Models comparison for the scattering of an acoustic wave on immersed targets

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1 Modls compariso for th scattrig of a acoustic wav o immrsd targts B. Lu (Ph.D. studt), M. Darmo, C. Potl ad V. Zrov 3 CEA LIT, Frch Atomic Ergy Commissio, F-99 Gifsur-Yvtt, Frac Laboratoir d Acoustiqu d l Uivrsité du Mai (LAUM), UMR CNR 663, 785 L Mas Cdx 9, Frac. 3 oud Mathmatics Ltd., Cambridg, U.K.

2 Cotxt: Ultrasoic tlmtry Missio: Dvlopmt of th simulatio tool to assist Ultrasoic tlmtry : a moitorig ad ispctio tchiqus for locatig various grad structur régulièr, liss, immrsd structurs (for istac, compots i th cor of fast brdr ractors). Istrumtatio of U tlmtry: Optical masurmt of th trasducr positio tructur ispcté : délimité par u arêt (diffractio) Liquid sodium ihomogous spcular rflctio diffractio of boudaris ad dgs U trasducr istalld i th cor of uclar ractor Primary aims U trasducr immrsd structurs Pricipl of Ultrasoic tlmtry corr ffct Pricipl: surfac wav Dtrmi th distac btw th trasducr ad th immrsd structurs by masurig th tim of flight of back scattrig wav. Modlig of wav propagatio i mdia with larg-scal radom ihomogitis.modlig of th scattrig of acoustic wav o immrsd structurs AFPAC Jauary 9- Fréjus Frac / B. Lu, M. Darmo, C. Potl ad V. Zrov

3 Outli Modls compariso for th : cattrig of a pla wav by a rigid halfpla cattrig of a pla wav by a rigid wdg cattrig of a pla wav by a fiit impdac wdg Coclusio AFPAC Jauary 9- Fréjus Frac / B. Lu, M. Darmo, C. Potl ad V. Zrov 3

4 cattrig of pla wav by a rigid halfpla Kirchhoff approximatio () Gr s thorm U x G x, x' ( ) (, ') ( ) cat U x G xx U x ds x High frqucy approximatio o th boudaris ( + & - ) U( x), U( x) U ( x), U( x). 5 4 Kirchhoff approximatio U ka for th scattrig fild U cat G x, x U ( x) U x dx 7.5 θ=5 ; r = λ 6 3 Kirchhoff (mm) (mm) Error distributio of (xact - ) % % -% -% Advatags : Ovrall good dscriptio of th scattrd fild Easily applicabl for complx structur shaps Dficicis: Errors ar th boudaris orrct amplitud of diffractio wav AFPAC Jauary 9- Fréjus Frac / B. Lu, M. Darmo, C. Potl ad V. Zrov 4

5 cattrig of pla wav by a rigid halfpla Gomtrical thory of diffractio (GTD) U U D GTD GO GTD (, ) ikr kr With D GTD : diffractio cofficits D GTD (, ) i /4 cos cos Thortical validatio cattrig filds compariso ( vs. GTD) D GTD hadow boudaris Numa =5 θ =5 pumbra ara GTD 3 θ=5 ; r = λ AFPAC Jauary 9- Fréjus Frac / B. Lu, M. Darmo, C. Potl ad V. Zrov θ=5 ; r = 5λ GTD 3 33 θ [dg] Advatags : impl formulatio corrct prdictio of diffractio phomo Dficicy: Iapplicabl i th pumbra aras 5

6 cattrig of pla wav by a rigid halfpla Rfimt of Kirchhoff approximatio (R) Cotributio to th Kirchhoff itgral G x, x U ( x) U x dx Diffractio cofficit of Kirchhoff itgral D To limiat th dficicis of ad GTD formalism ad combi thir advatags i 4 ta ta tatioary poit (spcular rflctio) lowr itgratio limit cotributio (diffractio x =) U U (GO) ( x) (diff) ( x) D (, ) ikr kr D GTD D kirchoff =5 Modificatio of U usig U GTD U U U U U R (GO) (diff) (diff) GTD(diff ) U D D GTD ikr kr [dg] D GTD - D Kirchoff ic =5 additioal corrctio AFPAC Jauary 9- Fréjus Frac / B. Lu, M. Darmo, C. Potl ad V. Zrov [dg] 6

7 cattrig of pla wav by a rigid halfpla Thortical validatio : Improvmt of rfid Rfid- 3 zoom Rfid- Good agrmt btw th xact solutio ad th rfid solutio 7 Error distributio compariso (xact - ) θ=5 (xact - R) θ=5 (mm) (mm) % (mm) % -% -% rfimt (mm).5% % % -% -% -.5% Coclusio : atisfyig validatio for ad slight improvmt du to th rfimt (ar fild ) AFPAC Jauary 9- Fréjus Frac / B. Lu, M. Darmo, C. Potl ad V. Zrov 7

8 5 cattrig of pla wav by a rigid wdg GTD for a rigid wdg D H (,, ) H(,, ) H GTD Wdg (,, ) ctg ( ) ctg ( ) Kirchhoff approximatio for a rigid wdg Wh both facs of th wdg (Ф > π) ar illumiatd by th icidt wav, itgral ds to b calculatd for ach fac U U (, ) U (, ) Thortical validatio for a rigid right-agld wdg Th mthods applid to rigid half-pla ar valid for rigid wdg Rfid Rafi zoom -Rafi 8 Rfid 33 zoom θ=5 ; Ф = 7 ;r = λ θ=35 ; Ф = 7 ;r = λ Coclusio : atisfyig validatio for ad slight improvmt du to th rfimt AFPAC Jauary 9- Fréjus Frac / B. Lu, M. Darmo, C. Potl ad V. Zrov 8

9 Modul Phas cattrig of a pla wav by a fiit impdac wdg Boudary coditios at wdg facs: U ( ikr ) U, at ad, Z R( ) si( ) R( ) wdg with. c.89 Rflctio cofficit ( liquid sodium/stl ) Rflctio Cofficit (odium/tl) GTD for a arly rigid wdg: [Pirc & Hadd 978 ] D D (, ) Z GTD Wdg Wdg U U R( ) U D (, ) cat Rf Z Wdg Validatio of Rfid- for a fiit impdac wdg ikr kr R( ) Agls ( / - ) [dg] solutio outsid pumbra Rfid- rigid fails o a fiit impdac wdg 4 7 GTD arly rigid Rfid- 33 rigid 3 θ=5 ;r = 5λ 4 AFPAC Jauary 9- Fréjus Frac / B. Lu, M. Darmo, C. Potl ad V. Zrov 7 GTD arly rigid Rfid- 33 rigid 3 θ= ;r = 5λ Nd to tak ito accout th surfac fiit impdac i. 9

10 Modul Phas cattrig of pla wav by a wdg with fiit impdac Dvlopmt of th Kirchhoff approximatio applid to a fiit impdac surfac: U x G x, x' ( ) (, ') ( ), cat U x G xx U x ds x Rflctio cofficit ( liquid sodium/stl ) Rflctio Cofficit (odium/tl) U x U x ( ) ( ) ( R), U ( x ) ( R) U ( x ).89 R = : rigid boudary (Numa) R = - : soft boudary (Dirichlt) Impdac : Z U x G x, x' U( x) G( x, x') ( R) U x ( R) ds( x ).8 R( ) Agls ( / - ) [dg] Proposal ad dvlopmt of a modifid rfid for a fiit impdac wdg: D H(,, ) H(,, ) GTD Wdg ikr Z Z GTD R wdg wdg U U D D H(,, ) ctg ( ) R* ctg ( ) D kr i 4 ta +R* ta AFPAC Jauary 9- Fréjus Frac / B. Lu, M. Darmo, C. Potl ad V. Zrov

11 cattrig of pla wav by a wdg with fiit impdac Validatio of modifid rfid Kirchhoff GTD arly rigid Rfid- rigid Rfid- rigid 33 Modifid-rfid- Impdac GTD arly rigid 33 Impdac Modifid-rfid θ=5 ;r = 5λ θ= ;r = 5λ Good agrmt btw th rsults giv by impdac ad GTD arly rigid outsid th pumbra aras. No sigificat corrctio with Modifid-rfid- AFPAC Jauary 9- Fréjus Frac / B. Lu, M. Darmo, C. Potl ad V. Zrov

12 Coclusio Modls applid to th scattrig of a pla wav by a rigid halfpla ad a rigid wdg Kirchhoff approximatio: Qualitativly corrct dscriptio of diffractio wav Possibl to us for flaw shaps for which a xact solutio is ot kow Ovrall corrct dscriptio of th scattrd fild GTD : accurat prdictio of th diffractio wav but o valid i pumbra ara Rfid Kirchhoff: light improvmt of i th diffractio modlig (ar fild) Th mthods applid to half-pla ar valid for wdg Modls applid to scattrig of a pla wav by a arly rigid wdg GTD arly rigid : xact solutio outsid of th pumbra ara. Kirchhoff approximatio: xtdd to accout for th fiit impdac of th wdg. Proposal of a modifid rfid Kirchhoff approximatio for a arly rigid wdg. Validatio by compariso with a rfrc GTD arly rigid solutio : Good agrmt obtaid for th Kirchhoff approximatio. No sigificat corrctio with modifid-rfid-

13 Thak you for your kid atttio! AFPAC Jauary 9- Fréjus Frac / B. Lu, M. Darmo, C. Potl ad V. Zrov 3

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