Estudo numerico de um escoamento bifasico, laminar : padrões anular e estratificado




A numerical solution of the two-dimensional momentum equations for a two-phase, Newtonian fluid(s), steady, laminar, axial, fully developed flow in a long, horizontal, circular pipe is conducted. The annular and stratified patterns are considered by assuming the interface between the phases to be either circular-cylindrical or an arc-segment of a cylindrical surface, possibly of zero curvature (chord). Mathematically, the physical phenomenon is described by conduction-type governing equations and represents a potential flow. To solve the problem, the Flux-Spline method (Varejão, 1979), built on the basis of the contral-volume formulation (Patankar, 1980), is used, because it shows to be more accurate and economic than other schemes. Besides, it was devised to handle homogeneous by parts source-terms, a feature particularly interesting in this type of question. Moreover, the presence of the interface, whose position is known in advance, imposes the use of a general curvilinear coordinates frame, hence the work of Hsu (1981), who extended the aforementioned concept, originally derived to Cartesian coordinates, is utilized. The results are confranted against the calculations carried out by Bentwich (1964) and comparisons in terms of volumetric flow rates show a very good match. That author constructed an analytical solution under the same assumptions made here, although the referred numerical technique is not restricted to such limitations: only, for a given problem, an apprapriate computing mesh must be placed to map the domain of calculation


analise numerica engenharia mecanica escoamento bifasico

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