Performance of an elasto-viscoplastic model in some benchmark problems

Abstract

A recent elasto-viscoplastic thixotropic model proposed by (de Souza Mendes in J. Non-Newton. Fluid Mech. 164:66-75, 2009; de Souza Mendes in Soft Matter 7:2471-2483, 2011) is applied to five benchmark problems: the flow in a lid cavity, the flow through an expansion followed by a contraction, the flow over a flat plate, the channel entry flow, and the flow around a cylinder confined between parallel plates. One of the main advantages of this approach is its ability to recover a model for elasto-viscoplastic materials in B M.F. Naccache a smooth fashion, i.e., in the limit where the characteristic thixotropic time tends to zero. These problems are numerically solved using the finite element method, with a four-field GLS-type formulation. While the simplified version is applied to the first three problems, the full model including thixotropy is applied to the channel entry flow and the flow around the cylinder. The elasto-viscoplastic problems analyzed show that, in general, elasticity tends to inhibit yielding and is more concentrated in unyielded regions. The thixotropic effects analyzed show that the delay in the microstructure response of the material significantly alters the problem when compared to the pure elasto-viscoplastic counterpart.

A finite volume method for the simulation of elastoviscoplastic flows and its application to the lid-driven cavity case

“…The lid-driven cavity test case is arguably the most popular benchmark test case for new numerical methods for flow simulations. As such, it has been used also as a benchmark problem for viscoplastic [24,34] and viscoelastic [35] flows; there exist also the EVP flow studies of [36,23], but with a different EVP model that incorporates a kind of regularisation. In the present study the parameters of the SHB model are chosen so as to represent Carbopol, which is regarded as a simple VP fluid (more complex behaviour such as thixotropy [37] and kinematic hardening [38] are not considered, but may be incorporated into the model in the future).…”

“…Usually, FEM solvers are employed in EVP flow simulations (e.g. [22,23,21]). An alternative, very popular discretisation / solution method in Computational Fluid Dynamics is the Finite Volume Method (FVM); it has been successfully applied to viscoplastic (e.g.…”

“…The lid-driven cavity test case is arguably the most popular benchmark test case for new numerical methods for flow simulations. As such, it has been used also as a benchmark problem for viscoplastic [24,34] and viscoelastic [35] flows; there exist also the EVP flow studies of [36,23], but with a different EVP model that incorporates a kind of regularisation.…”