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Finite element analysis of the duct flow of Bingham plastic fluids: an application of the variational inequality
Author(s) -
Wang Yeh
Publication year - 1997
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/(sici)1097-0363(19971115)25:9<1025::aid-fld601>3.0.co;2-3
Subject(s) - finite element method , bingham plastic , variational inequality , mathematics , duct (anatomy) , mathematical analysis , mechanics , geometry , physics , rheology , thermodynamics , medicine , pathology
The duct flow of Bingham plastic fluids is analysed with the variational inequality‐based finite element method. The problem of tracking the yield surface is solvable through the regularization technique which can be easily incorporated into the existing finite element code. The existence theorem of this method was established through the theory of variational inequalities. A small positive constant is added to the second shear rate invariant, resulting in an apparent viscosity of finite magnitude in the unyielding plug zone. This makes the minimization of the non‐differential variational integral possible. In order to achieve convergence at small regularization parameter, a zero‐order continuation is employed. It is also shown that a fine tessellation of the flow domain is necessary for tracking the yield surfaces unambiguously. Two classes of duct flow, namely axial flows in eccentric annuli and in an L‐shaped duct, were investigated. In both cases it was easy to show the presence of the mobile plugs around the duct centres from the axial velocity profiles; however, the stagnant plugs at the narrow side in eccentric annuli with large eccentricity and near the apex of right‐angled corners in an L‐shaped duct could only be identified from the calculation of the distributions of the second shear rate or shear stress invariant. © 1997 John Wiley & Sons, Ltd.