Jean-Francois Hetu

Adaptative remeshing for viscous incompressible flows

This paper presents an adaptive finite element procedure for solving viscous incompressible flows. The methodology is based on adaptive remeshing for steady-state problems. The Navier-Stokes equations for an incompressible fluid are solved in primitive variables by an Uzawa algorithm using a highly accurate element. The efficiency and convergence rate of the adaptive strategy are evaluated by solving problems with known analytical solutions. Finally, the methodology is applied to the flow over a backward-facing step and predictions are compared with experimental measurements. The use of the proposed adaptive procedure is shown to lead to improved accuracy of the finite element predictions. Nomenclature C = a constant e - error in the solution h - element size /(•) = dissipation energy n = number of elements in the mesh p = pressure 5 - step and fence height U = velocity vector u, v = velocity components x, y = coordinates V = gradient operator 6 = element size predicted by adaptation module e = strain rate tensor = 1A( V U + V UT) a = stress tensor = 2/*e £ = similarity variable in a boundary layer t\ - relative error on a mesh H = absolute viscosity of the fluid v - kinematic viscosity of the fluid

On stabilized finite element formulations for incompressible advective–diffusive transport and fluid flow problems

Abstract A new approach is presented to obtain stabilized finite element formulations such as streamline-upwind/Petrov–Galerkin (SUPG) and Galerkin-least-squares (GLS). The procedure consists in modifying the equations to be solved and then obtaining the variational equations by the standard Galerkin method. The new formulation generates additional terms involving boundary integrals to standard stabilization techniques. These terms compensate for the lack of consistency of the traditional SUPG and GLS methods for which stabilization terms are added only on the element interiors, while jumps of the residual across element faces are neglected. A physical interpretation is provided of how the modified equations are obtained. It is shown how stabilized formulations such as streamline-upwind (SU) and SUPG are recovered as special cases. Stabilization terms defined on the element interiors are always accompanied by additional boundary integrals. The presence of the boundary integrals is shown to improve the numerical prediction for various viscous and nearly inviscid flows.

Adaptive finite element method for thermal flow problems

This paper presents an adaptive finite element method based on remeshing to solve incompressible viscous flow problems including heat transfer effects by forced or free convection. Conjugate heat transfer problems are also considered. Solutions are obtained in primitive variables by an Uzawa algorithm using a highly accurate finite element approximation on unstructured grids. Two error estimators are presented and compared on problems with known analytical solutions. The methodology is then applied to a problem of practical interest and predictions are compared with experimental measurements and show very good agreement.

Adaptive remeshing for convective heat transfer with variable fluid properties

This article presents an adaptive finite element method based on remeshing to solve incompressible viscous flow problems for which fluid properties present a strong temperature dependence. Solutions are obtained in primitive variables using a highly accurate finite element approximation on unstructured grids. Two general purpose error estimators are presented, which take into account the temperature dependence of fluid properties. The methodology is applied to a problem of practical interest: the thermal convection of corn syrup in an enclosure with localized heating. Predictions are in good agreement with experimental measurements. The method leads to improved accuracy and reliability of finite element predictions. Nomenclature cp = specific heat

Galerkin gradient least-squares formulations for transient conduction heat transfer

This paper presents the benefits provided by the use of the Galerkin gradient least-squares (GGLS) method for transient conduction heat transfer. The consistency of the GLS method for this type of problem is also discussed. The GGLS method is compared with standard Galerkin formulation on problems having an analytical solution: a semi-infinite solid solved on one- and three-dimensional meshes and a three-dimensional thin plate. For three-dimensional applications, the principle of including gradient least-squares terms is extended to stabilize Robin (convection) boundary conditions. Numerical simulations show that additional boundary gradient least-squares terms improve the behavior of the solution on boundaries subject to convection boundary conditions. New procedures used to obtain the GLS and GGLS stabilized finite element formulations are also presented. The methodology consists in modifying the equation to be solved and then to obtain the variational equation by a standard Galerkin method.

Adaptive finite element method for turbulent flow near a propeller

We present an adaptive finite element method based on remeshing to solve incompressible turbulent free shear flow near a propeller. Solutions are obtained in primitive variables using a highly accurate finite element approximation on unstructured grids. Turbulence is modeled by a mixing length formulation. Two general purpose error estimators, which take into account swirl and the variation or the eddy viscosity, are presented and applied to the turbulent wake or a propeller. The proposed adaptive scheme is robust, reliable and cost effective

Numerical Simulation of the Flow and Fiber Orientation in Reinforced Thermoplastic Injection Molded Products

Abstract This paper describes a fully three-dimensional transient finite element method for calculating the flow behavior and fiber orientation during filling of injection molded parts. The fiber-fiber interaction is taken into account. The momentum and continuity equations are first solved with the viscoelastic stress treated as a fixed body force. The kinetic equation for the orientation tensor is then integrated with known kinematics using the standard Galerkin method. The calculation is performed on a time-dependent flow domain. Since the method is truly three-dimensional, singular regions such as the flow front or near injection gates and solid boundaries, where decoupled approximations are not valid, are naturally dealt with. The material anisotropy behavior is modeled by using the Doi-Doraiswamy-Metzner model. Numerical results, involving the Poiseuille flow and the filling of an end-gated plate, emphasizing the importance of the three-dimensional coupling calculations between the flow and orientation are presented.

On stabilized finite element formulations for incompressible flows

A new approach is presented to obtain stabilized finite element formulations such as SUPG and GLS. The procedure consists in modifying the equations to be solved and then to obtain the variational equations by a standard Galerkin method. The new formulation adds terms involving boundary integrals to the standard stabilization techniques. These terms compensate for a lack of consistency of the traditional SUPG and GLS methods for which stabilization terms are added only on the element interiors, while jumps of the residual across element faces are neglegted. A physical interpretation is provided of how the modified equations are obtained. It is shown how stabilized formulations such as SU, SUPG and GLS are recovered. In all cases stabilization terms defined on the element interiors are accompanied by additional boundary integrals. The presence of the boundary integrals is shown to improve the numerical prediction for various viscous and nearly inviscid flows. Finally, the present approach is directly applicable to higher order finite element discretizations.

THREE-DIMENSIONAL NUMERICAL SIMULATION OF TURBULENT FLOW AND HEAT TRANSFER IN A CONTINUOUS GALVANIZING BATH

This article presents the application of a three-dimensional finite-element solution algorithm for the prediction of velocity and temperature fields in an industrial continuous galvanizing bath. The effect of line speed, strip width, strip temperature, and inductor mixing are evaluated. Simulations were carried out using a parallel computational fluid dynamics (CFD) software developed at the Industrial Materials Institute, Natural Research Council of Canada. The incompressible Navier-Stokes equations are solved for turbulent flows using the k - k model. Both forced-convection and temperature-dependent density conditions are considered in order to assess the buoyancy effect. When considering the buoyancy, the flow induced by variations in density is especially apparent near the inductors and the melting makeup ingot, while little effect is observed in the sheet and rollers region. Thermal effects are also amplified when the inductor is at high capacity, during the ingot melting. Simulations allow visualization of regions of varying velocity fields and clearly illustrate the mixed and stagnant zones for different operating conditions.

Numerical simulation of flow, temperature and composition variations in a galvanizing bath

Abstract The modern hot dip galvanizing operation is a complex process subject to a number of configurational, physical, chemical and kinetic parameters. Small decreases in temperature can precipitate intermetallic dross particles, which can be entrained in the flow towards the strip leading to surface imperfections. The numerical simulations carried out in this study clearly define the spatial distribution of velocity, temperature and compositional variation in the bath. The modeling of the transient effects during ingot melting and non-melting periods have also identified the critical periods and zones within the bath where dross formation can occur within an operating cycle. L’opération moderne de galvanisation à chaud est un procédé complexe exposé à plusieurs paramètres configurationnels, physiques, chimiques et cinétiques. De petites diminutions de température peuvent précipiter des particules intermétalliques de scories, lesquelles peuvent être entraînées dans l’écoulement vers la bande, conduisant à des imperfections de surface. Les simulations numériques effectuées dans cette étude définissent clairement la distribution spatiale de la vitesse, de température et de la variation de composition dans le bain. La modélisation des effets transitoires lors des périodes de fonte et d’absence de fonte du lingot a également identifié les périodes critiques ainsi que les zones dans le bain où la formation de scorie peut se produire à l’intérieur d’un cycle d’opération.