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dc.contributor.authorCanright, David
dc.contributor.authorHenson, Van Emden
dc.dateSep 01, 1996en_US
dc.date.accessioned2018-09-27T00:06:53Z
dc.date.available2018-09-27T00:06:53Z
dc.date.issued1996-09
dc.identifier.other19970006869
dc.identifier.urihttp://hdl.handle.net/10945/60127
dc.identifier.urihttps://ntrs.nasa.gov/search.jsp?R=19970006869
dc.descriptionSEE ParentDocumentRecord|Ntt=19970006857 "Seventh Copper Mountain Conference on Multigrid Methods"; p. 147-166; Part 1; NASA-CP-3339en_US
dc.descriptionApproved for public release, distribution unlimiteden_US
dc.description.abstractSeveral 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.en_US
dc.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.en_US
dc.titleTowards and FVE-FAC Method for Determining Thermocapillary Effects on Weld Pool Shapeen_US
dc.typeConference Paper
dc.contributor.corporateLangley Research Center
dc.subject.authorFINITE VOLUME METHODen_US
dc.subject.authorLIQUID-SOLID INTERFACESen_US
dc.subject.authorCONVECTIVE HEAT TRANSFERen_US
dc.subject.authorWELDINGen_US
dc.subject.authorCAPILLARY FLOWen_US
dc.subject.authorINTERFACIAL TENSIONen_US
dc.subject.authorFLOAT ZONESen_US
dc.subject.authorPURIFICATIONen_US
dc.subject.authorCZOCHRALSKI METHODen_US
dc.subject.authorTEMPERATURE GRADIENTSen_US
dc.subject.authorLIQUID SURFACESen_US
dc.subject.authorCYLINDRICAL COORDINATESen_US
dc.subject.authorCONSERVATION EQUATIONSen_US
dc.subject.authorTIME DEPENDENCEen_US
dc.subject.authorPOSITIVE FEEDBACKen_US
dc.subject.authorCONDUCTIONen_US
dc.subject.authorCOMPUTATIONAL GRIDSen_US
dc.description.funderN00014-92-WR-24009


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