Direct Measurement of Wall Shear Stress
in Single- and Multiphase Flows
Valery Sheverev, Lenterra Inc.
and
Bruce Brown, Srdjan Nesic, Ohio University
presentation at the
Institute for Corrosion and Multiphase Technology
Ohio University
Athens, OH
October 11, 2011
1
Scope
We report measurements of wall shear stress taken at five
installations of the Institute for Corrosion and Multiphase
Technology, using the first of its kind Lenterra RealShearTM
sensor.
1.Single-phase flows
a.1” pipe flow loop (Britol 50T oil, flow rate < 9 gpm)
b.Thin Channel Flow Cell #1(water, flow rates < 25 gpm)
c.Thin Channel Flow Cell #2(water, flow rate < 80 gpm)
2.Multi-phase flows
a.Standing slug system
b.Moving slug installation
2
Presenter - Lenterra, Inc.
•
Privately-owned emerging company, a
provider of innovative sensor instrumentation
based on its proprietary technologies.
•
Located in the New Jersey Institute of
Technology (NJIT) Enterprise Development
Center (incubator) in Newark, NJ.
•
$2.6M in SBIR (Small Business Innovation
Research) grants from federal agencies (NSF,
DOE, NASA)
•
Sales started in 2011
•
3 patents granted, 4 pending
• Founder and current president:
Enterprise Development Center,
Newark, NJ
Valery A Sheverev
Industry Professor of Physics, Polytechnic Institute of New York University
3
Flow Force on the Wall
y
Flow
z

F x , z shear
Wall

Fy
normal force
u
y
x
force
WSS,
p
x


F
w 
dF y
dA

d Fx ,z
dA
Pressure,
scalar quantity
Wall shear stress (WSS),
vector in x,z plane

 w , is a product of velocity gradient (shear rate)

near the wall,  u  y
and dynamic viscosity of the fluid,  :
Slope=du/dy|y=0
Wall
Sensing area
 w     u y
y0
Therefore WSS is an indirect measure of dynamic viscosity of the fluid or shear rate.
4
WSS Measurement – Needs in Oil and Gas Industry
The breadth of applications in an industry that utilizes flows is evident when one
considers the common use of pressure transducers and the fact that shear
stress characterizes flow action much better than pressure
•Flow Assurance
• Single- and multiphase simulations – WSS is a critical parameter in most
models
•Characterization of multiphase flows (slug effects etc.)
•Direct detection of high and low viscosity components, especially in harsh
environments such as high pressure and low temperature of deep water
energy production
•Corrosion Analysis
•Direct relation: WSS ↑ → Corrosion Rate ↑ , via mass transfer
•Corrosion inhibitors testing: WSS ↑ → removes inhibitor from the
wall → Corrosion Rate↑
• Important parameter in corrosion models
5
WSS Measurement – History
• Indirect
measurements: WSS is inferred, through a set of
assumptions, from another flow property, such as
streamwise velocity or heat transfer rate measured at or
near the wall
• Require a model of the flow near the wall and knowledge
of flow parameters such as temperature and viscosity
• Examples:
• hot-wire/film-based anemometry – quite rude
estimate, no temporal resolution
• laser-based near-wall flow velocity measurement
• Laser-based or Particle Image Velocimetry (PIV)
methods are well developed but they work only in
transparent single-phase fluids (water, air)
6
WSS Measurement – Direct Methods u
Direct - measure motion of a floating element,
positioned flush within the wall.
Floating element displacement measured by :
• Electrical techniques
y
x
Wall
Floating element
a.
b.
Piezoelectric – shear deformation of a PZT element
Capacitor-based - floating element is one of the capacitor plates - shift of
the floating element changes the capacitance
•
Drawbacks:
- Susceptibility to electromagnetic interference
- Narrow temperature range
- Difficult to separate WSS from normal force (pressure)
• Optical techniques
• Variety of imaging or resonant methods (such as Fabry-Perot
interferometers) to monitor floating element
- not durable - require delicate alignment of the resonator
- the resonator to be optically clean - difficult to sustain
All earlier direct techniques not robust enough for use in-field
7
Lenterra WSS Measurement Technology
• Lenterra’s solution: Combine
floating element with mechanical
cantilever with micro-optical
strain gage that are durable and
not affected by the flow
Floating
element
Wall
Fiberoptical
- Preferred type of optical strain gage:strain gages
Fiber Bragg Grating (FBG)
Optical
fibers
• Optical strain gage (FBG) versus:
- resistive strain gages – not nearly sensitive
Cantilever
Sensor
enclosure
- semiconductor strain gages – sensitivity comparable but narrow
temperature range
- both types require delicate electronics (preamplifier) embedded in the
probe
• Robust: Materials used in our sensor: stainless steel + glass
8
Micro Optical Strain Gage - Fiber Bragg Grating
FBGs are periodic structures of varying refractive index embedded in
optical fibers.
• FBG is attached to the cantilever.
When the cantilever bends in
response to shear stress, the FBG is
strained which shifts its optical
spectrum.
Force
Dl ~ Force
• By interrogating FBG with a light
source, this strain (and therefore
WSS) can be measured by tracking
the shift in the resonant wavelength.
Dl
9
Temperature Compensation
• Strain shifts FBG spectrum, but so does temperature
• Solution: use two FBGs attached to opposite sides of cantilever
Temp
Strain
FBG 1 (strain due to
applied force increases
spectral shift due to
temperature)
Temp Strain
FBG 2 (strain decreases
temperature shift)
Differential signal (shift of FBG 1 spectrum less
shift of FBG 2 spectrum) is independent from
temperature
10
Spectrum Measurement and WSS Computation
• Using laser diode (LD):
Monochromatic light from a tunable
laser is directed to FBGs and reflected
light is recorded by photodiode
Scanning laser
Photodiode
Fibers
• As the laser frequency is tuned, reflection
spectra (reflected light intensity versus
wavelength) are recorded for FBG1 & FBG2
FBG
• Shift in the resonant wavelengths (Dl  lFBG1  lFBG2) calculated
•WSS is found from τw = kDl where k is the calibration coefficient
• Sensors are calibrated by applying a varying mechanical force F to the tip
of the cantilever and measuring Dl, τw = F/A (A-area of floating element)
• k it is determined by
-Properties of FBGs
-Area of the floating element
- Elastic modulus, length and diameter of the cantilever
11
Lenterra RealShear™ Sensor - Probe
The RealShear ™ sensor
•1/4″-80 threaded housing
•FBGs are attached (currently glued) to
cantilever
• Detailed Specifications are found at
www.lenterra.com
12
Lenterra RealShear™ Sensor – Complete
Measurement System
Includes :
• A probe with connecting fibers
• Controller combining optical components and data acquisition
electronics
• Computer
•Measurement Software
13
Sensitivity to Off-Axis Shear Stress
1.2
Normalized sensor response
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
-1.2
-20
0
20
40
60
80
100
120
140
160
180
200
Q, degrees
RealShear™ sensors have a bidirectional response and can be used to find
flow direction at the wall.
14
Multi-Phase Detection: Two Disks Apparatus
Apparatus: rotating disk testbed
Fluid - glycerin (viscosity 900 cP)
Lower disk rotating at 122 RPM
Smaller tooth gap 0.9 mm
Wider tooth gap 1.2 mm
Two full rotations shown
Plot on right: Air bubbles are induced behind teeth
The RealShear ™ sensor
15
Single-Phase Tests at OU: WSS in a 1”Metal Pipe
Test section: 1 m long
Sensor floating element flush with
the inner wall.
Laminar Flow (Remax=130)
Fluid: Britol 50T oil
16
Single-Phase Tests at OU: WSS in a 1”Metal Pipe
WSS vs. Flow Rate
100
 
4U 
Fluid: Britol 50T oil
R
Wall shear stress, Pa
80
Viscosity (μ =185 mPa-s) measured after
completion of tests using
a falling ball viscometer.
U - averaged velocity (from flow rate), R - pipe radius
Estimated data: analytical
solution of Navier-Stokes
equations for fully
developed flow in
cylindrical pipe.
60
40
Measured
10% uncertainty in the
estimated data is due to
uncertainty in viscosity
and flow rate
Estimated
20
0
0
300
600
900
1200
1500
1800
Pump motor RPM
17
Single-Phase Tests at OU – WSS in a 1”Metal Pipe
Instantaneous Signal
70
WSS in 1“ pipe
Britol 50T
Acquisition rate 10000 S/s
1100 rpm, flow rate 5.66 gpm
60
Wall shear stress, Pa
50
40
30
20
10
0
-10
0
2
4
6
8
10
12
14
16
18
20
Time, s
18
Single-Phase Tests at OU – WSS in a 1”Metal Pipe
Instantaneous Signal-Detail
80
Cantilever oscillation
Measured wall shear stress, Pa
70
60
50
40
30
20
10
Modulation frequency i18.3 Hz corresponds to the
pump's motor rotation frequency (1100 rpm=18.33 Hz)
0
8.00
8.03
8.06
8.09
8.12
8.15
8.18
8.21
8.24
8.27
8.30
Time, s
19
Ohio University - Institute for Corrosion and Multiphase Technology
Thin Channel Flow Cell (TCFC)
(3mm x 100mm x 600mm)
T]
T]
Flow cell
pH meter
Sensor’s
sensitive
surface
P]
Heat
exchanger
Ion
exchanger
T]
T]
P]
pump
tank
CO2
20
Single-Phase Tests at OU - Thin Channel Flow Cell #1
Instantaneous Signal
70
Random excitation of mechanical oscillations of
cantilever by eddies of turbulent flow
65
Wall shear stress, Pa
60
55
50
45
40
35
30
25
20
8.8
8.9
8.9
9.0
9.0
9.1
9.1
9.2
9.2
9.3
9.3
Time, s
21
Single-Phase Tests at OU - Thin Channel Flow Cell #1
WSS vs. Flow Rate
200
180
  f
Wall shear stress, Pa
160
U
8
2
Fluid: water
U is averaged velocity (from flow rate)
ρ is fluid density
f is Darcy friction factor
Room Temperature
Flow Rate measured
by a flowmeter
140
120
100
Estimated: from
Darcy–Weisbach
equation using Darcy
friction factor (found
from a Moody diagram,
assuming a particular
roughness),
80
60
40
Measured
Estimated (roughness 0.1 mm)
Estimated (roughness 0.015 mm)
20
0
0
5
10
15
Flow rate, gpm
20
25
30
Measurements arcing downwards – Why?
Bruce Brown: top plate of Plexiglas bows up at higher flow rate, increases channel height
22
Single-Phase Tests at OU - Thin Channel Flow Cell #2
Time evolution
Water
Room Temp.
Diff. Pressure 76 psi
Measurement rate 10
kS/s
23
Single-Phase Tests at OU - Thin Channel Flow Cell #2
Time evolution - detail
Separate
turbulences are
readily observable
24
Single-Phase Tests at OU - Thin Channel Flow Cell #2
WSS vs. Flow Rate
800
Measured
Re= 12350-73500
Estimated using Darcy-Weisbach equation
(0.1 mm roughness)
Estimated using Darcy-Weisbach equation
(0.015 mm roughness)
System pressure 40
psig - total pressure is
system pressure +
differential pressure
700
Wall shear stress, Pa
600
500
Differential pressure
between standard
ports was directly
measured
400
300
No saturation of WSS
at higher flow rates
(compare with TCFC
#1)
200
100
Estimate: same model
as with TCFC #1 data
0
0
5
10
15
20
25
30
35
40
45
50
55
Flow rate, gpm
25
Multi-Phase Tests at OU – Standing Slug (Water-Air)
4” Plexiglas pipe
Sensor flush with the wall
Sensor inserted here
Adapter
26
Multi-Phase Tests at OU – Standing Slug (Water-Air)
Adapter
27
Multi-Phase Tests at OU – Standing Slug (Water-Air)
Clear indication of slug
influence on WSS
Instantaneous values of
WSS in the slug are
several times higher
those observed in the
upstream region
◘ Maximum measured
WSS<100 Pa
28
Multi-Phase Tests at OU – Moving Slug (Water-Air)
Sensor at the bottom of
the pipe, flush with the
wall.
Water superficial velocity
0.3 m/s
Gas superficial velocity
3.6 m/s
No characteristic features
caused by moving slugs
observed
Thus WSS due to slug
< 4 Pa
29
What Did We Learn From the First Tests?
• WSS was measured from few Pa to over 1 kPa, at pressures <50
•WSS on the pipe wall in laminar flow was measured systematically
somewhat higher than predicted
•Possibly due to calibration that does not include pressure difference across
the floating element
•Average values of WSS in two TCFCs (turbulent flows) are in the
reasonable range of expected values
• Standing water-air slug produced slightly higher instantaneous WSS
(under 100 Pa).
• Moving water-air slug showed no increase in WSS (<4 Pa)
• High measurement rate allows to observe details of the turbulent flow
(eddies striking the floating element) that are however masked by
mechanical oscillations of the cantilever
• Last observation lead to a new combined Wall Shear Stress Corrosion Sensor concept:
30
Advanced Corrosion Sensor Concept
Based on Lenterra’s Sensor Design
•“When you say the corrosion sensor is flush mounted,
make sure it is flush” – words of a professional.
•Local fluid turbulence created by a protruding sensor can
have a major impact on the damage mechanisms and the
rate of damage
• Srdjan Nesic: “Lenterra’ WSS sensor can be modified to
directly measure corrosion rate!”
• V. Sheverev and S. Nesic “Methods And Devices For
Monitoring Interaction Between A Fluid And A Wall” – PPA
filed June 21, 2011.
31
State of the Art– Tuning Fork Corrosion Sensor
•Mechanical oscillator - tuning
fork tines attached to a
diaphragm that is driven by a
piezoceramic or another driver
•Resonance frequency
f0=(1/2π)√(k/m) m =system mass, k= stiffness
•Corrosion rate is incurred from change in f0
•Problems:
•Tuning forks needs to be immersed in the fluid – how to make it flush
with the wall?
• Some experiments resulted in decrease in f0 when loss of material
occurred. Why?
•Answer: Corrosion affects not only the tip, but also the base – not only
m is reduced, but k as well - f0 may change in any direction
32
Corrosion Sensor – New Concept
•Basic design similar to RealShear
sensor
•Oscillator consists of a cantilever and
floating element – the oscillator system
known as “cantilever with a tip mass”
•Only the outer surface of floating
element is corrodible (for example
coupon inserted)
•Due to corrosion, only mass of the
floating element reduces changing m,
stiffness k not changed since it is
determined by cantilever only
•The sensor is flush – minimal gaps are needed for detection of oscillation
33
Passive Excitation-Example
FFT Spectra
Signal from TCFC #1
140
400
120
Amplitude, arb. units
300
250
200
150
100
100
80
60
40
20
50
0
100
75.45
75.5
Time, seconds
75.55
110
120
75.6
130
140
150
160
Frequency, Hz
1000
140
120
100
80
60
40
20
0
Amplitude, arb. units
0
75.4
Amplitude, arb. Units
Singal, arb. units
350
100
10
1
0.1
0.01
129
130
131
Frequency, Hz
132
133
100
120
140
160
Frequency, Hz
34
Thank You
Any Questions?
35