Modelling III Hybrid FE-VIM Model of Eddy Current Inspection of Steam Generator Tubes in the Vicinity of Tube Support Plates S. Paillard, A. Skarlatos, G. Pichenot, CEA LIST, France G. Cattiaux, T. Sollier, IRSN, France ABSTRACT Modelling of eddy current inspection of Steam Generator (SG) tubes near tube support plate () is beneficial for the validation of existing industrial Non Destructive Testing (NDT). Eddy current inspection of Steam Generator tubes in the vicinity of tube support plates is an important aspect of the safety of the nuclear plants. The appearance of material defects like corrosion or cracking is frequent for alloy 600 MA in this particular region of the SG installations. The detection of defects in the proximity of support plate presents increased difficulties due to the perturbation signals arising from the presence of the plate. Additional effects like gradual deposit of conducting or/and ferromagnetic material in the gap between the plate hole and the tube external wall may create additional perturbations which have to be identified and distinguished from the flaw signature as well. The aim of this collaborative work between CEA and IRSN is to extend the capabilities of the CIVA software by developing a simulation tool for the evaluation of industrial non-destructive testing method used for the tube inspection in the support plate region. For the numerical modelling of this problem, a combination of the Finite Elements Method (FEM) with the Volume Integral Method (VIM) is used in order to combine the advantages of the two techniques. According to this approach, the primary field is calculated using the FEM for the tubeplate ensemble whereas the flaw response is calculated via the VIM. First, we will introduce the principle of the hybrid method, we will describe the Finite Element model (FLUX) and the Volume Integral Method (CIVA) used in this hybrid model. Then, we will summarize the most important validation results of our previous communication (inspection of Steam Generator tubes in the vicinity of quatrefoil-shaped holes tube support plates with a bobbin coil). These results show that the proposed hybrid method is able to handle such configurations. Finally, we will present a simulation taking into account quatrefoil-shaped holes support plates and magnetic material deposit support plates with a bobbin coil. All these results are validated by experimental data. Application cases concerning support plates with magnetic quatrefoil-shaped holes with or without magnetic material deposit are given in this article to illustrate the good agreement between simulation and experimental data. INTRODUCTION The aim of this collaborative work between CEA and IRSN is to extend the capabilities of the CIVA software by developing a simulation tool for the evaluation of industrial non-destructive testing method used for the tube inspection in the support plate region. For the numerical modeling of this problem, a combination of the Finite Elements Method with the Volume Integral Method is used in order to combine the advantages of the two techniques. According to this approach, the primary field is calculated using the FEM for the tube-plate ensemble whereas the flaw response is calculated via the VIM. In a previous communication [7], we presented application and simulation cases concerning support plates with circular and quatrefoil-shaped holes. The results show that the proposed method is enabling to handle such configurations. Since, we worked on taking into account quatrefoil-shaped holes support plates and magnetic material deposit in the same configuration. Application cases concerning support plates with magnetic quatrefoil-shaped holes with or without magnetic material in the same configuration will be given in this article to illustrate the good agreement between simulation and experimental data.
HYBRID FE-VIM MODEL inc The coupling approach adopted in this work is described in [3]. The primary field E 2, i.e. the electric field induced inside the tube wall in the absence of the flaw, is calculated using the FEM. Since the defect is usually of small volume in respect to the rest of the structure, one can consider that the perturbation to the eddy current flow is of local character and thus neglect its interaction with the. Hence, the flaw response can be calculated with good accuracy by solving the volume integral equation approach applied for the free span area [1, 2] E2 = 2 0, δσ ee ( r ) E ( r ) + jωµ G22 ( r r ) ( r ) E ( r ) dv inc 2 ee V f where the Green dyad G22 corresponds to the dyad of a cylindrical multilayered medium. In the above equation, the tube is described in terms of a cylindrical multilayered structure the second layered being assigned to the tube wall, the first and the third ones being referred to the interior and the exterior of the tube respectively. Once the total field E 2 has been evaluated, the mutual impedance between the driving coil and each of the receiving coils of the probe can be calculated using the reciprocity theorem [5]: Z ji 1 = I I j i V f (1) inc δσ ( r ) E ( r ) E ( ) d 2, j 2, i r V. (2) inc where E 2, j denotes the primary field that would be induced by the considered receiving coil j if it was excited with a current I j, and I i is the excitation current of the driving coil. E 2, i is the total field in the flaw region and is obtained by the solution of Eq. (1). The unperturbed values of the impedance matrix at the different scanning positions Z ji depend on the tube- configuration and are obtained by the post-processing of the FEM solution. The final probe response is then calculated using the above values of Z ji and Z ji taking into account the operational mode of the probe (function in absolute or differential mode). As in the case of the with circular and quatrefoil-holes, an optimization algorithm has been developed in order to estimate the most pertinent positions of the probe and hence to minimize the number of FEM simulations. APPLICATIONS PARAMETERS The presented model as been applied for the simula tion of eddy current inspection of a SG tube in
The EC signals are computed at three frequencies: 100 khz, 240 khz and 500 khz but illustrated in this article only for the most significant frequency for the signal, 100 khz. Both simulation and experimental results are calibrated in respect to the signals of a reference flaw. The reference flaw consists of a set of 4 through-holes of 1 mm diameter, circumferentially distributed every 90. 2 identical coils operating at differential mode Inner radius: 7.83 mm Outer radius: 8.5 mm Height: 2 mm Coils distance: 0.5mm Number of turns: 70 Figure 2 - Problem configuration: bobbin coil in a SG tube with a quatrefoil FEM calculation parameters The quatrefoil tube support plate () properties of the experimental mock-up (depicted in Figure 3) are representative of those met in a typical pressurized water reactor. The conductivity of the was measured at 1.4 MS/m and the relative permeability estimated at 30. Side Face Cross-Section Figure 3 - Problem configuration: SG tube with a quatrefoil The FEM calculations are carried our using the Flux-3D package. An important feature of the hybrid approach is that the primary field has to be calculated only once for a given tube, and probe configuration which makes the approach significantly faster than treating the entire problem (primary field and flaw interaction) using the FEM only. The FEM calculation needs to be done cautiously because of the high sensibility of the result to the mesh chosen. On the Figure 4 an FEM mesh is illustrated for the treatment of the tube-bobbin coil configuration described above. In order to reduce the time of FEM calculation, only a quadrant is really treated.
Figure 4 - Problem configuration: bobbin coil (blue) in a SG tube (yellow) with a quatrefoil (green). FEM mesh used for the calculation of the primary field and the self and mutual impedances of the two coils Semi-analytical calculation parameters Once the surrounding environment (influence on the probe of the ) calculated with FEM, the semi-analytical model takes this result in account in the calculation of flaw effect. The defects considered for the validation are representative of the typical tube degradations in the area of the, which are principally the Intergranular Stress Corrosion Cracking (IGSCC). More over another type of configuration is also considered: a magnetic deposit. The geometry and the dimensions of the considered flaws and deposit illustrated in this article are given in Table 1. Table 1 - Examined flaws for the validation of the developed combined formulation. The flaw radial dimensions are given as percentages of the tube thicknesse Flaws and deposit Dimensions / e Angular Extension Longitudinal Extension External Groove EG40 40 % 360º 1 mm External Longitudinal Notch ELN10 54 % 0.6º 10 mm Magnetic deposit 300 µm 360 50 mm APPLICATION TO A QUATREFOIL TUBE SUPPORT PLATE In a previous communication, we presented application and simulations cases concerning support plates with circular and quatrefoil-shaped holes. In order to introduce the latest results (magnetic deposit), we will summarize in this paragraph, the two most important validation results which are applications to SG tube with grooves and notches in the vicinity of tube support plate (). The model has been applied for the simulation of eddy current inspection of a SG tube with an external groove (EG40) and with an external notch (ELN10) in the vicinity of a quatrefoil. These results have been validated using experimental measurements.
Validation on an external groove For this application (Figure 5), we consider a centred on an external groove (EG40). The calculation of the is carried out by the FEM model and this result is taking into account in the semi-analytical calculation of the probe response to the groove. Figure 5 - Problem configuration: external groove in a SG tube with a quatrefoil External groove Experiment Experiment (without SP) Simulation External groove Figure 6 - Simulated vs. measured signals for EG40 at 100 khz: (blue) experimental signal with, (black) simulated signal with and (red) experimental signal without. The above plots give the signals on the complex plane (left side) and their real and imaginary parts as function of the probe scanning position. The above plots (Figure 6) give the signals on the complex plane (left side) and their real and imaginary parts as function of the probe scanning position. The simulated signal (Figure 6, black) is in good agreement with the experimental signal with (blue). For a better understanding of the effect, the experimental signal without (red) is also presented. Both and EG40 signatures appear clearly in the probe response because of the distance between the edges and the groove.
Validation on an external longitudinal notch This validation (Figure 7) considers an external longitudinal notch (ELN10) with a height of 10 mm (the height of the groove is 1 mm) centred on the quatrefoil (with a thickness of 30 mm). On Figure 8, we can notice that the both signatures appear closely and are well-combined by the hybrid model and these results are in good agreement with experimental data in the case of an ELN10 in a SG tube with a quatrefoil. Figure 7 - Problem configuration: longitudinal notch in a SG tube with a quatrefoil External longitudinal notch Experiment Experiment (without SP) Simulation longitudinal notch Figure 8 - Simulated vs. measured signals for ELN10 at 100 khz: (blue) experimental signal with, (black) simulated signal with and (red) experimental signal without. The above plots give the signals on the complex plane (left side) and their real and imaginary parts as function of the probe scanning position.
APPLICATION TO A QUATREFOIL TUBE SUPPORT PLATE WITH DEPOSIT The presented model has been validated on flaws such as grooves and notches. Now, the model has to be validated on more complex configurations: magnetic deposit. The model has been applied for the simulation of eddy current inspection of a SG tube in the vicinity of a quatrefoil. The results of the hybrid approach have been validated using experimental measurements. Validation with the centred on the deposit For this application, we consider a centred on a magnetic deposit (Figure 9). The calculation of the is carried out by the FEM model and this result is taking into account in the semi-analytical calculation of the probe response to the deposit with. Figure 9 - Problem configuration: SG tube with a quatrefoil centred on the deposit Deposit Experiment Experiment (without SP) Simulation Deposit Deposit Figure 10 - Simulated vs. measured signals for deposit centred on the at 100 khz: (blue) experimental signal with, (black) simulated signal with and (red) experimental signal without. The above plots give the signals on the complex plane (left side) and their real and imaginary parts as function of the probe scanning position.
These results are in good agreement with experimental data in the case of a deposit on a SG tube with a quatrefoil centred on the deposit presented above in Figure 10. Both and deposit signatures appear in the probe response (Figure 10) because of the distance between the edges and the deposit. Two magnetic elements are taking into account in this validation: the deposit, which is handling by the semi-analytical model and the, which is handling by the FEM model. The two signatures are well-combined by the hybrid model. Validation with the centred on an edge of the deposit For this application, we consider a centred on an edge of the magnetic deposit (Figure 10). The calculation of the is carried out by the FEM model and this result is taking into account in the semi-analytical calculation of the probe response to the deposit with. Figure 11 - Problem configuration: SG tube with a quatrefoil centred on an edge of a deposit Deposit Experiment Experiment (without SP) Simulation + Deposit Deposit Figure 12 - Simulated vs. measured signals for deposit centred on an edge of the at 100 khz: (blue) experimental signal with, (black) simulated signal with and (red) experimental signal without. The above plots give the signals on the complex plane (left side) and their real and imaginary parts as function of the probe scanning position.
These results are in good agreement with experimental data in the case of deposit on a SG tube with a quatrefoil centred on an edge of the deposit presented above in Figures 11 and 12. Even more than in the last validation ( centred on the deposit), this application show that the hybrid method is not a simple addition of signatures but a well-combination of surrounding effect on the probe and degradation interaction. CONCLUSION The hybrid FEM-VIM approach used for the simulation of eddy-current inspection of tubes near support plates with cylindrical openings presented