Changes between Version 5 and Version 6 of doc/tec/wtm

Timestamp:

May 17, 2019 3:34:36 PM (6 years ago)

Author:

witha

Comment:

--

doc/tec/wtm

@@ -1 +1 @@
 = Wind turbine model =
+
+[[NoteBox(note,**This page is under construction!, 400px)]]
 
 == Overview ==
@@ -8 +10 @@
 == 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 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 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.
-[[Image(ADM-R_neu.png,300px)]]
+
+[[Image(ADM-R_neu.png,150px)]]
+
+For each segment the local lift and drag forces ''f'',,l,, and ''f'',,d,, per unit area are calculated:
+{{{
+#!Latex
+\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*}
+}}}
+''U'',,rel,, 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. ''c'',,l,, and ''c'',,d,, are the lift and drag coefficients of the blades, respectively, which vary along the blade. The factor
+{{{
+#!Latex
+$N_{b}c / 2\pi r_{seg}$
+}}}
+represents the solidity ratio of the rotor blades (with the number of rotor blades ''N'',,b,,, the chord ''c'' and the distance of the segment from the centre of the rotor disk ''r'',,seg,,). 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 Jonkman et al., 2009]).
+
+to be continued...
 
 == How to use the PALM-WTM with other turbine data ==