Post on 24-Dec-2021
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.