Dynamic simulation of free surfaces in capillaries with the finite element method

✍ Scribed by R. Trutschel; U. Schellenberger

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 244 KB
• Volume: 26
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/(sici)1097-0363(19980228)26:4<485::aid-fld646>3.0.co;2-#

✦ Synopsis

The mathematical formulation of the dynamics of free liquid surfaces including the effects of surface tension is governed by a non-linear system of elliptic differential equations. The major dif®culty of getting unique closed solutions only in trivial cases is overcome by numerical methods. This paper considers transient simulations of liquid±gas menisci in vertical capillary tubes and gaps in the presence of gravity. Therefore the CFD code FIDAP 7.52 based on the Galerkin ®nite element method (FEM) is used. Calculations using the free surface model are presented for a variety of contact angles and cross-sections with experimental and theoretical veri®cation. The liquid column oscillations are compared for numerical accuracy with a mechanical mathematical model, and the sensitivity with respect to the node density is investigated. The ef®ciency of the numerical treatment of geometric non-trivial problems is demonstrated by a prismatic capillary. Present restrictions limiting ef®cient transient simulations with irregularly shaped calculational domains are stated.