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Advisor(s)
Abstract(s)
The log-conformation formulation, proposed by Fattal and Kupferman [J. Non-Newt. Fluid Mech. 123
(2004) 281], has helped to provide further insights into the High-Weissenberg Number Problem. In this work, we investigate the performance of the log-conformation formulation in the Finite Volume Method
(FVM) framework for creeping flows of viscoelastic fluids in steady and unsteady flows around a confined
cylinder. The Oldroyd-B and Phan-Thien–Tanner (PTT) constitutive equations were used to assess
the effect of different rheological behaviour on the flow patterns and solution stability. The calculation
of the polymer stress contribution is carried out with both the standard technique and with the logconformation
methodology. For all test cases, up to the critical conditions when both methods converge to a steady solution, the use of the log-conformation technique provides solutions with similar accuracy as the standard approach. In terms of stability the log-conformation formulation is found to be significantly
more robust, and solutions could be obtained at higher Deborah number flows.
Description
Keywords
Finite-volume method Log-conformation tensor Viscoelastic fluid Cylinder flow