Multi-Harnack smoothings of real plane branches

We introduce a new method for the construction of smoothings of a real plane branch $(C, 0)$ by using Viro Patchworking method. Since real plane branches are Newton degenerated in general, we cannot apply Viro Patchworking method directly. Instead we apply the Patchworking method for certain Newton non degenerate curve singularities with several branches. These singularities appear as a result of iterating deformations of the strict transforms of the branch at certain infinitely near points of the toric embedded resolution of singularities of $(C,0)$. We characterize the $M$-smoothings obtained by this method by the local data. In particular, we analyze the class of multi-Harnack smoothings, those smoothings arising in a sequence $M$-smoothings of the strict transforms of (C,0) which are in maximal position with respect to the coordinate lines. We prove that there is a unique the topological type of multi-Harnack smoothings, which is determined by the complex equisingularity type of the branch. This result is a local version of a recent Theorem of Mikhalkin

THEORETICAL PLASMA CHARACTERIZATION DURING CURRENT PULSE

International audienceThe economic/ecological contexts and the CO2 regulation lead the automotive industry to improve the spark ignited engines. A way of improvement is the admission of a lean mixture or of a diluted mixture by recirculation of exhaust gases in the combustion chamber. The main difficulty in these conditions is to start the combustion. To overcome this problem, ignition systems are studied and more particularly the spark one. This discharge leads to the apparition of plasma and the understanding of the energy transfer mechanisms between this plasma and the reactive mixture is essential. This work is focus on the modeling of a spark during its electrical arc phase in order to predict the hydrodynamic behavior of the arc and the shock wave propagation. The difficulty on the choice of initial conditions for the model is highlighted. A two dimensional model based on ANSYS Fluent software is developed. This model allows us to show the role of each initial parameter as well as their impacts on the plasma flow. One calculation case presents the shock wave propagation and the plasma kernel. Finally a parametric study is presented. Without a complete model describing all the phases of the spark the choice of initial conditions is essential, nevertheless experimental measurements are difficult to perform. The interdependence of the initial parameters is demonstrated and care is needed in case of incomplete set of initial conditions which should be completed

EXPERIMENTAL STUDY OF A PLASMA BUBBLE CREATED BY A WIRE EXPLOSION IN WATER

International audienceAn experimental setup is developed to study the bubble dynamic created by a wire explosion in a liquid. This arrangement can be encountered in many configurations and processes and differs by the level and frequency of the applied energy and of the liquid nature. In our study the wire explosion is due to a current intensity around one thousand amps during 10ms in a water medium and a distance between the electrodes of few millimeters. By fast imaging the bubble radius is determined versus time depending on the applied energy. The results indicate that the maximum radius of the bubble versus the applied energy leads to a linear variation of 2.3 cm/kJ roughly. A modification of the Rayleigh model is proposed to consider not an empty bubble but pressure variation inside. The experimental results coupled with the Rayleigh model allow determining the maximum bubble radius, the bubble dynamic and to evaluate its mean temperature. For electrical arc energy of 846 J and an inter-electrode distance of 1 mm, the bubble presents an expansion and a collapse. A maximal radius is reached near 4 cm before 1.5 ms the end of the half current period, due to the leak of energy to feed the bubble

Heat Transfer in the Solid Cathode of a Hollow Cathode Plasma Torch

After recalling the working principle of hollow cathode plasma torches, we evaluate the heat flux profile on the cathodic arc root. This evaluation takes into account the physics of the cathode sheath. Particular attention is devoted to electron emission from the cold copper cathode. This heat flux profile is then used as a moving boundary condition to obtain the temperature field in the solid cathode with a heat conduction study, with the aim of discussing the problem of its erosion

The Virial Effect—Applications for SF6 and CH4 Thermal Plasmas

International audienceA tool based on the mass action law was developed to calculate plasma compositions and thermodynamic properties for pure gases and mixtures, assuming a local thermodynamic equilibrium for pressures of up to 300 bar. The collection of the data that was necessary for tool calculation was automated by another tool that was written using Python, and the formats for the model were adapted directly from the NIST and JANAF websites. In order to calculate the plasma compositions for high pressures, virial correction was introduced. The influences of the parameters that were chosen to calculate the Lennard-Jones (12-6) potential were studied. The results at high pressure show the importance of virial correction for low temperatures and the dependence of the dataset used. Experimental data are necessary to determine a good dataset, and to obtain interaction potential. However, the data available in the literature were not always provided, so they are not well-adapted to a large pressure range. Due to this lack, the formulation provided by L. I. Stiel and G. Thodos (Journal of Chemical and Engineering Data, vol. 7, 1962, p. 234-236) is a good alternative when the considered pressure is not close to the critical point. The results may depend strongly on the system studied: examples using SF 6 and CH 4 plasma compositions are given at high pressure

A Pressure Based Compressible Solver for Electric Arc-plasma Simulation

The electric arc discharge in a liquid medium is used in several applications such as the sterilization of the liquid by UV radiation, the fracturing of rocks by shock wave, the circuit breakers in oil bath or the forming of mechanical parts. Thus, describing the physics of the arc in a liquid and in particular its interaction with a liquid interface is an important issue to better characterize this type of configuration. However, such a challenging task requires to couple high-fidelity solver for compressible two-phase flows with liquid phase change and a plasma solver to describe the plasma and its interaction with the bubble. To study this type of medium, we use a compressible formulation of the fluid equations. For this purpose, a pressure based solver has been developed for the computation of the energy conservation equation. Moreover, our numerical model uses the immersed boundary method to simulate the solid electrodes. The numerical model is briefly described in this paper and the first results of the electric arc discharge in steam water are presented. To our knowledge this pressure based model has never been used to describe plasmas and electric arc discharge

Interpretation of Stark broadening measurements on a spatially integrated plasma spectral line

In thermal plasma spectroscopy, Stark broadening measurement of hydrogen spectral lines is considered to be a good and reliable measurement for electron density. Unlike intensity based measurements, Stark broadening measurements can pose a problem of interpretation when the light collected is the result of a spatial integration. Indeed, when assuming no self-absorption of the emission lines, intensities simply add up but broadenings do not. In order to better understand the results of Stark broadening measurements on our thermal plasma which has an unneglectable thickness, a Python code has been developed based on local thermodynamic equilibrium (LTE) assumption and calculated plasma composition and properties. This code generates a simulated pseudo experimental (PE) H$\alpha$ spectral line resulting from an integration over the plasma thickness in a selected direction for a given temperature profile. The electron density was obtained using the Stark broadening of the PE spectral line for different temperature profiles. It resulted that this measurement is governed by the maximum electron density profile up until the temperature maximum exceeds that of the maximum electron density. The electron density obtained by broadening measurement is 70% to 80% of the maximum electron density.Comment: European Physical Journal: Applied Physics, EDP Sciences, 202

ARC MOTION IN LOW VOLTAGE CIRCUITBREAKER (LVCB) EXPERIMENTAL ANDTHEORETICAL APPROACHES

International audienceAbstract This paper is related to the study of the arc motion in simple low voltage circuit breaker geometry.Experimental and theoretical approaches are investigated respectively by fast camera and by a magneto hydrodynamicmodel. Two theoretical methods have been developed to characterize the arc movement called MECM (Mean ElectricalConductivity Method) and GCRM (Global Current Resolution Method). The results obtained by the two models are ingood agreement with the experimental observations. The MECM allows obtaining faster results but the stagnation phasesare well represented with the GRCM and this last method is easier to implement in more complex geometry. The resultsshow also the importance of the exhaust description on the arc behavior

A Dynamical scheme for a large CP violating phase

A dynamical scheme where the third generation of quarks plays a distinctive role is implemented. New interactions with a $\theta$ term induce the breaking of the electroweak symmetry and the top-bottom mass splitting. A large CP-violating phase naturally follows from the latter. Comment: 10 pages, LaTe

Etude expérimentale et numérique d’un procédé de coupage plasma intensifié

International audienceLe procédé de coupage plasma, mettant en œuvre un arc électrique transféré entre une torche et une pièce métallique à découper, fait l’objet de développements continus depuis les années 1970 et d’une utilisation industrielle aujourd’hui essentielle à la construction métallique. Des études de caractérisation expérimentale et de modélisation détaillée, n’ont en revanche débuté que plus récemment, en raison de la mobilisation nécessaire d’approches [1] alliant mesures spectrométriques et simulation CFD.Le corpus de connaissance, et les méthodes de simulation, constitués et enrichis depuis, permettent désormais d’aborder l’amélioration des technologies industrielles de coupage plasma avec une approche d’innovation par la connaissance, i.e. s’appuyant sur une compréhension plus fine de la phénoménologie de mise en forme du jet plasma de coupage.La caractérisation d’une approche innovante proposée par la société AKRYVIA [2], est présentée ici. Cette approche s’appuie sur une démarche d’intensification du jet de plasma augmentant l’effet de constriction par la pression d’alimentation de la tuyère primaire associé à un contrôle actif de la cohérence spatiale du jet ainsi formé dans la tuyère secondaire, et dans l’espace entre la torche et la tôle.Cette technologie a pu être caractérisée expérimentalement sur les installations d’AKRYVIA à travers des largeurs de saignée de découpe ayant des niveaux de précision deux fois meilleures que les références industrielles de même puissance, des mesures de champ électrique moyen dans le plasma atteignant 26 kV/m et des images de l’arc en sortie de tuyère.Dans ce papier, une modélisation CFD réalisée au laboratoire LAPLACE est confrontée à certains de ces résultats. En particulier, ce modèle a permis de prédire des températures au cœur de l’arc inédites, supérieures à 30 000 K (figure 1)