1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
|
# Title: Wingtip vortices behind a rectangular NACA 2414 wing
#
# Description:
#
# According to Wikipedia
# \url{http://en.wikipedia.org/wiki/Wingtip_vortices}{`Wingtip
# vortices'} \begin{quotation}are tubes of circulating air which are
# left behind a wing as it generates lift. One wingtip vortex
# trails from the tip of each wing. The cores of vortices spin at very
# high speed and are regions of very low pressure.\end{quotation}
#
# Vortex-lines cannot end in fluid (Milne-Thomson \cite{milne1973} 1973, p. 168); in
# three dimensions, the starting vortex shed by the trailing edge on
# take-off remains joined to the wing by counterrotating wingtip
# vortices, which are associated with the escape of air from the
# underside to above via the wingtips, following the negative pressure
# difference from below to above which must be present if the wing is
# generating lift.
#
# This vortex-line consisting of the starting vortex and pair of
# wingtip vortices is notionally continued and closed by the `bound
# vortex' inside the wing, associated with the circulation around the
# wing, and proportional to its lift in accordance with the
# Kutta--Joukowsky theorem.
#
# As the flow over the wing evolves from start-up to steady-state, the
# starting vortex recedes and the wing-tip vortices extend back to
# infinity. For sketches of this `horseshoe vortex' system (Glauert
# \cite{glauert1926} p. 130; Milne-Thompson \cite{milne1973} p. 172),
# see, e.g. Glauert (\cite{glauert1926} Figure 80, p. 131), Hanson
# \cite{hanson1970} (1970, Figure 2, p. 268) or Milne-Thomson
# \cite{milne1973} (1973, Figure 10-41, p. 186).
#
# \begin{figure}[htbp]
# \caption{\label{movie}Wingtip vortices behind a rectangular NACA 2414 wing.}
# \begin{center}
# \htmladdnormallinkfoot{\includegraphics[width=0.8\hsize]{wingtip.eps}}{wingtip.mpg}
# \end{center}
# \end{figure}
#
# Author: G. D. McBain
# Command: sh wingtip.sh n2414 6 | gfsview3D wingtip.gfv
# Version: 110213-051327
# Required files: n2414.dat wingtip.gfv wingtip.sh
# Running time: 26 minutes
# Generated files: wingtip.mpg wingtip.eps
Define FRAMEPERIOD 0.02
6 7 GfsSimulation GfsBox GfsGEdge {} {
Time { end = 1.5 } # exit - trailing edge = (3-0.5) - 1 = 1.5
RefineSolid 7
Solid AEROFOIL.gts { rz = -INCIDENCE }
Init {} { U = 1 }
AdaptVorticity { istep = 1 } { maxlevel = 6 cmax = 5e-2 }
OutputTime { step = FRAMEPERIOD } stderr
OutputSimulation { step = FRAMEPERIOD } stdout
GModule gfsview
OutputView { step = FRAMEPERIOD } { ppm2mpeg > wingtip.mpg } wingtip.gfv
OutputView { start = 1 } { convert ppm:- wingtip.eps } wingtip.gfv
}
# 123
# 456
GfsBox { left = GfsBoundaryInflowConstant 1 }
GfsBox { }
GfsBox { right = GfsBoundaryOutflow }
GfsBox { left = GfsBoundaryInflowConstant 1 }
GfsBox { }
GfsBox { right = GfsBoundaryOutflow }
1 2 right
2 3 right
4 5 right
5 6 right
1 4 front
2 5 front
3 6 front
|
