Optical measure (reference) Optical measure (reference)

22ndnd acoustic technique : bubbles radius histogram measure acoustic technique : bubbles radius histogram measure

11stst acoustic technique : void fraction measure acoustic technique : void fraction measure

Realized with the financial support of

regional council Provence-Alpes-Côte d’Azur

Towards Acoustic Characterization of the Gaseous Towards Acoustic Characterization of the Gaseous Microbubbles Applied to Liquid SodiumMicrobubbles Applied to Liquid Sodium

M.CAVARO1,2, J. MOYSAN2, C.GUEUDRÉ2, G. CORNELOUP2, F. BAQUÉ1

1 CEA Cadarache – DEN/DTN/STPA/Laboratoire des Technologies et de Traitement du Sodium – Bât 201, 13108 St Paul lez Durance CEDEX, France.2 Laboratoire de Caractérisation Non Destructive – Université de la Méditerranée – IUT Avenue Gaston Berger, 13625 Aix en Provence CEDEX, France.

Liquid sodium cooled fast nuclear reactors (SFR)Liquid sodium cooled fast nuclear reactors (SFR)

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PerspectivesPerspectives

MESANGE bench finalization ► Optical measure optimisation ► Bubbles generation optimisation

Experiments on presented acoustic techniques ► Bubble cloud characterization validation

Modelling and/or validation of existing models ► Transposition to the industrial case: the sodium-argon system

Nonlinear acoustic technique : the modulation frequency [2]Nonlinear acoustic technique : the modulation frequency [2]

Industrial contextIndustrial context

Liquid sodium cooled fast nuclear reactors (SFR) Liquid sodium cooled fast nuclear reactors (SFR) are considered as good candidates are considered as good candidates

for the fourth-generation reactor system for the fourth-generation reactor system

Liquid sodium = opaque Complex inspectability

Main sources of gaseous bubbles presence in the SFR primary sodium : Dissolution then nucleation of the cover gas (argon) due to ΔT° Entrainment due to the weir presence (“waterfall effect”) Possible emergence of vortex on the sodium surface Entrainment linked to the pump rotation Neutron reactions

GOAL : The development of monitoring methods to characterize the continuous presence of gas microbubbles in the SFR primary sodium (i.e. measure the radius bubbles histogram and the void fraction = gas volume fraction).

Why acoustic ? After a literature review concerning all the NDA and given the properties of sodium, it appears that acoustic seems to be the most appropriate way.

Acoustic experiments development in water : the bench MESANGEAcoustic experiments development in water : the bench MESANGEMESMESure AAcoustique de l’eNGNGazement en EEau

““Low frequency” celerity measure : the WOOD’s model [1]Low frequency” celerity measure : the WOOD’s model [1]

Bubble cloud generationBubble cloud generationUsed technique: the aeroflottation

The bubble resonance frequency The bubble resonance frequency The MINNAERT’s model The MINNAERT’s model

[3] (linear approach)[3] (linear approach)

Bench’s goalsBench’s goals Generate a bubble cloud representative of the SFR microbubbles presence in sodium. (cf. bubble cloud generation)

Reliably measure the characteristics of the generated cloud. (cf. optical measure)

Validate the void fraction measure via the Wood’s model. (cf. 1st acoustic technique)

Validate the bubbles radius histogram and void fraction measure via the two frequencies modulation. (cf. 2nd acoustic technique)

The stakes of the gas bubbles characterization :

The use in the primary pool of measures based on the propagation of acoustic waves (US telemetry, US thermometry…).

Indeed, the acoustic properties of a liquid are deeply affected by the presence of gas bubbles.

A better modelling of the gas-pocket accumulation phenomena under the submerged structures.

The control of different thresholds (threshold of neutron disturbance of the core, cover gas activity ...).

An answer to a requirement of the Safety Authorities.

The validation of computational simulation of the evolution of gas bubbles in a reactor (VIBUL code).

iii Hxp Henry’s law

(industrially used for the water filtration)

Generated bubbles radius : 10 to 15 10 to 15 μmμm

Compression pressure variation ► Radius of

generated bubbles variation

pi = gas partial pressurexi = dissolved gas concentrationHi = gas Henry’s law constant

Goal : get with reliability the bubble cloud characteristics in order to validate the acoustic measures.

IMAGE PROCESSINGIMAGE PROCESSING

Bubbles radius Bubbles radius histogramhistogram

Void fractionVoid fraction

cm = medium acoustic celerity

ρm = medium density

χm = medium compressibility

Goal : detect and quantify resonant bubbles owing to their nonlinear comportment.

r = bubble radius

ρl = liquid density

p = pressure

γ = isentropic gas coefficient

A sweeping of the pump frequency is done in order to know the resonance frequencies (and so the radius) of all the present bubbles owing to the

modulations appearance.

Celerity as a function of the frequency (r = 2mm, τ = 5,3.10-3) [4]

Very low void fractions induce strong

celerity variations

WOOD’s model allows to link WOOD’s model allows to link acoustic celerity with void acoustic celerity with void

fraction in a liquid-gas two-fraction in a liquid-gas two-phase mediumphase medium

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Wood’s model

p = pressure

τ = void fraction

γ = isentropic gas coefficient

~ “Bottle of champagne effect”

Principles :

A gas bubble has a resonance frequency linked with its radius (cf. Minnaert’s model in first approach).

The resonance of a bubble is a highly nonlinear phenomena.

Bubbles are excited with two acoustic waves: if one’s frequency correspond with the resonance frequency of some bubbles, resonance nonlinearities involve the modulation of the two signals (called pump frequency and imaging frequency).

Application : Bubbles radius histogram Bubbles radius histogram deductiondeduction

Void fraction deduction (if the Void fraction deduction (if the volume of the measure is known)volume of the measure is known)

An inversion is done to try to quantify the number of resonant bubbles (may be with

the modulation picks intensities)

Allows to link resonance frequency with the bubble radius

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ReferencesReferences [1] WOOD A. B. – A textbook of sound – Macmillan, New York, 1941

[2] NEWHOUSE V. L., SHANKAR P.M. – Bubble sizing using the nonlinear mixing of two frequencies – J. Acoust. Soc. Amer., vol.75, p.1473-1477,1984

[3] MINNAERT M. – On musical air-bubbles and the sounds of running water – Phil. Mag., vol 16, p.235-248, 1933

[4] COMMANDER K. W., PROSPERETTI A. – Linear pressure waves in bubbly liquids : comparison between theory and experiments – J. Acoust. Soc. Amer., vol.85, p.732-746,1989

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cm

Void fraction : τ

Void fraction as low as 10Void fraction as low as 10-8-8

Bubbles radius : Bubbles radius : from 10 to 100 from 10 to 100 μmμm

Main expected difficulties:Main expected difficulties:

Homogeneous generation of the bubble cloud.

Optical measurements (in particularly the calibration).

Measure of the low celerity variation for the very low void fractions.

Nonlinear phenomena quantification.

“Low frequency” domain of validity of the Wood’s model

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COMPRESSION DISSOLUTION RELAXATION NUCLEATION

WATER

AIR

P ~ 10 bars

Pump

Compressor

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INPUT

f2 f1

OUTPUT

Harmonics

Modulations

Imaging frequency(fixed high frequency)

Pump frequency

(bubbles resonance

frequencies sweep)

Nonlinear resonance

if f1 = fres

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