Towards and FVE-FAC Method for Determining Thermocapillary Effects on Weld Pool Shape
Henson, Van Emden
MetadataShow full item record
Several practical materials processes, e.g., welding, float-zone purification, and Czochralski crystal growth, involve a pool of molten metal with a free surface, with strong temperature gradients along the surface. In some cases, the resulting thermocapillary flow is vigorous enough to convect heat toward the edges of the pool, increasing the driving force in a sort of positive feedback. In this work we examine this mechanism and its effect on the solid-liquid interface through a model problem: a half space of pure substance with concentrated axisymmetric surface heating, where surface tension is strong enough to keep the liquid free surface flat. The numerical method proposed for this problem utilizes a finite volume element (FVE) discretization in cylindrical coordinates. Because of the axisymmetric nature of the model problem, the control volumes used are torroidal prisms, formed by taking a polygonal cross-section in the (r, z) plane and sweeping it completely around the z-axis. Conservation of energy (in the solid), and conservation of energy, momentum, and mass (in the liquid) are enforced globally by integrating these quantities and enforcing conservation over each control volume. Judicious application of the Divergence Theorem and Stokes' Theorem, combined with a Crank-Nicolson time-stepping scheme leads to an implicit algebraic system to be solved at each time step. It is known that near the boundary of the pool, that is, near the solid-liquid interface, the full conduction-convection solution will require extremely fine length scales to resolve the physical behavior of the system. Furthermore, this boundary moves as a function of time. Accordingly, we develop the foundation of an adaptive refinement scheme based on the principles of Fast Adaptive Composite Grid methods (FAC). Implementation of the method and numerical results will appear in a later report.
SEE ParentDocumentRecord|Ntt=19970006857 "Seventh Copper Mountain Conference on Multigrid Methods"; p. 147-166; Part 1; NASA-CP-3339
RightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
Showing items related by title, author, creator and subject.
Giraldo, F.X. (2001);The spectral element method for the two-dimensional shallow water equations on the sphere is presented. The equations are written in conservation form and the domains are discretized using quadrilateral elements obtained ...
Cleveland, William Bryant. (Monterey, California. Naval Postgraduate School, 2007-03);This thesis had 2 objectives. The first purpose of this thesis was to develop an experimental procedure to study electric current induced flow of liquid metal, similar to that found at the armature-rail contact due to ...
Fisher, Michael Robert. (Monterey, California. Naval Postgraduate School, 1996-09);Subjective and objective analyses of near-surface winds are utilized to estimate tropical cyclone (TC) size over a region of the western North Pacific. An empirical outer wind profile assuming partial conservation of angular ...