Direct Measurement of Wall Shear Stress in Single- and Multiphase Flows

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Valery Sheverev, Lenterra Inc.and

Bruce Brown, Srdjan Nesic, Ohio University

presentation at theInstitute for Corrosion and Multiphase Technology

Ohio UniversityAthens, OH

October 11, 2011

Scope

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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 RealShearLenterra RealShearTMTM sensorsensor.

1.Single-phase flowsa.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 flowsa.Standing slug systemb.Moving slug installation

Presenter - Lenterra, Inc.

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•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

Enterprise Development Center,Newark, NJ

• Founder and current president: Valery A SheverevIndustry Professor of Physics, Polytechnic Institute of New York University

Flow Force on the Wall

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Pressure, scalar quantity

dA

Fd

dA

dFp

zxw

y

,

Flow

Wall F

forceshearF zx,

yF

forcenormal

xz

y

Wall shear stress (WSS),

vector in x,z plane

u

Sensing areaWall

Slope=du/dy|y=0

y

x

WSS, , is a product of velocity gradient (shear rate)

near the wall,

and dynamic viscosity of the fluid, :

w

yu

0

yw yu

Therefore WSS is an indirect measure of dynamic viscosity of the fluid or shear rate.

WSS Measurement – Needs in Oil and Gas Industry

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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

WSS Measurement – History

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• 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)

WSS Measurement – Direct Methods

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Direct - measure motion of a floating element, positioned flush within the wall.

Floating element displacement measured by :

•Electrical techniques• 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)

a.Optical techniques a. 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

u

Floating elementWall

y

x

Lenterra WSS Measurement Technology

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Floating element

Sensor enclosure

CantileverFiber-optical strain gages

Optical fibers

Wall

• Lenterra’s solution: Combine floating element with mechanical cantilever with micro-optical strain gage that are durable and not affected by the flow

- Preferred type of optical strain gage: Fiber Bragg Grating (FBG)

• Optical strain gage (FBG) versus: - resistive strain gages – not nearly sensitive- 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

Micro Optical Strain Gage - Fiber Bragg Grating

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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.

• By interrogating FBG with a light source, this strain (and therefore WSS) can be measured by tracking the shift in the resonant wavelength.

Force

Force

Temperature Compensation

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Differential signal (shift of FBG 1 spectrum less shift of FBG 2 spectrum) is independent from temperature

Temp Strain

Temp Strain

FBG 1 (strain due to applied force increases spectral shift due to temperature)

FBG 2 (strain decreases temperature shift)

• Strain shifts FBG spectrum, but so does temperature• Solution: use two FBGs attached to opposite sides of cantilever

Spectrum Measurement and WSS Computation

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• Using laser diode (LD): Monochromatic light from a tunable laser is directed to FBGs and reflected light is recorded by photodiode

• As the laser frequency is tuned, reflection spectra (reflected light intensity versuswavelength) are recorded for FBG1 & FBG2

• Shift in the resonant wavelengths (FBG1FBG2calculated

•WSS is found from τw = kwhere k is the calibration coefficient

• Sensors are calibrated by applying a varying mechanical force F to the tip of the cantilever and measuring 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

Scanning laser

FBG

Photodiode

Fibers

Lenterra RealShear™ Sensor - Probe

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•1/4″-80 threaded housing •FBGs are attached (currently glued) to cantilever • Detailed Specifications are found at www.lenterra.com

The RealShear ™ sensor

Lenterra RealShear™ Sensor – Complete Measurement System

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Includes :

• A probe with connecting fibers• Controller combining optical components and data acquisition electronics• Computer•Measurement Software

RealShear™ sensors have a bidirectional response and can be used to find flow direction at the wall.

Sensitivity to Off-Axis Shear Stress

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Multi-Phase Detection: Two Disks Apparatus

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The RealShear ™ sensor

Apparatus: rotating disk testbedFluid - 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 shownPlot on right: Air bubbles are induced behind teeth

Single-Phase Tests at OU: WSS in a 1”Metal Pipe

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Test section: 1 m long

Sensor floating element flush with the inner wall.

Laminar Flow (Remax=130)

Fluid: Britol 50T oil

Single-Phase Tests at OU: WSS in a 1”Metal PipeWSS vs. Flow Rate

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Fluid: Britol 50T oil

Viscosity (μ =185 mPa-s) - measured after completion of tests using a falling ball viscometer.

Estimated data: analytical solution of Navier-Stokes equations for fully developed flow in cylindrical pipe.

10% uncertainty in the estimated data is due to uncertainty in viscosity and flow rate

R

U 4

U - averaged velocity (from flow rate), R - pipe radius

Single-Phase Tests at OU – WSS in a 1”Metal PipeInstantaneous Signal

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Single-Phase Tests at OU – WSS in a 1”Metal PipeInstantaneous Signal-Detail

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pump

P]

T] T]

pH meter

Ion exchanger

Flow cell

Heat exchanger

CO2

T] P]T]

tank

pump

P]

T] T]

pH meter

Ion exchanger

Flow cell

Heat exchanger

CO2

T] P]T]

tank

Sensor’ssensitive surface

Ohio University - Institute for Corrosion and Multiphase Technology

Thin Channel Flow Cell (TCFC)(3mm x 100mm x 600mm)

Single-Phase Tests at OU - Thin Channel Flow Cell #1Instantaneous Signal

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Random excitation of mechanical oscillations of cantilever by eddies of turbulent flow

Single-Phase Tests at OU - Thin Channel Flow Cell #1WSS vs. Flow Rate

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Measurements arcing downwards – Why?

Bruce Brown: top plate of Plexiglas bows up at higher flow rate, increases channel height

Fluid: water

Room Temperature

Flow Rate measured by a flowmeter

Estimated: from Darcy–Weisbach equation using Darcy friction factor (found from a Moody diagram, assuming a particular roughness),

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2Uf

U is averaged velocity (from flow rate) ρ is fluid density f is Darcy friction factor

Single-Phase Tests at OU - Thin Channel Flow Cell #2Time evolution

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Water

Room Temp.

Diff. Pressure 76 psi

Measurement rate 10 kS/s

Single-Phase Tests at OU - Thin Channel Flow Cell #2Time evolution - detail

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Separate turbulences are readily observable

Single-Phase Tests at OU - Thin Channel Flow Cell #2WSS vs. Flow Rate

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Re= 12350-73500

System pressure 40 psig - total pressure is system pressure + differential pressure

Differential pressure between standard ports was directly measured

No saturation of WSS at higher flow rates (compare with TCFC #1)

Estimate: same model as with TCFC #1 data

Multi-Phase Tests at OU – Standing Slug (Water-Air)

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4” Plexiglas pipe

Sensor flush with the wall

Adapter

Sensor inserted here

Multi-Phase Tests at OU – Standing Slug (Water-Air)

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Adapter

Multi-Phase Tests at OU – Standing Slug (Water-Air)

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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

Multi-Phase Tests at OU – Moving Slug (Water-Air)

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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

What Did We Learn From the First Tests?

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• 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:

Advanced Corrosion Sensor Concept Based on Lenterra’s Sensor Design

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•“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.

•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

State of the Art– Tuning Fork Corrosion Sensor

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•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 Sensor – New Concept

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•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

Passive Excitation-Example

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Signal from TCFC #1 FFT Spectra

Thank You

Any Questions?

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