scholarly journals A Novel Analytical Wake Model with a Cosine-Shaped Velocity Deficit

Energies ◽  
2020 ◽  
Vol 13 (13) ◽  
pp. 3353
Author(s):  
Ziyu Zhang ◽  
Peng Huang ◽  
Haocheng Sun
Keyword(s):  
Wind Turbine ◽  
Numerical Data ◽  
Streamwise Velocity ◽  
Momentum Conservation ◽  
Velocity Deficit ◽  
Proposed Model ◽  
Roughness Lengths ◽  
Wake Model ◽  
Aerodynamic Roughness ◽  
Ambient Turbulence

A novel analytical model is proposed and validated in this paper to predict the velocity deficit in the wake downwind of a wind turbine. The model is derived by employing mass and momentum conservation and assuming a cosine-shaped distribution for the velocity deficit. In this model, a modified wake growth rate rather than a constant one is chosen to take into account the effects of the ambient turbulence and the mechanical turbulence generated. The model was tested against field observations, wind-tunnel measurements in different thrust operations and high-resolution large-eddy simulations (LES) for two aerodynamic roughness lengths. It was found that the normalized velocity deficit predicted by the proposed model shows good agreement with experimental and numerical data in terms of shape and magnitude in the far wake region ( x / d 0 > 3 ). Based on the proposed model, predictions from multiple views and at different locations are demonstrated to show the spatial distribution of streamwise velocity downwind of a wind turbine. The result shows that the model is suitable for predicting streamwise velocity fields and thus could provide some references for the selection of wind turbine spacing.

scholarly journals An Analytical Model for the Effect of Vertical Wind Veer on Wind Turbine Wakes

Energies ◽  
2018 ◽  
Vol 11 (7) ◽  
pp. 1838 ◽  
Author(s):  
Mahdi Abkar ◽  
Jens Sørensen ◽  
Fernando Porté-Agel
Keyword(s):  
Wind Turbine ◽  
Input Parameter ◽  
Mass Conservation ◽  
Wake Flow ◽  
Mean Velocity ◽  
Gaussian Shape ◽  
Velocity Deficit ◽  
Proposed Model ◽  
The Mean ◽  
Wake Model

In this study, an analytical wake model for predicting the mean velocity field downstream of a wind turbine under veering incoming wind is systematically derived and validated. The new model, which is an extended version of the one introduced by Bastankhah and Porté-Agel, is based upon the application of mass conservation and momentum theorem and considering a skewed Gaussian distribution for the wake velocity deficit. Particularly, using a skewed (instead of axisymmetric) Gaussian shape allows accounting for the lateral shear in the incoming wind induced by the Coriolis force. This analytical wake model requires only the wake expansion rate as an input parameter to predict the mean wake flow downstream. The performance of the proposed model is assessed using the large-eddy simulation (LES) data of a full-scale wind turbine wake under the stably stratified condition. The results show that the proposed model is capable of predicting the skewed structure of the wake downwind of the turbine, and its prediction for the wake velocity deficit is in good agreement with the high-fidelity simulation data.

scholarly journals Characterization of Wind Turbine Wakes with Nacelle-Mounted Doppler LiDARs and Model Validation in the Presence of Wind Veer

2019 ◽  
Vol 11 (19) ◽  
pp. 2247 ◽  
Author(s):  
Peter Brugger ◽  
Fernando Carbajo Fuertes ◽  
Mohsen Vahidzadeh ◽  
Corey D. Markfort ◽  
Fernando Porté-Agel
Keyword(s):  
Wind Turbine ◽  
Model Validation ◽  
Cross Section ◽  
Model Prediction ◽  
Tilt Angle ◽  
Full Scale ◽  
Efficient Design ◽  
Velocity Deficit ◽  
Wake Model

Accurate prediction of wind turbine wakes is important for more efficient design and operation of wind parks. Volumetric wake measurements of nacelle-mounted Doppler lidars are used to characterize the wake of a full-scale wind turbine and to validate an analytical wake model that incorporates the effect of wind veer. Both, measurements and model prediction, show an elliptical and tilted spanwise cross-section of the wake in the presence of wind veer. The error between model and measurements is reduced compared to a model without the effect of wind veer. The characterization of the downwind velocity deficit development and wake growth is robust. The wake tilt angle can only be determined for elliptical wakes.

scholarly journals Modelling Yawed Wind Turbine Wakes: Extension of a Gaussian-Based Wake Model

Energies ◽  
2021 ◽  
Vol 14 (15) ◽  
pp. 4494
Author(s):  
De-Zhi Wei ◽  
Ni-Na Wang ◽  
De-Cheng Wan
Keyword(s):  
Transverse Velocity ◽  
Engineering Application ◽  
Streamwise Velocity ◽  
Steering Control ◽  
Eddy Simulation ◽  
Proposed Model ◽  
Large Eddy ◽  
Wake Model ◽  
Short Time ◽  
Far Wake

Yaw-based wake steering control is a potential way to improve wind plant overall performance. For its engineering application, it is crucial to accurately predict the turbine wakes under various yawed conditions within a short time. In this work, a two-dimensional analytical model is proposed for far wake modeling under yawed conditions by taking the self-similarity assumption for the streamwise velocity deficit and skewness angle at hub height. The proposed model can be applied to predict the wake center trajectory, streamwise velocity, and transverse velocity in the far-wake region downstream of a yawed turbine. For validation purposes, predictions by the newly proposed model are compared to wind tunnel measurements and large-eddy simulation data. The results show that the proposed model has significantly high accuracy and outperforms other common wake models. More importantly, the equations of the new proposed model are simple, the wake growth rate is the only parameter to be specified, which makes the model easy to be used in practice.

scholarly journals Wake Effect and Power Production of Wind Turbine Arrays

2015 ◽  
Vol 9 (11) ◽  
pp. 77
Author(s):  
Ismail Ismail ◽  
Samsul Kamal ◽  
Purnomo Purnomo ◽  
Sarjiya Sarjiya ◽  
Sulaiman Tampubolon
Keyword(s):  
Wind Turbine ◽  
Turbulence Intensity ◽  
Wake Flow ◽  
Mechanical Power ◽  
Centerline Velocity ◽  
Downwind Distance ◽  
Wake Effect ◽  
Velocity Deficit ◽  
Ambient Turbulence ◽  
Turbine Arrays

This study experimentally investigated the influence of wake effect and production of mechanical power in wind tunnel of wind turbine arrays. Wind turbine arrays consist of 2 rows with 3 columns for spacing wind turbines in rows apart in the windward direction 1.77 rotor diameters and apart in the crosswind direction 8.85 rotor diameters. The wake characteristics such as profiles of time averaged velocity, turbulence intensity, centerline velocity deficit and wake radius for far wake regions in position 1, 2, and 3 were measured and analysed. The vertical and lateral profiles of velocity and turbulence intensity were studied. Concerning the results from measured data, empirical relations for the centerline velocity deficit, turbulence intensity and wake radius were proposed. Based on the experimental results, the power loss is due to the wake flow of upwind turbine approximately 20% when the downwind distance 8.85 rotor diameters. This is different with numerical result study that 11% at downwind distance is 8.85 rotor diameters. This difference results from the influence of ambient turbulence on the production of mechanical power of the wind turbine.

scholarly journals A Theoretical Model with Which to Safely Optimize the Configuration of Hydraulic Suspension of Modular Trailers in Special Road Transport

2020 ◽  
Vol 11 (1) ◽  
pp. 305
Author(s):  
Rubén Escribano-García ◽  
Marina Corral-Bobadilla ◽  
Fátima Somovilla-Gómez ◽  
Rubén Lostado-Lorza ◽  
Ash Ahmed
Keyword(s):  
Theoretical Model ◽  
Wind Turbine ◽  
Optimization Algorithm ◽  
Hydraulic Cylinder ◽  
Road Transport ◽  
Automatic Testing ◽  
Transport Systems ◽  
The Road ◽  
Proposed Model ◽  
On The Road

The dimensions and weight of machines, structures, and components that need to be transported safely by road are growing constantly. One of the safest and most widely used transport systems on the road today due to their versatility and configuration are modular trailers. These trailers have hydraulic pendulum axles that are that are attached in pairs to the rigid platform above. In turn, these modular trailers are subject to limitations on the load that each axle carries, the tipping angle, and the oil pressure of the suspension system in order to guarantee safe transport by road. Optimizing the configuration of these modular trailers accurately and safely is a complex task. Factors to be considered include the load’s characteristics, the trailer’s mechanical properties, and road route conditions including the road’s slope and camber, precipitation and direction, and force of the wind. This paper presents a theoretical model that can be used for the optimal configuration of hydraulic cylinder suspension of special transport by road using modular trailers. It considers the previously mentioned factors and guarantees the safe stability of road transport. The proposed model was validated experimentally by placing a nacelle wind turbine at different points within a modular trailer. The weight of the wind turbine was 42,500 kg and its dimensions were 5133 × 2650 × 2975 mm. Once the proposed model was validated, an optimization algorithm was employed to find the optimal center of gravity for load, number of trailers, number of axles, oil pressures, and hydraulic configuration. The optimization algorithm was based on the iterative and automatic testing of the proposed model for different positions on the trailer and different hydraulic configurations. The optimization algorithm was tested with a cylindrical tank that weighed 108,500 kg and had dimensions of 19,500 × 3200 × 2500 mm. The results showed that the proposed model and optimization algorithm could safely optimize the configuration of the hydraulic suspension of modular trailers in special road transport, increase the accuracy and reliability of the calculation of the load configuration, save time, simplify the calculation process, and be easily implemented.

An Investigation of the Aerodynamic Response of a Wind Turbine Blade to Tower Shadow

2004 ◽  
Vol 126 (4) ◽  
pp. 1034-1040 ◽  
Author(s):  
Xabier Munduate ◽  
Frank N. Coton ◽  
Roderick A.McD. Galbraith
Keyword(s):  
Wind Turbine ◽  
Turbine Blade ◽  
Careful Consideration ◽  
Wind Turbine Blade ◽  
Small Scale ◽  
Force Coefficient ◽  
Velocity Deficit ◽  
Pressure Transducers ◽  
Aerodynamic Model ◽  
Tower Shadow

This paper presents results from a wind tunnel based examination of the response of a wind turbine blade to tower shadow in head-on flow. In the experiment, one of the blades of a small-scale, two-bladed, downwind turbine was instrumented with miniature pressure transducers to allow recording of the blade surface pressure response through tower shadow. The surface pressures were then integrated to provide the normal force coefficient responses presented in this paper. It is shown that it is possible to reproduce the measured responses using an indicially formulated unsteady aerodynamic model applied to a cosine wake velocity deficit. It is also shown that agreement between the model and the measured data can be improved by careful consideration of the velocity deficit geometry.

scholarly journals Improving the FLORIS wind plant model for compatibility with gradient-based optimization

2017 ◽  
Vol 41 (5) ◽  
pp. 313-329 ◽  
Author(s):  
Jared J Thomas ◽  
Pieter MO Gebraad ◽  
Andrew Ning
Keyword(s):  
Steady State ◽  
Wind Turbine ◽  
Case Studies ◽  
Wind Farm ◽  
Optimization Problems ◽  
Algorithmic Differentiation ◽  
Function Calls ◽  
Gradient Based ◽  
Wake Model ◽  
Yaw Angle

The FLORIS (FLOw Redirection and Induction in Steady-state) model, a parametric wind turbine wake model that predicts steady-state wake characteristics based on wind turbine position and yaw angle, was developed for optimization of control settings and turbine locations. This article provides details on changes made to the FLORIS model to make the model more suitable for gradient-based optimization. Changes to the FLORIS model were made to remove discontinuities and add curvature to regions of non-physical zero gradient. Exact gradients for the FLORIS model were obtained using algorithmic differentiation. A set of three case studies demonstrate that using exact gradients with gradient-based optimization reduces the number of function calls by several orders of magnitude. The case studies also show that adding curvature improves convergence behavior, allowing gradient-based optimization algorithms used with the FLORIS model to more reliably find better solutions to wind farm optimization problems.

Modeling of a Wind Turbine Rotor Blade System

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Dayuan Ju ◽  
Qiao Sun
Keyword(s):  
Wind Turbine ◽  
Rotor Blade ◽  
Simulation Software ◽  
Wind Flow ◽  
Coupling Effects ◽  
Horizontal Axis Wind Turbine ◽  
Blade Vibration ◽  
Proposed Model ◽  
Blade System ◽  
Coupling Terms

In wind turbine blade modeling, the coupling between rotor rotational motion and blade vibration has not been thoroughly investigated. The inclusion of the coupling terms in the wind turbine dynamics equations helps us understand the phenomenon of rotor oscillation due to blade vibration and possibly diagnose faults. In this study, a dynamics model of a rotor-blade system for a horizontal axis wind turbine (HAWT), which describes the coupling terms between the blade elastic movement and rotor gross rotation, is developed. The model is developed by using Lagrange's approach and the finite-element method has been adopted to discretize the blade. This model captures two-way interactions between aerodynamic wind flow and structural response. On the aerodynamic side, both steady and unsteady wind flow conditions are considered. On the structural side, blades are considered to deflect in both flap and edge directions while the rotor is treated as a rigid body. The proposed model is cross-validated against a model developed in the simulation software fatigue, aerodynamics, structure, and turbulence (fast). The coupling effects are excluded during the comparison since fast does not include these terms. Once verified, we added coupling terms to our model to investigate the effects of blade vibration on rotor movement, which has direct influence on the generator behavior. It is illustrated that the inclusion of coupling effects can increase the sensitivity of blade fault detection methods. The proposed model can be used to investigate the effects of different terms as well as analyze fluid–structure interaction.

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