Nonlinear Wake Model Research Articles

Erratum to: A nonlinear wake model of a wind turbine considering the yaw wake steering

Erratum to: A nonlinear wake model of a wind turbine considering the yaw wake steering

A nonlinear wake model of a wind turbine considering the yaw wake steering

A nonlinear wake model of a wind turbine considering the yaw wake steering

Power Prediction of Wind Farms via a Simplified Actuator Disk Model

This paper aims to demonstrate a simplified nonlinear wake model that fills the technical gap between the low-cost and less-accurate linear formulation and the high-cost and high-accuracy large eddy simulation, to offer a suitable balance between the prediction accuracy and the computational cost, and also to establish a robust approach for long-term wind farm power prediction. A simplified actuator disk model based on the momentum theory is proposed to predict the wake interaction among wind turbines along with their power output. The three-dimensional flow field of a wind farm is described by the steady continuity and momentum equation coupled with a k-ε turbulence model, where the body force representing the aerodynamic impact of the rotor blade on the airflow is uniformly distributed in the Cartesian cells within the actuator disk. The characteristic wind conditions identified from the data of the supervisory control and data acquisition (SCADA) system were employed to build the power matrix of these typical wind conditions for reducing the computation demands to estimate the yearly power production. The proposed model was favorably validated with the offshore measurement of Horns Rev wind farm, and three Taiwanese onshore wind farms were forecasted for their yearly capacity factors with an average error less than 5%, where the required computational cost is estimated about two orders of magnitude smaller than that of the large eddy simulation. However, the proposed model fails to pronouncedly reproduce the individual power difference among wind turbines in the investigated wind farm due to its time-averaging nature.

Development of an Equivalent Wind Farm Model for Frequency Regulation

The operational security of power systems for wind farm (WF) integration becomes more important as the penetration of wind generation increases. A WF may contain hundreds of wind turbines (WT) and thus the power system simulations based on the complex model of a WT consume much time. This article proposes an equivalent WF model with the frequency-regulation function. The main research works include the establishment of the generic model of a WT, the development of single- and multimachine equivalent models for a large WF, the clustering of WTs based on the developed nonlinear wake model and the fuzzy C-means (FCM) clustering algorithm, the integration of the frequency-regulation function into the equivalent WF model, and the validation of the developed equivalent WF model by various operating scenarios. The results demonstrate that the proposed multimachine equivalent method based on the FCM clustering provides a more accurate model than a single-WT equivalent model. Consequently, the research results provide a solution for simulating a large-scale wind power integration, providing efficient, accurate, and fast steady-state and dynamic analyses.

A nonlinear model for aerodynamic configuration of wake behind horizontal-axis wind turbine

Determination of the aerodynamic configuration of wake is the key to analysis and evaluation of the rotor aerodynamic characteristics of a horizontal-axis wind turbine. According to the aerodynamic configuration, the real magnitude and direction of the on-flow velocity at the rotor blade can be determined, and subsequently, the aerodynamic force on the rotor can be determined. The commonly employed wake aerodynamic models are of the cylindrical form instead of the actual expanding one. This is because the influence of the radial component of the induced velocity on the wake configuration proper is neglected. Therefore, this model should be called a “linear model”. Using this model means that the induced velocities at the rotor blades and aerodynamic loads on them would be inexact. An approximately accurate approach is proposed in this paper to determine the so-called “nonlinear” wake aerodynamic configuration by means of the potential theory, where the influence of all three coordinate components of the induced velocity on wake aerodynamic configuration is taken into account to obtain a kind of expanding wake that approximately looks like an actual one. First, the rotor aerodynamic model composed of axial (central), bound, and trailing vortexes is established with the help of the finite aspect wing theory. Then, the Biot-Savart formula for the potential flow theory is used to derive a set of integral equations to evaluate the three components of the induced velocity at any point within the wake. The numerical solution to the integral equations is found, and the loci of all elementary trailing vortex filaments behind the rotor are determined thereafter. Finally, to formulate an actual wind turbine rotor, using the nonlinear wake model, the induced velocity everywhere in the wake, especially that at the rotor blade, is obtained in the case of various tip speed ratios and compared with the wake boundary in a neutral atmospheric boundary layer. Hereby, some useful and referential conclusions are offered for the aerodynamic computation and design of the rotor of the horizontal-axis wind turbine.

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

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.

Research of the Nonlinear Wake Model of HAWT

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.

Contrasting the Cartesian and polar forms of the shedding-induced force vector in response to 12 subharmonic and superharmonic mechanical excitations

We mechanically excited the near-field shedding of the von Kármán vortex street of a stationary cylinder at Reynolds number 300 by moving it sinusoidally with 12 different frequencies. We first solved the incompressible Navier–Stokes equations using the finite difference method and obtained unexcited shedding, which occurs at the Strouhal frequency. Then, we applied six subharmonic excitations with rational frequency ratios (defined as the excitation frequency to the Strouhal frequency) in the form 1/n and six superharmonic excitations with frequency ratios n, where n is an integer taking values between 2 and 7. We compared the behavior of the shedding-induced force vector acting on the cylinder in each excitation case to their counterparts in the other excitation cases and to the case of the stationary cylinder. This force vector has two representations: lift and drag (Cartesian) or magnitude and direction (polar). Whereas the first representation is commonly used in theoretical fluid mechanics and engineering applications, we found that the second representation is favored in terms of revealing how the force vector responds to the applied excitations. For example, the mean and standard deviation of the drag do not show clear trends with the excitation frequency, whereas the force magnitude changes quadratically with it. We showed that the theoretical analysis of a simplified nonlinear wake model does in fact support this behavior. We found three modes of shedding-induced force in response to mechanical excitation, depending on the ratio of excitation frequency to Strouhal frequency. Near-field shedding is not entrained by excitation for all subharmonic excitations, but it is entrained for all superharmonic excitations. For entrained shedding, we found two behaviors of the shedding-induced force vector, which is periodic only at odd frequency ratios.

Experimental and Computational Investigation of the Knoller-Betz Effect

The ability of a sinusoidally plunging airfoil to produce thrust, known as the Knoller-Betz or Katzmayr effect, is investigated experimentally and numerically. Water-tunnel experiments are performed providing flow visualization and laser Doppler velocimetry data of the unsteady wakes formed by the plunging foils. Vortical structures and time-averaged velocity profiles in the wake are compared with numerical computations from a previously developed inviscid, unsteady panel code that utilizes a nonlinear wake model