like coned or swept rotors or shrouded turbines involve more complex blade functions than provided by the tip loss factor or its recent modifications. Even in the presence of significant wake expansion, the functions derived from the exact solution for the flow due to constant pitch and radius helical vortices provide accurate estimates for the axial and circumferential blade functions. Modifying the vortex pitch in response to the expansion improves the accuracy of the latter. The modified functions are more accurate than the tip loss factor for the test cases at high tip speed ratio that are studied here. The radial velocity is important for expanding flow as it has the magnitude of the induced axial velocity near the edge of the rotor. It is shown that the resulting angle of the flow to the axial direction is small even with significant expansion, as long is the tip speed ratio is high. This means that blade element theory does not have account for the effective blade sweep due to the radial velocity. Further, the circumferential variation of the radial velocity is lower than of the other components.

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Aerodynamic Design and Wind Tunnel Tests of Small-scale Horizontal-axis Wind Turbines for Low Tip Speed Ratio Applications

Journal of Solar Energy Engineering ◽

10.1115/1.4053453 ◽

2022 ◽

pp. 1-34

Author(s):

Ojing Siram ◽

Neha Kesharwani ◽

Niranjan Sahoo ◽

Ujjwal K. Saha

Keyword(s):

Wind Tunnel ◽

Wind Turbines ◽

Pitch Angle ◽

Horizontal Axis ◽

Power Coefficient ◽

Speed Ratio ◽

Small Scale ◽

Wind Tunnel Tests ◽

Tip Speed Ratio ◽

Horizontal Axis Wind Turbines

Abstract In recent times, the application of small-scale horizontal axis wind turbines (SHAWTs) has drawn interest in certain areas where the energy demand is minimal. These turbines, operating mostly at low Reynolds number (Re) and low tip speed ratio (λ) applications, can be used as stand-alone systems. The present study aims at the design, development, and testing of a series of SHAWT models. On the basis of aerodynamic characteristics, four SHAWT models viz., M1, M2, M3, and M4 composed of E216, SG6043, NACA63415, and NACA0012 airfoils, respectively have been developed. Initially, the rotors are designed through blade element momentum theory (BEMT), and their power coefficient have been evaluated. Thence, the developed rotors are tested in a low-speed wind tunnel to find their rotational frequency, power and power coefficient at design and off-design conditions. From BEMT analysis, M1 shows a maximum power coefficient (Cpmax) of 0.37 at λ = 2.5. The subsequent wind tunnel tests on M1, M2, M3, and M4 at 9 m/s show the Cpmax values to be 0.34, 0.30, 0.28, and 0.156, respectively. Thus, from the experiments, the M1 rotor is found to be favourable than the other three rotors, and its Cpmax value is found to be about 92% of BEMT prediction. Further, the effect of pitch angle (θp) on Cp of the model rotors is also examined, where M1 is found to produce a satisfactory performance within ±5° from the design pitch angle (θp, design).

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New airfoils for micro horizontal-axis wind turbines

Journal of Engineering Research ◽

10.36909/jer.10949 ◽

2021 ◽

Author(s):

Manoj Kumar Chaudhary ◽

◽

S. Prakash ◽

Keyword(s):

Reynolds Number ◽

Wind Turbines ◽

Low Reynolds Number ◽

Horizontal Axis ◽

Speed Ratio ◽

Maximum Output ◽

Horizontal Axis Wind Turbine ◽

Horizontal Axis Wind Turbines ◽

Low Reynolds ◽

Bem Theory

In this study, small horizontal-axis wind turbine blades operating at low wind speeds were optimized. An optimized blade design method based on blade element momentum (BEM) theory was used. The rotor radius of 0.2 m, 0.4 m and 0.6 m and blade geometry with single (W1 & W2) and multistage rotor (W3) was examined. MATLAB and XFoil programs were used to implement to BEM theory and devise a six novel airfoil (NAF-Series) suitable for application of small horizontal axis wind turbines at low Reynolds number. The experimental blades were developed using the 3D printing additive manufacturing technique. The new airfoils such as NAF3929, NAF4420, NAF4423, NAF4923, NAF4924, and NAF5024 were investigated using XFoil software at Reynolds numbers of 100,000. The investigation range included tip speed ratios from 3 to 10 and angle of attacks from 2° to 20°. These parameters were varied in MATLAB and XFoil software for optimization and investigation of the power coefficient, lift coefficient, drag coefficient and lift-to-drag ratio. The cut-in wind velocity of the single and multistage rotors was approximately 2.5 & 3 m/s respectively. The optimized tip speed ratio, axial displacement and angle of attack were 5.5, 0.08m & 6° respectively. The proposed NAF-Series airfoil blades exhibited higher aerodynamic performances and maximum output power than those with the base SG6043 and NACA4415 airfoil at low Reynolds number.

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Performance Characteristics of a Horizontal Axis Model Wind Turbine

Proceedings of the Institution of Mechanical Engineers ◽

10.1243/pime_proc_1981_195_023_02 ◽

1981 ◽

Vol 195 (1) ◽

pp. 223-229 ◽

Cited By ~ 1

Author(s):

A T Sayers ◽

A F Christopher Bsc

Keyword(s):

Low Power ◽

Wind Turbine ◽

Wind Turbines ◽

Horizontal Axis ◽

Performance Characteristics ◽

Coefficient Of Performance ◽

Speed Ratio ◽

Tip Speed Ratio ◽

And Performance ◽

Prototype Design

The performance characteristics of wind turbines should be thoroughly investigated prior to expending large amounts of capital on a prototype design. A low power dynamometer is described for measuring the power and torque output from a two-bladed model wind turbine, and performance characteristics relating coefficient of performance to tip speed ratio and blade geometric pitch are presented for three designs of blade.

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