Proceedings of the ENCIT 2014 Copyright c  2014 by ABCM 15th Brazilian Congress of Thermal Sciences and Engineering November 10-13, 2014, Belém, PA, Brazil EXTERNAL FLOWS OF ELASTO-VISCOPLASTIC MATERIALS OVER A BLADE Márleson R. S. Ferreira, marleson@mecanica.ufrgs.br Giovanni M. Furtado, giovannimf@mecanica.ufrgs.br Lober Hermany, hermany@mecanica.ufrgs.br Sérgio Frey, frey@mecanica.ufrgs.br Department of Mechanical Engineering, Federal University of Rio Grande do Sul, Rua Sarmento Leite 425, Porto Alegre, RS 90050- 170, Brazil Mônica F. Naccache, naccache@puc-rio.br Paulo R. de Souza Mendes, pmendes@puc-rio.br Department of Mechanical Engineering, Pontifícia Universidade Católica-RJ, Rua Marquês de São Vicente 225, Rio de Janeiro, RJ 22453-900, Brazil Abstract. A numerical investigation of external flows of elasto-viscoplastic materials around a flat plate is presented. The mechanical modeling herein considered makes use of the incompressible continuity and motion equations, coupled with the elasto-viscoplastic material equation introduced by de Souza Mendes (2011). The constitutive equation is based upon a modified Oldroyd-B model. The mechanical model is approximated by a stabilized finite element formulation, namely the three-field GLS-type method, using an equal-order combination of bi-linear Lagrangian interpolations – a very attractive choice from the computational point-of-view. The numerical results show a significant elastic deformation obtained far from the plate and the elasticity changes the shape of the yielded/unyielded regions. Keywords: elasto-viscoplastic fluid flow, external flow, finite element approximations, GLS method 1. INTRODUCTION The study of non-Newtonian fluids flows is of great interest in industrial processes, since most industrial fluids exhibit this behavior. Some examples are the petroleum, cosmetics, paints, drilling muds, food industry products among others. To represent the nonlinear behavior of the viscosity of these fluids it was adopted a elasto-viscoplastic model proposed by de Souza Mendes (2009), which is a modified version of the Oldroyd-B model. This model is approximated numerically by the Galerkin least squares method in terms of the extra-stress, pressure and velocity. This methodology – introduced by Hughes et al. (1986), for the Stokes problem, and later extended to mixed and multi-field Navier-Stokes equations in Franca and Frey (1992) and in Behr et al. (1993), respectively – does not need to satisfy the compatibility conditions arisen from finite element sub-spaces for extra-stress-velocity and pressure-velocity fields. It enhances the stability of the classical Galerkin method adding mesh-dependent terms, which are functions of the residuals of flow governing equations, evaluated element-wise. This article studies the inertialess steady state flow of elasto-viscoplastic fluids around a flat plate. In order to investi- gate the morphology of the yield stress surfaces, numerical simulation are performed varying the dimensionless flow-rate U * and the dimensionless relaxation time θ * 0 . In all simulations power-law index is n =0.5. 2. MECHANICAL MODELING The governing equations are given, respectively, by the continuity and the momentum conservation equations as: ∇· u = 0, ∈ Ω, ∇· τ -∇P = ρu ·∇u, ∈ Ω, (1)