Numerical methods for wave propagation and applications UPMC, 31st August – 1st September 2017 Overview of domain decomposition strategies applied to the simulation of electromagnetic testing by the boundary element method Practical examples & focus on the local multi-trace formalism Edouard DEMALDENT, CEA LIST, DISC (Department of Imaging and Simulation for the Control) In collaboration with Marc BONNET, POems, and Xavier CLAEYS, LJLL
INTRODUCTION NON DESTRUCTIVE TESTING DEPARTMENT Design & Evaluation of non destructive testing (NDT) processes Both modelling and instrumentation skills 70% Ultrasonic, 15% X-ray, 15% Electromagnetic (Eddy Current Testing) 100 people including 20 PhD/post-doc, 30 working on software issues, 3 on simulation by FEM/BEM 200 CIVA licenses worldwide (NDT simulation platform) DESIGN & EVALUATION INSTRUMENTATION MODELLING & IMAGING & SIMULATION www.extende.com Numerical methods for wave propagation and applications | E. Demaldent | 2
INTRODUCTION CIVAMONT PROJECT Scientific collaboration around the NDT simulation platform CIVA New trends such as statistical tools & meta-models It still motivates the search for fast and accurate direct models Favorable location for collaborating on BEM Numerical methods for wave propagation and applications | E. Demaldent | 3
CONTEXT & MOTIVATION PRACTICAL EXAMPLES NOTATIONS & BIE FORMALISM EXTENSION OF THE LOCAL MULTI-TRACE BIE TO THE EDDY CURRENT REGIME X. Claeys, E. Demaldent ASYMPTOTIC EXPANSION OF THE SINGLE-TRACE BIE OF THE FIRST KIND (PMCHWT) M. Bonnet, E. Demaldent, A. Vigneron OPTIMISATION ATTEMPT OF THE EDDY CURRENT MULTI-TRACE BIE
CONTEXT & MOTIVATIONS EDDY CURRENT TESTING INPUT OUTPUT Eddy Current Testing Sinusoidal current Variation of impedance 𝐽 COMPUTE • Detection of perturbations (crack, distortion) ∆𝑎 Eddy currents • Input: Loop sinusoidal current in vacuum (coil) • Compute: Eddy currents in the conductive medium • Output: Variation of impedance through a Reciprocity Th ∆𝑎 = 1 http://www.victor-aviation.com/ 𝐽 2 𝑜 ∙ ℰ 𝑡 × ℋ + ℋ 𝑡 × ℰ d𝜏 Eddy Current Testing Γ Working at low frequency to penetrate the conductive medium • Conductivity 𝜏 = 1𝑓6 S/m 𝜀 = 1 𝜌𝑔𝜈𝜏 ≃ 1.6 mm skin depth • Frequency 𝑔 = 100 kHz (half space) 2 = 𝜕 2 𝜁 0 𝜈 0 ≃ 4 × 10 −6 𝜆 0 2 = 𝜆 0 2 − 𝑡𝜅𝜕𝜈𝜏 ≃ 4 × 10 −6 − 𝑡𝜅 8 × 10 +5 𝑡 = ∓1 𝜆 1 2 ∼ −𝑡𝚥 8 × 10 +5 , 2 ∼ 0. 𝜆 1 𝜆 0 EC approximation: Numerical methods for wave propagation and applications | E. Demaldent | 5
CONTEXT & MOTIVATIONS ECT OF STEAM GENERATOR TUBES Major application: Inspection of steam generators in pressurized water reactors http://allthingsnuclear.org Thousands of tubes checked every year • Diameter ≈ 20 mm • Thickness ≈ 1 mm • Conductivity ≈ 1 MS/m Frequency of the testing ≈ 100 kHz 6000 U-bend tubes (L tot = 140 km, S tot = 8000 m 2 ) Numerical methods for wave propagation and applications | E. Demaldent | 6
CONTEXT & MOTIVATIONS ECT OF STEAM GENERATOR TUBES Various kinds of flaws Looking for the variation of impedance • Phase • Shape • Amplitude Eddy Current Testing, GP Courseware Various kinds of sensors http://www.zetec.com/ Multi-element probe US rotating probe Axial probe French rotating probes Numerical methods for wave propagation and applications | E. Demaldent | 7
CONTEXT & MOTIVATIONS ECT OF STEAM GENERATOR TUBES Various kinds of distortions Anti-vibration bar Ovalization, thickness variation… (naïve) pilger Friction wear noise Tube supports Dent Inner wall Outer wall (radius variation) (radius variation) Meta-parameters to be fixed, simplified modelling to be evaluated Numerical methods for wave propagation and applications | E. Demaldent | 8
CONTEXT & MOTIVATIONS SIMULATION TOOLS CIVA-ECT : Fast solution on canonical geometries (stratified media, pipes…) CIVA-ECT CIVA-ECT Defect’s response Field computation (VIM + Reciprocity Theorem) (Modal solution) Various alternative solutions to handle 3D components … Boundary Elements • From a modified Maxwell integral form • That exploits suitable domain decompositions • With the use of high-order approximation tools Numerical methods for wave propagation and applications | E. Demaldent | 9
PRACTICAL EXAMPLES FERRITE CORES Iterative coupling between a ferrite core (BEM) and a canonical conductive workpiece (modal) Real part of the impedance variation with a notch +Point-like probe Iterations of the coupling (Rototest probe) CIVA (+Point probe) Numerical methods for wave propagation and applications | E. Demaldent | 10
PRACTICAL EXAMPLES FERRITE CORES Iterative coupling between a ferrite core (BEM) and a canonical conductive workpiece (modal) CIVA 2D grid with respect to the ferrite’s border (no numerical parameter) Numerical methods for wave propagation and applications | E. Demaldent | 11
PRACTICAL EXAMPLES FERRITE CORES Iterative coupling between a ferrite core (BEM) and a canonical conductive workpiece (modal) CIVA Extraction & smoothing of the boundary (no numerical parameter) Numerical methods for wave propagation and applications | E. Demaldent | 12
PRACTICAL EXAMPLES FERRITE CORES Iterative coupling between a ferrite core (BEM) and a canonical conductive workpiece (modal) CIVA Axisymmetric extrusion (no numerical parameter) Numerical methods for wave propagation and applications | E. Demaldent | 13
PRACTICAL EXAMPLES FERRITE CORES Iterative coupling between a ferrite core (BEM) and a canonical conductive workpiece (modal) Here the coupling between the ferrite and the defect is simplified (ok with low-signal perturbations) Few min for pre-computation time (LU BEM) + few sec (iterative process & modal response) Hyp. Stable relative position of the probe (constant signal vs scan) 0 = 𝑍 𝑄 − 𝑄𝐺 𝐺𝐺 −1 𝑍 𝑄𝑄 𝑌 𝑄 𝑌 𝑄 = 𝑍 𝑌 𝐺 𝒦 𝑡 𝐺𝐺 𝐺𝑄 𝐺 𝐺 𝑄 𝑍 𝑗+1 − 𝑌 𝑄 = 𝑄𝐺 𝐺𝐺 −1 𝐺𝑄 𝑗 − 𝑌 𝑄 𝑄𝐺 𝑄𝑄 𝐺 𝑗 𝑗−1 𝑄𝑄 𝑌 𝑄 𝑌 𝑄 𝑄 Modal BEM 𝐺 𝑌 𝐺 = 𝑍 𝑄𝐺 𝐺𝐺 −1 ( 𝐺 𝐺𝐺 𝑄 Hyp. 𝑄 𝐺 𝑌 𝑄 − 𝐺𝑄 𝑌 𝑄 ) ≈ 0 𝑄 𝑍 𝑄𝐺 𝑄 𝑌 𝑄 𝒦 𝑡 𝑄 𝑄 𝐺 𝑄 𝑄 𝑄 − 𝑌 𝑄 = 𝑍 𝑄𝐺 𝑌 𝐺 VIM Simplified formalism Numerical methods for wave propagation and applications | E. Demaldent | 14
PRACTICAL EXAMPLES U-BEND TUBES Raising order reduces digital noise It allows movement of the probe (shift, tilt) Truncation of the workpiece by scanning subzones Meshing of a straight tube curved quadrilaterals, centered probe Distortion on the U-bend tube w.r.t. the targeted axial position of the probe A single calculation for all shift/tilt of the probe Numerical methods for wave propagation and applications | E. Demaldent | 15
PRACTICAL EXAMPLES U-BEND TUBES Simulation tools to help determine the path of the probe Envelope of the mechanically possible positions of the probe Computation of the EC signal on a representative basis Fast comparison of several parametric trajectories Hyp. Smooth ∆𝑦 ⟹ Smooth ∆𝑎 Numerical methods for wave propagation and applications | E. Demaldent | 16
PRACTICAL EXAMPLES U-BEND TUBES The simulation of a defect’s response for the chosen trajectory requires the full scan of the defect’s zone (increasing number of unknowns) Numerical methods for wave propagation and applications | E. Demaldent | 17
PRACTICAL EXAMPLES MAGNETIC FLUX LEAKAGE Magnetic testing of pipes Simplified model: linear regime, slow motion (no induced current) High contrast of scales: L tot ~ 1 x 1 m 2 , L def ~ 10 x 0.1 mm 2 Domain decomposition to isolate the defect Comparison with experimental data (Vallourec Research Center France) Solution without defect CIVA (no numerical parameter) Numerical methods for wave propagation and applications | E. Demaldent | 18
PRACTICAL EXAMPLES MAGNETIC FLUX LEAKAGE Magnetic testing of pipes Simplified model: linear regime, slow motion (no induced current) High contrast of scales: L tot ~ 1 x 1 m 2 , L def ~ 10 x 0.1 mm 2 Domain decomposition to isolate the defect Comparison with experimental data (Vallourec Research Center France) Extraction of the solution outside the defect’s area CIVA (no numerical parameter) Numerical methods for wave propagation and applications | E. Demaldent | 19
PRACTICAL EXAMPLES MAGNETIC FLUX LEAKAGE Magnetic testing of pipes Simplified model: linear regime, slow motion (no induced current) High contrast of scales: L tot ~ 1 x 1 m 2 , L def ~ 10 x 0.1 mm 2 Domain decomposition to isolate the defect Comparison with experimental data (Vallourec Research Center France) Solution in the defect’s area with the equivalent source CIVA (no numerical parameter) Numerical methods for wave propagation and applications | E. Demaldent | 20
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