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

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.

2021 ◽  
Author(s):  
David Wood ◽  
Eric Limacher

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.


Energies ◽  
2021 ◽  
Vol 14 (22) ◽  
pp. 7653
Author(s):  
David Wood

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.


2002 ◽  
Vol 26 (2) ◽  
pp. 109-116
Author(s):  
Sadhan Mahapatra ◽  
Subhasis Neogi

This paper is based on the studies made on a numerical model for calculating the turbine characteristics at low tip speed ratio for a Horizontal Axis Wind Turbine. The turbine characteristics are analysed for different configurations over the total operating range i.e. from tip speed ratio of zero to a maximum value where CP becomes zero. The simulation model provides acceptable results, however for the blade position near the hub, a non-convergent situation is observed i.e. the flow parameters converge to values outside those associated with turbine operation. This indicates the possibility of a multisolution.


2013 ◽  
Vol 860-863 ◽  
pp. 256-261
Author(s):  
Qiu Hua Chen ◽  
Xu Lai ◽  
Jin Zou

The present paper evaluates the tip vortex evolution of a horizontal axis wind turbine model using the stereo particle image velocimetry technology. The measurements of the wake region up to 2.7 diameters downstream are first conducted using the phase locked technique based on two high speed CCD cameras. Parameters that describe the helical vortex wake, such as the velocity, helicoidal pitch and vortex vorticity, are presented at two tip speed ratios. The vortex interaction and stability of helical vortex filaments within wind turbine wake are seen throughout the measurement domain. The results show the wake structure varies with tip speed ratio, and the helicoidal pitch of tip vortex trajectory reduces while the diffusion of tip vortex is faster with increasing tip speed ratio.


2021 ◽  
pp. 1-28
Author(s):  
Mehmet Numan Kaya ◽  
Faruk Köse ◽  
Oguz Uzol ◽  
Derek Ingham ◽  
Lin Ma ◽  
...  

Abstract The aerodynamic shapes of the blades are still of high importance and various aerodynamic designs have been developed in order to increase the amount of energy production. In this study, a swept horizontal axis wind turbine blade has been optimized to increase the aerodynamic efficiency using the Computational Fluid Dynamics method. To illustrate the technique, a wind turbine with a rotor diameter of 0.94 m has been used as the baseline turbine and the most appropriate swept blade design parameters, namely the sweep start up section, tip displacement and mode of the sweep have been investigated to obtain the maximum power coefficient at the design tip speed ratio. At this stage, a new equation that allows all three swept blade design parameters to be changed independently has been used to design swept blades, and the response surface method has been used to find out the optimum swept blade parameters. According to the results obtained, a significant increase of 4.28% in the power coefficient was achieved at the design tip speed ratio with the new designed optimum swept wind turbine blade. Finally, baseline and optimum swept blades have been compared in terms of power coefficients at different tip speed ratios, force distributions, pressure distributions and tip vortices.


2021 ◽  
Vol 294 ◽  
pp. 01003
Author(s):  
Somaya Younoussi ◽  
Abdeslem Ettaouil

In this paper, an optimization approach of a small horizontal axis wind turbine based on BEM theory including De Vries and Shen et al. tip loss corrections is proposed. The optimal blade geometry was obtained by maximizing the power coefficient along the blade using the optimal angle of attack and the optimal tip speed ratio. The Newton’s iterative method applied to axial induction factor was used to solve the problem. This study was conducted for a NACA4418 small wind turbine, at low wind velocity. Among the two used tip loss corrections, the De Vries correction was found to be the most suitable for this blade optimization method. The optimal design was obtained for a tip speed ratio of 5 and has recorded a power coefficient equal to 0.463.


This research paper presents a design and fabrication of 100 Watt small horizontal axis wind turbine with 0.24 m and 0.35 m rotor radius and tip speed ratio varies from 2 to 10 was designed and development for operated at low wind speed with Low Reynolds number. In this paper, a new airfoil profile was designed and developed, it’s denoted by MK115. The numerical and experimental analysis for 6 airfoils using Xfoil software was conducted with a view to evaluating the lift-to-drag ratio and angle of attack by means of the SD7024, SG6043, NACA2412, S1210, E213, and New Airfoil (MK115) tested. In simulation, new MK115 airfoil was the most convenient airfoil to start high energy production for low-wind applications, on the Reynolds number 25000, 50000, 75000, and 100000 in improved airfoil (MK115) tests an Open type wind tunnel. An Xfoil analysis to obtain further data on the flow characteristics was also conducted. (MK115) airfoil have CLmax of 0.92, 1.25, 1.69, 1.67 at Re=25k, 50k, 75k and 100k for an angle of attack is equal to 100 .A maximum lift to drag ratio (Cl/Cd) of 7,16,50,63 at Re=25k, 50k, 75k and 100k for New airfoil (MK115) at angle of attack (α) =40 , 40 , 80 , 80 . SG6043, NACA2412, E214, SD7034, S1210 and MK115 (New airfoil) have the Maximum Cp=0.37, 0.36, 0.4, 0.39, 0.44, and 0.44 at tip speed ratio (λ) =6 for Reynolds number is equal to 100000. MK115, Maximum Torque obtained 0.9744 Nm, 1.389 Nm and 2.4866 Nm at blade angle =0, 15 and 30 degrees respectively. Power coefficient (Cp) =0.51, 0.5, 0.46, and 0.4 at Rotor shaft angle=00 , 50 , 100 , and 150 respectively for the new airfoil results.


2003 ◽  
Vol 27 (4) ◽  
pp. 299-316 ◽  
Author(s):  
Matthew M. Duquette ◽  
Jessica Swanson ◽  
Kenneth D. Visser

Experimental studies were conducted on a modified Rutland 500 horizontal axis wind turbine to evaluate numerical implications of solidity and blade number on the aerodynamic performance. Wind tunnel data were acquired on the turbine with flat-plate, constant-chord blade sets and optimum-designed blade sets to compare with theoretical trends, which had indicated that increased solidity and blade number more than conventional 3-bladed designs, would yield larger power coefficients, CP. The data for the flat plate blades demonstrated power coefficient improvements as the range of solidities was increased from 7% to 27%, but did not indicate performance gains for increased blade numbers. It was also observed that larger pitch angles decreased the optimum tip speed ratio range significantly with a small (5% or less) change in maximum CP. The optimum-design 3-bladed rotors produced an increased experimental CP as solidity increased, with reduced tip speed ratio, at the optimum operating point. As blade number was increased at a constant solidity of 10% from 3 to 12 blades, aerodynamic efficiency and power sharply decreased, contrary to the numerical predictions and the flat plate experimental results. Low Reynolds numbers and wind tunnel blockage effects limit these conclusions and a full scale prototype rotor is being constructed to examine the results of the numerical and experimental studies using a side-by-side comparison with a commercially available wind turbine at the Clarkson University wind-turbine test site.


2021 ◽  
pp. 1-16
Author(s):  
Ojing Siram ◽  
Niranjan Sahoo ◽  
Ujjwal K. Saha

Abstract The small-scale horizontal-axis wind turbines (SHAWTs) have emerged as the promising alternative energy resource for the off-grid electrical power generation. These turbines primarily operate at low Reynolds number, low wind speed, and low tip speed ratio conditions. Under such circumstances, the airfoil selection and blade design of a SHAWT becomes a challenging task. The present work puts forward the necessary steps starting from the aerofoil selection to the blade design and analysis by means of blade element momentum theory (BEMT) for the development of four model rotors composed of E216, SG6043, NACA63415, and NACA0012 airfoils. This analysis shows the superior performance of the model rotor with E216 airfoil in comparison to other three models. However, the subsequent wind tunnel study with the E216 model, a marginal drop in its performance due to mechanical losses has been observed.


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