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The solution of viscous incompressible jet and free-surface flows using finite-element methods

Published online by Cambridge University Press:  29 March 2006

R. E. Nickell ,
R. I. Tanner  and
B. Caswell
R. E. Nickell
Affiliation:
Division of Engineering, Brown University
R. I. Tanner
Affiliation:
Division of Engineering, Brown University
B. Caswell
Affiliation:
Division of Engineering, Brown University
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Abstract

We discuss the creation of a finite-element program suitable for solving incompressible, viscous free-surface problems in steady axisymmetric or plane flows. For convenience in extending program capability to non-Newtonian flow, non-zero Reynolds numbers, and transient flow, a Galerkin formulation of the governing equations is chosen, rather than an extremum principle. The resulting program is used to solve the Newtonian die-swell problem for creeping jets free of surface tension constraints. We conclude that a Newtonian jet expands about 13%, in substantial agreement with experiments made with both small finite Reynolds numbers and small ratios of surface tension to viscous forces. The solutions to the related ‘stick-slip’ problem and the tube inlet problem, both of which also contain stress singularities, are also given.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 65 , Issue 1 , 12 August 1974 , pp. 189 - 206
Copyright
© 1974 Cambridge University Press

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