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Skin Friction Measurements
Using Elastic Films
Sergey Fonov, Robert Forlines, Larry Goss, Jim Crafton
Innovative Scientific Solutions, Inc.
Background
• Surface Stress Sensitive Film (S3F) ~2003
– elastic film that deforms under physical loads
– direct linear response to skin friction
– implementation as 2D point sensor or image based system
• Applications
– measurement of skin friction in fluids
– measurement of contact forces
• Advantages
– insensitive to static pressure
• Challenges
– apply film to complex surfaces
– establish the accuracy of the sensor
Response to Tangential Forces
Response to Normal Forces
S3F is a gradient sensor, not an absolute pressure sensor
• Place polymer film on model
– surface markers
– fluorescent dye
• Illuminate surface
– LED array
• Image surface
– wind-off & wind-on images
– surface marker pattern
• tangential deformation
– fluorescent dye
• film thickness normal
deformation
shear
deformation
x y
z
marker
pattern
Force
luminescent
film
Measurement System
wind-off image wind-on image ratio
Flo
w
Delta Wing
Pressure gradient from
leading edge vortex
Measurement Demonstration
The film is lightly doped with a fluorescent dye and
exposed to an illumination source to excite the dye
Flow ~ 10-m/s
Small markers are randomly applied to
the film surface. These markers are
tracked to determine the tangential
displacement of the film surface
Measuring Tangential Displacement
Combined normal (color map)
and tangential (vectors)
deformation field
Flow
ISSI & A. Fontaine (Penn State)
Strut End-wall Flow in
in a Water Tunnel
Saddle Point Stagnation Point
Tunnel ~ 3-m/s
Laminar Separation Bubble
L=200mm
40mm x 50mm x 1mm
Normal Deformation Field
A-A
Deformations in Section A-A
Tunnel Velocity 10-m/s
Inclined Jet Impingement
Delta Wing with Sprayed Film
Model ~ 8-cm span
Flow ~ 20-m/s
Data acquired with 2k X 2.5k
USB camera with CMOS chip
~ $800
7o Shock Generator
No discharge
Mach 5 Shock Boundary Layer
Görtler Vortices in
Reattaching Shear Flow
y, mm
Sp
an
wis
eT
an
ge
ntia
lS
tre
ss
(Pa
)
No
rma
lS
tre
ss
p(P
a)
-12 -8 -4 0 4 8 12-40
-30
-20
-10
0
10
20
30
40
-100
-80
-60
-40
-20
0
20
40
60
80
100
600 Spanwise Tangential Stress (Pa)
600 Normal Stress p (Pa)
PSP with N2 Injection
Data Fusion with PSP and S3F
Skin Friction (100-Pa) Combined
Pressure (PSP) and
Skin Friction (S3F)
L
2D linear FEA model for
elastic layer with thickness h
x=X/h
2D FEA Model
X
Y Applied load
),(),(
,(),(1)(
xx
xxx
yyyx
xyxxg
R(x)=(Rx,Ry) is the elastic reaction
of the film to an arbitrary load
L(x)=(Lx,Ly) xdxxxx )()()( LgR
Reaction Matrix
g(x) is the response matrix that
describes the films response to the
normal and tangential loads
Reaction Equation
Analytical Equations for Film Response
h
FT
FN
A
Applied force: FT or FN
Contact surface : A
Film
Contact surface
Film thickness: h
Spatial frequency: h/A
Amplitude – Frequency Plot for S3F
tangential
normal
cross-talk
Spatial Frequency h/A
Analytical Equations for Film Response
• Model film response mathematically
– Thickness
– Shear modulus
– Shear force
– Pressure
• Tangential reaction
– Directly proportional to shear
– Function of pressure gradient * thickness squared
• Use these equation as design tools
x
PhFhR XX
2
1 2
x
Fh
x
PhR X
Y23
1 2
2
23
Physical Quantities
• Film thickness – capacitance gauge
– luminescent signal from film
• Film Shear Modulus – static based on displacement to applied force
• response function (h/)
– dynamic based on excitation of tangential mode
• Tangential displacement – PIV, holography
• Normal displacement (thickness) – Stereo PIV
– luminescent signal (relative thickness)
Film Thickness
• Ultrasonic thickness gauge – range 25-m to 1500-m, accuracy 1-m + 1% of reading
– 1.1% - 5% error
• Interferometer – accuracy ~ l/10, error estimate ~ 0.1%
– index of refraction probably major error in this
• Luminescent coating (used during test) – relative thickness
– uncertainty ~ 0.01% film thickness
– error based on experience, dominated by camera noise
• Conservative estimate of error is up to 5% – 2% for a 100-m film that is commonly used
Measurement of Shear Modulus
Shear Modulus
• Looking for slope, plot F vs x
• F = m*g*Sin(a)
– 1 degree error in a ~ 1.7%
• Relative displacement
– cross-correlation with optical flow
• displacement accurate to up to 1/500 pixel
– PCO.1600
• 7.4-m per pixel, 1/100 pixel resolution >> 75-nm
• diffraction limit is closer to 300-nm
– Film thickness ~ 100-m
• displacement ~ film thickness
• error ~ 0.3%
• Applied force dominant error ~ 2%
Dynamic Calibration of S3F
Tangential Film Reaction
• Relative displacement, x
– cross-correlation with optical flow
• displacement accurate to up to 1/500 pixel
– PCO.1600
• 7.4-m per pixel, 1/100 pixel resolution >> 75-nm
• diffraction limit is closer to 300-nm
– Film thickness ~ 100-m
• displacement ~ 1/10 film thickness
• Tangential error ~ 3%
Normal Film Reaction
• Relative displacement, y
• Luminescent coating
– relative accuracy ~ 0.01% film thickness (need to average)
– error based on experience, dominated by camera noise
– PCO.1600
• full well is 40,000 photons, 0.7% noise
• low pass filter can easily drop to 0.1%
– This is relative thickness
– absolute is still ~ 2% + noise
• Normal error ~ 2%
Simple FEA model for = 0.5
• Unknown quantity
– tangential force (Fx)
– pressure gradient (dP/dx)
• Measured quantity
– film thickness (h) error estimate ~ 2%
– film shear modulus () error estimate ~ 2%
– reaction forces (Rx, Ry) error estimate ~ 3%
x
PhF
h
RX
X
2
x
F
x
Ph
h
R XY
2
1
3 2
2
2
tangential response normal response
Fully Developed Channel
• Constant Fx and linear pressure gradient
• Rearrange RX and substitute for pressure
gradient
L
PPhR
hF XX
21
2
2
1
02
1
3 2
22
x
F
x
PhhR X
Y
P2 P1
L
H
Fx h
Rx
L>>h
Fully Developed Channel
• Simple experimental setup
• Well known analytical solution
– Poiseuille flow
• Independent experimental measurement
– pressure gradient
Dh
fCRe
24
dx
dPHw
2
Camera
Channel
LED
Pressure
Measurement
System Flow
Controller
Poiseuille flow
Dh
fCRe
24
dx
dPHw
2
pressure gradient
h=0.8-mm
=312-Pa
H=0.8-mm
h=0.3-mm
=3035-Pa
H=0.75-mm
S3F
Skin
Fri
ctio
n (P
a)
Pressure Gradient Skin Friction (Pa)
Rx ~ 4.7-m
Rx ~ 0.25-m
error est. ~ 5%
dP/dx ~ 26 kPa/m
dP/dx ~ 182 kPa/m
Box – S3F data
O’s – pressure port data
brown line – “24/Re” model
Reynolds Number
Cf
Cf as function of Reynolds number
S3F and pressure gradient
data agree to better than
3% full scale
h=0.8-mm
=312-Pa
H=0.8-mm
h=0.3-mm
=3035-Pa
H=0.75-mm
Flow is Laminar
Channel with Backward Facing Step
Friction distribution
along channel
centerline for
different phase lags
Pressure variation along
channel centerline for
different phase lag Reattachment is unsteady
period ~ 0.1-s
High Reynolds Number Flow
• Turbulent boundary layer
• Penn State University 12-inch water tunnel
– well documented flow with good optical access
– skin friction measured with
• drag balance
• 2D-LDV velocity profile
– Reynolds number up to 11-million
– Velocity up to 20-m/s
– skin friction up to 500-Pa
• traditional S3F in air ~ 500-Pa,
• S3F in water ~ 20,000-Pa
Film
Plug
3 inch hole for Plug
Acrylic tunnel window
2D point gauge tunnel installation
Sensor is designed as a Plug.
Plug is mounted flush with
the tunnel wall.
Gen 1 package, hang a camera
from the sensor with set screws
Fx
Point Gage. FEA Model
S3F
Window
Objective Lens
LED
CCD (CMOS) matrix
S3F D=15mm, h=1mm
X displacement (mkm)
Y displacement (mkm)
A
A
Displacements in section A-A (mm)
X
Y
x
y
ROI ROI
compare smooth wall
drag balance to S3F
a-priori result
“perfect” result
m = 1.0
b = 0
offset likely a bias
error in displacement
Measurements repeatable to
better than 2% full scale
Integrated Package
Wall Shear Stress in an Artificial Heart Model
Shear Field (Pa) for phase time 300ms, single frame with exposure
time 2ms
Shear Field for phase time 55ms
Normal deformation field (false color)
and shear tension field (vectors)
for phase time 55ms,
phase locked averaged
LED Lamp
Heart Model
with S3F
CCD Camera
Pa
ISSI & A. Fontaine (Penn State)
CCD Camera
Normal and Shear Forces Under a Shoe Normal forces under a shoe.
Load on Heel
Load on Toe
Pressure Shear
Currently funded by NIH
Shear and Pressure on a Tire
CCD Camera LED
Film Layer
Glass Plate
Section 1
2D Finite Element Analysis results for plane strain field in Section
1. Note that while S3F measures absolute shear force, it measures
the variation of normal pressure on the contact surface.
Reconstructed pressure variation in Section 1Y-component of reconstructed
friction force in Section 1
Measured displacements in Section 1, normal (red),
shear Y-comp (blue), tire tread indicator (green)
Region used
for force reconstruction
x
y
Normal component of displacement field
Load Reconstruction with Ribbed Automotive Tire
Recent funding
from 88th test wing
USAF
Conclusions
• Sensitive to 2 components of skin friction – avoid elaborate calibrations or fluid analogies
– operate in air, water, other fluids
– measure shear and pressure from contact forces
• Tunable sensitivity – control shear modulus and thickness
• Point sensor – very accurate 2D skin friction measurements
– accuracy validated using fully developed channel • compared to experimental measurement to better than 5%
– measurements in high Re boundary layer (water) • Repeatable to better than 2%
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