ultrasonic measurement systemsstaff.johanc/e7021e/e7021e_lecture11.pdf2 d cot θ c 2 v, where d is...

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Last lecture

Measurement of volume flow rateDifferential pressure flowmetersMechanical flowmetersVortex flowmeters

Measurement of mass flowMeasurement of “tricky flows"

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Today’s menu

Ultrasonic measurement systemsWhat is ultrasound?What are the main properties we can measure?Application examples

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Ultrasonic measurement systems

What is ultrasound?Acoustics may be defined as the generation, transportation, and receptionof energy in the form of vibrational waves.

The sound propagation arises from internal elastic forces between atomsor molecules, when they are displaced from their equilibrium.

Ultrasound is defined as sound of frequencies above the audible range,that is above 20 kHz.

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What is Ultrasound (cont’d...)?

Compression waves: Particle displacement and wave propagation insame direction.

wave propagation

particle motion

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Transversal waves: Particle displacement normal to wave propagation.

wave propagation

particlemotion

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We differ between pulsed sound

time

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...and continuous-wave ultrasound

time

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Reflection and Transmission

When a sound wave encounters a boundary between two differentmaterials, part is reflected and part is transmitted.

The reflection coefficient (number between 0 and 1) is defined as

R12 =z2 − z1

z1 + z2,

where z1 and z2 are the acoustic impedances of medium 1 and 2,respectively.

This means that the amplitude of the reflected wave is A0 ·R12, where A0

is the amplitude of the incident wave.

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Reflection and Transmission (cont’d...)

The acoustic impedance of a material is given by:

z = ρ · c,

where ρ is the density and c is the speed of sound. The acousticimpedance is measured in Pa·s/m.

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Attenuation

When a sound wave propagates through a medium, its is also attenuatedwith distance, often modeled as:

A1 = A0e−αx,

where x is the propagation distance, α is the attenuation coefficient, and

A0 is the amplitude of the transmitted wave.

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What can we measure?

From the received sound waves we can directly measure attenuation(damping) and speed of sound, as a function of wavelength(frequency).From attenuation and speed of sound we can calculate variousproperties, such as:

Reflection and transmission coefficientsFluid densityElastic properties (viscosity, Young’s modulus, Bulk modulus, etc.)Since sound propagation is a particle motion, we can also usesound velocity measurements to estimate volume flow rate. Theperceived speed of sound is the sum of the flow rate and thewave propagation speed.

We can also model the physics of the wave propagation in terms ofother material/system properties and use numerical methods to solvethe inverse problem.

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Acoustic Properties of Materials

Speed of sound in different media:Gases: 250–400 m/s.Water: 1400–1550 m/s.Plastics: Very different, but typically in the range 2500-3000 m/s (forPMMA).Steel: ≈5800 m/s.Aluminium: ≈6420 m/s.

All depend on temperature, sound frequency, and pressure.

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Acoustic Properties of Materials

Speed of sound in Biological tissue (at 37◦C):Blood: 1560 m/s.Bone: 2700–4100 m/s (trabecular and cortical bone).Fat: 1450 m/s.Liver: 1560 m/s.

All depend on temperature, sound frequency, and pressure.

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Acoustic Properties of Materials (cont’d...)

Frequencies for different applications:Ultrasound in gases, typically below 1 MHz.Ultrasound in liquids, 500 kHz – 30 MHz, but often 3-10 MHz.Medical ultrasound, 3-10 MHz, in the most common systems.

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Application examples

Doppler flowmeter.Cross-correlation flowmeter.Transit-time flowmeter.Velocity profile measurements in multiphase flows(speckle-correlation).Characterization of multi-layered materials.Analysis of gas mixtures.

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Application examples (cont’d...)

Doppler flowmetertransmitter

flow containingscatterers

receiver

The frequency of the received signal will shift depending on the flowvelocity, i.e. a Doppler effect.

Δf = f ′′ − f =2f

ccos(θ)v,

where f ′′ is the frequency of the received wave, f is the frequency of thetransmitted wave, θ is the angle between the flow and the sensor, c is thespeed of sound, and v is the average flow velocity.

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Cross-correlation flowmeter


transducer

transmitted pulse

received backscatter signals

¢T

The signal received at one time instant is cross-correlated with a signalreceived a short time later. The shift of the signal in time depends on theflow velocity.

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Cross-correlation flowmeter (cont’d...)


receiving transducers

transmitting transducers

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Transit-time flowmeter

flow

transducer 1

transducer 2

¢x

The transit time of the sound differs upstream and downstream of the flow,as

ΔT =2D cot θ

c2v,

where D is the distance between the sensors, θ is the angle between theflow and the sensors, c is the speed of sound, and v is the average flowvelocity.

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Velocity profile measurementsGoing into more advanced instrumentation, it is possible to use thebackscattered signals as a “fingerprint" (speckle pattern) of the entire flowprofile. Cross-correlating two consecutive pattern, we can create avelocity profile of particles in the flow.

0

5

15

10

20

-20

10

0

-10

20

-20

10

0

-10ax

ialdis

tance

,y

(mm

)

axia

ldis

tance

,y

(mm

)

par

ticl

eve

loci

ty(c

m/s)

par

ticl

eve

loci

ty(c

m/s

)0

2

4

6

8

10-10 0 10 -10 0 10

transversal distance, x (mm) transversal distance, x (mm)

(a) (b)

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Velocity profile measurements (cont’d...)Looking at the velocity profile at the center of the pipe, we obtain thefollowing:

-15 -10 -5 0 5 10 15

axial distance, y (mm)

0

5

10

15

part

icle

velo

city

,v

(cm

/s)

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Characterization of multi-layered materials

layer 3

layer 1

layer 2

water

water

time

d0

d1

d2

d3

u ype

transducer

dh

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Characterization of multi-layered materials (cont’d...)Modeling the reflections and transmissions at boundaries between thelayers, and losses within the layers as a linear (dynamic) system and thenusing the measured pulse to estimate the model parameters, we get

1500 2000 2500 3000 3500 4000 4500 5000 5500 6000

−1 −0.5

0 0.5

1

n [sample]

Am

plitu

de

a) MeasuredEstimated

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Characterization of multi-layered materials (cont’d...)A look at the model error reveals that there are some un-modeledvariations, but not too much.

1500 2000 2500 3000 3500 4000 4500 5000 5500 6000−0.05

0

0.05

n [sample]A

mpl

itude

b) Residual

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Analysis of energy gases

ProblemEnergy content of gases (e.g. natural gas, biogas, synthesis gas)changes with composition.Producers and customers need to know what the produce/buy.Existing techniques are expensive.No available technique measures flow and composition in the sameinstrument.

IdeaSpeed of sound and attenuation depend on molecular properties ofgases, i.e. the composition.Gas flow can already be measured using ultrasound.

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Analysis of energy gases (cont’d...)

Research approachDevelop techniques for accurate and robust estimation of speed ofsound and attenuation, based on physical knowledge of the system.Use some empirical regression technique to connect acousticproperties to gas composition, including also knowledge oftemperature and pressure.

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The setup

Pressuretransmitter Gas inlet

Magneticvalve

Temp. probe

Electricalfeed-through

Pressurechamber

Transducer

Measurementcell

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Measurements on upgraded biogasFirst, we used the measured pulse to see how speed of sound andattenuation change with gas composition.

150 200 250 300 350 400

5

10

15

20

25

frequency (kHz)

�(N

p/m

)

0% CO2

10% CO2

150 200 250 300 350 400300

305

310

315

320

325

330

335

340

frequency (kHz)

c p(m

/s)

0% CO2

2% CO2

4% CO2

6% CO2

8% CO2

10% CO2

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Measurements on upgraded biogasThen, correlate the measured quantities (acoustic properties, pressureand temperature) with gas composition.

0 0.02 0.04 0.06 0.08 0.10

0.02

0.04

0.06

0.08

0.1

True volume fraction of CO2

Estim

ated

vol

ume

frac

tion

of C

O2

true vs. estimatedtrue vs. true

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Estimation of particle size distributions

World premiere!

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ProblemMany industrial processes use crushed materials.Crushing or grinding results in different particle size distributions.Particle sizes are important for process performance.How do we measure particle size distributions (for very smallparticles)?

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IdeaAttenuation of ultrasound depends on:

Ultrasound frequency (known).Particle and liquid densities (known).Particle sizes (unknown).

This can be modeled from physics, given the probability densityfunction of the particle sizes. Parameters of the probability densityfunctions are unknown.Attenuation as function of frequency can be measured.

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StrategyAssume particles follow a certain distribution, described by someparameters, θ1, θ2, and θ3. If the parameters were known, we couldestimate the attenuation of ultrasound.Make an initial guess of the parameters and compute the modeledattenuation as function of frequency, let’s call this α̂(f).Compare with the measured attenuation α(f) and form the costfunction

J =∑

(α− α̂)2

Use this error to update the guess of the parameters.Iterate!

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Measured and modeled ultrasound attenuation before algorithm was run,for three different suspensions of Dolomite particles and water:

1 2 3 4 5 6

2

4

6

8

10

12

14

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frequency, f [MHz]

atte

nuat

ion

coef

ficie

nt, α

(f)

2%, measured attenuation2%, initial estimate4%, measured attenuation4%, initial estimate8%, measured attenuation8%, initial estimate

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Measured and modeled ultrasound attenuation after the algorithm wasrun, for three different suspensions of Dolomite particles and water:

1 2 3 4 5 6

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

frequency, f [MHz]

atte

nuat

ion

coef

ficie

nt, α

(f)

2%, measured attenuation2%, final estimate4%, measured attenuation4%, final estimate8%, measured attenuation8%, final estimate

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Estimated particle size distribution before (dashed line) and after (solidline). True particle sizes are known to be approximately 37–54 μm.

0 20 40 60 80 1000

0.005

0.01

0.015

0.02

particle radius, a [μm]pr

obab

ility

den

sity

func

tion,

p(a

)

Final estimateInital estimate

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References

J. Carlson and R. K. Ing, “Ultrasonic Speckle Correlation Imaging of2D Particle Velocity Profiles in Multiphase Flows", Flow Measurementand Instrumentation, vol. 14, no. 4–5, pp. 193–200, 2003.F. Hägglund, J. Martinsson, and J. E. Carlson, “Model-BasedEstimation of Thin Multi-Layered Media using UltrasonicMeasurements", IEEE Trans. on Ultrason. Ferroelectr. and Freq.Contr., vol. 56, no. 8, pp. 1689–1702. 2009.J. E. Carlson, J. Martinsson, and M. Lundberg Nordenvaad,“Measurement of Methane Content in Upgraded Biogas UsingPulse-Echo Ultrasound", In Proc. of Int. Congr. on Ultrasonics, Paper1366, (Vienna, Austria), April 9–13, 2007.J. E. Carlson, “Estimation of Particle Size Distributions in Solid/LiquidSuspensions Based on Wide-Band Ultrasound AttenuationMeasurements", accepted for presentation at 2010 IEEE Int.Ultrasonics Symposium, (San Diego, USA), October 10–13, 2010.

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