Francisco Pena

A numerical method for transient simulation of metallurgical compound electrodes

The objective of this work is to introduce and numerically solve a mathematical model for unsteady thermoelectrical behavior of an electric arc electrode. The electrode is composed of several materials and one of them suffers a change of state during operation. Thermoelectric parameters depend on the temperature in each material. The volumetric heat source is the Joule effect. The mathematical model leads to a coupled non-linear system of partial differential equations. The axisymmetry of the domain allows us to simplify the problem when it is written in cylindrical coordinates. We use an implicit method for time discretization and a standard finite element method for space discretization. Numerical results corresponding to the simulation of a real industrial situation are given.

A finite element method for the thermoelectrical modelling of electrodes

In this paper we give a numerical method based on finite element discretizations to simulate the thermoelectrical behaviour of electrodes for electric reduction furnaces. After introducing the mathematical model we take advantage of the cylindrical symmetry of the problem to compute boundary conditions for the Maxwell equations. Thermal and electrical problems are coupled and non-linear because of the Joule effect and the fact that thermal conductivity and electrical resistivity depend on temperature. A classical piecewise linear finite element method on a triangular mesh is used to discretize weak formulations in cylindrical co-ordinates for the two problems. Then an iterative algorithm is proposed to solve the coupled discrete system. Numerical results are shown both for an analytical test and for a real industrial electrode.

Numerical computation of the electromagnetic field in the electrodes of a three-phase arc furnace

In this paper we introduce and numerically solve a mathematical model for numerical simulation of electro-magnetic field in a three-phase electric reduction furnace. The model allows us to compute the current distribution on a cross-section of the three electrodes. A combined boundary element/finite element method is used. Numerical results for real industrial furnaces are shown. As a by-product we compute the torque on the electrodes due to the Lorentz electromagnetic force. Copyright

19th European Conference on Mathematics for Industry: book of Abstracts, June, 13-17, 2016, Santiago de Compostela (Spain)

In the last decades, the biomedical relevance of mathematical models has been demonstrated and comparison of experiments against computer simulations has been encouraged. Blood circulation in the human liver and in particular perfusion, the process of delivering blood to the capillary bed, is an open problem and inherently multiscale in nature. Models currently available in the literature [2, 1] either present a macroscale approach in which liver is assumed as a homogeneous anisotropic porous medium and therefore flow within it is simulated using Darcy’s equation, or they work at the microscale where the vascular and extravascular domains need to be treated differently solving Stokes’ equation in the former and Darcy’s equation in the latter and applying suitable coupling condition at the interface. In this communication, instead, we present an approach where the Darcy-Stokes-Brinkmann [3] equation is used on the entire computational domain, different areas of the tissue being represented by a (possibly discontinuous) friction coefficient. This approach allows to run simulations at the capillary scale on real-life geometries deduced from medical images avoiding complex and costly preprocessing such as edge detection, and mesh generation. The peculiar properties of IsoGeometric discretization methods [4, 5] such as stability and ability to provide exactly divergence free velocity are exploited in the simulation. After validating the numerical method on 2D and 3D test cases based on syntetic images, we apply it to actual micro-CT images of the liver and perform an upscaling procedure to determine the macroscale parameters of the tissue such as the local permeability tensor.

Automatic Analysis of Floating Offshore Structures

In the coming years offshore wind energy will be one of the most promising areas in the renewable power generation field. Achieving the optimum design of floating platforms requires a rigorous analysis chain to establish the response of the whole platform under different scenarios. With this aim, we have developed a software package that automatically analyzes the feasibility of a floating structure. The structure of the platform is defined according to a very general set of parameters, allowing us to consider a wide range of designs. The package calls some commercial applications and some own codes, to complete the analysis process. Returned results include the hydrostatic equilibrium position, hydrodynamic pressure, RAOs (response-amplitude operators), material costs and static stresses.

The Galerkin Lumped Parameter Method for Thermal Problems

In this contribution, we present a method called Galerkin lumped parameter (GLP) method, as a generalization of the lumped parameter models used in engineering. This method can also be seen as a model-order reduction method. Similarities and differences are discussed. In the GLP method, introduced in [1], domain is decomposed into several sub-domains and a time-independent adapted reduced basis is calculated solving elliptic problems in each sub-domain. The method seeks a global solution in the space spanned by this basis, by solving an ordinary differential system. This approach is useful for electric motors, since the decomposition into several pieces is natural. Numerical results concerning heat equation are presented. Firstly, the comparison with an analytic solution is shown to check the implementation of the numerical algorithm. Secondly, the thermal behavior of an electric motor is simulated, assuming that the electric losses are known. A comparison with the solution obtained by the finite element method is shown.© 2012 ASME

Radiative Heat Transfer in Silicon Purification

We present a numerical model describing the thermal behavior of a silicon purification process which takes place into a so-called casting ladle. We consider, simultaneously, the phase change in the silicon and a nonlinear non-local boundary condition arising from the Stefan-Boltzmann radiation condition at the enclosure surfaces within the ladle. We also propose a numerical approximation using a finite element method. An iterative algorithm and numerical results are presented.