| Full text | |
| Author(s): |
Evans, J. D.
;
Palhares Junior, I. L.
;
Oishi, C. M.
;
Ruano Neto, F.
Total Authors: 4
|
| Document type: | Journal article |
| Source: | Physics of Fluids; v. 34, n. 11, p. 28-pg., 2022-11-01. |
| Abstract | |
We verify numerically the theoretical stress singularities for two viscoelastic models that occur at sharp corners. The models considered are the Giesekus and Phan-Tien-Tanner (PTT), both of which are shear thinning and are able to capture realistic polymer behaviors. The theoretical asymptotic behavior of these two models at sharp corners has previously been found to involve an integrable solvent and polymer elastic stress singularity, along with narrow elastic stress boundary layers at the walls of the corner. We demonstrate here the validity of these theoretical results through numerical simulation of the classical contraction flow and analyzing the 270 degrees corner. Numerical results are presented, verifying both the solvent and polymer stress singularities, as well as the dominant terms in the constitutive equations supporting the elastic boundary layer structures. For comparison at Weissenberg order one, we consider both the Cartesian stress formulation and the alternative natural stress formulation of the viscoelastic constitutive equations. Numerically, it is shown that the natural stress formulation gives increased accuracy and convergence behavior at the stress singularity and, moreover, encounters no upper Weissenberg number limitation in the global flow simulation for sufficiently large solvent viscosity fraction. The numerical simulations with the Cartesian stress formulation cannot reach such high Weissenberg numbers and run into convergence failure associated with the so-called high Weissenberg number problem. (C) 2022 Author(s). (AU) | |
| FAPESP's process: | 18/22242-0 - Free surface flows of complex fluids |
| Grantee: | Murilo Francisco Tome |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 21/13833-7 - Data-driven and machine learning in non-Newtonian fluid mechanics |
| Grantee: | Cassio Machiaveli Oishi |
| Support Opportunities: | Scholarships abroad - Research |
| FAPESP's process: | 21/05727-2 - Numerical analysis and computational implementations of non-Newtonian flow constitutive equations |
| Grantee: | Fabiano Ruano Neto |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry |
| Grantee: | Francisco Louzada Neto |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |