Numerical study of the stress singularity in stick-slip flow of the Phan-Thien Tanner and Giesekus fluids

Author(s)

Evans, J. D. ^[1] ; Cuminato, J. A. ^[2] ; Palhares Junior, I. L. ^[2] ; Oishi, C. M. ^[3]

Affiliation

^[1] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon - England

^[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Dept Matemat Aplicada & Estat, BR-13566590 Sao Carlos, SP - Brazil

^[3] Univ Estadual Paulista, Fac Ciencias & Tecnol, Dept Matemat & Comp, BR-19060900 Presidente Prudente, SP - Brazil

• Document type: Journal article
• Source: Physics of Fluids; v. 31, n. 9 SEP 2019.
• Web of Science Citations: 0

Abstract

Stick-slip flow is a challenging viscoelastic benchmark problem due to the presence of a separation or transition point at the die exit where a sudden change in flow boundary conditions occurs. We present numerical simulations of transient planar stick-slip flow of the Phan-Thien-Tanner (PTT) and Giesekus fluids, investigating the polymer stress behavior around the stress singularity at the stick-slip point, confirming the asymptotic results presented by Evans et al. {[}{''}Stresses of the Oldroyd-B, PTT and Giesekus fluids in a Newtonian velocity field near the stick-slip singularity,{''} Phys. Fluids 29, 1-33 (2017)]. In order to improve the numerical knowledge about this viscoelastic benchmark problem, two distinct mathematical methodologies are used for comparison in the computational simulations: the Cartesian and natural stress formulations. The former is widely applied in computational rheology, while the latter is used for the first time in the context of this problem. The natural stress formulation gives improved convergence results both temporally and spatially near to the singularity while maintaining the same global flow characteristics as the Cartesian. (AU)

• 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
• FAPESP's process: 18/22242-0 - Free surface flows of complex fluids
• Grantee: Murilo Francisco Tome
• Support Opportunities: Regular Research Grants
• FAPESP's process: 14/17348-2 - Stability of Numerical methods for Viscoelastic high Weissenberg number flows
• Grantee: Irineu Lopes Palhares Junior
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 16/20389-8 - Numerical study of the natural stress formulation for free surface problems
• Grantee: Irineu Lopes Palhares Junior
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate