In this study, the energy conservation equation in a cylindrical coordinate system and the moving heat source from the tool are used to establish a steady-state three-dimensional heat transfer model for the friction stir welding (FSW). Then, the simplified momentum conservation equation is employed to predict the material flow model for the FSW. Combining the effects of heat transfer and material flow, this numerical model successfully predicts the weld temperature field and the material flow for the FSW. Numerical results show that increasing the welding or translational speed of the tool has the effect of decreasing the magnitude of the temperature within the workpiece, while increasing the rotating speed has the opposite effect. During the feeding process, the material located on the back of the tool pin has higher temperature than that on the front. Moreover, the temperature profile are asymmetrical between the advancing and retreating sides due to the material flow stirred by the tool, and this temperature difference depends on the speed of material flow under the tool shoulder.

In order to simulate the histories of temperature distributions and plastic flow of the dwell phase during a friction stir welding process, the Newton-Raphson method is used to solve the simultaneous equations of energy and momentum in the cylindrical-coordinate system. Comparing the simulation with the results of experiment, results show that the contact condition between the tool and the workpiece is at pure sliding without plastic flow at the beginning of the dwell phase until the temperature rises to about 300¢XC at the depth of 1.5 mm. In this period, the heat generation comes from the sliding friction between two surfaces. After the plastic flow occurs, the heat generation rises rapidly, and then decreases to a saturated value so that the temperature rise also achieves a constant value. Thermal expansion of the workpiece will increase the plunge force, so that the heat generation and the temperature raise increase. At the steady state condition, with increasing sticking proportion, the heat generation and the temperature quickly achieve a saturated value. For the steady-state condition, results show that the speed of plastic flow and shear strain rate increase with increasing rotational speed. The control of the contact state variable can effectively describe the heat generation and the distribution of plastic flow in different contact conditions. Comparing the simulation with the results of experiment, the contact condition can be identified.

La simulation d'écoulements dans des cavités cylindriques en rotation présente une difficulté particulière en raison de l'apparition de singularités sur l'axe. Le présent travail propose une méthode collocative pseudospectrale suffisamment efficace et précise pour surmonter cette difficulté et résoudre les équations 3D de Navier-Stokes écrites en coordonnées cylindriques. Cette méthode a été développée dans le cadre des différentes études menées au laboratoire M2P2, utilisant une méthode collocative de type Chebychev dans les directions radiale et axiale et Fourier-Galerkin dans la direction azimutale [thêta]. Pour éviter de prescrire des conditions sur l'axe, une nouvelle approche a été développée. Le domaine de calcul est défini par (r,[thêta],z)∈[-1,1]×[0,2π]×[-1,1] avec un nombre N pair de points de collocation dans la direction radiale. Ainsi, r=0 n'est pas un point de collocation. La distribution de points de type Gauss-Lobatto selon r et z densifie le maillage seulement près des parois ce qui rend l'algorithme bien adapté pour simuler les écoulements dans des cavités cylindriques en rotation. Dans la direction azimutale, le chevauchement des points dû à la discrétisation est évitée par l'introduction d'un décalage égal à π/2K à [thêta]>π dans la transformée de Fourier. La méthode conserve la convergence spectrale. Des comparaisons avec des résultats expérimentaux et numériques de la littérature montrent un très bon accord pour des écoulements induits par la rotation d'un disque dans des cavités cylindriques fermées. / When simulating flows in cylindrical rotating cavities, a difficulty arises from the singularities appearing on the axis. In the same time, the flow field itself does not have any singularity on the axis and this singularity is only apparent. The present work proposes an efficient and accurate collocation pseudospectral method for solving the 3D Navier-Stokes equations using cylindrical coordinates. This method has been developed in the framework of different studies of rotor-stator flows, using Chebyshev collocation in the radial and axial directions and Fourier-Galerkin approximation in the azimuthal periodic direction [thêta]. To avoid the difficulty on the axis without prescribing any pole and parity conditions usually required, a new approach has been developed. The calculation domain is defined as (r,[thêta];,z)∈[-1,1]×[0,2π]×[-1,1] using an even number N of collocation points in the radial direction. Thus, r=0 is not a collocation point. The method keeps the spectral convergence. The grid-point distribution densifies the mesh only near the boundaries that makes the algorithm well-suited to simulate rotating cavity flows where thin layers develop along the walls. In the azimuthal direction, the overlap in the discretization is avoided by introducing a shift equal to π/2K for [thêta]>π in the Fourier transform. Comparisons with reliable experimental and numerical results of the literature show good quantitative agreements for flows driven by rotating discs in cylindrical cavities. Associated to a Spectral Vanishing Viscosity, the method provides very promising LES results of turbulent cavity flows with or without heat transfer.

This work has been aimed at developing a mechanistic, transient, 3-D numerical model to predict the behavior of an evaporating thin liquid film on a non-uniformly heated cylindrical rod with simultaneous parallel and cross flow of vapor. Interest in this problem has been motivated by the fact that the liquid film on a full-length boiling water reactor fuel rod may experience significant axial and azimuthal heat flux gradients and cross flow due to variations in the thermal-hydraulic conditions in surrounding subchannels caused by proximity to inserted control blade tip and/or the top of part-length fuel rods. Such heat flux gradients coupled with localized cross flow may cause the liquid film on the fuel rod surface to rupture, thereby forming a dry hot spot. These localized dryout phenomena can not be accurately predicted by traditional subchannel analysis methods in conjunction with empirical dryout correlations. To this end, a numerical model based on the Level Contour Reconstruction Method was developed. The Standard k- turbulence model is included. A cylindrical coordinate system has been used to enhance the resolution of the Level Contour Reconstruction Model. Satisfactory agreement has been achieved between the model predictions and experimental data. A model of this type is necessary to supplement current state-of-the-art BWR core thermal-hydraulic design methods based on subchannel analysis techniques coupled with empirical dry out correlations. In essence, such a model would provide the core designer with a "magnifying glass" by which the behavior of the liquid film at specific locations within the core (specific axial node on specific location within a specific bundle in the subchannel analysis model) can be closely examined. A tool of this type would allow the designer to examine the effectiveness of possible design changes and/or modified control strategies to prevent conditions leading to localized film instability and possible fuel failure.