The flow and solidification of a thin fluid film on an arbitrary three-dimensional surface
By T. Myers, J. Charpin, S. Chapman. 2002
169 citations recorded by the source corpus.
A model for the flow of a thin film, with and without solidification, on an arbitrary three-dimensional substrate is presented. The problem is reduced to two simultaneous partial differential equations for the film and solid layer thicknesses. The flow model (with the solidification rate set to zero) is the first such model to describe thin film flow on an arbitrary three-dimensional surface. Various limits are investigated to recover previous models for flow on flat, cylindrical and two-dimensional curved surfaces. With solidification a previous model for accretion on a flat substrate is retrieved. It is shown how the model may be reduced to standard forms, such as solidification on a flat surface, circular and non-circular cylinders, aerofoils and spheres. Numerical solutions are obtained by combining an ADI scheme with a shock capturing method. Results are presented for flow and accretion on a flat surface, aerofoil and sphere.
Subfields: Aerospace Engineering, Computational Mechanics
View Paper: https://www.semanticscholar.org/paper/042acfbe0b8f7a3ed29db69515d0aaa8da78fa7c
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In Aerospace Engineering
In Computational Mechanics
Citations in the corpus
- A simple embedding method for solving partial differential equations on surfaces (2008, background): “fields [7] and weathering [8], while applications in fluid dynamics include flows and solidification on surfaces [17,18], and the problem of evolving surfactants on interfaces [29].”
- Eulerian finite element method for parabolic PDEs on implicit surfaces (2008, unknown): “Models for thin fluid films on surfaces have been developed in [17, 20].”