Changes between Version 6 and Version 7 of doc/tec/wtm

Timestamp:

May 24, 2019 10:43:45 AM (6 years ago)

Author:

witha

Comment:

--

doc/tec/wtm

@@ -30 +30 @@
 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]).
 
+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):
+{{{
+#!Latex
+\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 
+{{{
+#!Latex
+\begin{equation*}
+   \phi  = \arctan{\frac{U_N}{\Omega r - U_{\theta}}}
+\end{equation*}
+}}}
+where ''U'',,N,, is the velocity in axial direction and ''U'',,θ,, 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...