Extraction of Skin Friction Fields from

Surface Flow Visualizations as an Inverse

Problem

Department of Mechanical & Aerospace Engineering

Western Michigan University, Kalamazoo, MI 49008

Tianshu Liu

Objective

To extract high-resolution skin friction fields

from surface flow visualization images by

using a unified approach of optical flow

Global luminescent oil-film (GLOF) visualization

Surface heat transfer visualization with TSP

Surface mass transfer visualization with PSP &

sublimating coatings in air and dye in water

Oil Film Thickness (h) Luminescent Intensity (g)

Global Luminescent Oil-Film (GLOF) Method

Surface in Object Space Image Plane

Equivalent Skin Friction:

2

3

i

ii

21a3

gg

x

p

x)g,x,x(f

Pressure Gradient and Gravity Terms:

fx/)ˆg(t/g jj

)2/(gHˆojiij

Thin-Oil Equation for GLOF is Recast into

Optical Flow Equation

Variational Formulation

The functional with a smoothness constraint:

The Euler-Lagrange equations:

where the Neumann condition

From two successive images, a snapshot solution is obtained.

0nˆ /

Superposition or averaging of snapshot solutions

21

2

2

2

1212

dxdxˆˆdxdxfˆgt/g)ˆ(J

0ˆfˆgt

gg 2

Low-AR Wing with NACA0012 Airfoil Section

Dow Corning silicone oil

with oil-based UV dye

Typical Experimental Setup for GLOF Method

Typical Luminescent Oil Image Skin Friction Vectors

Low-Aspect-Ratio Wing

The Upper Surface at AoA = 18 deg

Low-Aspect-Ratio Wing

Topological Analysis Based on the Poincare-Bendixson

Index Formula

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

Topological Change Caused by a Roughness Strip

along the Leading Edge at AoA = 18 deg

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

Square Cylinder Junction Flow

Experimental Setup Typical Luminescent Oil Image

Re = 2.03105 Local Re:

Square Size: 51 by 51 mm

Skin Friction Magnitude Skin Friction Vectors

Square Cylinder Junction Flow

(fusion of 300 snapshot solutions)

Square Cylinder Junction Flow

Skin Friction Lines

65o Delta Wing

Typical Luminescent Oil Image Skin Friction Lines

AoA = 13 deg AoA = 13 deg (Rec = 300,000)

Reattachment

line

Secondary

separation

line

AoA = 15 deg AoA = 20 deg

65o Delta Wing

Vortex Bursting

Double-Delta Wing

The Evolution of Skin Friction Topology

as AoA is Changed at Nominal Zero Yaw

AoA = 0 deg AoA = 16 deg

3 nodes

3 saddles

Double-Delta Wing

The Evolution of Skin Friction Topology

as AoA is Changed at Yaw Angle of 6 deg

AoA = 16 deg AoA = 24 deg

2 nodes

2 saddles 2 nodes

2 saddles

Skin Friction Field Mapped onto Surface

of a Wing-Body Junction

GLOF Intensity Distribution Surface Mesh

(240,372 grid points)

Five Views of Wing-Body Junction from at Different Positions

Reconstructed Skin Friction Field on Surface of

a Wing-Body Junction for AoA = 6 deg

0S#N#

6N#

6S#

Surface Heat and Mass Transfer Visualizations

with TSP, PSP and Sublimating Coatings

From the asymptotic forms of the energy transport

equation and the mass transport equation at wall,

the projected equation on the image plane is obtained:

0x/gˆG jj

Variational Formulation

The functional with a smoothness constraint:

The Euler-Lagrange equations:

where the Neumann condition 0nˆ /

21

2

2

2

1212

dxdxˆˆdxdxgˆG)ˆ(J

0ˆggˆG 2

If

can be obtained by solving the E-L equation.

are measured and known, &

)ˆ,ˆ(ˆ21

g G

Normal Impinging Air Jets with TSP

Normal Impinging Nitrogen Jet with PSP

PSP Intensity Ratio

Normalized skin friction field

Oscillating Impinging Nitrogen Jets at 9.4 kHz

Visualized with Fast PSP (Gregory et al. 2007)

0 s 20 s 40 s

0 s 20 s 40 s

Unsteady Skin Friction Fields Reconstructed by

Superposition of Quasi-Steady and Variation Fields

Sublimation Visualization with Pyrene PSP

on a 75-deg Delta Wing (Bouvier, Le Sant & Merienne 2001 ONERA)

Sublimation Visualization with Chemical on a Flat Plate

in Shock/Boundary-Layer Interaction over a Fin

at Mach 6 at AoA of 40 deg (Zemsch & Carbonaro VKI, 1995)

Surface Luminescent Dye Visualization on

a 65-deg Delta Wing in Water Tunnel

AoA = 10 deg, Rec = 40,000

Surface Luminescent Dye Visualization on

a 76/40-deg Double Delta Wing in Water Tunnel

AoA = 10 deg, Rec = 40,000

Conclusions

Global skin friction diagnostics is feasible based

on surface flow visualizations with luminescent

oil, TSP, PSP, sublimating coatings, and dye.

It is incorporated into a unified framework of

physics-based optical flow method in image

processing.