Numerical simulations in the development of the French radioactive waste vitrification processes using induction furnace

International audienceFor many years, the CEA (Commissariat à l’Énergie Atomique et aux Énergies Alternatives) Marcoule France has developed various processes dedicated to radioactive waste confinement, especially vitrification processes for HLLW. For 15 years now, the numerical simulation has become an important tool for research and developement projects held in the CEA-AREVA Joint Vitrification Laboratory (LCV). Induction heating, fluid mechanics and thermal simulations take part of all new R&D projects. The apports of such simulations are, first, the enhancement of the working knowledge of existing process. Those data are very useful to define optimisation choices, for example upgrades made on the hot metallic melter used since the 90s at LaHague facility. Second, the simulations are, of course, also used at the conception stage of new processes as a tool allowing wide ranges parametric tests. This has been extensively used in the design of the cold crucible inductive melter (CCIM) commissioned in 2010 at La Hague plant. Finally, it is a powerful and relatively cheap tool for prospective studies for processes of the future. Whatever the purpose, the potential benefits are gains on the reliability, the output capacity and the life time

A priori convergence estimates for a rough Poisson-Dirichlet problem with natural vertical boundary conditions

Stents are medical devices designed to modify blood flow in aneurysm sacs, in order to prevent their rupture. Some of them can be considered as a locally periodic rough boundary. In order to approximate blood flow in arteries and vessels of the cardio-vascular system containing stents, we use multi-scale techniques to construct boundary layers and wall laws. Simplifying the flow we turn to consider a 2-dimensional Poisson problem that conserves essential features related to the rough boundary. Then, we investigate convergence of boundary layer approximations and the corresponding wall laws in the case of Neumann type boundary conditions at the inlet and outlet parts of the domain. The difficulty comes from the fact that correctors, for the boundary layers near the rough surface, may introduce error terms on the other portions of the boundary. In order to correct these spurious oscillations, we introduce a vertical boundary layer. Trough a careful study of its behavior, we prove rigorously decay estimates. We then construct complete boundary layers that respect the macroscopic boundary conditions. We also derive error estimates in terms of the roughness size epsilon either for the full boundary layer approximation and for the corresponding averaged wall law.Comment: Dedicated to Professor Giovanni Paolo Galdi 60' Birthda

2D and 3D reconstructions in acousto-electric tomography

We propose and test stable algorithms for the reconstruction of the internal conductivity of a biological object using acousto-electric measurements. Namely, the conventional impedance tomography scheme is supplemented by scanning the object with acoustic waves that slightly perturb the conductivity and cause the change in the electric potential measured on the boundary of the object. These perturbations of the potential are then used as the data for the reconstruction of the conductivity. The present method does not rely on "perfectly focused" acoustic beams. Instead, more realistic propagating spherical fronts are utilized, and then the measurements that would correspond to perfect focusing are synthesized. In other words, we use \emph{synthetic focusing}. Numerical experiments with simulated data show that our techniques produce high quality images, both in 2D and 3D, and that they remain accurate in the presence of high-level noise in the data. Local uniqueness and stability for the problem also hold

Mathematical analysis of plasmonic nanoparticles: the scalar case

Localized surface plasmons are charge density oscillations confined to metallic nanoparticles. Excitation of localized surface plasmons by an electromagnetic field at an incident wavelength where resonance occurs results in a strong light scattering and an enhancement of the local electromagnetic fields. This paper is devoted to the mathematical modeling of plasmonic nanoparticles. Its aim is threefold: (i) to mathematically define the notion of plasmonic resonance and to analyze the shift and broadening of the plasmon resonance with changes in size and shape of the nanoparticles; (ii) to study the scattering and absorption enhancements by plasmon resonant nanoparticles and express them in terms of the polarization tensor of the nanoparticle. Optimal bounds on the enhancement factors are also derived; (iii) to show, by analyzing the imaginary part of the Green function, that one can achieve super-resolution and super-focusing using plasmonic nanoparticles. For simplicity, the Helmholtz equation is used to model electromagnetic wave propagation

Gas bubbling modeling in vitrification processes

International audienceA direct induction process using the cold crucible technology has been developed by the French Alternative Energies and Atomic Energy Commission and AREVA-NC for 25 years. In this process, walls of the crucible are cooled by internal water circulation which protects them from the corrosion and allow higher temperature of the molten glass. Moreover, a mechanical stirrer and air bubbling system promote a good homogeneity of the melt. In results, the lifetime of the crucible as the incorporation rate of the nuclear waste is increased.The 3D numerical simulation of glass elaboration by induction in cold crucible needs a coupled approach of the different phenomena induction, thermal and hydrodynamic. Indeed, those three phenomena are strongly coupled because of the temperature dependence of the glass properties.This presentation describes how the air bubbling in the glass is modelled in our simulation and enlightens its important role in the homogenisation of the glass during its elaboration. Air bubbling in liquids as viscous as the glass (viscosity up to 10 Pa.s) is not common and specific models have to be built. Two different models are used. The first one is a semi-empirical based model and the second is a two phase model (VOF). In order to model air bubbling in the molten glass, specific experiments have been performed based on the principle of hydraulic similarity. They consist in replacing the glass by silicon oil of equivalent viscosity in a tank of the same size. Non-dimensional Reynolds number as Galilee numbers are well respected between the two configurations. Only the Morton number differs, but it reflects tension surface effect which has been proven to have a weak effect on the formation of air bubbles in a very viscous liquid. This experiment facility allows us to acquire data as bubbles size, bubbles velocity and their behaviour. These data are used to build specific correlations for the semi-empirical model and also to validate the two phase model.The importance of air bubbling is quantified in simulations of the cold crucible process in a case with thermal convection forces only compared with a case with the air bubbling.Thanks to this numerical simulation new capability, the internal design of the crucible can be optimized and the comprehension of glass elaboration can be improved

Enhanced Resolution in Structured Media

The aim of this paper is to prove that we can achieve a resolution enhancement in detecting a target inclusion if it is surrounded by an appropriate structured medium. The physical notions of resolution and focal spot are revisited. Indeed, the resolution enhancement is estimated in terms of the material parameters of the structured medium. Copyright by SIAM

Electrical impedance tomography by elastic deformation

This paper presents a new algorithm for conductivity imaging. Our idea is to extract more information about the conductivity distribution from data that have been enriched by coupling impedance electrical measurements to localized elastic perturbations. Using asymptotics of the fields in the presence of small volume inclusions, we relate the pointwise values of the energy density to the measured data through a nonlinear PDE. Our algorithm is based on this PDE and takes full advantage of the enriched data. We give numerical examples that illustrate the performance and the accuracy of our approach