Optical measure (reference) 2 nd acoustic technique : bubbles radius histogram measure 1 st acoustic technique : void fraction measure Realized with the financial support of regional council Provence-Alpes-Côte d’Azur Towards Acoustic Characterization of the Gaseous Microbubbles Applied to Liquid Sodium M.CAVARO 1,2, J. MOYSAN 2, C.GUEUDRÉ 2, G. CORNELOUP 2, F. BAQUÉ 1 1 CEA Cadarache – DEN/DTN/STPA/Laboratoire des Technologies et de Traitement du Sodium – Bât 201, St Paul lez Durance CEDEX, France. 2 Laboratoire de Caractérisation Non Destructive – Université de la Méditerranée – IUT Avenue Gaston Berger, Aix en Provence CEDEX, France. Liquid sodium cooled fast nuclear reactors (SFR) Perspectives 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] Industrial context Liquid sodium cooled fast nuclear reactors (SFR) are considered as good candidates 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 MESANGE MESANGE MESure Acoustique de l’eNGazement en Eau “Low frequency” celerity measure : the WOOD’s model [1] Bubble cloud generation Used technique: the aeroflottation The bubble resonance frequency The MINNAERT’s model [3] (linear approach) Bench’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. 1 st acoustic technique)  Validate the bubbles radius histogram and void fraction measure via the two frequencies modulation. (cf. 2 nd 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). Henry’s law (industrially used for the water filtration) 10 to 15 μm Generated bubbles radius : 10 to 15 μm Compression pressure variation ► Radius of generated bubbles variation p i = gas partial pressure x i = dissolved gas concentration H i = gas Henry’s law constant Goal : get with reliability the bubble cloud characteristics in order to validate the acoustic measures. IMAGE PROCESSING Bubbles radius histogram Bubbles radius histogram Void fraction Void fraction c m = medium acoustic celerity ρ m = medium density χ m = medium compressibility Goal : detect and quantify resonant bubbles owing to their nonlinear comportment. r = bubble radius ρ l = 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, ) [4]  Very low void fractions induce strong celerity variations WOOD’s model allows to link acoustic celerity with void fraction in a liquid-gas two- phase medium 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 deduction Bubbles radius histogram deduction Void fraction deduction (if the volume of the measure is known) Void fraction deduction (if the 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 _Surveillance_ ________Safety________ References [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 ,1984 [3] MINNAERT M. – On musical air-bubbles and the sounds of running water – Phil. Mag., vol 16, p , 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 ,1989 Celerity : c m Void fraction : τ Void fraction as low as Bubbles radius : from 10 to 100 μm 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 Bubbles resonance frequency COMPRESSIONDISSOLUTIONRELAXATIONNUCLEATION WATER AIR P ~ 10 bars Pump Compressor f 2 + f 1 f 2 - f 1 f2f2 f1f1 Freq. INPUT f2f2 f1f1 OUTPUT HarmonicsHarmonicsModulationsModulations Imaging frequency (fixed high frequency) Pump frequency (bubbles resonance frequencies sweep) Nonlinear resonance if f 1 = f res R