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Version 8 (modified by witha, 5 years ago) (diff)

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Wind turbine model

This page is under construction!

Overview

Since r1916 a wind turbine model (WTM) is included in PALM that parameterises the effect of individual wind turbines on the flow. The PALM WTM is based on an advanced actuator disk model approach. It contains a turbine controller including speed control, pitch control and yaw control. By default, the PALM-WTM includes the publicly available data for the NREL 5 MW reference turbine (Jonkman et al., 2009), but it can be adapted for "real" turbine data as described below.

Technical description of the PALM-WTM

The PALM-WTM is based on the common actuator disk model (ADM) approach in which the rotor of a wind turbine is represented by a permeable disk that extracts energy from the flow by applying a thrust force at the disk. While in the frequently used simple version of the ADM (e.g. as proposed by Calaf et al. (2010) the forces are uniformly distributed and only the thrust force is considered (thus ignoring the torque), the WTM provides an advanced ADM (ADM-R) that considers varying forces over the rotor disk and rotation of the rotor blades although these are not resolved. The basic concept is similar to the ADM-R proposed by Wu and Porté-Agel (2011) with several modifications. The rotor plane is divided into rings and segments such that the segments have an equal size which is a function of the grid spacing.

Figure 1 (right): Schematic representation of the advanced actuator disk method with the rotor disk segments and the axial (blue arrows) and tangential (red arrows) forces acting on the flow. The grey arrows are representing the tower thrust force.

Figure 1 (left): Descriptive illustration of the forces acting on a blade element.

For each segment the local lift and drag forces fl and fd per unit area are calculated:

\begin{equation*} f_l = \frac{1}{2}\rho U^{2}_{rel}c_l\frac{N_{b}c}{2\pi r_{seg}} \end{equation*} \begin{equation*} f_d = \frac{1}{2}\rho U^{2}_{rel}c_d\frac{N_{b}c}{2\pi r_{seg}} \end{equation*}

Urel is the local relative velocity in the centre of the segment. It is calculated from the local wind speed components (interpolation from the nearest grid points) and the velocity of the blades. cl and cd are the lift and drag coefficients of the blades, respectively, which vary along the blade. The factor

$N_{b}c / 2\pi r_{seg}$

represents the solidity ratio of the rotor blades (with the number of rotor blades Nb, the chord c and the distance of the segment from the centre of the rotor disk rseg). The blade properties have to be specified by the user. By default, the WTM includes publicly available data for the NREL 5 MW reference turbine (Jonkman et al., 2009).

In a second step, the lift and drag forces are projected onto the axial and tangential planes, multiplied by a factor of -1 (Newton's third law):

\begin{equation*} f_{\theta} = -f_l \sin{\phi} - f_d \cos{\phi} \end{equation*} \begin{equation*} f_{N} = -f_l \cos{\phi} - f_d \sin{\phi} \end{equation*}

with

\begin{equation*} \phi = \arctan{\frac{U_N}{\Omega r - U_{\theta}}} \end{equation*}

where UN is the velocity in axial direction and Uθ the velocity in tangential direction (along the circular movement of the rotor blade element, as shown in Figure 2). Ω denotes the rotational speed of the rotor.

Finally, the forces are smeared and interpolated to the PALM grid points. To optimise the performance of the time-consuming 3d smearing process. the smearing is done with a Polynomial function instead of the standard Gaussian smearing and confined to the region around the rotor ().

to be continued...

How to use the PALM-WTM with other turbine data

References

  • Jonkman JM, Butterfield S, Musial W, Scott G 2009. Definition of a 5-MW reference wind turbine for offshore system development. Technical Report NREL/TP-500-38060, National Renewable Energy Laboratory, Golden, Colorado.

old

A description of the wind turbine model will follow soon.

So far, you will find an example case in your PALM distribution (starting from r1914) under ​trunk/EXAMPLES/wind_turbine. The text file ​example_wtm.txt includes some instructions how to use the wind turbine model.

We recommend using the most recent PALM version as the wind turbine model is updated from time to time and only recently a bug has been fixed which caused problems with one compiler.

The steering parameters for the wind turbine model are listed and described here.

In case of any question, please do not hesitate to contact Dr. Björn Witha (ForWind, Carl von Ossietzky Universität Oldenburg): bjoern.witha <at> uol.de

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