Research of the Nonlinear Wake Model of HAWT

2013 ◽  
Vol 448-453 ◽  
pp. 1747-1753
Author(s):  
Rui Yang ◽  
Sheng Long Zhang ◽  
Jiu Xin Wang
Keyword(s):  
Radial Component ◽  
Wake Vortex ◽  
Surface Model ◽  
Trailing Edge ◽  
Vortex Sheets ◽  
Central Vortex ◽  
Actuator Disc ◽  
Horizontal Axis Wind Turbines ◽  
Wake Model ◽  
Induced Velocity

In the existing linear wake (cylindrical surface) model of horizontal axis wind turbines, the rotor was taken as the actuator-disc composed of infinite blades with infinitesimal chords. The distribution of variable circulation along blade was not taken into account and the span-wise (or radial) component of induced velocity is totally ignored. And assumed that the all trailing vortex filament shed from blade trailing edge would locate on their own cylindrical stream-surface. This aerodynamic model for determination of wake configuration is obviously different from that actually observed wake in wind tunnel experiment. Therefore, a "nonlinear" wake model was proposed, in this model the wake vortex system was divided into the central vortex along rotor axis, the bound vortex along blade axis, the wake vortex sheets shed from blade trailing edge and extent into infinity behind the rotor. Then, on the basis of potential theory in fluid mechanics a set of integral equations for evaluation of induced velocity in wake were derived with Biot-Savarts formula.

Analysis on Aerodynamic Performance of Horizontal Axis Wind Turbine Based on Nonlinear Wake Model

2013 ◽  
Vol 448-453 ◽  
pp. 1716-1720
Author(s):  
Rui Yang ◽  
Jiu Xin Wang ◽  
Sheng Long Zhang
Keyword(s):  
Wind Turbine ◽  
Wind Turbines ◽  
Optimization Design ◽  
Aerodynamic Performance ◽  
Horizontal Axis ◽  
Wake Vortex ◽  
Horizontal Axis Wind Turbine ◽  
Horizontal Axis Wind Turbines ◽  
Wake Model ◽  
Induced Velocity

A computational method based on nonlinear wake model was established for horizontal axis wind turbines aerodynamic performance prediction. This method makes use of finite difference method to solve the integral differential equation of the model, the induced velocity of wake vortex can be calculated from equations and compared with the induced velocity of wake vortex in linear model. The comparison between the calculated results of wind turbine under axis flow condition, including tip vortex geometry and aerodynamic performance, and available experimental data shows that this method is suitable for wind turbine aerodynamic performance analysis. Finally, a series of numerical calculations were made to investigate the change of wake geometry and aerodynamic performance of the wind turbine when yawing and pitch angle increasing, which provide foundations for aerodynamic optimization design of horizontal axis wind turbines.

On the Optimum Pressure Drop of Axial Kinetic Turbines Operating Within Nozzles

2018 ◽  
Author(s):  
Jaime Moreu ◽  
Ricardo García-Morato ◽  
Jesús Valle ◽  
Santiago de Guzmán ◽  
Miriam Terceño
Keyword(s):  
Pressure Drop ◽  
Turbine Blades ◽  
Radial Component ◽  
Optimum Pressure ◽  
Cost Of Energy ◽  
Actuator Disc ◽  
Points Of View ◽  
Ultimate Objective ◽  
Induced Velocity ◽  
Energy Harnessing

Kinetic turbines harnessing tidal and ocean currents make use, in some designs, of nozzles and/or diffusers. Nozzles come at a cost, but they can help from the structural, hydrodynamic or positioning points of view. In those cases, they might make sense as long as they drive the LCoE (Levelized Cost of Energy) down, which is the ultimate objective of energy-harnessing devices. The design must then optimize the combined performance of both blades and nozzle. However, the interaction between turbine blades and nozzle is not always fully clear, and even less its optimization. A relevant amount of efficiency can be lost if the design spiral is not appropriate. The authors have suggested in [1] an approach for the optimization of turbines within nozzles. This approach was followed in [2] and validated with model tests. In the approach, the turbine is initially substituted by an actuator disc that applies a radially constant pressure drop. But in these references, the optimum pressure drop in the actuator disc was the same as if there was no nozzle at all, i.e., 4/9ρv2. This is equivalent to considering the nozzle coefficient does not depend on the pressure drop, and thus, on the induced velocity field. Hence it is a somewhat arbitrary assumption. This paper describes, using actuator disc theory, how nozzles affect the disc optimum pressure drop in uniform flow conditions. The effect of a hub is also analyzed. Then, using a viscous FVM CFD code, the variation of the pressure drop is quantified for two different acceleration nozzles, one suffering flow separation and the other one not. As the pressure drop increases, so does the flow expansion downstream. This rises the average radial component of velocity at the nozzle, increasing the thrust and nozzle coefficient. Therefore the optimum pressure drop goes up compared to that without nozzle. The increment in efficiency that can be obtained with this approach is quantified for the studied nozzles. Finally, the integration of this effect into the blade design is discussed.

The aerodynamics of hovering insect flight. V. A vortex theory

1984 ◽  
Vol 305 (1122) ◽  
pp. 115-144 ◽  
Keyword(s):  
Correction Factor ◽  
Insect Flight ◽  
Vortex Sheet ◽  
Hovering Flight ◽  
Vortex Theory ◽  
Actuator Disc ◽  
Temporal Pressure ◽  
The Mean ◽  
Wake Model ◽  
Induced Velocity

A full derivation is presented for the vortex theory of hovering flight outlined in preliminary reports. The theory relates the lift produced by flapping wings to the induced velocity and power of the wake. Suitable forms of the momentum theory are combined with the vortex approach to reduce the mathematical complexity as much as possible. Vorticity is continuously shed from the wings in sympathy with changes in wing circulation. The vortex sheet shed during a half-stroke convects downwards with the induced velocity field, and should be approximately planar at the end of a half-stroke. Vorticity within the sheet will roll up into complicated vortex rings, but the rate of this process is unknown. The exact state of the sheet is not crucial to the theory, however, since the impulse and energy of the vortex sheet do not change as it rolls up, and the theory is derived on the assumption that the extent of roll-up is negligible. The force impulse required to generate the sheet is derived from the vorticity of the sheet, and the mean wing lift is equal to that impulse divided by the period of generation. This method of calculating the mean lift is suitable for unsteady aerodynamic lift mechanisms as well as the quasi-steady mechanism. The relation between the mean lift and the impulse of the resulting vortex sheet is used to develop a conceptual artifice - a pulsed actuator disc - that approximates closely the net effect of the complicated lift forces produced in hovering. T he disc periodically applies a pressure impulse over some defined area, and is a generalized form of the Froude actuator disc from propeller theory. The pulsed disc provides a convenient link between circulatory lift and the powerful momentum and vortex analyses of the wake. The induced velocity and power of the wake are derived in stages, starting with the simple Rankine-Froude theory for the wake produced by a Froude disc applying a uniform, continuous pressure to the air. The wake model is then improved by considering a ‘modified’ Froude disc exerting a continuous, but non-uniform pressure. This step provides a spatial correction factor for the Rankine-Froude theory, by taking into account variations in pressure and circulation over the disc area. Finally, the wake produced by a pulsed Froude disc is analysed, and a temporal correction factor is derived for the periodic application of spatially uniform pressures. Both correction factors are generally small, and can be treated as independent perturbations of the Rankine-Froude model. Thus the corrections can be added linearly to obtain the total correction for the general case of a pulsed actuator disc with spatial and temporal pressure variations. The theory is compared with Rayner’s vortex theory for hovering flight. Under identical test conditions, numerical results from the two theories agree to within 3%. Rayner presented approximations from his results to be used when applying his theory to hovering animals. These approximations are not consistent with my theory or with classical propeller theory, and reasons for the discrepancy are suggested.

Optimal Placement of Horizontal- and Vertical-Axis Wind Turbines in a Wind Farm for Maximum Power Generation Using a Genetic Algorithm

2011 ◽  
Author(s):  
Xiaomin Chen ◽  
Ramesh Agarwal
Keyword(s):  
Genetic Algorithm ◽  
Wind Turbines ◽  
Wind Farm ◽  
Optimization Problem ◽  
Vertical Axis ◽  
Optimal Placement ◽  
Vertical Axis Wind Turbines ◽  
Wake Effects ◽  
Horizontal Axis Wind Turbines ◽  
Wake Model

In this paper, we consider the Wind Farm layout optimization problem using a genetic algorithm. Both the Horizontal–Axis Wind Turbines (HAWT) and Vertical-Axis Wind Turbines (VAWT) are considered. The goal of the optimization problem is to optimally place the turbines within the wind farm such that the wake effects are minimized and the power production is maximized. The reasonably accurate modeling of the turbine wake is critical in determination of the optimal layout of the turbines and the power generated. For HAWT, two wake models are considered; both are found to give similar answers. For VAWT, a very simple wake model is employed.

A modified near wake dynamic model for rotor analysis

1999 ◽  
Vol 103 (1021) ◽  
pp. 143-146 ◽  
Author(s):  
T. Wang ◽  
F. N. Coton
Keyword(s):  
High Resolution ◽  
Dynamic Model ◽  
Numerical Evaluation ◽  
Helicopter Rotor ◽  
Vortex Interaction ◽  
Near Wake ◽  
Blade Vortex Interaction ◽  
Wake Model ◽  
Induced Velocity

Abstract The Beddoes near wake model, developed for high resolution blade vortex interaction computations, enables efficient numerical evaluation of the downwash due to trailed vorticity in the near wake of a helicopter rotor. The model is, however, limited by the assumption that the near wake lies in the plane of the rotor and, in some cases, by its inability to accurately evaluate the induced velocity contribution from vorticity trailed from inboard blade sections. In this paper, modifications to the method are proposed which address these issues and allow it to be used with confidence over a wider range of rotor flows.

scholarly journals A Modified Free Wake Vortex Ring Method for Horizontal-Axis Wind Turbines

Energies ◽  
2019 ◽  
Vol 12 (20) ◽  
pp. 3900 ◽  
Author(s):  
Jing Dong ◽  
Axelle Viré ◽  
Carlos Simao Ferreira ◽  
Zhangrui Li ◽  
Gerard van Bussel
Keyword(s):  
Wind Turbine ◽  
Vortex Ring ◽  
Horizontal Axis ◽  
Wake Vortex ◽  
Horizontal Axis Wind Turbine ◽  
Vortex Model ◽  
Ring Method ◽  
Wake Model ◽  
Free Wake ◽  
Platform Motions

A modified free-wake vortex ring model is proposed to compute the dynamics of a floating horizontal-axis wind turbine, which is divided into two parts. The near wake model uses a blade bound vortex model and trailed vortex model, which is developed based on vortex filament method with straight lifting lines assumption. By contrast, the far wake model is based on the vortex ring method. The proposed model is a good compromise between accuracy and computational cost, for example when compared with more complex vortex methods. The present model is used to assess the influence of floating platform motions on the performance of a horizontal-axis wind turbine rotor. The results are validated on the 5 MW NREL rotor and compared with other aerodynamic models for the same rotor subjected to different platform motions. The results show that the proposed method is reliable. In addition, the proposed method is less time consuming and has similar accuracy when comparing with more advanced vortex based methods.

Investigation and validation of 3D wake model for horizontal-axis wind turbines based on filed measurements

2020 ◽  
Vol 260 ◽  
pp. 114272 ◽  
Author(s):  
Xiaoxia Gao ◽  
Bingbing Li ◽  
Tengyuan Wang ◽  
Haiying Sun ◽  
Hongxing Yang ◽  
...  
Keyword(s):  
Wind Turbines ◽  
Horizontal Axis ◽  
Horizontal Axis Wind Turbines ◽  
Wake Model

A numerical investigation of the rolling-up of vortex sheets

1980 ◽  
Vol 373 (1752) ◽  
pp. 67-91 ◽  
Keyword(s):  
Numerical Integration ◽  
Numerical Investigation ◽  
Equations Of Motion ◽  
Additional Term ◽  
Vortex Sheet ◽  
Time Step ◽  
Vortex Sheets ◽  
Numerical Instabilities ◽  
Sinusoidal Disturbance ◽  
Induced Velocity

In this paper the development of a vortex sheet due to an initially sinusoidal disturbance is calculated. When determining the induced velocity in points of the vortex sheet, it can be represented by concentrated vortices but it is shown that it is analytically more correct to add an additional term that represents the effect of the immediate neighbourhood of the point considered. The equations of motion were integrated by a Runge-Kutta technique to exclude numerical instabilities. The time step was determined by the requirement that a quantity (Hamiltonian) that remains invariant as a result of the equations of motion, should not change more than a certain amount in the numerical integration of the equations of motion. One difficulty is that if a greater number of concentrated vortices are introduced to represent the vortex sheet, the effect of round-off errors becomes more important. The number of figures retained in the computations limits the number of concentrated vortices. Where the round-off errors have been kept sufficiently small, a process of rolling-up of vorticity clearly occurs. There is no point in pursuing the calculations much beyond this point, first because the representation of the vortex sheet by concentrated vortices becomes more and more inaccurate and secondly because viscosity will have the effect of transforming the rolled-up vortex sheet into a region of vorticity.

Analysis and optimization of morphing wing aerodynamics

2019 ◽  
Vol 91 (3) ◽  
pp. 538-546 ◽  
Author(s):  
Witold Artur Klimczyk ◽  
Zdobyslaw Jan Goraj
Keyword(s):  
Optimal Solution ◽  
Design Sensitivity ◽  
Substantial Improvement ◽  
Surface Model ◽  
Morphing Wing ◽  
Trailing Edge ◽  
Significant Information ◽  
Content Type ◽  
Additional Information ◽  
Wing Optimization

PurposeThe purpose of this paper is to present a method for analysis and optimization of morphing wing. Moreover, a numerical advantage of morphing airfoil wing, typically assessed in simplified two-dimensional analysis is found using higher fidelity methods.Design/methodology/approachBecause of multi-point nature of morphing wing optimization, an approach for optimization by analysis is presented. Starting from naïve parametrization, multi-fidelity aerodynamic data are used to construct response surface model. From the model, many significant information are extracted related to parameters effect on objective; hence, design sensitivity and, ultimately, optimal solution can be found.FindingsThe method was tested on benchmark problem, with some easy-to-predict results. All of them were confirmed, along with additional information on morphing trailing edge wings. It was found that wing with morphing trailing edge has around 10 per cent lower drag for the same lift requirement when compared to conventional design.Practical implicationsIt is demonstrated that providing a smooth surface on wing gives substantial improvement in multi-purpose aircrafts. Details on how this is achieved are described. The metodology and results presented in current paper can be used in further development of morphing wing.Originality/valueMost of literature describing morphing airfoil design, optimization or calculations, performs only 2D analysis. Furthermore, the comparison is often based on low-fidelity aerodynamic models. This paper uses 3D, multi-fidelity aerodynamic models. The results confirm that this approach reveals information unavailable with simplified models.

Optimization of Wind Turbine Blades Using Lifting Surface Method and Genetic Algorithm

2011 ◽  
Author(s):  
Xin Shen ◽  
Xiao-cheng Zhu ◽  
Zhao-hui Du
Keyword(s):  
Genetic Algorithm ◽  
Design Method ◽  
Turbine Blades ◽  
Optimization Method ◽  
Efficient Design ◽  
Wind Turbine Blades ◽  
Surface Method ◽  
Lifting Surface ◽  
Horizontal Axis Wind Turbines ◽  
Wake Model

This paper describes an optimization method for the design of horizontal axis wind turbines using the lifting surface method as the performance prediction model and a genetic algorithm for optimization. The aerodynamic code for the design method is based on the lifting surface method with a prescribed wake model for the description of the wake. A micro genetic algorithm handles the decision variables of the optimization problem such as the chord and twist distribution of the blade. The scope of the optimization method is to achieve the best trade off of the following objectives: maximum of annual energy production and minimum of blade loads including thrust and blade rood flap-wise moment. To illustrate how the optimization of the blade is carried out the procedure is applied to NREL Phase VI rotor. The result shows the optimization model can provide a more efficient design.

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