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%