Stabilized finite element approximation of the incompressible MHD equations

No es frecuente encontrar un campo donde dos ramas principales de la Física estén involucradas. La Magnetohidrodinámica es uno de tales campos debido a que involucra a la Mecánica de Fluidos y al Electromagnetismo. Aun cuando puede parecer que esas dos ramas de la Física tienen poco en común, comparten similitudes en las ecuaciones que gobiernan los fenómenos involucrados en ellas. Las ecuaciones de Navier-Stokes y las ecuaciones de Maxwell, ambas en la raíz de la Magnetohidrodinámica, tienen una condición de divergencia nula y es esta condición de divergencia nula sobre la velocidad del fluido y el campo magnético lo que origina algunos de los problemas numéricos que surgen en la modelación de los fenómenos donde el flujo de fluidos y los campos magnéticos están acoplados.El principal objetivo de este trabajo es desarrollar un algoritmo eficiente para la resolución mediante elementos finitos de las ecuaciones de la Magnetohidrodinámica de fluidos incompresibles.Para lograr esta meta, los conceptos básicos y las características de la Magnetohidrodinámica se presentan en una breve introducción informal.A continuación, se da una revisión completa de las ecuaciones de gobierno de la Magnetohidrodinámica, comenzando con las ecuaciones de Navier-Stokes y las ecuaciones de Maxwell. Se discute la aproximación que da origen a las ecuaciones de la Magnetohidrodinámica y finalmente se presentan las ecuaciones de la Magnetohidrodinámica.Una vez que las ecuaciones de gobierno de la Magnetohidrodinámica han sido definidas, se presentan los esquemas numéricos desarrollados, empezando con la linealización de las ecuaciones originales, la formulación estabilizada y finalmente el esquema numérico propuesto. En esta etapa se presenta una prueba de convergencia.Finalmente, se presentan los ejemplos numéricos desarrollados durante este trabajo.Estos ejemplos pueden dividirse en dos grupos: ejemplos numéricos de comparación y ejemplos de internes tecnológico. Dentro del primer grupo están incluidas simulaciones del flujo de Hartmann y del flujo sobre un escalón. El segundo grupo incluye simulaciones del flujo en una tobera de inyección de colada continua y el proceso Czochralski de crecimiento de cristales.It is not frequent to find a field where two major branches of Physics are involved. Magnetohydrodynamics is one of such fields because it involves Fluid Mechanics and Electromagnetism. Although those two branches of Physics can seem to have little in common, they share similarities in the equations that govern the phenomena involved. The Navier-Stokes equations and the Maxwell equations, both at the root of Magnetohydrodynamics, have a divergence free condition and it is this divergence free condition over the velocity of the fluid and the magnetic field what gives origin to some of the numerical problems that appear when approximating the equations that model the phenomena where fluids flow and magnetic fields are coupled.The main objective of this work is to develop an efficient finite element algorithm for the incompressible Magnetohydrodynamics equations.In order to achieve this goal the basic concepts and characteristics of Magnetohydrodynamics are presented in a brief and informal introduction.Next, a full review of the governing equations of Magnetohydrodynamics is given, staring from the Navier-Stokes equations and the Maxwell equations. The MHD approximation is discussed at this stage and the proper Magnetohydrodynamics equations for incompressible fluid are reviewed.Once the governing equations have been defined, the numerical schemes developed are presented, starting with the linearization of the original equations, the stabilization formulations and finally the numerical scheme proposed. A convergence test is shown at this stage.Finally, the numerical examples performed while this work was developed are presented. These examples can be divided in two groups: numerical benchmarks and numerical examples of technological interest. In the first group, the numerical simulations for the Hartmann flow and the flow over a step are included. The second group includes the simulation of the clogging in a continuous casting nozzle and Czochralski crystal growth process.Postprint (published version

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Thermal-Hydraulics in Nuclear Fusion Technology: R&D and Applications

In nuclear fusion technology, thermal-hydraulics is a key discipline employed in the design phase of the systems and components to demonstrate performance, and to ensure the reliability and their efficient and economical operation. ITER is in charge of investigating the transients of the engineering systems; this included safety analysis. The thermal-hydraulics is required for the design and analysis of the cooling and ancillary systems such as the blanket, the divertor, the cryogenic, and the balance of plant systems, as well as the tritium carrier, extraction and recovery systems. This Special Issue collects and documents the recent scientific advancements which include, but are not limited to: thermal-hydraulic analyses of systems and components, including magneto-hydrodynamics; safety investigations of systems and components; numerical models and code development and application; codes coupling methodology; code assessment and validation, including benchmarks; experimental infrastructures design and operation; experimental campaigns and investigations; scaling issue in experiments

Magnetohydrodynamic equilibrium and stability of centrifugally confined plasmas

Centrifugal confinement is an alternative approach to magnetic fusion, employing a magnetic field with an open field line configuration. In this scheme, a plasma with magnetic mirror geometry is made to rotate azimuthally at supersonic speeds. The resulting centrifugal forces, given the field line curvature, prevent the plasma from escaping along the field lines. This dissertation addresses the equilibrium and stability of this configuration within the framework of magnetohydrodynamics (MHD). Well confined equilibrium with desirable profiles is demonstrated by numerical simulation. As far as stability is concerned, four types of magnetohydrodynamic modes determine the overall stability of centrifugally confined plasmas: flute interchanges and the Kelvin--Helmholtz instability, in a low $\beta$ system, and the magnetorotational instability (MRI) and the Parker instability, in a high $\beta$ system. One of the underpinnings of the centrifugal confinement is that flute interchanges could be stabilized by the strong velocity shear accompanying the rotation. Numerical simulations show strong evidence of stabilization, provided that the shear flow is not unstable to Kelvin--Helmholtz (KH) modes. The KH modes are ideally stable if the generalized Rayleigh's Inflexion criterion is satisfied. Particle sources and shown to be important to both equilibrium and stability. In the absence of particle sources, density profiles relax under resistive diffusion to pile up to the outboard side of the confining vessel. Tailoring the density profiles by appropriately placing the particle sources could be used to achieve control over MHD stability, for both interchanges and KH modes. Analytic analysis of interchanges based on an extension of MHD which applicable for low density plasmas with $V_A \sim c$ is presented. The interchange growth rates are reduced by a factor of $\sqrt{1+V_A^2/c^2}$ compared to the usual MHD prediction. The physical mechanisms of both the MRI and the Parker instability are examined and an explanation of why the MRI mechanism is insufficient to destabilize the system while the Parker instability could occur is given. Numerical simulations of the nonlinear behavior of the Parker instability are presented. It is shown that clumping from the Parker instability could reinforce centrifugal confinement

Bibliography of Lewis Research Center technical contributions announced in 1976

Abstracts of Lewis authored publications and publications resulting from Lewis managed contracts which were announced in the 1976 issues of STAR (Scientific and Technical Aerospace Reports) and IAA (International Aerospace Abstracts) are presented. Research reports, journal articles, conference presentations, patents and patent applications, and these are included. The arrangement is by NASA subject category. Citations indicate report literature (identified by their N-numbers) and the journal and conference presentations (identified by their A-numbers). A grouping of indexes helps locate specific publications by author (including contractor authors), contractor organization, contract number, and report number