Summary
The stream-tube analysis is considered for the problem of the free surface determination for a 3D duct. The method allows computation of the unknown free surface by only considering a “peripheral stream tube”limited by the wall and the free surface and an inner stream surface, in a mapped computational domain where streamlines are rectilinear. The unknowns are determined by considering the conservation equations together with an optimization criterion, solved by using the Levenberg-Marquardt optimization algorithm. The number of degrees of freedom and the storage area are reduced. Similarly to previous 2-D studies, singularity problems in the vicinity of the junction points of the wall and the free surface are avoided. However, the stress peaks due to the singularity at the exit may still be evaluated. Results are presented, using a Newtonian fluid and a memory-integral constitutive equation, for a duct of square cross-section.
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© 1996 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
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Normandin, M., Clermont, JR. (1996). Three-Dimensional Study of Extrusion Processes by the Stream-Tube Method: Newtonian and Viscoelastic Results. In: Deville, M., Gavrilakis, S., Ryhming, I.L. (eds) Computation of Three-Dimensional Complex Flows. Notes on Numerical Fluid Mechanics (NNFM), vol 49. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-89838-8_26
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DOI: https://doi.org/10.1007/978-3-322-89838-8_26
Publisher Name: Vieweg+Teubner Verlag
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