KR9700258 KAERI/RR-1680/96
Development of Nuclear Fuel Rod Testing Technique Using the Ultrasonic Resonance Phenomena
29 - 0
j KAERI/RR-1680/96
Development of Nuclear Fuel Rod Testing Technique Using the Ultrasonic Resonance Phenomena
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iation examination facility: PIEF)^
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vii ISSXT FAGE(S) left BLANK SUMMARY
I. Project Title
Development of Nuclear Fuel Rod Inspection Technique Using Ultrasonic
Resonance Phenomena
II. Objective and Importance of the Project
The core of the pressurized water reactors contain about three hundred fuel bundles. Each fuel bundle, which is of type of rectangular parallelpipe, consists of about two hundred fuel rods, some guide tubes, spacer grids, and top and bottom nozzles. Each fuel rod consists of uranium dioxide pellets, a Zircaloy-4 cladding tube, plenum spring(s), etc. The ends of the rod are sealed with end plugs by welding. Plenum is the internal space for accumulating the fission gases. For the safe and economic operation of a nuclear power plant, it is very important to secure the structural integrity of the cladding tube, which is the first barrier against the release of radioactive fission gases. Therefore a number of non-destructive testing (NDT) methods have been applied in the various stages of fuel manufacturing, in-service inspection (ISI) and post-irradiation examination
(PIE).
The current NDT methods to evaluate the extent of failure of in-service or spent fuel rods are the eddy current testing (ECT) and the ultrasonic testing (UT). The former is used to examine flaws in the cladding tube and the latter to detect the presence of water in the gap between cladding tube and pellet, which is indicative of cladding tube
ix failure. ECT is also used to measure the thickness of oxide layer on the outside surface of the cladding tube and it is rather simpler than UT in view point of detecting flaws in the cladding tube, but it requires disassembling of the fuel bundle for testing. UT does not require the disassembling but its reliability is not so high that, in ISI, the leak-defective fuel rods detected by UT have been re-examined by ECT. There were many cases that a rod evaluated as a leak-defective fuel rod by UT is evaluated as a sound rod by ECT, and vice versa.
Recently, a new UT technique has been developed, which has potential of detecting the water presence as well as flaws, dimensions and material property change of the cladding tube. This new technique takes advantage of ultrasonic resonance phenomenon which is attributed to elastic waves circumnavigating the tube (so-called
"circumferential waves"). In the simulation experiment using a pre-irradiated fuel rod, it was already shown that this technique can detect the presence of water clearly. The purpose of this project is to apply the new UT technique to ISI and PIE.
HI. Scope and Contents of the Project
In the first year (1995) of this project, some basic techniques had been developed for modeling of the acoustic resonance scattering (ARS) by a nuclear fuel rod, measurement of ultrasonic resonances, and design and manufacturing process of thin
(less than 2 mm) ultrasonic sensors. Particularly, an experimental system for measuring the resonances of a disassembled spent fuel rod was constructed at the post-irradiation examination facility (PIEF) in our institute and excellent detection ability of the new UT for the leak-defective fuel rods was successfully demonstrated.
In the second year(1996), the ARS modeling code developed in the first year has been extended to be applicable to an multilayered cylindrical shell. An empty cladding tube, a fluid-filled cladding tube, a pre-irradiated fuel rod with helium gas gap, a leak- defective fuel rod with water gap, and an in-service or spent fuel rod with zirconium oxide layer on the outer and/or inner surfaces of the cladding tube can be dealt as an example of the multilayered cylindrical shell. And the resonant ultrasound spectroscopy system (RUSS) has been constructed to evaluate the effectiveness of the developed ARS modeling code. The leak-defective fuel rod detection system (LFRDS) of a laboratory scale has been also constructed to develop the ISI technique taking advantage of the resonances of the cladding tube.
IV. Results and Proposal for Applications
The scattering of plane acoustic waves normally incident on a multilayered cylindrical shell has been formulated using the global matrix approach. This is to represent each boundary condition as a matrix (so-called "boundary matrix") equation and to simply add all boundary matrix equations. Therefore this approach allows us to represent all boundary conditions as a single matrix (so-called "global matrix" or
"system matrix") equation and to obtain the elements of the system matrix for any shell with arbitrary structure easily and correctly.
A simple approach to formulate a non-resonant background component in the field scattered by an empty elastic shell has been founded. This is to replace the surface
XI admittance for the shell with the zero-frequency limit of the surface admittance for the analogous fluid shell (i.e., where the shear wave speed in the elastic shell is set to zero).
Justification for this replacement comes from noticing that, when the waves that give rise to resonances in the shell are damped out, the surface admittance is well approximated by that for the analogous fluid shell and is practically constant as a function of frequency.
Therefore it can be hypothesized that the constant part of the surface admittance should be used to obtain the background and the simplest way to obtain this part for a nonattenuating shell, given there are no resonances to modify the surface admittance at zero frequency, is to extract it as the zero-frequency limit of the surface admittance for the fluid shell. It has been analytically and numerically shown that the background thus obtained, which is named "inherent background" here, is exact and applicable for shells of arbitrary thickness and material makeup, and over all frequencies and mode numbers.
The exact expressions of the background components for multilayered shells of arbitrary structure have been founded using the inherent background approach and their effectiveness has been also demonstrated. The inherent background approach is applicable to other goemetries; for an example, the approach for spherical geometry is identical to that for cylindrical geometry, with the exception of replacing the cylinder functions by the corresponding spherical functions.
RUSS has been constructed to measure the resonance spectrum of a single fuel rod and to evaluate the effectiveness of the developed ARS modeling code. It consists of an ultrasonic system, a scanner system, and a computer system. The ultrasonic system contains ultrasonic transducers, a pulser and receiver, and a waveform digitizer. The
xu scanner system contains a water tank, a stepping motor driving turn-table and two-axis slide unit, and a motor controller. The computer system controls the scanner controller, the pulser and receiver, and the waveform digitizer, and it acquires and analyzes the scattered signals. The resonance spectrum of a fuel rod is obtained using the mono-static pulse-echo method, and the order of each resonance is determined using the bi-static pulse-echo method. The measured resonance spectrum is in good agreement with the spectrum predicted by the ARS modeling code.
LFRDS of a laboratory scale has been constructed to develop the ISI technique. It consists of an ultrasonic flaw detector, an ultrasonic probe of thin (thickness of 1.2 mm) strip type, a scanner system, a standard (non-irradiated) fuel bundle, and a computer system. The scanner system contains an water tank, a stepping motor driving three-axis slide unit, and a motor controller. The computer system controls the scanner controller and it acquires and processes signals from the flaw detector. Particularly, all techniques and processes necessary for manufacturing the ultrasonic probe have been developed and some prototype probes have been manufactured.
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«-S. A vfl^.7^ ^l^-o] cj-* jL^l ^oil tfl^- #£«8t «-S- B. A% €°fl tfl^ «-S- C. V-fl^-7} ^l*?! °1^ aLSfl ^ofl tfl^j. AV^^tS] li H5 t^r^ 119 xvi Figure 2-1. (a) The modal surface admittance (divided by the fluid-loading- parameter) GJ,L) of the lowest order (« = 0) partial wave for the liquid shell l (h = 05 and CL=57%Qms~ ) without any consideration of structural damping in water (C, = 1480 m.?"1), and (b) the real parts of the modal surface admittance for various structural-damping coefficients /3L, plotted as a function of frequency. 13 ( L) + Figure 2-2. G n (0 ) of the first six (n = 0 ~ 5) partial waves plotted as a function of relative shell-thickness. 17 Figure 2-3. (a) Moduli and (b) phases (in radian) of the total backscattering form functions of the inherent backgrounds for the 2% (dash-and-dot line) and 99% (solid line) thick, empty, stainless-steel shells in water, as well as those of the rigid (dotted line) and soft (dash-and-two dots line) backgrounds. 19 (A) Figure 2-4. Moduli of the residual backscattering form functions, |/n -/n |, for the lowest six (n - 0 ~ 5) partial waves for the 2% thick, empty, stainless- steel shell in water. 21 Figure 2-5. Geometry of a plane acoustic wave scattering from a multilayered cylindrical shell. 25 Figure 2-6. Geometry of a plane acoustic wave scattering from an empty doublelayered elastic cylindrical shell. 45 Figure 2-7. Comparison between the inherent background amplitudes(dotted line) and the backscattering amplitudes (solid line) of the partial waves for an 12% thick, empty Zircaloy shell with 10// m thick ZrO2 layer. 47 Figure 2-8. Resonance spectra of the partial waves for an 12% thick, empty Zircaloy shell with 10 // m thick ZrO2 layer. 48 Figure 2-9. Resonance spectra of the (a) «=4 and (b) n=10 partial waves for 12% thick, empty Zircaloy shells with the various thickness (10/an, 20//m, 50/an, 100/an) of ZrO2 layer 49 xvu Figure 3-1. Schematic diagram of the resonant ultrasound spectroscopy system. • • 53 Figure 3-2. Overall view of the resonant ultrasound spectroscopy system: (a) scanner, (b) turn table, (c) computer, (d) scanner controller, (e) waveform digitizer, and (f) pulser & receiver. 54 Figure 3-3. Signal waveform and frequency spectrum of the 0.5 MHz transducer 57 Figure 3-4. Signal waveform and frequency spectrum of the 1.0 MHz transducer. 58 Figure 3-5. Signal waveform and frequency spectrum of the 2.25 MHz transducer. 59 Figure 3-6. Signal waveform and frequency spectrum of the 3.5 MHz transducer. 60 Figure 3-7. Signal waveform and frequency spectrum of the 5.0 MHz transducer. 61 Figure 3-8. Signal waveform and frequency spectrum of the 7.5 MHz transducer. 62 Figure 3-9. Signal waveform and frequency spectrum of the 10 MHz transducer. 63 Figure 3-10. Drawing of the turn table. 64 Figure 3-11. Photograph of the turn table. 65 Figure 3-12. Backscattering echoes obtained from the fuel rod using the 1 MHz transducer. c-i Figure 3-13. Backscattering echoes obtained from the fuel rod using the 2.25 MHz transducer. 68 Figure 3-14. Resonance spectrum of the cladding tube obtained using 1 MHz transducer. Here, n denotes the normal mode number. Left number in the parenthesis is resonance frequency measured experimentally and right number is resonance frequency calculated theoretically. 70 xvin Figure 3-15. Resonance spectrum of the cladding tube obtained using 2.25 MHz transducer. Here, n denotes the normal mode number. Left number in the parenthesis is resonance frequency measured experimentally and right number is resonance frequency calculated theoretically. 71 Figure 4-1. Different vendors' probes of ultrasonic testing (quoted from Reference [2]). 74 Figure 4-2. Schematic diagram of the leak-defective fuel rod detection system. • • • 78 Figure 4-3. Overall view of the leak-defective fuel rod detection system: (a) scanner, (b) xy slide unit, (c) fuel assembly, (d) computer, (e) scanner controller, (f) flaw detector, and (g) waveform digitizer. 79 Figure 4-4. Photograph of the ultrasonic probe. 82 Figure 4-5. The ultrasonic probe mounted in the xy slide unit. 84 Figure 4-6. Drawing of the slide unit. 85 Figure 4-7. Schematic diagram of the ultrasonic sensor designed for fuel assembly inspection. 87 Figure 4-8. Drawing of the ultrasonic sensor housing. 90 Figure 4-9. Drawing of the probe strip 92 Figure 4-10. Drawing of the probe strip holder. 94 xix ^^(pressurized water reactor: PWR)^ ^ 300 7fl5] te^^Kfuel assembly)!-^- if-^4- 44 *)1TT 200 ^7flS} 3 *}-^ it- fll n -^^^. #£-!§-& UO2 1^!, Zircaloy-4 a| ^(cladding tube), 1-el^(plenum) ^S^ f-^.S ^sM ^^r^l -g-^: n>7flS. 7}iffi] ^r^dfl tfl^- Al-g-^^A>(in-service inspection: ISI)°fl, H5lJL ^A>^:A1 ^(post- irradiation examination: PIE) -^^l ^ -1- il(leak-defetive) scattering) .[3, 4] (resonance scattering) *fl^ ^ ^-^ ^^ 34-8- W^ i-l-4 5] 'S^i.^l 2:^|-^Al^Al4i (post-irradiation examination facility: PIEF)°fl ^^1*> MI-?-^ #S] ^^ ^-^--i- uB-f ^^ 4!SUES. ^Til t^l ^ ^r SI (multilayered) -2- . I151JL 2.^-4 ^^mS-^SU] AliEfl(reSonant ultrasound spectroscopy system: RUSS)^: n1^^1^. ^E^(leak-defective fuel rod detection system: LFRDS)# -7fl 1.2 -3- 2.1. 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D?£r ^11 £>„ ^ ^^^l-o]4. ^^ "fl^olli ^(surface admittance)^ ] ^4 s^fl ^l^f. Murphy ^ plateau S. 51 ^-ol^^r €^1 -g-^^lS^l rfl^-SlJI, plateau^ ^1 intermediate background^ ifl-g-^cf. ^-tf^, °1 plateau unique *}*1 ^4^ ^-^1^°1 Si°1 intermediate background -9- B Q = (p, / p2)/h S, ^ 5] £)^ -B-*|)-f Sr- fl 7fl ^(fluid-loading-parameter) 3,[ll,13, 14] ^S.^: ^ GB-§- t)-g-3r 2°1 33^ ^r $14: f^ G/ 14 «14 -fMl^ D^£ «1 ^ -¥-^:«rtr. ^^l-^l-^^fl^^r^ null frequency e^-jLJE. l-^-?-^, &£ U^l ^^(soft) 2.2.2. Neper/m^ -10- LJ = xLJ(\-h), (6) €- ^3-i- pt>r 3.5L, ^- 3x3 5. -11- = m L Jn(yL)Yn(xL)-Jn(xL)Yn(yL) (liquid-shell background) 1480 5aJl 1 0.5°lJI ^4 ^£(Ci)7> 5780 ms" ^! stainless steel H](Q/C,)7]- ZLZJE.3., 2-l(b)Sr plateau °1 plateau^ ^ -12- (a) 200 -200 60 80 100 (b) 10 - P. =7 P. =5 4 PL=3 2 o -2 . P.-o> 20 40 60 80 100 Figure 2-1. 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(10) ^ 10 •§- q 7°fl tfl^t)-^, "t^ G^^ zero frequency limit £• ^-§-4 7^°1 ^ -15- n>\ (lib) l-(l-A) 2" -2^ *{•%• *)^- null frequency fi^ ^V +)fe ^^}s)-(generalized) null frequency 11 5] G(i)(Q+)^ «^«]:S}- null frequency 7]- ^^g- |«| # null frequency, Q (L) + null frequency °1I ^^f^ l^S]^, x, « Fn (0 ) ?1 2.2.4. -16- + o 0.0 0.2 0.4 0.6 0.8 1.0 Figure 2-2. GJ,L) (0+ ) of the first six ( n = 0 ~ 5) partial waves plotted as a function of relative shell-thickness. -17- /,,(A)(Tt,*, )•§•*,= 0-20 S] ^4^ <£ <* ofl Ai Til^^JL, „ = 25 4*1 (b) (n,xl)3\- f {n,xx) stainless-steel ^«fl cflsfl Ax, =0.01 OJJL, ^£3^ ^flS.^ #^^ cf-g- 3 3 1 1 4 W: p, =1.0gcm- , p2 =7.9gcm" , C, = 1480ms" , Ct= 5780ms" , 1 CT = 3090 ms" . 99% . 2o/o . 99% o| -18- - 0.4 10 15 20 k,a (b) 8 jS 0 a, -3 10 15 20 k,a Figure 2-3. 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Moduli of the residual backscattering form functions, b) for I fn ~ fn \> ^ lowest six (n = 0 ~ 5) partial waves for the 2% thick, empty, stainless-steel shell in water. -21- 20 514; -22- 2.3. £!#ii c|-g 10o|| s|oh ^o| 3 7} .[20, 21] ol £-*H tfl*> °l^-^tl *fl^ a^AS^ Thomson Haskell ^ [22, 23] ^iil:39!(transfer matrix)^ 4 Knopoff 5] [24] ^^, 2.3.1 2.3.2 *HH^ uLSfl/uLS||, - -23- ^ Til 5., 2.3.3 2.3.1. 2-5 . o) Pj 44 C} Cj (12) $= AA j dJ=aj_]-ajO)jL, Ol^O] y].^- 711S} Hi, -24- Figure 2-5. Geometry of a plane acoustic wave scattering from a multilayered cylindrical shell -25- x}-T=y}J(l-hj). (13) = 0 c R H P\ = p'r + Pi = > en/"[/n(V) + n ; (V)]cos«e, (14) n=0 en^r Neumann ^K^o = 1 > e«i=2), tfl ^*fi^c>> ^ <1^ Tfl^(scattering coefficient)^4. 4* (15a) n=0 ;)^ i;(Arjr)]sin«G . (15b) n=0 Bessel (i6a) (16b) n=0 -26- (i) r = a, r -Pi, u 2=u[, T?=0, (17a) (ii) r = ajU = - u)=u%x, (17b) Trr*- Oj ^ o] A^ ^17 (18) (4/w - 5) x (4m - 5) 2.1 . 4 -§- matrix)^ • -27- 2.3.2. ffl U1 (global matrix) (19) (Kh ^ 3x4 «91, r^(scattered) ^"i", '^'^ . o) ^tl; (20) -28- (21) . ZLE}JL, (22) 20-22 o] Aj^^o^ ^. R \ n A* - {0} x2 {0} ' Xj_i • = . {«} , (23) Jm-\ Um [x. {0} 23^- ^ 18 4 -29- D\ - D7-1 (24) o;m-1 nfl, tfl-^-S] ' —n T'9 — n m-1 (25) -1 - U> Xm-\ ~ U 22^ cf-g- (26) 2x4 (27) n=0 -30- (28) 22 4 24 4 A, 4 3x4 ^14 3x1 Xm=(T,,)m. (29) r J+x = u j, zf_]J+] = 0 (30) 24 4 A,2?" ££ B1 2.3.3. -31- 18 4 q 23°IM, #£ 7j)^ Rn±r Cramer , (31) \Dn\£r *)^ «8! Dn$\ ^t^(determinant)^i \Bn\-& Dn$ ^ ^ A u 2^ Z)^ 4:^to)tf. flJBnl^i(surface admittance)^, -ir^-f ^ a], ^^ ^5] tfl^. ^s, Zl^JL ( } Hankel W -32- Hankel ^ H™{x)$= complex conjugate <>]4. 22))^, ^^-^-^r Sn-& (scattering phase shift) 5n ^^.S. i^^ ^ $icf: 5n=exp(2/5J. (35) -33- 2.4. 2.2 ^nl1i^£l zero- frequency limits. tflSfl^f-^- 3H4. ol ofl^ul^^^ AOU|. -^-^1 ^ofl o] ^-^ AJ W.-O- ^^ 7].^- ^-^-^ HOV^^. zero frequency e^ ^^r-s ^^^1^ ^^°1 §1^ AoV4 -n-^11 €^1 zero-frequency limit ^1 °] ^ ^^1 Wf ^ ^14 ^^1, W -fV^ll ^^ ^^l^r S^ afl-Einm^-I- -fVS^cf. H?)3L 0} ^1^^^ zero-frequency limit 1- Zircaloy-4 -34- 2.4.1. -^(analogous) T 2-5 -9-si y(=2,3,..., m- (36) »=o n=0 (I) =£eBi-[(7; )>yj,(*wr)]cosiie . (38) N=0 36-38 U U ^7 =^+i ' J = J+I U = l2,...,m-\). (40) 2.3.2^H H^ 5J4 ^-^ €^1-1- 4^^, ^ 23 4 ^-4- -35- (41a) (41b) J { ) n Xj (41c) XjJn'(Xj) Pm-l (41d) (41e) (41f) E - (41g) -§•4 (42) P2 -36- *-y2^±. (45) P2 Jniyi) 44 ^ 4A] l) Hankel ^-^ /^ (^2)4 °1^ Hankel 2)^1 Ai ^Aj^o^w.^ ^ 1 °14. o] nfl, -37- P. ,. ^•(y )(SiL)) H?)'(y ) 2 2+ 1 (47) £>„ (48) Pi P2 P2 434 AI 44 (49) " P2 Bessel tHr^ Neumann f-^rt- Hankel ^1: 49 fe- 4^4 47 40.4 -38- D = {0} i$ n 0 (50) - 0 P2 o J, 0 x^ 44 ^ 4^4 7^-0) (51) 2Hn (52) J P3 J ^ ^ 45 °11 . Bessel tJ^rir Hankel 52 47 01 (53) (5^)3 = 1. -39- {L)) =^±v. -i ^ — (55) 53 1- ^ 55°fl tfl^*}1^, 4-5-^f ££ ^^^(recurrence relation)^: JYB (56a) JYD = Jn'(yJ)Yn'(xJ)-Jn'(xJ)Yn'(yj) , (56b) = Jn\yj)Yn{xJ)-Jn(xj)Yn\yj) , (56c) = Jn(yJ)Yn'(xj)-Jn'(xJ)Yn(yJ) , (56d) = y, (^. )yB (Xj ) - yB (x,. )Yn (yj ) . (56e) ^ 1 °)B.S., -40- (57) » D 2.4.2. :H 2.2.5 ofl^ol^i^o] Zero-frequency limit 10o)l M-E^vfl Bessel -%^ Neumann ^-^r^ ^4^1:^: ^ 56 °fl (i) + (58a) P, l-ln(l-A,)(Fn (0 (58b) q.=n J-^ . (58c) -41- (59) (L) + ^n]^^ Fn (0 )^ ^ 58^1 (60) ^g-f, 2.2.3 11-1- -42- (62) (63) .+£- 2.4.3. 10-200^m^^^ oiA]-^-xl5.3.^-(ZrO2) -43- 2-6 4 1, *\ 3, ZL51JL ^] 9^ D? D: {0,} {0} (64) {0} {0} D] + -Pi Fn^(0 ) = (65a) 1 + 1 ( )2 \2n F£Ho*)=*±n . ,, ; !.-*' ' (65b) P2 p3 1-O- l, Df±. 3x1, £)^ 3x2, D*^ D^ 4x4, ^ 2x4 9x9 Ci -44- Figure 2-6. Geometry of a plane acoustic wave scattering from an empty doublelayered elastic cylindrical shell. -45- fe JL ZrO2 Zircaloy-4 ^4^6fl ^^fl ^^tt4. ^^-^^] ^fl D A >JL ^B] -]-fi) J"ifl-T^ll(/»2)^ 0.1%, 0.2%, 0.5%, 1. 19mm ?1 9|l^*)~f^ 17x17 =0-100, Ax, =0.05 3 3 1 p2=5.6gcm- , p3 =6.55gcm- , C, = 1480ms" , £ 1 1 1 r C2 =7100ms- , C^SSOOms" , C\ = 4600ms" , C3 = Zl^ 2-7^ 0.1% ^M|i*l -a-^-^nj.^- ^^- s]^-^ofl tfl*> ^ cf^ 7fl 2-8 Lamb 4°fl 7l«]^4. ^^ 2-9 -46- 20 40 60 80 100 Figure 2-7. Comparison between the inherent background amplitudes(dotted line) and the backscattering amplitudes(solid line) of the lowest five(n=0~4) partial waves for the 12% thick, empty Zircaloy shell with lOfam thick ZrO2 layer. -47- n=0 n=1 n=2 n=3 3 n=4 O n=12 n=16 n=20 20 40 60 80 100 k.,a Figure 2-8. Resonance spectra of the partial waves for the 12% thick, empty Zircaloy shell with lOjam thick ZrO2 layer. -48- 20 40 60 80 100 60 80 100 k.,a Figure 2-9. Resonance spectra of the (a) «=4 and (b) «=10 partial waves for 12% thick, empty Zircaloy shells with the various thickness , 20fim, 50|am, lOO^m) of ZrO2 layer. -49- rt]. 33.^ -50- 3.1. ol ^-(resonance scattering theory: RST)°fl : 1981 Vl S.^ Le Havre tfl^ RipOche iL^r ^H 5]«fl ^ ^- JL^S] $4.[25-28] Quasi-harmonic MIIR(Method of Isolation and Identification of Resonances)^. toneburst 4 ^fl^Hl ^3. 7} , Rayleigh normal mode number)"^) -51- short-pulse MIIR ofl ^«fl #^€ T£ &4.[29-30] FFT(Fast Fourier Transform)^"°-£.tf ^ i^jS^^- Q&ty. °1 yo> wJ-^l-(quasi-harmonic MIIR 4 short-pulse ^ o) 3.2. 3-1 4 H^ 3-2^ -52- Transmitter/Receiver Pulser & Receiver Transducer (Ritec RAM 10000) Receiver Transducer Waveform Digitizer (Tek.RTD710A) Water ADAC4801A GPIB Computer RS232C Scanner Controller Printer Figure 3-1. Schematic diagram of the resonant ultrasound spectroscopy system -53- Figure 3-2. Overall view of the resonant ultrasound spectroscopy system: (a) scanner, (b) turn table, (c) computer, (d) scanner controller, (e) waveform digitizer, and (f) pulser & receiver. -54- S]^ 3(x, y, z) ^ scanner^ turntable, H^JL J2.B]- 5.*}- ^Sl-ei, ^^ ^ monostatic pulse-echo (MPE) uj"^AS <^o] xl^ z]- ^-^o) ^>^^ ^A| &• ^•AQ ^r^l ^-#^1-71- ^e)5i^ bistatic pulse-echo (BPE) "J^ BPE 1WH ^r^l ^^rfe turn table . 4 -¥-^-^ Litec 4^1 RAM-0.25-17.5 Mark VI Mr *}-%-*}Sm. °1 ^^1^ 250 ^i 10 MHz ^ofH ^cfl 1.5 kW (in RMS), 17.5 MHz 1.0 kW(in RMS)^ RF toneburst ^^1- ^V^A1^ ^r 9X^-, 78 dB ADAC4801A ?>=.-!• -i-«l| IBM 586PC °fl Tektronix/Sony RTD 710A1- ^}-%-t}<^t\; ^ cfl sampling rate fe 200 MHz, ^^r 10 bit, ^lliel^ 640kB <>14. GPIB 5 -55- -^c: Tektronix SPD(signal processing and display) i5.S Panametrics *H VideoScan series(0.50, 1.00, 2.25, 3.50, 5.00, 7.50, 10.00 MHz)t- 4-g-*>^4. ^ 3-3 "l-5f Metrotek 4^ C403 system^- 1.1 m(L) x 0.6 m(W) x 0.5 m(H) olcf. ^2: o]^ol ig;E<>11 5]«fl ^p-g-ilfe 3(x, y, z)-% scanner 7> ^2)"^cf. o] scanner fe ^ 0.05 mm o)cf. %$-B\9}- SLt\- fe RS232CS <31€4. i]^^^ ^^ ^^ ^^\] %n^= BPE turn table °fl £]«fl QtfQty. ^l^Nl-c- °1 turn tabled QQ ^- 3^ scanner °fl ^2}-^ -^-^^1 ll^ll^ jig °fl 3-10 4 ^-^ 3-11 ^r turn tabled 7])x\ -56- SIGNAL WAVEFORM ( 2 USEC / DIVISION ) FREQUENCY SPECTRUM 1.0 - j( ^ 0.8 - 0.6 ~ \ .31 V615 - -6dB 0.4 — j 1 \ - \ 0.2 — / ^ _. \ 0.0 —I k 00 0.5 1.0 (MHz) Figure 3-3. Signal waveform and frequency spectrum of the 0.5 MHz transducer. -57- SIGNAL WAVEFORM 0.8 - - 0.4 - - A 1 0.0 - \fV -0.4 — - - -0.8 ( 1 USEC / DIVISION ) FREQUENCY SPECTRUM 1.0 - / 0.8 — \ / - \ 0.6 — \ 6 .2 - / j 6dB V 0.4 - \ I \ - 0 2 V 0.0 . .. 1 (MHz) Figure 3-4. Signal waveform and frequency spectrum of the 1.0 MHz transducer. -58- WAVEFORM 200 mv/div VERTICAL SENSITIVITY: .50 us/div HORIZONTAL RESOLUTION: —— JL. A L r — \ \ \ \ \ \ \ / \ \ 0 2.5 5.0 SPECTRUM VERTICAL: LINEAR FORMAT HORIZONTAL: (MHZ) Figure 3-5. Signal waveform and frequency spectrum of the 2.25 MHz transducer. -59- SIGNAL WAVEFORM 0.8 - - - A 0.0 < 1\ \l / ' - -0.4 — - - -0.8 ( .2 USEC / DIVISION ) FREQUENCY SPECTRUM 1.0 - /'\ 0.8 - \ - 0.6 - I - 2.2 > / \j4.4 IdB 0.4 - / - \ - / \ / 0.2 - r / J y 0.0 0.0 5.0 130 (MHz) Figure 3-6. Signal waveform and frequency spectrum of the 3.5 MHz transducer. -60- WAVEFORM VERTICAL SENSITIVITY: BOO mv/div HORIZONTAL RESOLUTION: .20 us/div r Y \ / / \ \ s 0 5.0 10.0 SPECTRUM VERTICAL: LINEAR FORMAT HORIZONTAL: (MHZ) Figure 3-7. Signal waveform and frequency spectrum of the 5.0 MHz transducer. -61- WAVEFORM 200 mv/dlv VERTICAL SENSITIVITY: .10 us/div HORIZONTAL RESOLUTION: A I 1\ /I 111 sJ V / \ \ f \ \ \ T~/ J \ / \ \ 0 10.0 20.0 SPECTRUM VERTICAL: LINEAR FORMAT HORIZONTAL: (MHZ) Figure 3-8. Signal waveform and frequency spectrum of the 7.5 MHz transducer. -62- WAVEFORM VERTICAL SENSITIVITY: 200 mv/rliv HORIZONTAL RESOLUTION: • 1° us/1i\ A A A 1.1 M / 1 / \ \ / : \ / V / \ 0 10.0 20.0 SPECTRUM VERTICAL: LINEAR FORMAT HORIZONTAL: (MHZ) Figure 3-9. Signal waveform and frequency spectrum of the 10 MHz transducer. -63- mracnoN TABU Figure 3-10. Drawing of the turn table. Figure 3-11. Photograph of the turn table. -65- turn table 3\$\ sliding guided *!*13£- jig °fl Turn tabled 33£r 500 mm °\5L IM^r^r ^?H1 A}°)^\ 7]$^ 200 mm turn tabled i^^ S-Er^ EJ-O|XJJ ^E^] s]«fl scanner 5] z 5 turn tabled 0.5 3.3. £ 3-12 ^ H^ 3-13 o] 10.6 mm <^]J1 ^^^ 0.6 mm H.2% Westinghouse 14x14 44 1 MHz Sf 2.25 MHz MPE ^^A . Zircaloy-4 2)4^ «e|-g- 7>^5] ^- *}6\7} 3-13 -66- liSllli I i 1 - I » 0 f 3 | ffTfw -1 - •Hil 11 N H 50}isec I -2 • i Time ( Figure 3-12. Backscattering echoes obtained from the fuel rod using the 1 MHz transducer. I 20 40 60 Time(^s) Figure 3-13. Backscattering echoes obtained from the fuel rod using the 2.25 MHz transducer. fnJ|- FFT &6. 3- 14 3-15 °1 BPE 14 , 1 MHz So 2.25 MHz A, 0} n^i- -69- 1.0 - n=8 (1.035, 1.032) n=9 (1.157, 1.156) n=10 (1.284, 1.280) n=11 (1.401, 1.402) n=12 (1.523, 1.523) n=13 (1.641, 1.642) 0.0 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 Frequency (MHz) Figure 3-14. Resonance spectrum of the cladding tube obtained using 1 MHz transducer. Here, n denotes the normal mode number. Left number in the parenthesis is resonance frequency measured experimentally and right number is resonance frequency calculated theoretically. 1.0 n=13 (2.705, 2. n=14 (2.788, 2.780) 0.8 n=16 (2.954, 2.952) 0.0 2.1 2.4 2.7 3.0 3.3 Frequency (MHz) Figure 3-15. Resonance spectrum of the cladding tube obtained using 2.25 MHz transducer. Here, n denotes the normal mode number. Left number in the parenthesis is 5B resonance frequency measured experimentally and right number is resonance frequency calculated theoretically. 4.1. MB BBR *\4\ FFRDS(failed fuel rod detection system),[31] D]^- B&W(Bobcock and Wilcox) 45] Echo330,[32] ANF(American Nuclear Fuel) *}$] Ultratest [33] %-°) £ 2-3 mm) ^L^S ^e 7r ) 100% (Zircaloy-4/1-) ^^1^ ^HH ^^ -73- Path of Ultrasonic Pulse Receiver Transmitter Fuel Rod Probe a) B & W Type Fuel Rod Transmitter Receiver Path of Ultrasonic Pulse b) BBR Type Fuel Rod Probe Path of Ultrasonic Pulse c) ANF Type Figure 4-1. Different vendors' probes of ultrasonic testing (quoted from Reference [2]). -74- 34. o] 2:^. i~2 ^isec Si71 nfl-g-o]cf. FFRDS ^ ^ , 36] BBR FFRDS °fl^ 3.7] 34. O] 7^^ tfl7fl -75- 30 S. zM- 330^: ^r^l^ i^g-4 ^151^ $3.^ #3^7} ^fi.^- ifl^-5] #21 ^ o^H-cHl n^-E). ^Al^ ^^-^ A}Jr^ 717]- ^*>4. nl£) £33 ^^1- ^'HM-^ 3713] Echo330^r . Ultratest ° 71 fi] 9\^$\ ^^1^4. Echo330^1M- Ultratest^ ^- 7fl^-ofl xltj.. o] wave)S -76- (So) . So MHz ^-4 -ffl^S #1-71 3 MHz 4 dB ^£21 «OU} (A,) a.-9-s. 4.2. 4-2 Sf a^ 4-3^8: 44 711^3. -77- Ultrasonic strip sensor Flaw Detector (Sonic 237) AD Waveform Digitizer (Tek. RTD710A) GPIB Water \ Fuel rods Computer RS232C Scanner Controller Printer Figure 4-2. Schematic diagram of the leak-defective fuel rod detection system -78- Figure 4-3. Overall view of the leak-defective fuel rod detection system: (a) scanner, (b) xy slide unit, (c) fuel assembly, (d) computer, (e) scanner controller, (f) flaw detector, and (g) waveform digitizer. -79- ^ 3(x, y, z) ^ scanner, o] ^#3}- ^^-*}^ ^-g-4 H.S.«-1- slide unit, ^L^Jl SLE]- ^S 4.2.1. S^ Staveley Instruments ^>^ Sonic 237 i-i-^ ^^7] (flaw detector)!- ^ . °1 ^^1^" dual voltage square wave pulser, RF display mode, dual flaw gates ^--i: S.®*\JL &6.*\ RS232 1- ^-*fl Pulser Type Square wave Pulse Amplitude Selectable 150 or 300 volts Pulse Width 30 to 1,000 ns Modes Pulse Echo, Dual, or Through Transmit Receiver Bandwidth 0.3 to 20 MHz (-3dB) -80- Gain Oto lOOdB in 0.2dB steps Display RF, Halfwave+, Halfwave-, Fullwave Timebase Pulse Repetition Rate 150 Hz to 10 kHz in 50 Hz steps Delay Range -10 to 3,200 \is DualjGate Gate Functions Gate 1: peak detection and flaw alarm Gate 2: peak detection and selectable thickness or flaw alarm Gate Start and Width 0 to 3,200 us Analog Output 0 to 5 volts full scale for 0 to 100% full screen height signal. Updated at the repetition rate. *J J xJS.ui H PE Id 4 *L»L* -*— n -**r —- -— 4-4 : 1.2 mm) i, BNC Tfl ?) BNC -81- Figure 4-4. Photograph of the ultrasonic probe. -82- 4.3 ^H *HI*1 4.23. Metrotek A>^ C403 system^: 1.1 m(L)x0.6m(W)x0.5 m(H) }^ 3(x, y, z)# scanner 7} ^^^tj-. ZL^ 4-5 °fl l^ slide unit oil #^4. °1 slide unit ^ z scanner^ 2 ^-al- £SHf (x, y) ^ 0.05 mm RS232 °1 (x, y) lfe slide unit 7>o] 4-6^: slide unit £] 4.2.4. Westinghouse 14x14 -83- Figure 4-5. The ultrasonic probe mounted in the xy slide unit. -84- ,1 „ Iw I, 0- -~- 8 Fi .j I j. I l±JLd 8 m X-AX/S SMOKE 250 X-JX/S © IT-AXB SUDE UNIT ,.. i- — i—. Figure 4-6. Drawing of the slide unit. 4.3. 4.3.1. 1.2 mm mechanical damping factor 1- ^)^ air backing *1 °fl JE. V ^^r cfl^^-^: ^ JL, £;E<2}- »8-A].^O)| HIJE^ ^^ lead metaniobate 4|]]§ ll>^4 l J^f^ ^ ^^^ 4 Frequency : 3.0 MHz Thickness: 0.5 mm Acoustic impedance : 20.5x10^ kg/m^sec -86- LM Crystal (0.5 mm) Backing Layer (0.5 mm) Figure 4-7. Schematic diagram of the ultrasonic sensor designed for fuel assembly inspection. -87- 1 °J A 4 (= sin" (CxICp)* 14.3° .6 min) 1480 m/s o]5L Cp^ 3.0 MHz °1H A, 6000 m/s air backing^ . Air backing^: ^l*f^i 0.2 mm -T^II^ aluminum foill- 0.5 mm 7> "3! -i" Teknovit 3040^1 1/4 Acoustic impedance : 2.6x10^ kg/m^sec Acoustic velocity : 2400 m/sec Density: 1.1 g/m^ o] 3.0 MHz ^^-4^ 1/4 4^^: 0.2 mm -88- 4.3.2. impulse response Impulse response ^^ ^wls.^ UltraPac ^1^.^-i- 4-§-^>S^^. °1 Al^ 2\ ^-§-4 ^^Ai7]^ Accu-TronInc.^ Model 101OPR 4-8^: 4.3.1 ^H ^^^ ^j^S] ^if -fr*W7l^ €>H housing ^f. °1 housing^ 4^^ ^•^•a 1.2 mm ^. €^# strip ^ 7} -g-olsl-SL^ o] housing^ tfl^el^ 2^^-S. ^3j-i|$jl4. vfl-?- ^B^-el^ 7V slit 4 ^-^^r z|^ ^^r^l tf^ldfc^H ^^^^ silver ribbon^ v)*H -§- die die $] ^fl^-cr ^•is^-T?!om-. ^Ai ^l2l'A] housing £• -89- 0.3 2-00.6 0.6 Figure 4-8. Drawing of the ultrasonic sensor housing -90- °1 die ^ 33 8 mm, £°1 0.25 mm 0.2 mm Micro-Coax Components, 0.58 mm °]JL 3.°}$] ^j^^r 0.13 mm ^°fl, ^l31!^ sensor housing 3) slit °fl housing^ silver ribbon «>fl ^1 «B Silver ribbon •a-^i^-^- *H ^^ >floll"i- ^l*>7l fl«fl A>-g-^cf. n]^- California Fine Wire Company 5] *flf-°-5. 3.7)^ 0.001 x 0.025 (mil) °}JL £5.^ 99.99% Probe strip -g-1- 4°lS. €%^1 °1^1 ^r 51^^- 0.5 mm ^1^ SUS plate -91- Ur. A 7 I T . in L| VB 112 11 . 910 11 109 ~^ 3340 I Figure 4-9. Drawing of the probe strip. fixture 7} ^.1 ^2S £M $1 cf Strip holder 4-10 £ 1S1 ill W^l *H4 £^ol4. °1 *^, ^ 4-5 , slide unit°fl ^^"S]^ HSH iS^^l 'S-S.-g-i: ^}°}S. . °] *C1 ^°fl^ *M) -^^ 711 o]#3)- BNC 4.3.3. . -g- 1) ^ul^ ^rM"5! impulse response -t #^^f^ ^4) ^4^r(3.0 MHz 2) \kn3--z: 2M- ^r-g-^M impulse reponse 4r 4^1 -93- 1EL NO|P/NUIC MATERM. | Q'TY | SPEOTICWON j RCMARK SSgSraB * s ™ ~"- • —* •u U/T PROBE HOLDER YL-KO2OO ""* ntOBEDO |" Figure 4-10. Drawing of the probe strip holder. 3) °^±7\-S.t^ 0.2 mm ^i ^ 3.7]$] aluminum foil •§• 4) irul€ aluminum foil ^ -fre)^: ^ofl ^-JL H $)<=)) silver ribbon tfi°] 10 mm ^JE) #^-g- ^H^tf. ^nfl, snVer ribbon °1 4*\ housing £] -f- ^ aluminum foil °fl tfl ^ silver ribbon ^ $\ *) °ll - 5) 4^ 4)°fl>H §«1^ aluminum foil 4 silver ribbon-§: ^ SJ-g- ^ tape S., ] *}-^ 7}#z}B\7} silver ribbon ^^| aluminum foil 5] 71-^fel-i- 0.1 mm 6) 4^ 5)^1 141-i- -n-^^r°flAi tfl^^^ aluminum foil tape i ^ °fl#Al7> aluminum foil 4 air backing ^3°1 7) #Sli*f3 a)"^ ^ 71-^)-^^ tape^. ^.s H3^vfl 4 silver ribbon ^ -r" ^^^-S. *}<$ impulse response 1r 8) ^ 4^ 1)~8)^- ^-^-*>^ air backing -g- aluminum foil 4 silver ribbon 9) ^o]7> 40 mm ^§£^1 ^1^1 -^^ ?H^1- 2 7flt- -95- 11) housing^ housing •§- ^J^ ^il^-R- die 3] ^°o> l-#^-7> ^^ housing^ die ^ 14) 4Ui housing ^^-°fl^1 ^^^.4^1 silver ribbon #^"4 ^Afl 24?} housing 4 3#3*1 #^ 15) silver ribbon 4 silver ribbon A housing^ w>^ofl f-^- ^-g.^- ^ iJE^# die -96- die die housing^ >H housing T2-^ -SMW silver paste 20) Teknovit 3040 ^-^* ^^-^ofl ^^ #4 housing Ml-^-ofl 7rt.Vcf. ol 21)ol)S.A]7l- ^^i*l ^-^ cf-g- ^M^ dieoflA^ t^)^ vflc}. ^1^ housing tb ^, impulse response 23) €>H housing^ slit -¥-fl ^^<^1 ^ 2mm ^£^) ^'S-i- # 24) Siver ribbon 5] ^ #-^-^-ofl ^"^r ^=7fl ^^1 ^, 10 mm #4. 4^ 24) °1 Sa^- -¥-fl^- °J"^4iXH ^oi ^-o} oj^ «-^^ ^Q^ housing^ slit ofl fl^l^tj-. ^^4i45| -2.*!34 silver ribbon^: ^7l«?]^^ °H •y^^i "S^ •y*!! °J-^4i^7r £#3*1 ^^^- ^^t>4. Silver ribbon #-8: ^l^i housing 2] slit -97- 25) Teknovit 3040 ^-^* housing vflofl &^r ##4:*1- ^^^ 71-3:4. °H. Si^^ 4^ 24)^>H , housing^ sand paper 3. i^^i^Tfl ^^j-^A^ ^JA^O] impuise response 28) ^M^4 BNC ^oll-g- ^S^ ^C-H ^-oj^. ^ o] ^d ifloJH n]Afl BNC Tflol-g-g. 0^^3:4 o] -98- #?*:•§• ^3) I'll (global matrix approaches *r*l3j- t\ ^l(boundary matrix)" o) «OV^^. 40^^ tfl«. ^t- ^-^ ^^ *n ii(jn.^n n vfl^si ^41- ^I^- ^-fH tfltt i^ "D^Dj^^o] zero. frequency limits, cfl^l^^ ^°14. °1 $\*\}^ 4^4 o) 1) 430] zero. frequency limit S.^ 0} #>=. ^H.^. ^.O]- ufl^ ^ -99- £1 . O] X\ + , i>a^ S.4°fl 2(x, y) ^ slide unit 4 turn table, ^l-ei -f- ^. ^§1-^ monostatic pulse-echo (MPE) U V) bistatic pulse-echo (BPE) O ^^- BPE turn table -100- ^ 3(X) y> z) ^ slide unit, 3.^3. £.Ef HiXT left BLANK A. 5x5 2 2 rf!3 =(2« -xr )yn(xi)-2^iKrt'(^)) rfI4 =2n[xTJn\xT)-Jn{xT)l i 1) dl5 =2n[xTYn'(xT)-Yn(xT)], d2l =-xlH n '(xi), d2i^xLJn'(xL), dn=xLYn'(xL), du=nJn(xT), d25=nYn(xT), di2 =2n[Jn(xL)-xLJn'(xL)], di3 =2n[Yn{xL)-xLYn\xL)], 2 2 2 2 du=2xTJn'(xT) + [xT -2n )Jn(xT), d35 =2xTYn'(xT) + [xT -2n ]Yn(xT), 2 2 2 2 dn =(2n -yT )Jn(yL)-2yLJn'(yL), dA3={2n -yT )Yn(yL)-2yLYn\yL), d44 =2n[yTJn'(yT)-Jn(yT)], d45 =2n[yTYn\yT)- Yn(yT)], d* -2n[Jn(yL)-yLJn'(yL)], d5i =2n[Ytt(yL)-yLYn'(yL)], z 2 2 2 [yT -2n ]Jn(yT), d55 =2yTYn<(yT) + [yT -2n ]Yn(yT), -103- B. c« S2|- ZL scattered P2 1st medium top du dn dn du d2l d22 d2i d24 *31 33 2nd layer 2 T 2 du =[2n -{y 2) \Jn{y^-2y$Jn'{yh 2 T 2 L L L dn =[2n -(y 2) ]Yn(y$)-2y2 Yn'(y2 ) d22=y2Yn\y 2) T T T du=2rHy 2Yn\y 2)-Yn{y 2)] l L L dn=2n[Yn(y2 )-y2 Yn'(y2 )] T T 2 T 2 T dv=2y 2Jn'(y 2)-[2n -{y 2) ]Jn{y 2) 2 T 2 T ^34 =2ylYn'(yl)-[2n -(y 2) }Yn{y 2) -105- top dn dn dn dH i\ i\ 42 7th layer d3l = 2 22 -{2n - (yjj )) }Y}Y(yjn(yj -106- bottom du dn du du d d n d22 d23 * d d d dn n ll u d d dn dn t3 AA yth layer du=nYn(xJ) T T 2 =Yij[2x jJn'{x j)-{2n - -107- top d2X d22 mth layer T d22=yl,Jn\y m) T T T mJn'{y m)- Jn{y m)} T T 2 T 43 =iim[2y mJn'(y m)-{2n -(y m — P2 ^ 71 xjT=yj'T(l-hj) (J=2,3,..,m-\) y (/=2,3,...,/«)^ 4 Lame constant^ -108- dn i-l)th layer 2 T dn={2n -{x m_x T T dn=2n[x m_xJn\x m_x)- 2 T -2n ]JAx m_x), -109- bottom (m-l)th layer 2 du={2n 2 du={2n diA = "21 = Xm- L L L dn=2n[Yn{x m-X)-x m_xYn'{x m-X)l T T T 2 2 d,3=2x m_xJn'(x m_x) + [(x m_x) -2n ]Jn(xLx), T T T 2 2 T d» =2x m_xYn'(x m_x) + [(x m_x) -2n ]Yn(x m_x). -110- top u [".]• 0 with layer d2l=-ymrn'(ym) bottom M3 U14 Kl- "23 "24 '31 *32 ^33 ^34 (/-l)thlayer 2 du={2n -(xU) 2 du={2n -{xl, dn=2n[xlxJn\xJ_x)-Jn{xU)\ d24=nYn(xlx). 2 d33 =2xJ_xJn'{ -2n ]Jn(xU), 2 di4 =2xlxYn\ -2n \Yn{xlx). -Ill- top "12 "21 *22 0 0 Ah fluid layer — Pf-l bottom ^11 dn "21 "22 0 0 fth fluid layer P/+1 Pi -112- top ^11 ^12 ^13 ^14 d2\ d22 d2l d2i d d d d 3i n a Mj (/+l)th layer 2 dn={2n -(ylx 2 2 yix) -2n }Jn(ylx) 2 2 J+x) -2n ]YM(ylx). -113- = m-\ %•*] 3x2 DflE^i top 22 mth layer 2 T 2 L L du ={2n -{y m) Jn{y!;,)-2y mJn<{y a), T T T dn=2n[y mJn\y m)-Jn{y m)l 2 T 2 T T T n={2n -{y m) )Jn{y m)-2y mJn\y m). -114- Mi o|^ 9x9 '(*,), 2 T 2 ={2n -{y 2) }JM)-2y^Jn\ L L 1 dv=2r,[Yn(y2 )-y2 Yn'(y2 )], T u =nJn{x 2), T T T 2 2 T i5=2y2 Yn'(y2 ) + [(y2 ) -2n ]Yn{y 2), d s2 ="Jn(x2), L 15i=nYn(x2 ), dsl=-nYn{y$] d59=-y^ -115- 2 T 2 L L L d62 ={2n -(x2 ) }Jn(x2 )-2x2 Jn'(x2 ), 2 T 2 L L L db,={2n -(x2 ) }Yn(x2 )-2x2 Yn'(x2 ), T T T dM=2n[x2 Jn'(x2 )-Jn(x2 )], T r T d65=2n[x2 Yn'(x2 )-Ytt(x2 )], r d69 = -(fi3/fi2 )2»D>3 Yn\yl) - Yn(yl)l L L L d72=2n[x2 Jn'(x2 )-Jn(x2 )], L L L dn=2n[x2 Yn'(x2 )-Yn(x2 )], 2 T 2 T T dli={2n -{x 2) }Jn(x 2)-2xlJn\x 2), 2 T 2 T T T d15={2n -{x 2) )Yn{x 2)-2x 2Yn\x 2), L L L d16 =-(ii3/ii2 )2n[y3 Jn • (y3 ) - Jn (y, )], L r 2 2 L = 2x\Jn'(x3 [(jc3 ) - 2n ]Jn (xt), d96=xlJn'(xi ), 2 2 L L L [(xl) -2n ]Yn(x3 ), dg7=x, Yn'(Xi ), d9S = -116- T x}=k}aJt x]=k]Oj, y^-k^aj, yl,=k J+xaJ (,=1,2) o) ^(/=2,3)^ 4 *^ Lame constants «i* (e,,«2,0,0,0,0,0,0,0)^.3. 4 HiXT PAQI(S) I !ef 18LANK S" 1. J. T. A. Roberts, "Nuclear fuel NDE", The 3rd International Conference Proceedings on the Nondestructive Evaluation in the Nuclear Industry(1980), pp. 23-45. 2. 3$if, "CE^ fS\<^S. Ai«|i 7|# £>*J", KAERI/EP-113/88 (1988), pp. 24, 66; "KWU 4^1 *%<&£- -HH1^ 7]£ £-^ ", KAERI/IM-95/87 (1987), pp. 5. 3. M. S. Choi, M. S. Yang and H. C. Kim, "Detection of leak-defective fuel rods using the circumferential Lamb waves excited by the resonance backscattering of ultrasonic pulses", Ultrasonics 30, 221-223 (1992). 4. 3M 34*1, "-S-4^ *1 ^ 074872 3. (1994). 5. 3^ ^2?1, «a-S-3| # 7fl^",KAERI/RR-1545/94 (1995). 6. J. D. Murphy, J. George, A. Nagl and H. Uberall, "Isolation of the resonance component in acoustic scattering from fluid-loaded elastic spherical shells", J. Acoust. Soc. Am. 65, 368-373 (1979). 7. V. M. Ayres and G. C. Gaunaurd, "Acoustic resonance scattering by viscoelastic objects", J. Acoust. Soc. Am. 81, 301-311 (1987). 8. N. D. Veksler, "Intermediate background in problems of sound waves scattering by elastic shells", Acustica 76, 1-9 (1992). -119- 9. M. F. Werby, "The acoustical background for a submerged elastic shell", J. Acoust. Soc. Am. 90, 3279-3287 (1991). 10. G. C. Gaunaurd, "Hybrid background coefficients to isolate the resonance spectrogram of submerged shells", J. Acoust. Soc. Am. 92, 1981-1984 (1992). 11. A. N. Norris and N. Vasudevan, "Acoustic wave scattering from thin shell structures", J. Acoust. Soc. Am. 92, 3320-3336 (1992). 12. P. M. Morse and K. U. Ingard, Theoretical Acoustics (McGraw-Hill, Inc., New York, 1968), pp. 425-426. 13. D. G. Crighton, A. D. Dowling, J. E. Ffowcs Williams, M. Heckl, and F. G. Leppington, Modern Methods in Analytical Acoustics: Lecture Afote^Springer- Verlag, New York, 1992), pp.510-523. 14. A. N. Norris and D. A. Rebinsky, "Acoustic coupling to membrane waves on elastic shells," J. Acoust. Soc. Am. 95, 1809-1829 (1994). 15. X. Y. Huang, "Energy dissipation in sound scattering by a submerged cylindrical shell," Acustica 77, 221-231 (1992). 16. L. W. Anson and R. C. Chivers, "Ultrasonic scattering from spherical shell including viscous and thermal effects," J. Acoust. Soc. Am. 93, 1687-1699 (1993). 17. J. P. Lee, J. H. Song, and M. S. Choi, "The effects of material attenuation on acoustic resonance scattering from cylindrical tubes, Ultrasonics 34, 737-745 (1996). 18. G.N. Watson, A Treatise on the Theory ofBessel Functions(Cambridge University Press, London, 1966), 2nd ed., pp.199. -120- 19. G.C. Gaunaurd and M.F. Werby, "Acoustic resonance scattering by submerged elastic shells," Appl. Mech. Rev. 43, 171-208 (1990). 20. M. J. Lowe, "Matrix techniques for modeling ultrasonic waves in multilayered media," IEEE Trans, on ultrasonics, ferroelectrics and freq. control, 42(4), 525-542 (1995). 21. C. Randall and F. E. Stanke, "Mathmatical model for internal ultrasonic inspection of cylindrically layered structures," J. Acoust. Soc. Am. 83, 1295-1305 (1988). 22. W. T. Thomson, "Transmission of elastic waves through a stratified solid medium," J. Appl. Phys. 21, 89-93 (1950). 23. N. A. Haskell, "Dispersion of surface waves on multilayered media," Bull. Seism. Soc. Am. 43, 17-34(1953) 24. L. Knopoff, "A matrix method for elastic wave problems," Bull. Seism. Soc. Am. 54,431-438(1964) 25. G. Maze, B. Taconet, and J. Ripoche, "Influence des ondes de "galeri a echo" sur la diffusion d'une onde ultrasonore plane par un cy;indre," Physics Letters 84A, 309- 312(1981). 26. G. Maze, J. Ripoche, A. Derem, and J. L. Rousselot, "diffusion d'une onde acoustique plane par des cylindres solides immerges: etude experimentale et theorie des resonances," Austica 50, 39-50 (1982). 27. A. Derem, J. L. Rousselot, G. Maze, J. Ripoche, and A. Faure, "Diffusion d'une onde ultrasonore par des tubes remplis d'air immerges dans I'eau," Austica 55, 69- 85(1984). -121- 28. J. Ripoche, G. Maze, and J. L. Izbicki, " A new acoustic spectroscopy: resonance spectroscopy by the MIIR," J. of NDE 5, 69-79 (1985). 29. G. Quentin, M. de Billey, and Hayman, "Comparison of backscattering of short pulse by solid spheres and cylinders at large ka" J. Acoust. Soc. Am. 70, 870-878 (1981). 30. M. de Billey, "Determination of the resonance spectrum of elastic bodies via the use of short pulse and Fourier transform theory," J. Acoust. Soc. Am. 79, 219-221 (1986). 31. F. D'Annucci and R. Scharpenberg, "Operational experience of ultrasonic testing on fuel assemblies with FFRDS", Nuclear Europe .5, 23-24 (1985). 32. Bobcock and Wilcox, "Echo sounds out failed fuel", Nucl. Eng. Int. 31, 45-46 (1986). 33. T.R. Blair and L.F. Van Swam, "Looking for leaks with ultratest", Nucl. Eng. Int. 31,44-45(1986). 34. %%^ $\ 5*1, "3^3. 4£«l££. ^^l-f^H^", KAERI/RR-638/87 (1987). 35. £^«£, %1^ 2] 23 «?!, ", KRC-88N- T02 (1990). 36. #31 3} 4 1609/96 (1996). -122- 37. H. C. Kim, M. S. Choi and M. S. Yang, "Resonance scattering of acoustic waves from circular cylindrical shell and circumferential wave propagation", J. Korean Phys. Soc., Vol.22(1989), pp. 176-180 38. M. S. Choi, H. C. Kim and M. S. Yang, "Propagation characteristics of elastic circumferential waves in nuclear fuel cladding tubes", Ultrasonics.30, 213-219 (1992). -123- INIS KAERI/RR-1680/96 ^ ^ -9(»1 Bj-^iS 7}7l# 1997. 2. 123 p. -B-(O), -¥-( ) 71 26 cm «i ^^(scattered field)ofl>H ll ^(background) 105] ^Di^A-s. ^(analogous) i^Pl^i^ zero-frequency limits, 1.2 Bibliographic Information Sheet Performing Org. Sponsoring Org. Standard IMS Subject Report No. Report No. Report No Code KAERI/RR-1680/96 Development of Nuclear Fuel Rod Inspection Technique Uing Title Ultrasonic Resonance Phenomenon Project Manager Myoung-Seon Choi (NDE R&D Dept.) Young-Sang Joo, Hyun-Kyu Jung, Yong-Moo Cheong Researcher and Dep. (NDE R&D Dept.) Pub. Place Taejon Pub. Org. KAERI Pub. Date 1997. 2 Page 123 p. 111. and tab. Yes(O), No( ) Size 26 cm Note 1996 Research Project Classified Open(O), Outside( ), Class Report Type Research Report Sponsor Contract No. Abstract The scattering of plane acoustic waves normally incident on a multilayered cylindrical shell has been formulated using the global matrix approach And a simple way to fomulate the non-resonant background component in the field scattered by an empty elastic shell has been found. This is to replace the surface admittance for the shell with the zero-frequency limit of the surface admittance for the analogous fluid shelKi.e., the shear wave speed in the elastic shell is set to zero). It has been shown that the background thus obtained is exact and applicable to shells of arbitrary thickness and material makeup, and over all frequencies and mode numbers. This way has been also applied to obtain the expressions of the backgrounds for multilayered shells. The resonant ultrasound spectroscopy system has been constructed to measure the resonance spectrum of a single fuel rod. The leak-defective fuel rod detection system of a laboratory scale has been also constructed. Prticularly, all techniques and processes necessary for manufacuring the ultrasonic probe of thin (1.2 mm) strip type have been developed. Keywords resonance, scattering, fuel rod, multilayered shell, ultrasonic testing