Hot-pressing process modeling for medium density fiberboard (MDF)

In this paper we present a numerical solution for the mathematical modeling of the hot-pressing process applied to medium density fiberboard. The model is based in the work of Humphrey[82], Humphrey and Bolton[89] and Carvalho and Costa[98], with some modifications and extensions in order to take into account mainly the convective effects on the phase change term and also a conservative numerical treatment of the resulting system of partial differential equations.Comment: LaTeX, 11 figures. Added references. Fixed some errors. To appear in International Journal of Mathematics and Mathematical Sciences, http://jam.hindawi.co

Resolución de flujos potenciales compresibles no-estacionarios por el método de los elementos finitos

Son considerados flujos alrededor de perfiles aerodinámicos que evolucionan en el tiempo en forma rígida. Para evitar el uso de mallas deformables la ecuación potencial completa es transformada a un sistema de referencia no-inercial donde el dominio de integración es fijo. En este sistema las ecuaciones son discretizadas y resueltas por un método de minimización en direcciones dadas por los vectores de Lanczos. Para casos con sustentación se tiene en cuenta la vorticidad concentrada en el borde de fuga siguiendo el modelo de Giesing-Maskeli el cual, para frecuencias reducidas muy pequeñas, es equivalente a la condición de Kutta-Joukowski estacionaria. Varios ejemplos numéricos son presentados.In this work inviscid irrotational flows around aerodynamic profiles which experiment rigid motions are studied. To avoid the use of deformable grids the fuli potential equation is transformed to a non-inertial frame of reference where the domain of integration is fixed. The problem is discretized in this frame of reference and the resulting system of equations is resolved via a minimization along Lanczos vectors algorithm. In lift problems, the vorticity concentrated in the wake is taken account. This vorticity is produced in the trailing edge foilowing the model of Giesing & Maskeil, which reduces to the steady Kutta-Joukowski condition for low reduced frequencies. Finally several numerical examples are presented.Peer Reviewe

A Coupling Strategy for a Chimera Method Applied to Thermal Conduction Optimization Problems

The main idea of the Chimera method is to generate independent meshes for the objects present in a computational domain and to couple them by a coupling strategy in order to obtain a unique solution of the system. The method has appealing characteristics that are convenient for applications like simplified mesh generation, moving components, local refinement and optimization. The optimization process is a straightforward application where several objects, each one with its respective mesh, can be moved around without the need to remesh the whole computational domain. Then, different optimization techniques can be used to find the optimum configuration of the system in terms of an objective function. In a previous work (B. Storti et al., “A chimera method based on Dirichlet-Dirichlet coupling and pasting penalization operators”, Mecánica Computacional, vol. XXXIV, 2016), we have presented and validated a Chimera scheme in the finite element context for structured meshes, and we have proven that it has a good convergence rate solving the system iteratively with BiCGStab (BiConjugate Gradient Stabilized method). In the present work, we improve the Chimera method to solve thermal conduction problems on overlapping unstructured meshes and then we test it in several optimization cases. A Dirichlet-Dirichlet coupling imposes the continuity of the unknown on overlapping subdomains and to transfer these values between the multiples domains, a third order interpolation method is used in conjunction with a "pasting" penalization operator. Several numerical examples are also shown in order to validate the proposed interpolation method. Finally a variety of optimization problems are solved under the pyOpt framework, either using gradient-free or gradient based optimizers, running in the CIMEC cluster Seshat (http://www.cimec.org.ar/c3/seshat/equipos.php), where every evaluation test of the objective function is compute on each core. Seshat is a 69 nodes cluster, which has an Infiniband network and a computing power of almost 7 TFLOPS.Publicado en: Mecánica Computacional vol. XXXV, no. 28.Facultad de Ingenierí

Modelización numérica de un motor de combustión interna monocilíndrico encendido por chispa

El objetivo de este trabajo fue el desarrollo de un código computacional para la resolución de problemas de dinámica de gases en su escurrimiento a través de ductos y toberas y su posterior inserción dentro de un código que simule el ciclo de potencia y el de bombeo en un motor de combustión interna encendido por chispa. Es sabido que los motores de combustión interna son altamente influenciados por el diseño de los múltiples de admisión y escape. Factores como el ruido, la emisión y el rendimiento volumétrico son algunos de los principales temas de actualidad en el área de motores térmicos. Es por esto que en pos de poder modelar un motor y sus partes pensamos que será muy provechoso contar con un desarrollo previo en el flujo en tubos de sección arbitraria, siendo los ductos y las toberas sólo una aplicación particular del código generado. Se utilizó una discretización espacial unidimensional en elementos _nitos con una discretización temporal según un esquema de Lax-Wendro de dos pasos. La física del problema es gobernada por las ecuaciones de Euler, flujo invíscido, con el agregado de términos fuentes para incluir los efectos de la fricción en las paredes del tubo, la variabilidad de la sección de paso del fluido y la transferencia de calor a través de las paredes del ducto. Las primeras secciones introducen acerca de la dinámica de gases en sus aspectos teóricos básicos incluyendo el análisis de discontinuidades tipo ondas de choque. Posteriormente se analizan aspectos numéricos como la formulación empleada, el tratamiento de las condiciones de contorno y las técnicas de resolución numérica del sistema resultante. A continuación se presentan una gran variedad de resultados y su comparación con sus contrapartes analíticas. Finalmente se presentan algunos aspectos computacionales acerca del modelo completo de simulación de un motor de combustión interna encendido por chispa y las curvas características obtenidas para un caso test.Peer Reviewe

Modelización numérica de un motor de combustión interna monocilíndrico encendido por chispa

El objetivo de este trabajo fue el desarrollo de un código computacional para la resolución de problemas de dinámica de gases en su escurrimiento a través de ductos y toberas y su posterior inserción dentro de un código que simule el ciclo de potencia y el de bombeo en un motor de combustión interna encendido por chispa. Es sabido que los motores de combustión interna son altamente influenciados por el diseño de los múltiples de admisión y escape. Factores como el ruido, la emisión y el rendimiento volumétrico son algunos de los principales temas de actualidad en el área de motores térmicos. Es por esto que en pos de poder modelar un motor y sus partes pensamos que será muy provechoso contar con un desarrollo previo en el flujo en tubos de sección arbitraria, siendo los ductos y las toberas sólo una aplicación particular del código generado. Se utilizó una discretización espacial unidimensional en elementos _nitos con una discretización temporal según un esquema de Lax-Wendro de dos pasos. La física del problema es gobernada por las ecuaciones de Euler, flujo invíscido, con el agregado de términos fuentes para incluir los efectos de la fricción en las paredes del tubo, la variabilidad de la sección de paso del fluido y la transferencia de calor a través de las paredes del ducto. Las primeras secciones introducen acerca de la dinámica de gases en sus aspectos teóricos básicos incluyendo el análisis de discontinuidades tipo ondas de choque. Posteriormente se analizan aspectos numéricos como la formulación empleada, el tratamiento de las condiciones de contorno y las técnicas de resolución numérica del sistema resultante. A continuación se presentan una gran variedad de resultados y su comparación con sus contrapartes analíticas. Finalmente se presentan algunos aspectos computacionales acerca del modelo completo de simulación de un motor de combustión interna encendido por chispa y las curvas características obtenidas para un caso test.Peer Reviewe

CFD presenta compresible + incompresible un matrimonio por conveniencia

Este trabajo presenta por un lado una breve síntesis de algunas importantes contribuciones dirigida a la unificación de códigos computacionales para flujos tanto compresible como incompresible y por otro un eficiente precondicionador local para todo el rango de números de Mach y Reynolds implementado sobre un esquema iterativo tipo GMRES con una estrategia que evita el ensamblaje de matrices llamada matriz-free usando como discretización espacial una formulación en elementos finitos. El principal objetivo de esta investigación es lograr un tratamiento unificado de flujo de fluidos tanto compresible como incompresible, viscoso o inviscido apto para simulaciones a gran escala y capaz de ser utilizado sobre plataformas de hardware paralelas.This paper presents a brief review of important contributions towards the unification of compressible and incompressible flow solvers and an efficient local preconditioner for al1 Mach and Reynolds numbers implemented with a matrix-free GMRES iterative scheme and a finite element method. The main goal of this research is the unified treatment of fluid flow at al1 speeds for large scale simulation capable of being implemented over parallel platforms.Peer Reviewe

GMRES physics‐based preconditioner for all Reynolds and Mach numbers: numerical examples

This paper presents several numerical results using a vectorized version of a 3D finite element compressible and nearly incompressible Euler and Navier–Stokes code. The assumptions were set on laminar flows and Newtonian fluids. The goal of this research is to show the capabilities of the present code to treat a wide range of problems appearing in laminar fluid dynamics towards the unification from incompressible to compressible and from inviscid to viscous flow codes. Several authors with different approaches have tried to attain this target in CFD with relative success. At the beginning the methods based on operator splitting and perturbation were preferred, but lately, with the wide usage of time‐marching algorithms, the preconditioning mass matrix (PMM) has become very popular. With this kind of relaxation scheme it is possible to accelerate the rate of convergence to steady state solutions with the modification of the mass matrix under certain restrictions. The selection of the mass matrix is not an easy task, but we have certain freedom to define it in order to improve the condition number of the system. In this paper we have used a physics‐based preconditioner for the GMRES implicit solver developed previously by us and an SUPG formulation for the semidiscretization of the spatial operator. In sections 2 and 3 we present some theoretical aspects related to the physical problem and the mathematical model, showing the inviscid and viscous flow equations to be solved and the variational formulation involved in the finite element analysis. Section 4 deals with the numerical solution of non‐linear systems of equations, with some emphasis on the preconditioned matrix‐free GMRES solver. Section 5 shows how boundary conditions were treated for both Euler and Navier–Stokes problems. Section 6 contains some aspects about vectorization on the Cray C90. The performance reached by this implementation is close to 1 Gflop using multitasking. Section 7 presents several numerical examples for both models covering a wide range of interesting problems, such as inviscid low subsonic, transonic and supersonic regimes and viscous problems with interaction between boundary layers and shock waves in either attached or separated flows

Improving the convergence rate of the Petrov‐Galerkin techniques for the solution of transonic and supersonic flows

This paper report progress on a technique to accelerate the convergence to steady solutions when the streamline‐upwind/Petrov‐Galerkin (SUPG) technique is used. Both the description of a SUPG formulation and the documentation of the development of a code for the finite element solution of transonic and supersonic flows are reported. The aim of this work is to present a formulation to be able to treat domains of any configuration and to use the appropriate physical boundary conditions, which are the major stumbling blocks of the finite difference schemes, together with an appropriate convergence rate to the steady solution. The implemented code has the following features: the Hughes' SUPG‐type formulation with an oscillation‐free shock‐capturing operator, adaptive refinement, explicit integration with local time‐step and hourglassing control. An automatic scheme for dealing with slip boundary conditions and a boundary‐augmented lumped mass matrix for speeding up convergence. It is shown that the velocities at which the error is absorbed in and ejected from the domain (that is damping and group velocities respectively) are strongly affected by the time step used, and that damping gives an O(N2) algorithm contrasting with the O(N) one given by absorption at the boundaries. Nonetheless, the absorbing effect is very low when very different eigenvalues are present, such as in the transonic case, because the stability condition imposes a too slow group velocity for the smaller eigenvalues. To overcome this drawback we present a new mass matrix that provides us with a scheme having the highest group velocity attainable in all the components. In Section 1 we will describe briefly the theoretical background of the SUPG formulation. In Section 2 it is described how the foregoing formulation was used in the finite element code and which are the appropriate boundary conditions to be used. Finally in Section 3 we will show some results obtained with this cod

Two‐phase flow modelling in gas‐stirred liquid vessels with SUPG‐stabilized equal‐order interpolations

The modelling of liquid flow in gas‐stirred vessels is described. A simple two‐phase model accounts for the buoyancy effect of bubbles. Friction between liquid and gas is modelled with the hypothesis of independent bubbles. The resulting PDE system is discretized with an original version of the SUPG‐FEM technique which stabilizes both the convection term and equal‐order interpolations for velocity and pressure, which are known to be unstable for incompressible flows. The resulting steady state discrete system is solved via pseudotemporal explicit iteration with a local time step and a preconditioning to homogenize the temporal scales for liquid and gas

Numerical methods in phase-change problems

This paper summarizes the state of the art of the numerical solution of phase-change problems. After describing the governing equations, a review of the existing methods is presented. The emphasis is put mainly on fixed domain techniques, but a brief description of the main front-tracking methods is included. A special section is devoted to the Newton-Raphson resolution with quadratic convergence of the non-linear system of equations