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# Title: Starting vortex of a NACA 2414 aerofoil
#
# Description:
#
# According to Wikipedia a
# \url{http://en.wikipedia.org/wiki/Starting_vortex}{`Starting
# vortex'} \begin{quotation}is a vortex which forms in the air
# adjacent to the trailing edge of an airfoil as it is accelerated
# from rest in a fluid. It leaves the airfoil\ldots, and remains
# (nearly) stationary in the flow. \end{quotation} Or in the frame of
# reference of the aerofoil, it appears to recede behind the wing.
# The phenomenon is fundamental to the understanding of the generation
# of lift by aerofoils; see e.g. \cite{glauert1926} (Figure 69, p. 121) or
# \cite{videler2006} (Figure 1.5, p. 21).
#
# A starting vortex is easily generated in a Gerris simulation, as
# shown here. It does not depend for its existence on the viscosity
# of the air, or the third dimension, so here we solve the
# two-dimensional Euler equations.
#
# The phenomenon does depend on the trailing edge being sharp, as it
# is for most aerofoils. There is a great collection of such shapes
# at the
# \url{http://www.ae.illinois.edu/m-selig/ads/coord\_database.html}{UIUC
# Airfoil Coordinates Database}. The coordinates from these files can
# be converted to a Gerris solid surface using the Gerris command line
# utility \url{http://gfs.sourceforge.net/wiki/index.php/Shapes}{shapes}.
# Here we use a classic aerofoil, the NACA 2414 \cite{jacobs1933}, from
# \url{http://www.ae.illinois.edu/m-selig/ads/coord/n2414.dat}{n2414.dat}.
#
# Static refinement around the wing section is necessary to capture
# the shape well in a Cartesian quad-tree grid. The grid is also
# adaptively refined on the vorticity to resolve the trailing vortex
# as it recedes into the wake.
#
# \begin{figure}[htbp]
# \caption{\label{movie}Generation of a starting vortex in plane flow
# over a NACA 2414 aerofoil at 6$^\circ$ incidence. The colour is vorticity
# (red positive anticlockwise).}
# \begin{center}
# \htmladdnormallinkfoot{\includegraphics[width=0.8\hsize]{starting.eps}}{starting.mpg}
# \end{center}
# \end{figure}
#
# Author: G. D. McBain
# Command: sh starting.sh n2414 6 | gfsview2D starting.gfv
# Version: 110213-051327
# Required files: starting.sh starting.gfv n2414.dat
# Running time: 5 minutes
# Generated files: starting.mpg starting.eps
Define FRAMEPERIOD 0.02
3 2 GfsSimulation GfsBox GfsGEdge {} {
Time { end = 1.5 } # exit - trailing edge = (3-0.5) - 1 = 1.5
RefineSolid 9
Solid AEROFOIL.gts { rz = -INCIDENCE }
Init {} { U = 1 }
AdaptVorticity { istep = 1 } { maxlevel = 8 cmax = 5e-2 }
OutputTime { step = FRAMEPERIOD } stderr
OutputSimulation { step = FRAMEPERIOD } stdout
GModule gfsview
OutputView { step = FRAMEPERIOD } { ppm2mpeg > starting.mpg } {
width = 720 height = 240
} starting.gfv
OutputView { start = 1. } { convert ppm:- -geometry 720x240 starting.eps } {
format = PPM width = 1440 height = 480
} starting.gfv
}
GfsBox { left = GfsBoundaryInflowConstant 1 }
GfsBox { }
GfsBox { right = GfsBoundaryOutflow }
1 2 right
2 3 right
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