Elastodynamic models for nuclear tanks

[sachaalidadi]

My internship occurred in the R&D team of Avnir Energy as part of the SINDYN project (SImulation NUmérique DYNamique). This project aims to develop a default monitoring method for nuclear tanks using time reversal technique. This technique is composed of two phases:

In the learning phase, a hit (e.g a hammer) is applied to the structure we want to watch. The hit is propagated as a wave throughout the structure until the accelerometers register the acceleration at their location as a signal. The figure below illustrates this phase.

In the focalization phase, the signals registered are inverted in time and emitted throughout the structure at the locations of the accelerometers, as explained in the following figure.

The waves emitted will converge to the origin of the hit and form a peak. If a default appears between the learning and focalization phases, the signal at the origin of the hit will be more diffuse.

This technique is impossible to perform on a nuclear tank because it implies hitting the tank containing high-temperature liquid inside. That's why we want to perform the learning phase on the digital twin of the tank. However, this simulation requires solving a PDE called elasticity equation. This equation requires a high computation time to obtain a precise solution in finite element method (FEM). The goal of my internship is to develop a fast and precise numerical method with the spectral element method.

Spectral element method

The spectral element method consists of using high-degree polynomials as basis functions. Thus, ensuring a better precision than the FEM and a better computation time with the Dubiner function basis.

Results

For the first case, I simulated a 2D plate with null displacement on the right boundary, and a wavelet was applied in the middle of the left side. The simulation can be watched here

I also launched a simulation on a 3D plate with free displacement everywhere. The plate is in steel, contains holes, and comes from a small model of a nuclear tank. The simulation can be watched here

Finally, I launched a simulation on a cylindrical plate with null displacement on the upper and lower boundary. The video of the simulation is available here