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Application of numerical analysis techniques to eddy current testing for steam generator tubes
ELSEVIER
Nuclear Engineering and Design 153 (1994) I-9
Nuclear Engmeen.ng andDemgn
Application of numerical analysis techniques to eddy current testing for steam generator tubes Kazuo Morimoto +', Koji Satake +', Yasui Araki b, Koichi Morimura c, Michio Tanaka c, Naoya Shimizu d, Yoichi lwahashi d " Advanced Technology Researcl; Center, Mitsubishi Heao' hl&tstries Ltd., Kanagawa-ku, Yokoh,ma 236, Japan b Takasago Research anti Deveh~pment Center, Mitsubishi Henry buhtstries, Ltd: .~,ai-cho, Takasago 670, Japan c Electronics Division, Mitsubishi Hetwy bt&tstries Ltd., tl)'ogo-ku, K:,be 652, Japan d Kobe Shipyard and Engine Works, Mitsuhishi Heat,y b~&tstries Ltd., Hyogo-ku, Kobe 652, Japan
Abstract
This paper describes the application of numerical analysis to eddy current testing (ECT) for steam generator tubes. A symmetrical and three-dimensional sinusoidal steady state eddy current analysis code was developed. This code is formulated by future element method-boundary elemen! method coupling techniques, in order not to regenerate the mesh data in the tube domain at every movement of the probe. The calculations were carried out under various conditions including those for various probe types, defect orientations and so on. Compared with the experimental data, it was shown that it is feasiblc to apply this code to actual use. Furthermore, we have developed ~ total eddy current analysis system which consists of an ECT calculation code, an automatic mesh generator for analysis, a database and display software for calculated results.
I. Introduction
Eddy current testing (ECI') techniques have been applied to in-service inspection of steam generator (SG) tubes, because of their high speed and ease of operation. Various types of probe are needed according to the defect type ~u~d orientation. Recently it has become cle='~."th.ut a probe for detecting smaller cracks must be dc,:~:loped. Since in actual inspections the detectc+_~ E( F signals are caused not only by defects but al:+o by the support plates and deposit around the tubes and so on, we have to analyze the signals and to determine the sources of the signals. To meet these require-
ments, we have developed numerical analysis techniques which calculate eddy current distribution in SG tubes, coil impedance and other factors in order to develop a new probe and to analyze the actual signals. Regarding this development, the following factors had to be considered. In actual testing, several kinds of probe are used, such as a bobbin coil probe, a pancake coil probe, and a probe which includes magnetic materials. The coil impedance change caused by defects is very little, e.g. a li:w tenths of a per cent of the coil impedance. Therefore, threediemsional high accuracy analysis would be needed. Moreover, the numerical analysis must be easily
0029-5493/94/$07.00 ,~" 1994 Elsevier Science S.A. All rights reserved SSD! 0029-5493( 94)00807-B
2
K. Morimoto et al. / Nuch,ar b.)agineer#tg and Des(gn 153 (19941 ! 9
carried out, even if there are many procedures for calculating the coil impedances at every posititon while the coil is moving.
2. Analysis method
The equations for this analysis are Maxwell's electromagnetic equations. However, because of the low frequency range, the displacement current can be ignored in these equations, so that these equations are reduced as follows:
V x E-
(I) ~B Ot
(2)
B = pH
(3)
J = irE
(4)
V. B = 0
(5)
V. J = O
(6)
where H is the magnetic field J is the current density, E is the electric field, B is magnetic flux density, p is the magnetic permeability and tr is the electric conductivity. To solve these equations, a vector potential (A = V x B) and a scalar potential q~ are used. Using A, Eq. (5) is automatically satisfied. The differential operator c~B/~,t is replaced by h:h since the eddy current is sinusoidal steady state. From these considerations and Eqs. (1)-(4), the following equation can be obtained: I V2A P
a(itoA + VO)
(7)
where t,J is the angular frequency. Also, the electric field is described by E = - itoA - V~b
! --V2A Po
=-J
(!0)
2.2. Formulations
2. i. Basic equation
V×H=J
On the contrary, in a domain including current sources, the equation is as follows:
For the ECT problems, we must calculate the eddy current distributions and coil impedances at every position for a coil, which moves in a tube axially or circumferentiaily. In these cases, input data for calculation have to be found at each position, because the models are different from position to position. In order to obtain input data easily, a finite element method (FEM) and a boundary element method (BEM) are used for a tube domain and a domain including a coil respectively. According to these combinations, we do not have to redivide, the tube area in spite of the moving coil, so that it shortens the preparation time for the calculation. From these ideas, the formulations were carried out as follows. The Calerkin method was used for the formulation of FEM; Eqs. (7) and (9) give
where [K] is the coefficient matrix and {F} is the nodal flux vector. Applying Gren's theorem to the BEM area, the following equation can be obtained from Eq. (10): :
--
.tB i
(12)
where [H] and [6-] are the coefficient matrices and {B} is the surface flux vector induced by the coil current. Superimposing Eq. (12) on Eq. ( ! ! ), the formulation can be obtained in the manner of the FEM. The coil impedance can be calculated from the magnetic vet!or potential A as follows:
(8) itoA" dl
Eq. (6) is converted to the following equation, using Eqs. (4) and (8)' V " a(io~A + Vrk) = 0
(9)
Z -
I
(13)
where I is the source current density; A is obtained from the equations mentioned above and
K. Morimoto et al. / Nuclear Engineering and Design 153 (1994) i - 9
the integral is conducted along the center of the coil.
3. Numerical analysis and results Using the analysis code developed, we calculated the eddy current and the coil impedance in various cases of ECT, and we investigated the calculation accuracy, by comparing it with the experiment results.
3.1. Two-dimensional analysis First, axially symmetrical problems were dealt with for the case of a bobbin coil, in order to reduce the central processing unit (CPU) time and memories. The calculated results and the experimental data, in which the models were straight tubes with an entire wall thinning, are shown in Fig. 1. The impedance changes calculated in various cases between 10% and 75% of full circumferential wall thinnings are almost the same as the experimental results. This shows that these small changes of coil impedance could be calculated with high accuracy. Secondly, a model which simulates a tube with a support plate was calculated. In this case, the
• Analysis at 100 kHz = Analysis at 400 kHz
[~1
I
40
I
• Experiment at 100 kHz x Experiment at 4001kHz~
3
permeability of the support plate is so high that the skin depth of the eddy current is as small as approximately a few tens of micrometers, which shows that the eddy current decreases suddenly near the surface. If normal rectangular elements were used as FEM elements, a sufficient accuracy could not be obtained. Therefore, the higher order rectangular elements were used. Fig. 2 shows an eddy current distribution in the tube and the support plate. A probe impedance trajectory obtained by numerical analysis and experiments are also shown in Fig. 3. From this result, it is recognized that our analysis code has sufficient accuracy to calculate the effect of a support plate. Thirdly, we investigate a way of calculating a model which simulated a tube with a higher conductive deposit on the outer surface. In SG tubes, the conductivity of the adherent materials is about 30 times the tube's conductivity, but the thickness is extremely small about a few micrometers, compared with the tube. Therefore, for 100 kHz, the eddy current skin depth is about 200 lam, the eddy current density flowing in the deposit mentioned above seems to be almost uniform in depth. In the calculation, a surface current flowing in it was supposed. Fig. 4 shows the eddy current distribution which was calculated according to these ideas. This result shows that the eddy current distribution in the tube was affected by the eddy current in the high conductivity material. In Fig. 5, the calculated and experimental coil impedances are shown. In this case, both results are almost the same.
3.2. Three-dimensional analysis
-~- 10 o c
,~
4
,/100
[kHz]
o 0 o c el
E
0.4
0.1
0
25
50
75
1O0
Depth of outer surface wall thinning [%] Fig. i. Comparison between the calculated and experimental impedances.
In order to calculate the eddy current in testing actual SG tubes, the models must be three dimensional. We developed a three-dimensional analysis code for various ECT probes, and invetigated the calculation accuracy in comparison with the experimental data. First, we applied this code to testing by bobbin coils, which were usually used at normal inspections. The calculated model and the eddy current distribution are shown in Fig. 6, and the calculated and experimental coil impedances are also shown in Fig. 7. The calculated value is in close agreement with the experimental value.
K. Morimoto et ai. / Nuclear Engineering and Design 153 (1994) i - 9
4
II Coil
~:~
(a)
(b)
Fig. 2. Calculated eddy current distribution in tubes and support plate caused by bobbin coil at 100 kHz: (a) analyzed model; (b) eddy current distribution. :-,,, ------------
Calculation Ex ~erimenl
0.2
½
X
I° m
_E --0.2
.I. -0.2
i 0
Real (&R) [t31
0.2
Secondly, we considered a pancake coil as an ECT probe coil, which has recently been used as frequently as the bobbin coil. Circumferential defects in the tube were calculated as a test model. The eddy current distribution for a slit are Fig. 8. Calculated and experimental coil impedances are also shown in Fig. 9. These results agree with each other. Thirdly, we also use ECT probes which inc!ude high permeability materials such as a ferrite. In these cases, the FEM was applied to such materi. als to link it to the BEM, because the area including such an ECT probe cannot be analyzed only by BEM.
Fig. 3. Comparison between the calculated and experimental impedances of bobbin coil for wall ~hinning at 100 kHz.
K. Morimoto et al. / Nuclear Engineering and Design 153 (1994) ! - 9
5
Coil
Adhered material Contour l e v e l s •
W •
\ S/G tubes
(a)
(b)
1.032E+01 2.054E÷Ol 3.096E+01 4.12gE+01
m • •
• • • • •
5.z61E+01
• •
6.193E+01
•
7.225E÷01 8.257E+01
• •
•
B.QBBE÷OI
•
= =
• *
=
1.030E+02 1.140E+02 1.240E÷02 1.340E+02 1.440E+OZ 1.550E+02 1.650E+02 1.750E÷02 I.BGO£*02 1.960E+02
= •
m
2.060E÷0~
•
1 O0 [kHz]
Fig. 4. Calculated eddy current distribution affected by the high conductivity of deposit at 100 kHz: (a) analyzed model; (b) eddy current distribution.
....
(3 . . . .
Calculation " Experiment
i
0 e-
E
Using this F E M - B E M technique, we calculated a test model where a longitudinal slit was tested by the probe with a ferrite core surrounded by a coil. The eddy current distribution and coil impedance are shown in Fig. 10 and Fig. 11 respectively. The coil impedance is in agreement with the experimental value. From the results mentioned above, it was recognized that our developed analysis code had sufficient capability, to solve the ECT for SG tubes, although the model size was limited by the calculation time and the memory size.
-1
m'
0 Real (&R) [Q]
1
Fig. 5. Comparison between the calculated and experimental impedances of bobbin coil caused by a deposit at 100 kHz.
K. Morimoto et ai./Nuclear Engineering and Design 153 (1994) 1-9
6
Q
Longitudinal slit
f
Coil
S/G tubes
(a)
Inner surface
Outer surface
Fig. 6. Calculated eddy current distribution caused by bobbin coil (5 mm long; 50% deep slit at outer surface: 100 kHz): (a) analyzed model: (b) eddy current distribution.
Calculation Experiment
~" " "'---'----
~. t.llll,¢ r,.ul*lJ i a,~JLt~. jL
_
0.1
..h~l,fl
X
t
| -0.1
0
f 0 Real (~R) [D]
L" rE
-0.1
0.1
Fig. 7. Comparison between the calculated and experimental bobbin coil impedances (5 mm long; 50% deep slit at outer surface; 100 kHz).
4. Eddy current testing analysis system The capability of the analysis codes was confirmed, as described above. However, in order to use these codes to develop probes or estimate the ECT signal in actual testing, it was necessary to make various software to support the analysis. From this point of view, we have developed the ECT analysis system, in which an analysis can be done following the flow chart shown in Fig. 12. This system is based on a high speed engineering
Density of current Eddy current distribution
Fig. 8. Calculated eddy current distribution caused by pancake coil (10ram long; 50% deep slit at outer surface; 100 kHz).
work station (EWS). The reasons for using the EWS are as follows: the calculation cost is low; the turn-around time is short because there is no waiting time, although the calculation speed is not faster than a super computer. The specifications of the EWS, used in this system are listed in Table 1. A calculation time of the case shown in Fig. 8 was about 20 min. The software environments of this system are also shown in Table 2. These were selected so this system could be installed in other EWSs easily and so a multiwindow system could
K. Morimoto et al./ Nuclear Engineering and Design 153 (1994) 1-9 0.1
.-
.o- - . ........
7
Calculation Experiment
Calculation
~Q
- --* Experiment 0 O.
,-.,
05
0.2
._. u
xm
er-
O
A X
m
E
-0.05
0
0.05
l
I
(&R) [hi Reactance component
-0.2
Fig. 9. C:mparison between the calculated and experimental pancake coil impedances (i0 mm long; 50% deep slit at outer surface; I00 k~7.~.
be utilized to display the results. The characteristics of this system are described as follows. (1) If the information concerning the tube, the defects and so on are inputted as shown in Fig. 13, the input data for the calculation code are generated automatically. This function allows one to calculate any model easily, even if the particular operations to create the necessary elements, nodes and so on, for FEM or BEM are not known.
-0.2
0
0.2
Real (&R) [Q]
Fig. 1I. Comparison between the calculated and experimental special coil impe~dances (10 mm long; 50°,4 deep slit at outer surface; 100 kHz).
(2) Previously retrieved analyzed data can be stored ~ad searched, because this system has a relational database for past data. Cc,nsidering the EWS performance, it takes little more than 20 rain to calculate a three-dimensional model. Storing and searching for previously analyzed data allow
~
s.~,T.0¢/, ~.llllWl
~, ' , l q k
1.~;l*lM I.~B:q
: j..r~.~ll
Circumferential slit
Coil
(a)
~Ferrite
core
~
(b)
Fig. I0. Calculated eddy current distribution caused by special coil including ferrite core: (a) analyzed model; (b) eddy current distribution.
8
K. Morimoto et aL/ Nuclear Engineering and Design 153 (1994) 1-9
Table ! Specifications of engineering work station
Input data for analysis
]
CPU Speed
eady calculated
Memory
IBM RS-6000 25.6 Mflops 128 Mbl/3
Table 2
I Generate data automatically ,]
Software environment
[
Operating System Window
! Calcula,ion
1
Language
i
UNIX X-window FORTRAN C
I, arrangements simultaneously, as shown in Fig. 14. Using these display facilities, evaluation or comparison of various data is easy.
1 ( r-n.) Fig. 12. Flow chart for the ECT analysis system.
unnecessary recalculation to be avoided and the total calculating time to be shortened. ~-,Jla~ Using the multiwindows, the analyzed data and the experimental data can be seen in various
5. Conclusions Two-dimensional and three-dimensional eddy current analysis codes were developed to be ap-
Fig. 13. Cathode-ray tube for input procedure.
K. Morimoto et al. / Nuclear Engineering and Design 153 (1994) 1-9
9
150n~pr Ig 1gqTq8 Igg2
Z
[~lfl
il
0.1K 102.00 ...0.03
o.L6
k~ta] ?SgOD 0.2! 115.00 -0.09 f'-lOOId~
0.19
Axial 50Y,OD t'mlOOidr~ m
g G
(olml
x
Axt~*l lOOgOD 1.02 136.00 -0.71
fo|OOId~
-0.75
0
-0,75
g [olml
y
.
-.q
i
o.10
gxum-e
°to*.3 -0.10
P,rc,a 50gOD Ututnne© Im)
R lukml
r,q~kh
Fig. 14. Sample screen '~f displayed result.
plied to the ECT problems. Comparing the calculated data with the experimental data, it was proven that these codes had sufficient accuracy to analyze various models, and that was feasible to use the codes at practical levels• We have also developed an ECT analysis system which includes an automesh generator, a database, and various display functions. This system will be used and continuously improved for many applications.
Acknowledgment The authors are grateful to Professor K. Miya of the University of Tokyo for his useful suggestions.
References K. Morimoto, Y. Araki, M. Tanaka, K. Satake, N. Shimizu and Y. Iwahashi, Development on numerical anlaysis techniques for ECT, JNDT Spring Conf., 1993. K. Satake, M. Tanaka, N. Shimizu, Y. Araki and K. Morinoto, Three-dimensional analysis on eddy current testing for SG tubes, IEEE Trans. on Mag. 28(2) (1992) 1466-1468.
Nuclear Engineering and Design 153 (1994) I-9
Nuclear Engmeen.ng andDemgn
Application of numerical analysis techniques to eddy current testing for steam generator tubes Kazuo Morimoto +', Koji Satake +', Yasui Araki b, Koichi Morimura c, Michio Tanaka c, Naoya Shimizu d, Yoichi lwahashi d " Advanced Technology Researcl; Center, Mitsubishi Heao' hl&tstries Ltd., Kanagawa-ku, Yokoh,ma 236, Japan b Takasago Research anti Deveh~pment Center, Mitsubishi Henry buhtstries, Ltd: .~,ai-cho, Takasago 670, Japan c Electronics Division, Mitsubishi Hetwy bt&tstries Ltd., tl)'ogo-ku, K:,be 652, Japan d Kobe Shipyard and Engine Works, Mitsuhishi Heat,y b~&tstries Ltd., Hyogo-ku, Kobe 652, Japan
Abstract
This paper describes the application of numerical analysis to eddy current testing (ECT) for steam generator tubes. A symmetrical and three-dimensional sinusoidal steady state eddy current analysis code was developed. This code is formulated by future element method-boundary elemen! method coupling techniques, in order not to regenerate the mesh data in the tube domain at every movement of the probe. The calculations were carried out under various conditions including those for various probe types, defect orientations and so on. Compared with the experimental data, it was shown that it is feasiblc to apply this code to actual use. Furthermore, we have developed ~ total eddy current analysis system which consists of an ECT calculation code, an automatic mesh generator for analysis, a database and display software for calculated results.
I. Introduction
Eddy current testing (ECI') techniques have been applied to in-service inspection of steam generator (SG) tubes, because of their high speed and ease of operation. Various types of probe are needed according to the defect type ~u~d orientation. Recently it has become cle='~."th.ut a probe for detecting smaller cracks must be dc,:~:loped. Since in actual inspections the detectc+_~ E( F signals are caused not only by defects but al:+o by the support plates and deposit around the tubes and so on, we have to analyze the signals and to determine the sources of the signals. To meet these require-
ments, we have developed numerical analysis techniques which calculate eddy current distribution in SG tubes, coil impedance and other factors in order to develop a new probe and to analyze the actual signals. Regarding this development, the following factors had to be considered. In actual testing, several kinds of probe are used, such as a bobbin coil probe, a pancake coil probe, and a probe which includes magnetic materials. The coil impedance change caused by defects is very little, e.g. a li:w tenths of a per cent of the coil impedance. Therefore, threediemsional high accuracy analysis would be needed. Moreover, the numerical analysis must be easily
0029-5493/94/$07.00 ,~" 1994 Elsevier Science S.A. All rights reserved SSD! 0029-5493( 94)00807-B
2
K. Morimoto et al. / Nuch,ar b.)agineer#tg and Des(gn 153 (19941 ! 9
carried out, even if there are many procedures for calculating the coil impedances at every posititon while the coil is moving.
2. Analysis method
The equations for this analysis are Maxwell's electromagnetic equations. However, because of the low frequency range, the displacement current can be ignored in these equations, so that these equations are reduced as follows:
V x E-
(I) ~B Ot
(2)
B = pH
(3)
J = irE
(4)
V. B = 0
(5)
V. J = O
(6)
where H is the magnetic field J is the current density, E is the electric field, B is magnetic flux density, p is the magnetic permeability and tr is the electric conductivity. To solve these equations, a vector potential (A = V x B) and a scalar potential q~ are used. Using A, Eq. (5) is automatically satisfied. The differential operator c~B/~,t is replaced by h:h since the eddy current is sinusoidal steady state. From these considerations and Eqs. (1)-(4), the following equation can be obtained: I V2A P
a(itoA + VO)
(7)
where t,J is the angular frequency. Also, the electric field is described by E = - itoA - V~b
! --V2A Po
=-J
(!0)
2.2. Formulations
2. i. Basic equation
V×H=J
On the contrary, in a domain including current sources, the equation is as follows:
For the ECT problems, we must calculate the eddy current distributions and coil impedances at every position for a coil, which moves in a tube axially or circumferentiaily. In these cases, input data for calculation have to be found at each position, because the models are different from position to position. In order to obtain input data easily, a finite element method (FEM) and a boundary element method (BEM) are used for a tube domain and a domain including a coil respectively. According to these combinations, we do not have to redivide, the tube area in spite of the moving coil, so that it shortens the preparation time for the calculation. From these ideas, the formulations were carried out as follows. The Calerkin method was used for the formulation of FEM; Eqs. (7) and (9) give
where [K] is the coefficient matrix and {F} is the nodal flux vector. Applying Gren's theorem to the BEM area, the following equation can be obtained from Eq. (10): :
--
.tB i
(12)
where [H] and [6-] are the coefficient matrices and {B} is the surface flux vector induced by the coil current. Superimposing Eq. (12) on Eq. ( ! ! ), the formulation can be obtained in the manner of the FEM. The coil impedance can be calculated from the magnetic vet!or potential A as follows:
(8) itoA" dl
Eq. (6) is converted to the following equation, using Eqs. (4) and (8)' V " a(io~A + Vrk) = 0
(9)
Z -
I
(13)
where I is the source current density; A is obtained from the equations mentioned above and
K. Morimoto et al. / Nuclear Engineering and Design 153 (1994) i - 9
the integral is conducted along the center of the coil.
3. Numerical analysis and results Using the analysis code developed, we calculated the eddy current and the coil impedance in various cases of ECT, and we investigated the calculation accuracy, by comparing it with the experiment results.
3.1. Two-dimensional analysis First, axially symmetrical problems were dealt with for the case of a bobbin coil, in order to reduce the central processing unit (CPU) time and memories. The calculated results and the experimental data, in which the models were straight tubes with an entire wall thinning, are shown in Fig. 1. The impedance changes calculated in various cases between 10% and 75% of full circumferential wall thinnings are almost the same as the experimental results. This shows that these small changes of coil impedance could be calculated with high accuracy. Secondly, a model which simulates a tube with a support plate was calculated. In this case, the
• Analysis at 100 kHz = Analysis at 400 kHz
[~1
I
40
I
• Experiment at 100 kHz x Experiment at 4001kHz~
3
permeability of the support plate is so high that the skin depth of the eddy current is as small as approximately a few tens of micrometers, which shows that the eddy current decreases suddenly near the surface. If normal rectangular elements were used as FEM elements, a sufficient accuracy could not be obtained. Therefore, the higher order rectangular elements were used. Fig. 2 shows an eddy current distribution in the tube and the support plate. A probe impedance trajectory obtained by numerical analysis and experiments are also shown in Fig. 3. From this result, it is recognized that our analysis code has sufficient accuracy to calculate the effect of a support plate. Thirdly, we investigate a way of calculating a model which simulated a tube with a higher conductive deposit on the outer surface. In SG tubes, the conductivity of the adherent materials is about 30 times the tube's conductivity, but the thickness is extremely small about a few micrometers, compared with the tube. Therefore, for 100 kHz, the eddy current skin depth is about 200 lam, the eddy current density flowing in the deposit mentioned above seems to be almost uniform in depth. In the calculation, a surface current flowing in it was supposed. Fig. 4 shows the eddy current distribution which was calculated according to these ideas. This result shows that the eddy current distribution in the tube was affected by the eddy current in the high conductivity material. In Fig. 5, the calculated and experimental coil impedances are shown. In this case, both results are almost the same.
3.2. Three-dimensional analysis
-~- 10 o c
,~
4
,/100
[kHz]
o 0 o c el
E
0.4
0.1
0
25
50
75
1O0
Depth of outer surface wall thinning [%] Fig. i. Comparison between the calculated and experimental impedances.
In order to calculate the eddy current in testing actual SG tubes, the models must be three dimensional. We developed a three-dimensional analysis code for various ECT probes, and invetigated the calculation accuracy in comparison with the experimental data. First, we applied this code to testing by bobbin coils, which were usually used at normal inspections. The calculated model and the eddy current distribution are shown in Fig. 6, and the calculated and experimental coil impedances are also shown in Fig. 7. The calculated value is in close agreement with the experimental value.
K. Morimoto et ai. / Nuclear Engineering and Design 153 (1994) i - 9
4
II Coil
~:~
(a)
(b)
Fig. 2. Calculated eddy current distribution in tubes and support plate caused by bobbin coil at 100 kHz: (a) analyzed model; (b) eddy current distribution. :-,,, ------------
Calculation Ex ~erimenl
0.2
½
X
I° m
_E --0.2
.I. -0.2
i 0
Real (&R) [t31
0.2
Secondly, we considered a pancake coil as an ECT probe coil, which has recently been used as frequently as the bobbin coil. Circumferential defects in the tube were calculated as a test model. The eddy current distribution for a slit are Fig. 8. Calculated and experimental coil impedances are also shown in Fig. 9. These results agree with each other. Thirdly, we also use ECT probes which inc!ude high permeability materials such as a ferrite. In these cases, the FEM was applied to such materi. als to link it to the BEM, because the area including such an ECT probe cannot be analyzed only by BEM.
Fig. 3. Comparison between the calculated and experimental impedances of bobbin coil for wall ~hinning at 100 kHz.
K. Morimoto et al. / Nuclear Engineering and Design 153 (1994) ! - 9
5
Coil
Adhered material Contour l e v e l s •
W •
\ S/G tubes
(a)
(b)
1.032E+01 2.054E÷Ol 3.096E+01 4.12gE+01
m • •
• • • • •
5.z61E+01
• •
6.193E+01
•
7.225E÷01 8.257E+01
• •
•
B.QBBE÷OI
•
= =
• *
=
1.030E+02 1.140E+02 1.240E÷02 1.340E+02 1.440E+OZ 1.550E+02 1.650E+02 1.750E÷02 I.BGO£*02 1.960E+02
= •
m
2.060E÷0~
•
1 O0 [kHz]
Fig. 4. Calculated eddy current distribution affected by the high conductivity of deposit at 100 kHz: (a) analyzed model; (b) eddy current distribution.
....
(3 . . . .
Calculation " Experiment
i
0 e-
E
Using this F E M - B E M technique, we calculated a test model where a longitudinal slit was tested by the probe with a ferrite core surrounded by a coil. The eddy current distribution and coil impedance are shown in Fig. 10 and Fig. 11 respectively. The coil impedance is in agreement with the experimental value. From the results mentioned above, it was recognized that our developed analysis code had sufficient capability, to solve the ECT for SG tubes, although the model size was limited by the calculation time and the memory size.
-1
m'
0 Real (&R) [Q]
1
Fig. 5. Comparison between the calculated and experimental impedances of bobbin coil caused by a deposit at 100 kHz.
K. Morimoto et ai./Nuclear Engineering and Design 153 (1994) 1-9
6
Q
Longitudinal slit
f
Coil
S/G tubes
(a)
Inner surface
Outer surface
Fig. 6. Calculated eddy current distribution caused by bobbin coil (5 mm long; 50% deep slit at outer surface: 100 kHz): (a) analyzed model: (b) eddy current distribution.
Calculation Experiment
~" " "'---'----
~. t.llll,¢ r,.ul*lJ i a,~JLt~. jL
_
0.1
..h~l,fl
X
t
| -0.1
0
f 0 Real (~R) [D]
L" rE
-0.1
0.1
Fig. 7. Comparison between the calculated and experimental bobbin coil impedances (5 mm long; 50% deep slit at outer surface; 100 kHz).
4. Eddy current testing analysis system The capability of the analysis codes was confirmed, as described above. However, in order to use these codes to develop probes or estimate the ECT signal in actual testing, it was necessary to make various software to support the analysis. From this point of view, we have developed the ECT analysis system, in which an analysis can be done following the flow chart shown in Fig. 12. This system is based on a high speed engineering
Density of current Eddy current distribution
Fig. 8. Calculated eddy current distribution caused by pancake coil (10ram long; 50% deep slit at outer surface; 100 kHz).
work station (EWS). The reasons for using the EWS are as follows: the calculation cost is low; the turn-around time is short because there is no waiting time, although the calculation speed is not faster than a super computer. The specifications of the EWS, used in this system are listed in Table 1. A calculation time of the case shown in Fig. 8 was about 20 min. The software environments of this system are also shown in Table 2. These were selected so this system could be installed in other EWSs easily and so a multiwindow system could
K. Morimoto et al./ Nuclear Engineering and Design 153 (1994) 1-9 0.1
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be utilized to display the results. The characteristics of this system are described as follows. (1) If the information concerning the tube, the defects and so on are inputted as shown in Fig. 13, the input data for the calculation code are generated automatically. This function allows one to calculate any model easily, even if the particular operations to create the necessary elements, nodes and so on, for FEM or BEM are not known.
-0.2
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Fig. 1I. Comparison between the calculated and experimental special coil impe~dances (10 mm long; 50°,4 deep slit at outer surface; 100 kHz).
(2) Previously retrieved analyzed data can be stored ~ad searched, because this system has a relational database for past data. Cc,nsidering the EWS performance, it takes little more than 20 rain to calculate a three-dimensional model. Storing and searching for previously analyzed data allow
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8
K. Morimoto et aL/ Nuclear Engineering and Design 153 (1994) 1-9
Table ! Specifications of engineering work station
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I, arrangements simultaneously, as shown in Fig. 14. Using these display facilities, evaluation or comparison of various data is easy.
1 ( r-n.) Fig. 12. Flow chart for the ECT analysis system.
unnecessary recalculation to be avoided and the total calculating time to be shortened. ~-,Jla~ Using the multiwindows, the analyzed data and the experimental data can be seen in various
5. Conclusions Two-dimensional and three-dimensional eddy current analysis codes were developed to be ap-
Fig. 13. Cathode-ray tube for input procedure.
K. Morimoto et al. / Nuclear Engineering and Design 153 (1994) 1-9
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plied to the ECT problems. Comparing the calculated data with the experimental data, it was proven that these codes had sufficient accuracy to analyze various models, and that was feasible to use the codes at practical levels• We have also developed an ECT analysis system which includes an automesh generator, a database, and various display functions. This system will be used and continuously improved for many applications.
Acknowledgment The authors are grateful to Professor K. Miya of the University of Tokyo for his useful suggestions.
References K. Morimoto, Y. Araki, M. Tanaka, K. Satake, N. Shimizu and Y. Iwahashi, Development on numerical anlaysis techniques for ECT, JNDT Spring Conf., 1993. K. Satake, M. Tanaka, N. Shimizu, Y. Araki and K. Morinoto, Three-dimensional analysis on eddy current testing for SG tubes, IEEE Trans. on Mag. 28(2) (1992) 1466-1468.