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Numerical simulation of complex flows of non‐Newtonian fluids using the stream tube method and memory integral constitutive equations
Author(s) -
Bereaux Yves,
Clermont JeanRobert
Publication year - 1995
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650210502
Subject(s) - streamlines, streaklines, and pathlines , constitutive equation , singularity , mechanics , mathematics , newtonian fluid , total variation diminishing , rotational symmetry , flow (mathematics) , geometry , mathematical analysis , classical mechanics , finite element method , physics , thermodynamics
In this paper a memory integral viscoelastic equation is considered for simulating complex flows of non‐Newtonian fluids by stream tube analysis. A formalism is developed to take into account co‐deformational memory equations in a mapped computational domain where the transformed streamlines are parallel and straight. The particle‐tracking problem is avoided. Evolution in time and related kinematic quantities involved with a K‐BKZ integral constitutive model are easily taken into account in evaluating the stresses. Successive subdomains, the stream tubes, may be considered for computing the main flow in abrupt axisymmetric contractions from the wall to the central flow region. The ‘peripheral stream tube’ close to the duct wall is determined by developing a non‐conventional modified Hermite element. A mixed formulation is adopted and the relevant non‐linear equations are solved numerically by the Levenberg‐Marquardt algorithm. Although the singularity at the section of contraction is not involved explicitly, the results obtained for the peripheral stream tube clearly show the singularity effects and the extent of the recirculating zone near the salient corner. The algorithm is stable even at high flow rates and provides satisfactory solutions when compared with similar calculations in the literature.