Electric Transverse Emissivity of Sinusoidal Surfaces Determined by a Differential Method: Comparison with Approximation of Geometric Optics

We present in this paper a numerical study of the validity limit of the optics geometrical approximation in comparison with a differential method which is established according to rigorous formalisms based on the electromagnetic theory. The precedent studies show that this method is adopted to the study of diffraction by periodic rough surfaces. For periods much larger than the wavelength, the mechanism is analog to what happens in a cavity where a ray is trapped and undergoes a large number of reflections. For gratings with a period much smaller than the wavelength, the roughness essentially behaves as a transition layer with a gradient of the optical index. Such a layer reduces the reflection there by increasing the absorption. The code has been implemented for TE polarization. We determine by the two methods such as differential method and the optics geometrical approximation the emissivity of gold and tungsten cylindrical surfaces with a sinusoidal profile, for a wavelength equal to 0.55 microns. The obtained results for a fixed height of the grating allowed us to delimit the validity domain of the optic geometrical approximation for the treated cases. The emissivity calculated by the differential method and that given on the basis of the homogenization theory are satisfactory when the period is much smaller than the wavelength.

Plastic forming processes of transverse non-homogeneous composite metallic sheets

In this work an analysis of the radial stress and velocity fields is performed according to the J 2 flow theory for a rigid/perfectly plastic material. The flow field is used to simulate the forming processes of sheets. The significant achievement of this paper is the generalization of the work by Nadai & Hill for homogenous material in the sense of its yield stress, to a material with general transverse non-homogeneity. In Addition, a special un-coupled form of the system of equations is obtained where the task of solving it reduces to the solution of a single non-linear algebraic differential equation for the shear stress. A semi-analytical solution is attained solving numerically this equation and the rest of the stresses term together with the velocity field is calculated analytically. As a case study a tri-layered symmetrical sheet is chosen for two configurations: soft inner core and hard coating, hard inner core and soft coating. The main practical outcome of this work is the derivation of the validity limit for radial solution by mapping the “state space” that encompasses all possible configurations of the forming process. This configuration mapping defines the “safe” range of configurations parameters in which flawless processes can be achieved. Several aspects are researched: the ratio of material's properties of two adjacent layers, the location of layers interface and friction coefficient with the walls of the dies.

Time-Splitting Coupling of WaveDyn with OpenFOAM by Fidelity Limit Identified from a WEC in Extreme Waves

Survivability assessment is the complexity compromising Wave energy development. The present study develops a hybrid model aiming to reduce computational power while maintaining accuracy for survivability assessment of a Point-Absorber (PA) Wave Energy Converter (WEC) in extreme Wave Structure Interaction (WSI). This method couples the fast inviscid linear potential flow time-domain model WaveDyn (1.2, DNV-GL, Bristol, UK) with the fully nonlinear viscous Navier–Stokes Computational Fluid Dynamics (CFD) code OpenFOAM (4.2, OpenFOAM.org, London, UK). The coupling technique enables the simulation to change between codes, depending on an indicator relating to wave steepness identified as a function of the confidence in the linear model solution. During the CFD part of the simulation, the OpenFOAM solution is returned to WaveDyn via an additional load term, thus including viscous effects. Developments ensure a satisfactory initialisation of CFD simulation to be achieved from a ‘hot-start’ time, where the wave-field is developed and the device is in motion. The coupled model successfully overcomes identified inaccuracies in the WaveDyn code due to the inviscid assumption and the high computational cost of the OpenFOAM code. Experimental data of a PA response under extreme deterministic events (NewWave) are used to assess WaveDyn’s validity limit as a function of wave steepness, in order to validate CFD code and develop the coupling. The hybrid code demonstrates the applicability of WaveDyn validity limit and shows promising results for long irregular sea-state applications.

Quasi-Static Solution for ELF/SLF near-Zone Field of a Vertical Magnetic Dipole near the Surface of a Lossy Half-Space

Dipole antennas over the boundary between two different media have been widely used in the fields of geophysics exploration, oceanography, and submerged communication. In this paper, an analytical method is proposed to analyse the near-zone field at the extremely low frequency (ELF)/super low frequency (SLF) range due to a vertical magnetic dipole (VMD). For the lack of feasible analytical techniques to derive the components exactly, two reasonable assumptions are introduced depending on the quasi-static definition and the equivalent infinitesimal theory. Final expressions of the electromagnetic field components are in terms of exponential functions. By comparisons with direct numerical solutions and exact results in a special case, the correctness and effectiveness of the proposed quasi-static approximation are demonstrated. Simulations show that the smallest validity limit always occurs for component H2z, and the value of k2ρ should be no greater than 0.6 in order to keep a good consistency.

The family of Quasi-satellite periodic orbits in the circular co-planar RTBP

In the circular case of the coplanar Restricted Three-body Problem, we studied how the family of quasi-satellite (QS) periodic orbits allows to define an associated libration center. Using the averaged problem, we highlighted a validity limit of this one: for QS orbits with low eccentricities, the averaged problem does not correspond to the real problem. We do the same procedure to L3, L4 and L5 emerging periodic orbits families and remarked that for very high eccentricities ${\cal F}_{L_4}$ and ${\cal F}_{L_5}$ merge with ${\cal F}_{L_3}$ which bifurcates to a stable family.

Modeling of Solution Renewal with the Kindis Code: Example of R7T7 Glass Dissolution at 90°C

The deep underground environment that would correspond to a geological repository is a system open to fluid flow. It is therefore necessary to investigate the effects of solution renewal on the long-term behavior of glass in contact with water. These effects can now be simulated using the new version of the geochemical Kindis model (thermodynamic and kinetic model).We tested the model at 90°C with an SAIV ratio of 400 m−1 at twelve renewal rates of pure water ranging from 200 to 0 vol% per day. With renewal rates between 200 and 0.065 vol% per day, steady-state conditions were obtained in the reaction system: i.e. the glass corrosion rate remained constant as did the concentrations of the dissolved species in solution (although at different values depending on the renewal rate). The ionic strength never exceeded 1 (the validity limit for the Debye-Huckel law) and long term predictions of the dissolved glass mass, the solution composition and the potential secondary mineral sequence are possible. For simulated renewal rates of less than 0.065 vol% per day (27 vol% per year), the ionic strength rose above 1 (as in a closed system) before steady-state conditions were reached, making it critical to calculate long-term rates; A constant and empirical long-term rate, derived from laboratory measurement, have to be extrapolated. These calculations were based on a first order equation to describe the glass dissolution kinetics. The results obtained with the KINDIS code show discrepancies with some major experimental kinetic data (the long term rate must decrease with the « glass-water » reaction progress, under silica saturation conditions). This clearly indicates that a more refine kinetic relation is needed for the glass matrix.