Simulation Of Thin Film Flow Around A Cylinder
On An Inclined Plane Using The Boundary
Element Method
Author(s)
S. J. Baxter, H. Power, K. A. Cliffe & S. Hibberd
Abstract
Steady Stokes flow driven by gravity down an inclined plane wall around a circular
cylinder attached to the wall is considered. The effects of the cylinder are examined
for various flow configurations. Values for the unit normal and curvature of the
free surface are found using a Hermitian radial basis function interpolation. All
free surface profiles indicate an upstream peak, followed by a trough downstream
of the obstacle with the peak decaying in a \“horseshoe” shaped deformation. Flow
profiles are governed by four parameters; the plane inclination, the Bond number,
the contact angle and the obstacle geometry.
Keywords: BEM, three-dimensional, thin film, Newtonian viscous flow, cylinder.
1 Introduction
Thin film flows down an inclined plane wall driven by gravity can often be modelled
as an incompressible Stokes flow. Flows usually involve interaction with an
obstacle either fully submerged of protruding through the film surface.
Early published works considering two-dimensional film flows over obstacles
utilized a variety of techniques for the numerical procedures required to obtain
solutions.An overviewof these publications is presented in Blyth and Pozrikidis [1].
Hayes et al. [2] considered a three-dimensional steady, thin, viscous liquid film
down an inclined plane driven by gravity and over small topographies. The lubrication
approximation was used as the basis for their model and formulates a single
linear inhomogeneous evolution equation. The free surface shape was then
obtained by formation of the appropriate Green’s function.
Keywords
BEM, three-dimensional, thin film, Newtonian viscous flow, cylinder.
Related Book
Other papers in this volume
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