<figure><img src="image_1.png" /></figure>

IRSN
INSTITUT DE RADIOProtection
ET DE SûRETE NuCLÉAIRE

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# Modelling the Influence of the Tube Support Plate on the Eddy Current Testing of the Steam Generator: Numerical Tools and Experimental Validation

[Audrey Vigneron]¹, Edouard Demaldent¹, Thierry Sollier², Jean-Marc Decitre²

¹ Université Paris-Saclay, CEA LIST

² IRSN
# Modelling the Influence of the Tube Support Plate on the Eddy Current Testing of the Steam Generator: Numerical Tools

Audrey Vigneron, Edouard Demaldent, Jean-Marc Decitre, Thierry Sollier

► To cite this version:

Audrey Vigneron, Edouard Demaldent, Jean-Marc Decitre, Thierry Sollier. Modelling the Influence of the Tube Support Plate on the Eddy Current Testing of the Steam Generator: Numerical Tools. NDE in Nuclear 2023, Jun 2023, Sheffield, United Kingdom. 10.58286/28669. cea-04487893

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<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Context and motivation

☐ Tube support plates (TSP) are positioned at regular intervals to
secured the tubes in place

- ☐ Anti Vibration Bars (AVBs) limit vibratory phenomena in the top of tubular bundle (U-Bend)

- ☐ Steam generator (SG) tubes are regularly inspected as part of eddy current non destructive inspection

> To assess the tube integrity and prevent tube rupture

☐ The aim of the study between CEA LIST and IRSN is to validate simulation tools for the eddy current inspection of SG tubes, enabling the implementation of parametric studies

<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /></figure>
# Modelling the Influence of the Tube Support Plate on the Eddy Current Testing of the Steam Generator: Numerical Tools

Audrey VIGNERON<fnref n="1" />, Edouard DEMALDENT<fnref n="1" />, Jean-Marc DECITRE<fnref n="2" />, Thierry SOLLIER<fnref n="2" />

## Abstract

Eddy current testing (ECT) of Steam Generator (SG) tubes is part of the maintenance program of Nuclear Power Plants. Tube Support Plates (TSP) are usually only considered as extraneous signals for tube inspection. However, for long-term operation of SGs, there is a safety concern related to the build-up of deposits in the TSPs flow holes. The clogging-up of the TSPs flow holes affect the safe thermal-hydraulic operation of SGs. The deposits come from the feedwater train and are mostly iron oxides (magnetite) with a weak electrical conductivity and magnetic permeability.

The ability of ECT probes to detect and characterize TSPs deposits is therefore of great interest. The most common and industrial ECT technique, the bobbin coil, averages the surrounding electromagnetic field over 360°, whereas the geometry of tri-foiled and quadri-foiled TSPs, and thus of clogging, is rather complex and non-axisymmetric, hence motivating the evaluation of the performance of conventional ECT rotating probes used for SGs tubes inspection. Although simulation is a powerful tool to support such a study, it requires dedicated models to be made available to NDT experts, and CEA develops ECT physical models in CIVA for this purpose. In addition to standard fast CIVA modules based on 3D semi-analytical or 2D numerical calculations restricted to canonical or axisymmetric parts, respectively, CEA develops a module dedicated to the simulation of SG tube inspection based on a 3D numerical simulation. This module allows tube deformation such as ovalization, bending or tube expansion. It also allows the addition of external objects such as anti-vibration bars, different geometries of tube support plates and now their clogging by deposits. This model is used to study various influent parameters and to perform benchmarks in the framework of a scientific collaboration between the CEA and the IRSN, related for example to the inspection of the U-bend tubes or of a friction wear under the anti-vibration bars. Here, the specificity of the TSPs and their clogging justifies further investigations between CEA and IRSN to qualify the simulation model before evaluating the influence of material and geometry properties of the deposit as well as the performance of the inspection techniques. We present the main characteristics of the simulation module in CIVA.

**Keywords:** Eddy current testing, modelling, steam generator tubes, nuclear, clogging, tube support plate

## 1. Introduction

Steam generators (SGs) play a crucial role in French PWR (Pressurised Water Reactor) nuclear power plants. These plants typically have three or four SGs housed within the reactor building, consisting of several thousand tubes shaped like an inverted 'U' and measuring around twenty meters in length. The combined surface area of these steam generator tubes is equivalent to the size of a soccer field and carries out the exchange of heat between the primary circuit (inside the tubes) and the secondary circuit (outside the tubes). Due to their key role in ensuring nuclear safety, the SG tubes undergo periodic non-destructive examinations to detect any indications or defects.

Eddy current testing (ECT) techniques are employed for the in-service inspection of SG tubes. New indications produced by active degradation mechanisms can be detected and the evolution of previously identified flaws can be monitored. If the indications identified during an inspection are characterized as flaws having critical dimensions with respect to structural integrity analysis, the affected tube is plugged to maintain the integrity of the barrier between the primary and secondary circuits. If the tubes plugging ratio is too high for a safe operation, steam generators can be replaced.

<figure><img src="image_2.png" /></figure>

<footnote n="1">¹ Université Paris-Saclay, CEA LIST, France; E-mail: audrey.vigneron@cea.fr,</footnote>

<footnote n="2">² IRSN, France; E-mail: jean-marc.decitre@irsn.fr</footnote>
# Context and motivation

<figure><img src="image_5.png" /></figure>

Semi-analytical approaches (modal methods)

<figure><img src="image_6.png" /></figure>

Very fast and accurate

<figure><img src="image_7.png" /></figure>

Limited to canonical geometries

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>

2D solver based on Finite Integration Technique (FIT)

<figure><img src="image_11.png" /></figure>

2D numerical approach

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

3D solver based on Boundary elements

<figure><img src="image_14.png" /></figure>

Pieces and sensors with complex geometries

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /></figure>
The ongoing research conducted by CEA and IRSN aims to enhance the detection and characterization of defects through ECT. In this context, simulation tools are being utilized to assess the effectiveness of existing and upcoming ECNDT techniques.

Tube support plates (TSP) are designed to hold the tubes along their height and to maintain a sufficient distance between the tubes in order to avoid tube-to-tube fretting. TSP provide also support for different mechanical loading during normal and accidental conditions such as seismic loading. TSPs are broached to allow fluids to flow outside the tubes. The foliage (or flow hole) may be subject to a build-up of corrosion products or residues of elements present in the feedwater train. This clogging phenomenon reduces the flow section of water inside the SGs with a detrimental effect on the safe operation of this equipment [1]-[5]. A chemical cleaning of SGs might be required to restore sufficient safety margins for operation.

## 2. Modelling tools

A specific module within the CIVA software has been developed to simulate the ECT inspection of SG tubes. This module relies on a 3D solver based on the boundary element method, as detailed in [6] and [7]. Designed to accommodate non-standard geometries, the SG tube inspection module is capable of handling various external objects such as the AVB and support plates, as depicted in Figure 1.

<figure><img src="image_3.png" /><figcaption>Figure 1: Steam Generator Tube Inspection module in CIVA software.</figcaption></figure>

The SG tubes inspection module is specifically designed for the inspection of steam generator tubes and includes a list of industrial probes (CIVA2023 restricted to the axial probe). These probes have predefined and simplified parameters, encompassing the various components of the probe and optimized trajectory control through the definition of a probe body. Additionally, small variations between elements have been incorporated to account for manufacturing irregularities that may occur.

In the module, four types of tube support plates can be defined: two types of quadrifoiled plates, one type of trifoiled plates, and cylindrical plates, as shown in Figure 2. The module takes input data for the different dimensions and material parameters (electrical conductivity and magnetic permeability). For trifoiled plates and type B quadrifoiled plates, it is possible to incorporate
# CIVA ET module « Steam Generator Inspection »

- ☐ Development and validation of a steam generator tube

CIVA
ND≡I

module dedicated to the complete eddy current inspection of

<figure><img src="image_17.png" /></figure>
clogging with various geometries and defined value of magnetic permeability and electrical conductivity.

This module has undergone experimental validation in [8], using experimental configurations that include an axial probe, a tube with straight wear with flat bottom, and anti-vibration bars. The calculation kernels remain the same for all external objects, whether they are anti-vibration bars or tube support plates.

<figure><img src="image_4.png" /><figcaption>Figure 2. Defining dimensional parameters for tube support plates in the steam generator tube inspection module.</figcaption></figure>

## 2. Simulation results

In this section, we present the simulation results obtained using the tools developed in CIVA. All results are presented without calibration for a frequency of 280 kHz. The probe is composed of two identical bobbin coils spaced 1 mm apart. The coils have an internal radius of 14 mm,
<figure><img src="image_18.png" /></figure>

* Tube geometry: U-bend, expanded tube, section distorsion, pilging, distorsion, deposit

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /></figure>

* External objects: antivibration bars, trifoiled support plate, quadrifoiled support plate, cylindrical plate,

* Clogging

* Wear defect due to the external objects

<figure><img src="image_23.png" /></figure>

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<figure><img src="image_28.png" /></figure>
an external radius of 14.8 mm, a height of 2 mm, and consist of 40 turns. The specimen is a ¾" outer diameter tube with a thickness of 1.09 mm and an electrical conductivity of 0.87 MS/m. The tube support plate is the type A of quadrifoiled plate with the dimensions mentioned in Figure 2 and an electrical conductivity of permeability of 1.75 MS/m and a relative magnetic permeability of 50.

The developed modeling tools allow for conducting parametric studies to assess the influence of various parameters. One such application is the investigation of the impact of tube support plate clogging on the eddy current (EC) signal. In Figure 3, the initial simulated configuration is presented, aiming to observe the effect of the axial position of the clogging on the EC signal. The clogging fills the holes of the plate with a height of 5 mm and a relative magnetic permeability of 2, placed at different axial positions. Figure 4 displays the EC signal corresponding to the different axial positions of the clogging. As anticipated, the signal associated with the plate alone is anti-symmetrical, while the signal related to the presence of the clogging demonstrates similar amplitudes across the three positions.

<figure><img src="image_5.png" /><figcaption>Figure 3. Horizontal section of the configuration, top left, axial displacement of the probe, top right. The different axial positions of the clogging are represented at the bottom.</figcaption></figure>
<figure><img src="image_29.png" /></figure>

* Defect: Calibration defects, hole, straight wear, bump, groove, progressive groove, notch

<figure><img src="image_30.png" /></figure>

<figure><img src="image_31.png" /></figure>

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<figure><img src="image_33.png" /></figure>

* Probes: bobbin coils, rotating probes, +point, multi-element

Version under development

<figure><img src="image_34.png" /></figure>

<figure><img src="image_35.png" /></figure>

<figure><img src="image_36.png" /></figure>
<figure><img src="image_6.png" /><figcaption>Figure 4. EC signal for the different axial positions of the clogging.</figcaption></figure>

Figure 5 shows the configuration used to observe the effect of the magnetic permeability value of the clogging for a full clogging with a height of 5 mm. Figure 6 shows the EC signal for a relative magnetic permeability value of 2 (red) and 6 (black), observing that the amplitude of the EC signal increases with permeability.

<figure><img src="image_7.png" /><figcaption>Figure 5. Horizontal and axial sections of the configuration used to assess the effect of magnetic permeability.</figcaption></figure>
# Experimental validations: configuration

* Probe: bobbin coils

* Device: Impedance analyzer

* Frequency: 280 kHz (Differential mode)

* Calibration defect: 4 through wall Φ1 holes (Amplitude = 1700 mV, Phase = -35°)

* Samples of ¾" OD SG tube made in alloy 690 with calibration defects and straight wears with rectangular bottom flat

* AVB in alloy 600

<figure><img src="image_37.png" /></figure>

<figure><img src="image_38.png" /></figure>
<figure><img src="image_8.png" /><figcaption>Figure 6. EC signal for different magnetic permeability values, $\mu_r$ = 2 in red and $\mu_r$ = 6 in black.</figcaption></figure>

Figure 7 shows the configuration simulated to observe the effect of the clogging shape on the EC signal. The clogging is placed at the edge of the plate with a height of 5 mm and a relative magnetic permeability of 2. A hole in the clogging is placed at different positions. Figure 8 shows the EC signal for the different positions of the hole in the clogging. It can be seen that the signal obtained for the hole placed in the center and against the edge of the plate is very similar, which is due to the fact that it is too far from the probe to be taken into account.

<figure><img src="image_9.png" /><figcaption>Figure 7. Axial displacement of the probe, top left, axial position of the clogging, top right. Different clogging geometries are shown below.</figcaption></figure>
# Experimental validation: Calibration defect and straight wear

<table><thead><tr><th></th><th>Amplitude<br>Difference (%)</th><th>Phase<br>Difference (°)</th></tr></thead><tbody><tr><td>Internal Groove<br>10%</td><td>1,31</td><td>0,07</td></tr><tr><td>External Groove<br>40%</td><td>3,45</td><td>4,57</td></tr><tr><td>Large External<br>Groove 30%</td><td>0,74</td><td>4,33</td></tr><tr><td>4Φ1</td><td>0</td><td>0</td></tr><tr><td>Straight Wear<br>20%</td><td>4,80</td><td>3,91</td></tr><tr><td>Straight Wear<br>40%</td><td>4,54</td><td>4,77</td></tr><tr><td>Straight Wear<br>60%</td><td>3,69</td><td>4,33</td></tr></tbody></table>

<figure><img src="image_39.png" /></figure>

<figure><img src="image_40.png" /></figure>
<figure><img src="image_10.png" /><figcaption>Figure 8. EC signal for different clogging shapes.</figcaption></figure>

Finally, it may be important to estimate the effect of the presence of a plate with and without clogging on the EC signal of a defect, in order to assess the detectability of defects in this zone. The configuration presented in Figure 9 shows in black an internal groove 10% deep and 1 mm opening, in red the presence of a quadrifoiled plate and in blue a full clogging placed at the edge of the plate. Figure 10 presents the EC signal obtained for these three configurations, showing that the fault signal is minimized in the presence of the plate and even more so in the presence of the clogging. It is therefore important to take into account elements external to the tube when assessing fault detectability.

<figure><img src="image_11.png" /><figcaption>Figure 9. Internal groove, on left, internal groove and tube support plate, on center, internal groove with tube support plate and clogging, on right.</figcaption></figure>
Experimental validation: 20 % straight wear with AVB

<figure><img src="image_41.png" /></figure>

<figure><img src="image_42.png" /></figure>

<figure><img src="image_43.png" /><figcaption>AVB at 90°</figcaption></figure>

<table><tr><td></td><td>-0.2 mm</td><td>0.0 mm</td><td>0.2 mm</td></tr><tr><td>Amplitude (mV)</td><td>245</td><td>216</td><td>205</td></tr><tr><td>Phase (°)</td><td>-5</td><td>-19</td><td>-35</td></tr></table>

<figure><img src="image_44.png" /></figure>
<figure><img src="image_12.png" /><figcaption>Figure 10. EC signal for an internal groove with and without tube support plate and clogging.</figcaption></figure>

## 4. Conclusion

The development of modelling tools for eddy current testing of steam generator tubes in the presence of tube support plate with clogging has been presented in this document. It is possible to perform parametric studies in order to evaluate the performances of probes in various situations: with or without magnetite deposit at TSPs, with or without flaws and to mix these situations in order to evaluate the ability to detect flaws or magnetite or a combination of both. These tools are available in the commercial software CIVA and have been experimentally validated.

The modelling tools provided by CEA enable IRSN to conduct parametric studies for evaluating the detection and characterization performance of defects in steam generator tubes.

## References

[1] S. Girard, "Diagnostic du colmatage des générateurs de vapeur à l'aide de modèles physiques et statistiques," PhD Thesis, 2012.

[2] G. Yang et al., "A review on clogging of recirculating steam generators in Pressurized-Water Reactors", Progress in Nuclear Energy, vol. 97, 2017.

[3] H. Bodineau and T. Sollier, "Tube support plate clogging up of French PWR steam generators," Eurosafe, 2008.

[4] N. Le Lostec et al., "Tube support plate clogging and secondary side deposit: performance evaluation using simulation and site results", JRC-NDE, 2013.

[5] T. Prusek et al., "Deposit models for tube support plate flow blockage in Steam Generators," Nuclear Engineering and Design, vol. 262, 2013.

[6] M. Bonnet and E. Demaldent, "The eddy current model as a low-frequency, high-conductivity asymptotic form of the Maxwell transmission problem," in Computers & Mathematics with Applications, vol. 77, n°18, 2019.
# Experimental validations: work in progress

□ The 3D solver has been experimentally validated for

➤ Calibration defects (holes and grooves), straight wears

➤ Bobbin coils

➤ Anti-vibration bars

→ Configurations available in commercial version are experimentally validated, the calculation kernels are the same for the different external objects (AVB, TSP)

<figure><img src="image_45.png" /></figure>

CIVA
ND= 2023

□ In progress

➤ Tube support plate (cylindrical and quadrifoiled)

➤ Clogging

➤ Rotating probes

*All the simulations presented after are not calibrated and balanced*

<figure><img src="image_46.png" /></figure>
[7] M. Bonnet and E. Demaldent, “Eddy-current asymptotics of the Maxwell PMCHWT formulation for multiple bodies and conductivity levels,” in *Computers & Mathematics with Applications*, vol. 141, 2023.

[8] A. Vigneron, et al., “Modelling of wear defects under Anti Vibration Bars in U-bend for the Eddy Current inspection of Steam Generator tube,” in *Journées COFREND*, Marseille, France, 2023.
# Simulation of quadrifoiled tube support plate

* EC signal at 280 kHz in differential mode for bobbin coils and quadrifoiled plate ($\sigma=1.75$ MS/m, $\mu_r = 50$)

<figure><img src="image_47.png" /><figcaption>CIVA panel</figcaption></figure>

<figure><img src="image_48.png" /></figure>

<figure><img src="image_49.png" /></figure>

CIVA
NDE 2023

<figure><img src="image_50.png" /></figure>

IRSN
# Simulation of trifoiled tube support plate

* EC signal at 280 kHz in differential mode for bobbin coils and trifoiled plate (σ=1.75 MS/m, μ<sub>r</sub> = 50)

<figure><img src="image_51.png" /><figcaption>CIVA panel</figcaption></figure>

<figure><img src="image_52.png" /></figure>

CIVA
NDE 2023
# Simulation of trifoiled TSP with clogging

* EC signal at 280 kHz in differential mode for bobbin coils and trifoiled plate (σ=1.75 MS/m, μ<sub>r</sub> = 50) with clogging (μ<sub>r</sub> = 2)

<figure><img src="image_53.png" /></figure>

<figure><img src="image_54.png" /></figure>

CIVA panel

<figure><img src="image_55.png" /></figure>

CIVA
NDE 2023

<figure><img src="image_56.png" /></figure>

IRSN
# Simulation of quadrifoiled tube support plate

* EC signal at 280 kHz in differential mode for bobbin coils and quadrifoiled plate ($\sigma$=1.75 MS/m, $\mu_r$ = 50)

<figure><img src="image_57.png" /><figcaption>CIVA panel</figcaption></figure>

<figure><img src="image_58.png" /></figure>

<figure><img src="image_59.png" /></figure>

CIVA
ND= 2023

<figure><img src="image_60.png" /></figure>

IRSN
# Simulation of quadrifoiled TSP with clogging

* EC signal at 280 kHz in differential mode for bobbin coils and quadrifoiled plate ($\sigma=1.75$ MS/m, $\mu_r = 50$) with clogging ($\mu_r = 2$)

<figure><img src="image_61.png" /><figcaption>CIVA panel</figcaption></figure>

<figure><img src="image_62.png" /></figure>
# Quadrifoiled TSP with clogging: position effect

* EC signal at 280 kHz in differential mode for bobbin coils and quadrifoiled plate (σ=1.75 MS/m, μ<sub>r</sub> = 50) with clogging (μ<sub>r</sub> = 2) at different positions

<figure><img src="image_63.png" /><figcaption>Probe
displacement</figcaption></figure>

<figure><img src="image_64.png" /><figcaption>Clogging
geometry</figcaption></figure>

<figure><img src="image_65.png" /><figcaption>Variation of the clogging position</figcaption></figure>

<figure><img src="image_66.png" /></figure>
# Quadrifoiled TSP with clogging: position effect

* EC signal at 280 kHz in differential mode for bobbin coils and quadrifoiled plate (σ=1.75 MS/m, μ<sub>r</sub> = 50) with clogging with different magnetic permeability

<figure><img src="image_67.png" /><figcaption>Probe
displacement</figcaption></figure>

<figure><img src="image_68.png" /><figcaption>Clogging
geometry</figcaption></figure>

<figure><img src="image_69.png" /><figcaption>Clogging
position</figcaption></figure>

<figure><img src="image_70.png" /></figure>
# Quadrifoiled TSP with clogging: filling effect

* EC signal at 280 kHz in differential mode for bobbin coils and quadrifoiled plate (σ=1.75 MS/m, μ<sub>r</sub> = 50) with clogging (μ<sub>r</sub> = 2) with different filling

<figure><img src="image_71.png" /><figcaption>Probe
displacement</figcaption></figure>

<figure><img src="image_72.png" /></figure>

<figure><img src="image_73.png" /></figure>

<figure><img src="image_74.png" /><figcaption>Clogging
position</figcaption></figure>

<figure><img src="image_75.png" /></figure>

<figure><img src="image_76.png" /><figcaption>Variation of the filling</figcaption></figure>

<figure><img src="image_77.png" /></figure>

<figure><img src="image_78.png" /></figure>

<figure><img src="image_79.png" /></figure>

<figure><img src="image_80.png" /></figure>
# Quadrifoiled TSP with clogging: filling effect

* EC signal at 280 kHz in differential mode for +point and quadrifoiled plate (σ=1.75 MS/m, μ<sub>r</sub> = 50) with clogging (μ<sub>r</sub> = 2) with different filling

<figure><img src="image_81.png" /><figcaption>Probe
displacement
(45°)</figcaption></figure>

<figure><img src="image_82.png" /><figcaption>Variation of the filling</figcaption></figure>

<figure><img src="image_83.png" /><figcaption>Probe position</figcaption></figure>

<figure><img src="image_84.png" /><figcaption>Clogging
position</figcaption></figure>

<figure><img src="image_85.png" /><figcaption>Version under development</figcaption></figure>

<figure><img src="image_86.png" /></figure>
# Quadrifoiled TSP with clogging: filling effect

* EC signal at 280 kHz in differential mode for +point and quadrifoiled plate ($\sigma=1.75$ MS/m, $\mu_r = 50$) with clogging ($\mu_r = 2$) and internal groove (opening 1mm, depth 10%)

<figure><img src="image_87.png" /><figcaption>Internal groove</figcaption></figure>

<figure><img src="image_88.png" /><figcaption>Internal groove+TSP</figcaption></figure>

<figure><img src="image_89.png" /><figcaption>Internal groove+TSP+clogging</figcaption></figure>

<figure><img src="image_90.png" /></figure>

<figure><img src="image_91.png" /></figure>

<figure><img src="image_92.png" /></figure>
# Conclusions

□ Collaborative study between CEA LIST and IRSN for the simulation of eddy current inspection of steam generator tubes

□ Module dedicated to the inspection of SG tubes in CIVA

□ Experimental validation for bobbin coils

□ Modelling of TSP with different geometries and clogging

□ Study in progress on the experimental validation of clogging of tube support plates for various probes

□ Numerical tools for sensitivity study of the parameters influencing the EC signal

□ Clogging geometry and position

□ Presence of clogging

→ Civa users can quickly assess the sensitivity of their inspection setup settings

<figure><img src="image_93.png" /></figure>

Multi-element probe numerical settings in development

<figure><img src="image_94.png" /></figure>
<figure><img src="image_95.png" /></figure>

Thank you for your attention.

Audrey VIGNERON
audrey.vigneron@cea.fr