Finite element formulation for filling a thin section cavity

Abstract

Presents a quasi three‐dimensional formulation for filling a thin section cavity which is derived under the assumption that no transverse flow occurs in the gap. A no‐slip condition was applied on all surfaces occupied by the fluid and a slip condition on all air‐filled (empty) surfaces. The formulation was developed to analyse the sections which lie in the xy‐plane or may be oriented arbitrarily in three‐dimensional space. Solves the discretized thickness‐integrated finite element flow equations by using the implicit mixed velocity‐pressure formulation, and uses the volume of fluid (VOF) method to track the free surfaces. Presents numerical examples which confirm the accuracy of the formulation and demonstrate how it can be used to model the filling of planar and three‐dimensional thin section cavities of irregular shape.

Citation

Gethin, D.T. and Abdullah, S. (1997), "Finite element formulation for filling a thin section cavity", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 7 No. 4, pp. 344-366. https://doi.org/10.1108/09615539710165822