Steam Generator Tube Inspection I

Transcription

1 Steam Generator Tube Inspection I 3D emote Field-Eddy Current Simulation of the Support Plates of the Magnetic Steam Generator Tubes in FB O. Mihalache, T. Yamaguchi, M. Ueda, S. Miyahara, Japan Atomic Energy Agency, Japan ABSTACT The paper presents three dimensional numerical simulations of the in-service inspection using eddy currents of the support plates of steam generator tubes in a fast breeder reactor. A numerical finite element code, named 3D-FECT, developed in-house, was parallelized and implemented to be used on a supercomputer. 3D numerical analysis are conducted to establish variations in the support plate signal when remote field eddy current probes runs inside steam generator tubes. INTODUCTION In Fast Breeder eactors (FBs), one of the techniques used in the In-Service Inspection (ISI) of magnetic steam generator (SG) tubes is the remote field eddy current technique (F-ECT) [1]. The SG tubes, made of 2.25Cr-1Mo alloy are fixed in a helical structure shape using multiple support plates (SP) which are also ferromagnetic. The complicated shape of the SP and the multiple connections of several tubes to the SP can be quantitatively analyzed only in a full 3-dimensional (3D) analysis, in order to evaluate the influences in the ECT signal due to the close proximity of the SG tubes. In a SG mock-up, the SG tubes are supported using only a reduced geometry version of the SP. However, in the reactor, there are multiples SG tubes connected to a big SP and the ECT signal from the SP can varies according to the position of the SG tube in SP. In the paper are presented full 3D finite element simulations (FEM) of the eddy current effect of the SP using an in-house developed numerical ECT code [2]. The 64-bit code, fully parallelized, is based on the reduced magnetic vector potential in a FEM environment. Femap 8.3 was employed for both pre-processor (meshing) and post-processor analysis (field visualization) [3]. The 3D numerical analysis are conducted to establish variations in the SP signal when F-ECT probes runs inside SG tubes and several tubes are connected to the SP. Variations of a defect under SP signal is computed and visualized in the above situations in order to identify the defect signal sensitivity in different locations under SP. 3D-FECT FINITE ELEMENT CODE Earlier work for the three dimensional remote field eddy current (3D-FECT) code was previously reported in [4-6]. The code is based on the FEM in the Galerkin approach, starting from the Maxwell electromagnetic equations and uses the magnetic vector potential defined as B = A. 1 (1) ( / µ A) + σ ( jωa v A) ν A = J s where µ is the magnetic permeability, σ is the electrical conductivity, v is the material velocity, and J s is the imposed current density in the excitation system. The 3D FEM model is based on (A-V) field formulation with the gauge of the electric scalar potential V=0 (in order to reduce the computational burden due to the 3D model). The magnetic vector potential A is divided in two terms as follows: the vector potential of the source field in the free air A S (calculated with the Biot-Savart law) and presence of the ferromagnetic region. A the reduced magnetic vector potential, due to the

2 A = A S + A (2) By adopting the reduced magnetic vector potential, the source and detection ECT coils are not meshed in the FEM model. The domain of the problem (Ω) is divided in two areas: air region (Ω 1 ) and tube region (Ω 2 ). By using Eqs. (1-2), the electromagnetic field in the 3D-FECT code is modeled by the Eq. (3). ( ν A ) ( ν A ) = 0, in Ω1 A AS ( ν A ) ( ν A ) + σ = ( ν A ) σ, in Ω 2 t The boundary conditions in Eq. (4) show that the normal component of flux is prescribed on Г B and the tangential component of magnetic field intensity is given on Г H, where Г=Г B +Г H is the boundary of volume Ω. The Coulomb gauge is weakly imposed (in order to assure the uniqueness of the problem) using the boundary conditions in Eq. (4) and the term ν A is added in the field Eq. (3) as a supplementary penalty factor. On the interface Г 12 between air-tube, the continuity of the tangential component of magnetic field intensity is expressed using Eq. (5), where n 1 and n 2 are the normal at the Г 12 at volume Ω 1 and Ω 2 respectively. ν A n = 0, on Γ A n = 0 H ; ν A = 0, on ΓB A n = 0 S t (4) (3) ν A 0 1 n1 + ν 0 AS n1 + + ν A n + ν A 2 2 S n 2 = 0, on Γ 12 (5) The system of Eqs. (3,4,5) are solved using nodal elements in a finite element model. The solution of the FEC problem is obtained by calculating the induced voltage V in the detection coils, base on the formula: V = jω A dl. (6) Coil In the numerical simulation of the ECT signal, the excitation probe move over the defect zone, and the detection coil signal is computed at every step using Eq. (6). The code was parallelized in order to take advantage of the multiple CPUs available on today PCs and supercomputers and to speed up the execution time. The parallel performance of the code is presented in Figure 1, for up to 64CPUs for two supercomputer configurations: HPC2500 and ALTIX3700. The speed of the code is 30 times faster, when using 64 CPUs in parallel, for the iterative matrix solver. The FEM matrix is solved using: a) a developed parallel iterative matrix solver based on the GMES method; b) or using the INTEL MKL library available on ALTIX3700. The advantage of the iterative solver is that it requires a small amount of memory. However, when computing the ECT signal in successive points, as the probe scans the defect area, the INTEL MKL solver is faster, as is updating only the field from the excitation coil in the next simulation step. In the iterative solver, the solution is recomputed in the next simulation step starting from the previous simulation electromagnetic field results. Table 1 shows the computational burden, using 8 CPUS and the iterative matrix solver for a 3D simulation problem (with 500,000 degrees of freedom, and 1,200,000 linear order tetrahedral elements), in which an ECT signal is composed of 120 distinct simulation points. Table 2 shows the computation burden for the same 3D geometries, but using 2 nd order tetrahedral nodal elements (5,000,000 degrees of freedom). In order to use Intel MKL solver for the same problem, at least 400 GB memory is required.

3 Figure 1 - Parallel performance of the 3D-FECT code on supercomputer Memory Time Time.. Time Total time [GBytes] 1st point 2nd point 120th point Developed iterative solver 1 GB 347 sec 170 sec sec 5.5 hours Intel MKL 27 GB 1140 sec 12 sec.. 12 sec 45 minutes solver Table 1 - Computational burden for the 3D-FECT code using 1st order elements (8CPUs) Memory [GBytes] Time Time.. 1st point 2nd point Time 120th point Total time Developed iterative solver 30 GB 1 hour 0.5 hour hour 60 hours Table 2 - Computational burden for the 3D-FECT code using 2nd order elements (8CPUs) The pre-processor FEM meshing and the post-processing and visualization/animation of the eddy current field distribution was linked with the FEMAP 8.3 [3]. 3D NUMEICAL SIMULATIONS AND ESULTS FO THE SP In the SG mock-up, smaller versions of the SP are available, as shown in Figure 2a. But, in a FB, the SG tubes are bundled and closed to each other and connected to a bigger SP structure as is illustrated in Figure 2c. In the 3D numerical simulation it is also analyzed the model from Figure 2b, in which one tube is connected to a bigger SP, in order to asses the variations in the SP signal. In Figure 2c, four tubes were identified and labelled with different colours. These tubes have various positions (middle - the black label, left the green label, up the red label, diagonal the blue label) regarding the SP, and the simulations take into account the ECT signal from the SP recorded as the F-ECT probes enter and scan each of these tubes separately.

4 a) b) c) Figure 2 - View of various geometries of SP and SG tubes connected to it: a) small SP structure with only one SG tube; b) big SP strcuture with only one SG tube; c) big SP structure with multiple SG tubes. Acurrate representation of the distribution of the eddy current around SP are calculated using 2nd order tetrahedral nodal elements. The finite element mesh for the reduced SP in Figure 3a has 1,200,000 tetrahedrons, and 5,000,000 degrees of freedom (DOF). The tube and SP includes around 1/3rd of finite elements, while the others are used to discretized the air surounding them. Figure 3a shows a visualization of eddy current distribution in tube and SP, using the postprocessor capabilties of FEMAP, while in Figure 3b is presented the hidden tube zone situated in the shadow of the plate connecting the two legs of the SP. The 3D simulation shows a smaller eddy current distribution in this area, resulting in a smaller defect disturance for a defect localized in this area. In Figure 4 are shown eddy current distribution for a full SP with multiple tubes connected to it. The FEM mesh has 1,700,000 2 nd order tetrahedrons and 7,000,000 DOF. Aproximatively 700,000 finite elements are used to discretized the SP and the tube structure. In Figure 4a and 4b, a double excitation F-ECT probe enter and scan the diagonal and the middle tube, respectively. Some parts of tubes and SP were cut out from the picture in order to visualize the field distribution in the area between the exitation probes, where the detection coils exists. It can be seen that smaller field values are present in the midle tube compared to the diagonal tube, resulting a smaller SP signal, as will be shown later, in the next paragraph.

5 a) b) Figure 3 - Distribution of electro-magnetic field generated in SP and SG tube by a double F-ECT probe: a) small SP structure; b) the hidden zone of the SG tube under the plate that connects the two legs of the SP. a) b) Figure 4 - Distribution of electro-magnetic field generated in the big SP structure by a double F-ECT probe when the excitation coil system is located into the: a) diagonal SG tube; b) middle SG tube Figure 5a shows a comparison between SP signals calculated with a 2-dimensional axisymmetric (2D) code [2] and the 3D code. This simulation took into consideration the reduced SP structure (see Figure 3). The 2D code calculates a 30-40% larger SP signal and gives a 30 degrees phase difference compared to the 3D code result. In the next step it was analyzed the influence of the size of SP (reduced and full SP model) with only one tube connected to it (the middle tube). Figure 5b shows that there is no additional variation in the SP signal as only one tube is connecting to the big SP structure. However, the SP signal varies (see Figure 6) as multiples tubes are connected to the SP and the ISI of tubes is performed by ECT probes entering separately in each tube, as was shown previously in Figure 2c. Numerical simulations showed that SP signal has the smallest amplitude when the probe enters in the middle tube. Overall, a 20% variation in the SP signal can be expected, due to the position of the tubes regarding the SP. The phase of the SP signal varies by up to 5 degrees.

6 a) b) Figure 5 - a) Comparison between numerical simulations of the small SP structure using a twodimensional (2D) axysimmetric FEM code and the three-dimensional (3D) FECT code; b) Comparison between 3D simulations of the small SP and big SP structure with only one tube connected to it. Figure 6 - ECT signal of the SP when only one tube in different positions (middle, up, left, diagonal) is connected to the SP. In the next simulation it was evaluated again the influences of the tube position on the SP signal, but taking into account the full SP model and only one SG tube, as shown in Figure 7. The four tube positions were identified as: middle, up, left and diagonal. The simulations (see Figure 8) show the same pattern in variations of the SP signal when all tubes were connected to the full SP model. The only difference in the SP signal is that its signal amplitude is 20% smaller when all SG tubes connect to SP than the case of only one tube connect to it. Figure 7 - Local position of the SG tube in the big SP structure.

7 Figure 8 - Variation in the ECT signal of SP, when the F-ECT probe scan each of the representative tube (middle, up, left; diagonal). Three dimensional numerical FEM simulations were conducted to investigate the sensitivity of the defect detection, when these defects are located under SP in two positions as indicated in Figure 9. In order to asses the most difficult situation, it was considered that the defects were on the SG tube located in the middle of the SP. For the middle tube it was shown previously in the paper that it is subjected to the strongest influence from the neighbouring SG tubes. Also, the SP model took into consideration the multiple SG tubes, as shown in Figure 2. The sketch of the SP and positions of outer tube defects is presented in Figure 9. The SP has two legs, one of them being in close contact with the SG tube trough an austenitic stainless steel ring, while the other is let free. Defects are most likely to appear in these areas mainly due to the friction between SP and SG tube. In the ISI of FB tubes using ECT it is required to be detected a defect with a signal equal with the signal from an outer groove OD 20%, 10 mm wide. Figure 10 shows the ECT signal from an OD 50% groove, 10 mm, while Figures 11 and 12 present the signal from OD 20% groove, 10 mm. Figure 9 - elative position of the defect hidden under the SP. Figure 10 - Simulation of ECT signal detection for OD50% groove under SP in position P1.

8 Figure 11 - Simulation of ECT signal detection for OD20% groove under SP in position P1. Figure 12. Simulation of ECT signal detection for OD20% groove under SP in position P2. In the simulations scan, were computed up to 120 simulations points, with a scan step of 3 mm, in order to build the SP signal. 3D numerical simulations, from Figure 10-12, showed and confirmed, that even in the case when multiple SG tubes are connected to a big SP structure, a 20 % OD groove under the SP can be easily identified using either Lissajous X-Y curve, or each component of the ECT signal: resistance X and reactive Y. CONCLUSIONS 3D numerical simulations based on the FEM method were conducted to asses the sensitivity of defects detection under a full 3-dimensional model of support plates of magnetic steam generator tubes of FB. The FECT signal of the SP decreases by up to 20% in amplitude, but remain constant in phase, only when multiple SG tubes are connected to the full model of the SP. The 3D simulations showed up to 5 0 variations in the phase of the SP signal, depending on the location of the inspected SG tube on the SP. Even in the full SP model, with multiple SG tubes connected to it, an OD20% groove 10 mm wide under SP can be easily identified, using either the X or Y component of the ECT signal, or the Lissajous diagram. EFEENCES

9 1) D. L. Atherton, S. Sullivan and M. Daly, Br. J. Nondestructive Testing, 30, No. 1, pp , Jan ) O. Mihalache, Advanced emote Field Computational Analysis of Steam Generators Tubes, IOS Press, Electromagnetic Nondestructive Evaluation VII, Studies in Applied Electromagnetics and Mechanics 26, pp , ) Femap User Guide, Version 8.3, ) O. Mihalache, T. Yamaguchi, M. Ueda and T. Yamashita, Experimental Confirmation of 3D Numerical Simulations of emote Field Signal from Defects in Magnetic Steam Generator Tubes, eview of Progress in Quantitative Nondestructive Evaluation, American Institute of Physics, Vol. 25, pp , ) O. Mihalache, Y. Imai, M. Ueda and T. Yamashita, Finite Element Simulations of the emote Field Eddy Current Signal in Steam generator Tubes of Monju Fast Breeder eactor, 2004 ASME/JSME Pressure Vessels and Piping Conference, PVP-VOL. 484, pp , ) Ovidiu Mihalache, Toshihiko Yamaguchi, Masashi UEDA, Shinya Miyahara, Eddy Current Simulations and Measurements of Sodium Effect for Magnetic and non-magnetic steam generator tubes of FB, eview of Progress in Quantitative Nondestructive Evaluation, American Institute of Physics, Vol. 28A, pp , 2008.