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Skin Friction Topology of Wing-
Body Junction Flows
H. Zhong, P. Wang, J. Shang, X. Cui AVIC Aerodynamics Research Institute, Shenyang, China
J. Wang Shenyang Aerospace University, Shenyang, China
Sudesh Woodiga, Tianshu Liu Western Michigan University, Kalamazoo, MI, USA
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Objectives
To obtain high-resolution skin friction
fields in wing-body junction flows from
luminescent oil-film images taken at
multiple viewing angles and positions
To examine the skin friction topology
of wing-body junction flows based on
the topological rules
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Topological Rule of Hunt et al. (1978)
for Junction Flows
In fact, this is a reduced case in
the collapsed sphere method
developed by Foss (2004, 2007)
0S#N#
Illustration of Wing-Body
Junction Flow (Simpson 2001)
The number of nodes equals
to that of saddles, i.e.,
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The Poincare-Bendixson Index Formula
A conservation law between the number of the singular points
in a region and the number of the switch points on the boundary:
In simple notation:
Negative Switch Point Positive Switch Point
k
k
k
k
k
k ZZ2
11I
2/)Z#Z#(1S#N#
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Topological Rule of Hunt et al. as a Reduced Case
of the P-B formula Applied to Junction Flow
02/)Z#Z#(1S#N#
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Oil Film Thickness (h) Luminescent Intensity (g)
Global Luminescent Oil-Film (GLOF)
Skin Friction Diagnostics
03
hg
X
p
2
h
Xt
h 3
i
i
2i
i
Thin-Oil Film Equation:
2
3
i
ii
2
i
i a3
gg
X
p
Xa2
g
Xt
g
)2,1i(
)2,1i(
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Surface in Object Space Image Plane
Projection onto Image Plane
k
ki2
i
2
3
i
n
ni
k
kik
k
x
h
a2
g
a3
gg
x
ph
xhg
xt
g
)a2/(gˆkk
Equivalent Skin Friction:
Projective Skin Friction:
ikik hˆ 0|h| ki
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)a2/(g
Equivalent Skin Friction:
)g,x,x(f 21Pressure Gradient and Gravity Terms:
)g,x,x(fgt/g 21
Liu & Shen, “Fluid Flow and Optical Flow”, JFM, 2008
Liu et al. “Global Luminescent Oil-Film Skin Friction Meter,”
AIAA Journal 2008
Liu et al. “Skin Friction Topology in a Region Enclosed by
Penetrable Boundary,” Exp. Fluids, 2011
Form of Physics-Based Optical Flow Equation
Inverse Problem:
To determine the equivalent skin friction field
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21
2
2
2
1212
dxdxdxdxfgt/g)(J
Variational Formulation
The functional with a smoothness constraint:
0fgt
g
xg 1
2
1
0fgt
g
xg 2
2
2
The Euler-Lagrange equations:
0n /where the Neumann condition
From two successive images, a snapshot solution is obtained.
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Fusion of Snapshot Solutions
Heuristic Fusion Methods:
(1) Superposition for Direct Fusion
(2) Wavelet-Based Fusion in Transform Domain
A sequence of snapshot solutions captures the major skin
friction signatures in different regions at different moments
in the whole process of oil film evolution.
This is due to different time scales in different regions .
Observation:
Snapshot solutions are not invariant in the process of oil
evolution unless the process is self-similar t/sh
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Mapping Skin Friction Vectors from Images onto Surface
1XmXmXm
mXmXmXmx
333232131
143132121111
1XmXmXm
mXmXmXmx
333232131
243232221212
Direct Linear Transformation (DLT):
0
nnn
X
x
X
x
X
x
X
x
X
x
X
x
2
1
1
321
3
2
2
2
1
2
3
1
2
1
1
1
3
2
1
Mapping from image onto surface:
is the unit normal vector of a surface 321 n,n,nnwhere
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Setup at Shenyang Aerospace University 最大分辨率为1280X1024,14bit灰阶,最大分辨率时采集频率
为112帧/秒。
图 1 风洞的照明与采集光路布置
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The Rood Wing:
Chord: 383.3 mm
Max Thickness: 90 mm
Height: 235.1 mm
Dow Corning silicone oil
(200 cs) with oil-based
UV dye: Coating sprayed
using air gun.
072.0*e /z82.0U/u
Boundary Layer Velocity Profiles
Boundary Layer Parameters
x (mm) xRe * (mm) (mm) Shape Factor
388 7.17×105 1.39 1.18 1.18
402 7.43×105 1.68 1.28 1.28
416 7.69×105 1.49 1.19 1.19
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GLOF Images Taken at Five Viewing Angles and Positions
AoA = 6 deg,
U = 27 m/s,
Re based on max
thickness:
151,000,
UV LED Power:
12 W
Long-pass Filter:
550 nm
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Reconstructed Intensity Distribution on Surface of
the Wing-Body Junction via Photogrammetry
GLOF Intensity Distribution Surface Mesh
(240,372 grid points)
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Skin Friction Vectors Extracted from Images (AoA = 6 deg)
Superposition of
30-80 snapshot solutions;
About 2 million vectors
extracted;
Isolated singular points
in Regions A, B, C &
D
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Reconstructed Skin Friction Field on Surface of
the Wing-Body Junction for AoA = 6 deg
0S#N#
6N#
6S#
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Zoomed-in Views of Topological Details (AoA = 6 deg)
Region A Region B
12/)Z#Z#(1S#N#
02/)Z#Z#(1S#N#
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Region C Region D
Zoomed-in Views of Topological Details (AoA = 6 deg)
12/)Z#Z#(1S#N#
02/)Z#Z#(1S#N#
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Skin Friction Vectors Extracted from Images (AoA = 0 deg)
Isolated singular points
in Regions A & B
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Reconstructed Skin Friction Field on Surface of
the Wing-Body Junction for AoA = 0 deg
0S#N#
6N#
6S#
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Zoomed-in Views of Topological Details (AoA = 0 deg)
Region A Region B
02/)Z#Z#(1S#N#
02/)Z#Z#(1S#N#
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Reconstructed Skin Friction Field on Surface of
the Wing-Body Junction for AoA = 12 deg
5N#
5S#
0S#N#
![Page 24: Skin Friction Topology of Wing- Body Junction Flows · 2017. 3. 15. · 2, g ) Liu & Shen, “Fluid Flow and Optical Flow”, JFM, 2008 Liu et al. “Global Luminescent Oil-Film Skin](https://reader034.vdocument.in/reader034/viewer/2022051822/5fec7b270136ba67347ed3e7/html5/thumbnails/24.jpg)
Zoomed-in View near the Leading Edge of the
Wing-Body Junction for AoA = 0 deg
Reconstructed Skin
Friction Field
Oil-Streak Visualization
(Devenport & Simpson 1990)
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(a) (b)
Crescent-Shaped Pattern and Line of Low Shear
Near the Wing-Body Junction for AoA = 6 deg
GLOF Image Skin Friction Magnitude
and Lines
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(a) (b)
Crescent-Shaped Pattern and Line of Low Shear
Near the Circular Cylinder Junction
GLOF Image Skin Friction Magnitude
and Lines
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Conclusions
● The high-resolution skin friction fields in wing-body junction
flows are reconstructed from GLOF images taken at different
viewing angles and positions;
● The isolated singular points and the boundary switch points
are identified on the entire surface and regions of interest,
and their distribution and conservation are analyzed by using
the Poincare-Bendixson index formula; ● This work gives experimental verification of the topological
rule of Hunt et al. (1978) for junction flows.