Filling of a circular pipe with a viscous fluid accounting for the surface tension forces

Abstract

In the framework of this paper, an investigation of the vertical axisymmetric pipe filling with a viscous fluid against the gravity force is implemented. The fluid flow is described by Navier-Stokes and continuity equations. On the free surface, the shear stress is equal to zero and the normal stress is equal to the sum of external and capillary pressure. The free surface motion is defined by the kinematic condition. On the solid wall, the velocity is set to zero. At the inlet section, the Poiseuille profile is used. Along the symmetry axis, the symmetry condition is assigned. A numerical solution to the problem is obtained using the control volume method and SIMPLE algorithm. The method of invariants is applied for compliance of the natural boundary conditions on the free surface. The effect of dimensionless criteria on the steady-state shape of the free surface was parametrically studied.