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

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

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.,

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#

Topological Rule of Hunt et al. as a Reduced Case

of the P-B formula Applied to Junction Flow

02/)Z#Z#(1S#N#

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(

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

)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

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.

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

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

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

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

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

Reconstructed Intensity Distribution on Surface of

the Wing-Body Junction via Photogrammetry

GLOF Intensity Distribution Surface Mesh

(240,372 grid points)

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

Reconstructed Skin Friction Field on Surface of

the Wing-Body Junction for AoA = 6 deg

0S#N#

6N#

6S#

Zoomed-in Views of Topological Details (AoA = 6 deg)

Region A Region B

12/)Z#Z#(1S#N#

02/)Z#Z#(1S#N#

Region C Region D

Zoomed-in Views of Topological Details (AoA = 6 deg)

12/)Z#Z#(1S#N#

02/)Z#Z#(1S#N#

Skin Friction Vectors Extracted from Images (AoA = 0 deg)

Isolated singular points

in Regions A & B

Reconstructed Skin Friction Field on Surface of

the Wing-Body Junction for AoA = 0 deg

0S#N#

6N#

6S#

Zoomed-in Views of Topological Details (AoA = 0 deg)

Region A Region B

02/)Z#Z#(1S#N#

02/)Z#Z#(1S#N#

Reconstructed Skin Friction Field on Surface of

the Wing-Body Junction for AoA = 12 deg

5N#

5S#

0S#N#

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)

(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

(a) (b)

Crescent-Shaped Pattern and Line of Low Shear

Near the Circular Cylinder Junction

GLOF Image Skin Friction Magnitude

and Lines

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.