scholarly journals Wake Expansion and the Finite Blade Functions for Horizontal-Axis Wind Turbines

Energies ◽  
2021 ◽  
Vol 14 (22) ◽  
pp. 7653
Author(s):  
David Wood
Keyword(s):  
Radial Velocity ◽  
Wind Turbines ◽  
Loss Factor ◽  
Axial Direction ◽  
Horizontal Axis ◽  
Speed Ratio ◽  
Tip Speed Ratio ◽  
Constant Pitch ◽  
Horizontal Axis Wind Turbines ◽  
Blade Element

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.

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

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).

scholarly journals New airfoils for micro horizontal-axis wind turbines

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.

scholarly journals Some effects of flow expansion on the aerodynamics of horizontal-axis wind turbines

2021 ◽  
Author(s):  
David Wood ◽  
Eric Limacher
Keyword(s):  
Axial Velocity ◽  
Momentum Equation ◽  
Horizontal Axis ◽  
Speed Ratio ◽  
Axial Component ◽  
Horizontal Axis Wind Turbine ◽  
Tip Vortices ◽  
Tip Speed Ratio ◽  
Constant Pitch ◽  
Far Wake

Abstract. Upwind of an energy-extracting horizontal-axis wind turbine, the flow expands as it approaches the rotor, and the expansion continues in the vorticity-bearing wake behind the rotor. The upwind expansion has long been known to influence the axial momentum equation through the axial component of the pressure, although the extent of the influence has not been quantified. Starting with the impulse analysis of Limacher & Wood (2020), but making no further use of impulse techniques, we demonstrate that the expansion redistributes momentum from the external flow to the wake and derive its exact expression when the rotor is circumferentially uniform. This expression, which depends on the radial velocity and the axial induction factor, is added to the thrust equation containing the pressure on the back of the disk. Removing the pressure to obtain a practically useful equation shows the axial induction in the far-wake is twice the value at the rotor only at high tip speed ratio and only if the relationship between vortex pitch and axial induction in non-expanding flow carries over to the expanding case. At high tip speed ratio, we assume that the expanding wake approaches the "Joukowsky'' model of a hub vortex on the axis of rotation and tip vortices originating from each blade. The additional assumption that the helical tip vortices have constant pitch, allows a semi-analytic treatment of their effect on the rotor flow. Expansion modifies the relation between the pitch and induced axial velocity so that the far-wake area and induction are significantly less than twice the values at the rotor. There is a moderate decrease – about 6 % – in the power production and a similar size error occurs in the familiar axial momentum equation involving the axial velocity.

Design of Horizontal-Axis Wind Turbines with Six Blades by the Blade Element Momentum Method

2003 ◽  
Vol 2003.2 (0) ◽  
pp. 97-98
Author(s):  
Yutaka HARA ◽  
Tsutomu HAYASHI ◽  
Masatoshi KAJIWARA ◽  
Toshimasa MATSUOKA
Keyword(s):  
Wind Turbines ◽  
Horizontal Axis ◽  
Horizontal Axis Wind Turbines ◽  
Blade Element

scholarly journals Some effects of flow expansion on the aerodynamics of horizontal-axis wind turbines

2021 ◽  
Vol 6 (6) ◽  
pp. 1413-1425
Author(s):  
David H. Wood ◽  
Eric J. Limacher
Keyword(s):  
Axial Velocity ◽  
Momentum Equation ◽  
Horizontal Axis ◽  
Speed Ratio ◽  
Axial Component ◽  
Horizontal Axis Wind Turbine ◽  
Tip Vortices ◽  
Tip Speed Ratio ◽  
Constant Pitch ◽  
Far Wake

Abstract. The flow upwind of an energy-extracting horizontal-axis wind turbine expands as it approaches the rotor, and the expansion continues in the vorticity-bearing wake behind the rotor. The upwind expansion has long been known to influence the axial momentum equation through the axial component of the pressure, although the extent of the influence has not been quantified. Starting with the impulse analysis of Limacher and Wood (2020), but making no further use of impulse techniques, we derive its exact expression when the rotor is a circumferentially uniform disc. This expression, which depends on the radial velocity and the axial induction factor, is added to the thrust equation containing the pressure on the back of the disc. Removing the pressure to obtain a practically useful equation shows the axial induction in the far wake is twice the value at the rotor only at high tip speed ratio and only if the relationship between vortex pitch and axial induction in non-expanding flow carries over to the expanding case. At high tip speed ratio, we assume that the expanding wake approaches the Joukowsky model of a hub vortex on the axis of rotation and tip vortices originating from each blade. The additional assumption that the helical tip vortices have constant pitch allows a semi-analytic treatment of their effect on the rotor flow. Expansion modifies the relation between the pitch and induced axial velocity so that the far-wake area and induction are significantly less than twice the values at the rotor. There is a moderate decrease – about 6 % – in the power production, and a similar size error occurs in the familiar axial momentum equation involving the axial velocity.

Optimal Design of Horizontal-Axis Wind Turbines Using Blade-Element Theory and Evolutionary Computation

2002 ◽  
Vol 124 (4) ◽  
pp. 357-363 ◽  
Author(s):  
Ernesto Benini ◽  
Andrea Toffolo
Keyword(s):  
Wind Turbines ◽  
Accurate Solution ◽  
Function Optimization ◽  
Horizontal Axis ◽  
Geometrical Parameters ◽  
Multi Objective ◽  
Blade Element Theory ◽  
Horizontal Axis Wind Turbines ◽  
Element Theory ◽  
Blade Element

This paper describes a multi-objective optimization method for the design of stall-regulated horizontal-axis wind turbines. Two modules are used for this purpose: an aerodynamic model implementing the blade-element theory and a multi-objective evolutionary algorithm. The former provides a sufficiently accurate solution of the flow field around the rotor disc; the latter handles the decision variables of the optimization problem, i.e., the main geometrical parameters of the rotor configuration, and promotes function optimization. The scope of the method is to achieve the best trade-off performance between two objectives: annual energy production per square meter of wind park (to be maximized) and cost of energy (to be minimized). Examples of the best solutions found by the method are described and their performance compared with those of commercial wind turbines.

Performance Characteristics of a Horizontal Axis Model Wind Turbine

1981 ◽  
Vol 195 (1) ◽  
pp. 223-229 ◽  
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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