Numerical approximations for flow of viscoplastic fluids in a lid-driven cavity

• Published in: Journal of non-Newtonian fluid mechanics 2011-07, Vol.166 (12), p.667-679
• Main Authors: dos Santos, Daniel Dall’Onder, Frey, Sérgio, Naccache, Mônica F., de Souza Mendes, P.R.
• Format: Article
• Language: English
• Subjects: Approximation; Computational fluid dynamics; Exact sciences and technology; Fluid dynamics; Fluid flow; Fluids; Fundamental areas of phenomenology (including applications); Holes; Laminar flows; Laminar flows in cavities; Lid-driven cavity flow; Mathematical analysis; Mathematical models; Multi-field GLS method; Non-newtonian fluid flows; Physics; Regularized models; Rheological properties; SMD fluid; Viscoplasticity
• ISSN: 0377-0257; 1873-2631
• DOI: 10.1016/j.jnnfm.2011.03.004

► The flow of viscoplastic fluids inside a lid-driven cavity is studied. ► The mechanical behavior is assumed to obey the GNF constitutive model. ► The SMD viscosity function is used with thd GNF model. ► Results are presented for a wide range of the governing parameters. The effect of inertia and rheology parameters on the flow of viscoplastic fluids inside a lid-driven cavity is investigated using a stabilized finite element approximation. The viscoplastic material behavior is described by the model introduced by de Souza Mendes and Dutra [30] – herein called SMD fluid – which is essentially a regularized viscosity function that involves only rheological properties of the material. The incompressible balance equations are coupled with the non-linear SMD model and are approximated by a multi-field Galerkin least-squares method in terms of extra-stress, pressure and velocity. The results obtained confirm the stability features of the multi-field formulation and the appropriateness of the rheological stress regularization introduced by the SMD fluid. The influence of inertia and rheological parameters on the morphology of the material yield surfaces is analyzed and discussed.