DYNAMIC SIMULATION OF FREE SURFACES IN CAPILLARIES WITH THE FINITE-ELEMENT METHOD

The mathematical formulation of the dynamics of free liquid surfaces i ncluding the effects of surface tension is governed by a non-linear sy stem of elliptic differential equations. The major difficulty of getti ng unique closed solutions only in trivial cases is overcome by numeri cal methods. This paper considers transient simulations of liquid-gas menisci In vertical capillary tubes and gaps in the presence of gravit y. Therefore the CFD code FIDAP 7.52 based on the Galerkin finite elem ent method (FEM) is used, Calculations using the free surface model ar e presented for a variety of contact angles and cross-sections with ex perimental and theoretical verification. The liquid column oscillation s are compared for numerical accuracy with a mechanical mathematical m odel, and the sensitivity with respect to the node density is investig ated. The efficiency of the numerical treatment of geometric non-trivi al problems is demonstrated by a prismatic capillary. Present restrict ions limiting efficient transient simulations with irregularly shaped calculational domains are stated. (C) 1998 John Wiley & Sons, Ltd.