A simplified vortex model of propeller and wind-turbine wakes

2013 ◽  
Vol 725 ◽  
pp. 91-116 ◽  
Author(s):  
Antonio Segalini ◽  
P. Henrik Alfredsson
Keyword(s):  
Wind Turbine ◽  
Vortex Core ◽  
Roller Bearing ◽  
Operating Conditions ◽  
Tip Vortex ◽  
Speed Ratio ◽  
Core Size ◽  
Vortex Model ◽  
Momentum Theory ◽  
Good Agreement

AbstractA new vortex model of inviscid propeller and wind-turbine wakes is proposed based on an asymptotic expansion of the Biot–Savart induction law to account for the finite vortex core size. The circulation along the blade is assumed to be constant from the blade root to the tip approximating a turbine with maximum power production for given operating conditions. The model iteratively calculates the tip-vortex path, allowing the wake to expand/contract freely, and is afterward able to evaluate the velocity field in the whole domain. The ‘roller-bearing analogy’, proposed by Okulov and Sørensen (J. Fluid Mech., vol. 649, 2010, pp. 497–508), is used to determine the vortex core size. A comparison of the main outcomes of the present model with the general momentum theory is performed in terms of the operating parameters (namely the number of blades, the tip-speed ratio, the blade circulation and the vortex core size), demonstrating good agreement between the two. Furthermore, experimental data have been compared with the model outputs to validate the model under real operating conditions.

Experimental Investigation on the Tip Vortex of a Wind Turbine With and Without a Slotted Tip

2017 ◽  
Author(s):  
Pengyin Liu ◽  
Jinge Chen ◽  
Shen Xin ◽  
Xiaocheng Zhu ◽  
Zhaohui Du
Keyword(s):  
Experimental Data ◽  
Flow Field ◽  
Wind Turbine ◽  
Vortex Core ◽  
Control Method ◽  
Tip Vortex ◽  
Wake Flow ◽  
Core Model ◽  
Near Wake ◽  
Measured Velocity

In this paper, a slotted tip structure is experimentally analyzed. A wind turbine with three blades, of which the radius is 301.74mm, is investigated by the PIV method. Each wind turbine blade is formed with a slots system comprising four internal tube members embedded in the blade. The inlets of the internal tube member are located at the leading edge of the blade and form an inlet array. The outlets are located at the blade tip face and form an outlet array. The near wake flow field of the wind turbine with slotted tip and without slotted tip are both measured. Velocity field of near wake region and clear images of the tip vortex are captured under different wake ages. The experimental results show that the radius of the tip vortex core is enlarged by the slotted tip at any wake age compared with that of original wind turbine. Moreover, the diffusion process of the tip vortex is accelerated by the slotted tip which lead to the disappearance of the tip vortex occurs at smaller wake age. The strength of the tip vortex is also reduced indicating that the flow field in the near wake of wind turbine is improved. The experimental data are further analyzed with the vortex core model to reveal the flow mechanism of this kind of flow control method. The turbulence coefficient of the vortex core model for wind turbine is obtained from the experimental data of the wind turbine with and without slotted tip. It shows that the slotted tip increases the turbulence strength in the tip vortex core by importing airflow into the tip vortex core during its initial generation stage, which leads to the reduction of the tip vortex strength. Therefore, it is promising that the slotted tip can be used to weaken the vorticity and accelerate the diffusion of the tip vortex which would improve the problem caused by the tip vortex.

An Experimental Study of the Aerodynamics and Performance of a Vertical Axis Wind Turbine in a Confined and Unconfined Environment

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Vincenzo Dossena ◽  
Giacomo Persico ◽  
Berardo Paradiso ◽  
Lorenzo Battisti ◽  
Sergio Dell'Anna ◽  
...  
Keyword(s):  
Experimental Study ◽  
Wind Tunnel ◽  
Wind Turbine ◽  
Vertical Axis ◽  
Tip Vortex ◽  
Speed Ratio ◽  
Vertical Axis Wind Turbine ◽  
Tip Speed Ratio ◽  
And Performance ◽  
Power Curves

This paper presents the results of a wide experimental study on an H-type vertical axis wind turbine (VAWT) carried out at the Politecnico di Milano. The experiments were carried out in a large-scale wind tunnel, where wind turbines for microgeneration can be tested in real-scale conditions. Integral torque and thrust measurements were performed, as well as detailed aerodynamic measurements to characterize the flow field generated by the turbine downstream of the rotor. The machine was tested in both a confined (closed chamber) and unconfined (open chamber) environment, to highlight the effect of wind tunnel blockage on the aerodynamics and performance of the VAWT under investigation. The experimental results, compared with the blockage correlations presently available, suggest that specific correction models should be developed for VAWTs. The experimental thrust and power curves of the turbine, derived from integral measurements, exhibit the expected trends with a peak power coefficient of about 0.28 at tip-speed ratio equal to 2.5. Flow measurements, performed in three conditions for tip speed ratio equal to 1.5, 2.5, and 3.5, show the fully three-dimensional character of the wake, especially in the tip region where a nonsymmetrical wake and tip vortex are found. The unsteady evolution of the velocity and turbulence fields further highlights the effect of aerodynamic loading on the wake unsteadiness, showing the time-dependent nature of the tip vortex and the onset of dynamic stall for tip speed ratio lower than 2.

scholarly journals Geometrical Design of a Rotor Blade for a Small Scale Horizontal Axis Wind Turbine

2019 ◽  
Vol 8 (3) ◽  
pp. 3390-3400
Keyword(s):  
Wind Turbine ◽  
Rotor Blade ◽  
Operating Conditions ◽  
Horizontal Axis ◽  
Small Scale ◽  
Horizontal Axis Wind Turbine ◽  
Geometrical Properties ◽  
Momentum Theory ◽  
Bem Theory ◽  
Blade Element

In the present study, Blade Element Momentum theory (BEMT) has been implemented to heuristically design a rotor blade for a 2kW Fixed Pitch Fixed Speed (FPFS) Small Scale Horizontal Axis Wind Turbine (SSHAWT). Critical geometrical properties viz. Sectional Chord ci and Twist distribution θTi for the idealized, optimized and linearized blades are analytically determined for various operating conditions. Results obtained from BEM theory demonstrate that the average sectional chord ci and twist distribution θTi of the idealized blade are 20.42% and 14.08% more in comparison with optimized blade. Additionally, the employment of linearization technique further reduced the sectional chord ci and twist distribution θTi of the idealized blade by 17.9% and 14% respectively, thus achieving a viable blade bounded by the limits of economic and manufacturing constraints. Finally, the study also reveals that the iteratively reducing blade geometry has an influential effect on the solidity of the blade that in turn affects the performance of the wind turbine.

Wake and Performance Predictions of Two- and Three-Bladed Wind Turbines Based on the Actuator Line Model1

2021 ◽  
Vol 143 (5) ◽  
Author(s):  
Sebastian Henao Garcia ◽  
Aldo Benavides-Morán ◽  
Omar D. Lopez Mejia
Keyword(s):  
Wind Turbine ◽  
Three Dimensional ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Speed Ratio ◽  
Power Extraction ◽  
Low Incidence ◽  
And Performance ◽  
Turbine Design ◽  
Simulation Parameters

Abstract This paper challenges the standard wind turbine design numerically assessing the wake and aerodynamic performance of two- and three-bladed wind turbine models implementing downwind and upwind rotor configurations, respectively. The simulations are conducted using the actuator line model (ALM) coupled with a three-dimensional Navier Stokes solver implementing the k−ω shear stress transport turbulence model. The sensitivity of the ALM to multiple simulation parameters is analyzed in detail and numerical results are compared against experimental data. These analyses highlight the most suitable Gaussian radius at the rotor to be equal to twice the chord length at 95% of the blade for a tip-speed ratio (TSR) of ten, while the Gaussian radius at the tower and the number of actuator points have a low incidence on the flow field computations overall. The numerical axial velocity profiles show better agreement upstream than downstream the rotor, while the discrepancies are not consistent through all the assessed operating conditions, thus highlighting that the ALM parameters are also dependent on the wind turbine's operating conditions rather than being merely geometric parameters. Particularly, for the upwind three-bladed wind turbine model, the accuracy of the total thrust computations improves as the TSR increases, while the least accurate wake predictions are found for its design TSR. Finally, when comparing both turbine models, an accurate representation of the downwind configuration is observed as well as realistic power extraction estimates. Indeed, the results confirm that rotors with fewer blades are more suitable to operate at high TSRs.

scholarly journals Study the Effect of Blade Angles on the Performance of Axial Six Blades Wind Turbine

2018 ◽  
Vol 7 (4.19) ◽  
pp. 945
Author(s):  
Mishaal A AbdulKareem ◽  
Ammar A Hussain ◽  
Raid S Fahad
Keyword(s):  
Wind Speed ◽  
Wind Turbine ◽  
Operating Conditions ◽  
Power Coefficient ◽  
Maximum Value ◽  
Speed Range ◽  
Electrical Generator ◽  
Flow Through ◽  
High Level ◽  
Good Agreement

In this paper, the performance of a six blades axial type wind turbine has been studied experimentally to estimate the wind power, the electrical generated power and-the modified power-coefficient of the wind-turbine. This study was conducted under different operating conditions assuming steady-state, incompressible and isothermal air flow through the wind-turbine. The range of operating condition was (2 to 5.6 m/s wind speed), (10% to 100% of electrical load that is applied on the terminals of the electrical generator) and (10° to 80° blades angle of the wind-turbine). A good agreement was obtained when comparing the results of the present work with those of a previously published article. The predicted results showed that increasing the wind speed and-the blades angle of the wind-turbine will increase the generated power from the wind-turbine. The maximum-value of the modified power-coefficient was (0.57) at a wind velocity value of (5.6 m/s) and at a blades angle value of (80°). It is found that it’s not recommended to operate the wind-turbine at (80°) blades angle associated with a wind speed range that is above (3.8 m/s) due to a high level of wind-turbine vibration. 

Development of an Analytical Unsteady Model for Wind Turbine Aerodynamic Response to Linear Pitch Changes

2016 ◽  
Vol 138 (5) ◽  
Author(s):  
Mohamed M. Hammam ◽  
David H. Wood ◽  
Curran Crawford
Keyword(s):  
Wind Turbine ◽  
Pitch Angle ◽  
Turbine Rotor ◽  
Speed Ratio ◽  
Element Analysis ◽  
Tip Speed Ratio ◽  
First Order ◽  
Vortex Model ◽  
Constant Pitch ◽  
Induced Velocity

A simple unsteady blade element analysis is used to account for the effect of the trailing wake on the induced velocity of a wind turbine rotor undergoing fast changes in pitch angle. At sufficiently high tip speed ratio, the equation describing the thrust of the element reduces to a first order, nonlinear Riccti's equation which is solved in a closed form for a ramp change in pitch followed by a constant pitch. Finite tip speed ratio results in a first order, nonlinear Abel's equation. The unsteady aerodynamic forces on the NREL VI wind turbine are analyzed at different pitch rates and tip speed ratio, and it is found that the overshoot in the forces increases as the tip speed ratio and/or the pitch angle increase. The analytical solution of the Riccati's equation and numerical solution of Abel's equation gave very similar results at high tip speed ratio but the solutions differ as the tip speed ratio reduces, partly because the Abel's equation was found to magnify the error of assuming linear lift at low tip speed ratio. The unsteady tangential induction factor is expressed in the form of first order differential equation with the time constant estimated using Jowkowsky's vortex model and it was found that it is negligible for large tip speed ratio operation.

Including Swirl in the Actuator Disk Analysis of Wind Turbines

2007 ◽  
Vol 31 (5) ◽  
pp. 317-323 ◽  
Author(s):  
D.H. Wood
Keyword(s):  
Wind Turbine ◽  
Vortex Structure ◽  
General Model ◽  
Power Coefficient ◽  
Speed Ratio ◽  
Core Radius ◽  
Simple Analysis ◽  
Tip Speed Ratio ◽  
Vortex Model ◽  
Actuator Disk

It is shown that the presence of swirl in the wake of a wind turbine complicates the simple actuator disk analysis that provides such basic results as the Lanchester-Betz limit on the power coefficient. The simple analysis remains valid at high tip speed ratio for a sufficiently small core radius of the hub vortex. As the tip speed ratio decreases, the present analysis eventually becomes invalid. It is, however, reasonable to conclude that including the effects of the hub vortex causes the maximum power coefficient to increase above the Lanchester-Betz limit with decreasing tip speed ratio. The extent to which this conclusion depends on the assumed vortex model was investigated briefly by considering a more general model for the hub vortex. The results strongly imply that some account of the vortex structure of the wake will be required to resolve fully the effects of swirl. Unfortunately there are no measurements currently available for the hub vortex.

An Experimental and Theoretical Investigation of the Structure of a Trailing Vortex Wake

1977 ◽  
Vol 28 (1) ◽  
pp. 39-50 ◽  
Author(s):  
R G Sampson
Keyword(s):  
Significant Proportion ◽  
Vortex Sheet ◽  
Transverse Plane ◽  
Tip Vortex ◽  
Turbulent Vortex ◽  
Vortex Model ◽  
Vorticity Distribution ◽  
Pressure Distributions ◽  
Improved Technique ◽  
Good Agreement

SummaryAn improved technique for the use of a five-hole yaw probe has been used in determining velocity, vorticity and pressure distributions over a transverse plane five chords downstream of a lifting wing. A well-defined tip vortex is shown to exist, together with a vortex sheet which contains a significant proportion of the total vorticity. The vorticity distribution is compared with that predicted by the calculation of vortex sheet roll-up using a two-dimensional array of line vortices. Good agreement is obtained, and the validity of using time steps large enough to inhibit the chaotic motion found in some calculations of this type is demonstrated. The structure of the tip vortex is found to be well described by the turbulent vortex model of Hoffman and Joubert.

Lift Limit of Horizontal Axis Wind Turbine

2014 ◽  
Vol 1070-1072 ◽  
pp. 1869-1873
Author(s):  
Hai Bo Jiang ◽  
Yun Peng Zhao ◽  
Zhong Qing Cheng
Keyword(s):  
Wind Turbine ◽  
Lift Coefficient ◽  
Speed Ratio ◽  
Theoretical Limit ◽  
Horizontal Axis Wind Turbine ◽  
Tip Speed Ratio ◽  
Momentum Theory ◽  
Fluid Environment ◽  
Drag Ratio ◽  
Blade Element

The lift coefficient of any wind turbine must have highest limit. In this paper, an analytical expression of lift coefficient associated with tip-speed ratio and lift-drag ratio of airfoil of wind turbine with ideal chord has been deduced by integrating along the blade wingspan using the blade element - momentum theory, which can be used for pre-estimating lift coefficient of actual wind turbine in design. Further, considering ideal fluid environment ( the drag coefficient is close to 0 ), an expression of the highest performance of lift only associated with tip-speed ratio has been deduced too, which is the highest boundary of lift coefficient of any actual wind turbine with same tip-speed ratio. The results show that for the wind turbine in steady state, there is a theoretical limit of the lift coefficient, 0.57795, which is the highest boundary that any actual wind turbine can not be crossed; if the tip-speed ratio is greater than 6 and lift-drag ratio less than 200, the lift coefficient is unlikely to exceed 0.2.

Investigation of Flatback Airfoil Effect in the Wind Turbine Blade

2015 ◽  
Author(s):  
Jae-Ho Jeong ◽  
Soo-Hyun Kim
Keyword(s):  
Wind Turbine ◽  
Turbine Blade ◽  
Vortex Core ◽  
Pressure Difference ◽  
Wind Turbine Blade ◽  
Tip Vortex ◽  
Suction Surface ◽  
Pressure Surface ◽  
Large Pressure ◽  
Flatback Airfoil

The flatback airfoil effect in the inboard region of large wind turbine blade has been investigated by numerical analysis. Complicated flow phenomena in the wind turbine blade were captured by Reynolds-averaged Navier-Stokes flow simulation (RANS) with SST (Shear Stress Transport) turbulence model. The inboard region of the blade without the flatback airfoils is dominated by the separated vortex. The separated vortex starts to be formed near the blade mid-chord. The separated vortex core is generated by the large pressure difference in the blade inboard trailing edge region. The separated vortex grows nearly in the outboard direction, which is so-called secondary flow on the blade surface. The flatback airfoils are designed, and applied to the wind turbine inboard region. The scale of the separated vortex can be decreased, and the blade performance enhanced up to nearly 6% in the flatback airfoil region. However, the blade with large wake thickness due to the flatback airfoil has a negative impact on the aerodynamic noise. Regardless of the flatback airfoils, the tip vortex core of the outboard region is formed on the suction surface leading edge, and strongly rolled-up by the pressure surface boundary layers due to the large pressure difference between the suction surface and the pressure surface in the blade tip region. This remarkably strong tip vortex develops downstream, and rakes up the blade trailing edge boundary layer with low energy.

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