Numerical simulation of non-isothermal viscoelastic fluid flows using a VMS stabilized finite element formulation

Abstract

The effect of temperature in viscoelastic fluid flows is studied applying a stabilized finite element formulation based on both a standard and a log-conformation reformulation (LCR), and the Variational Multiscale (VMS) method as stabilization technique. The log-conformation reformulation turns out to be crucial to solve the cases with a high Weissenberg number. Regarding temperature coupling, a two-way coupling strategy is employed: on the one hand, the dependence of viscoelastic fluid parameters on temperature is established, together with the addition of a new term to the energy equation which takes into account the stress work. The formulations and the iterative algorithms are validated in the well-known flow past a cylinder benchmark. Besides, the extension 1:3 case is studied, in which several scenarios are explored varying the values of the main dimensionless numbers that characterize the problem to see how the flow pattern and temperature distribution change along the channel. • A new formulation for solution of thermally coupled viscoelastic flows is presented. • The new formulation is based on the Variational Multiscale Method. • Both a standard and a logarithmic conformation reformulation approach are presented. • The behavior of the proposed methodology is tested in several numerical examples.