Technique for obtaining the algebraic PTT models, applications and analysis in two-dimensional flows

Abstract

This project proposes the theorical study about the calculation to obtain an algebraic model from a differential model PTT (Phan-Thien--Tanner) as well as its implementation and numerical results for viscoelastic confined and free surface flows on the high performance code called FREEFLOW-2D. The advantage for using algebraic models is the CPU time, because only one differential equation must be solved, instead of the differential model which requires the calculation of three differential equations, in case bidimensional. To validate the algebraic methodology implemented for PTT model it will be simulate the fully developed flow in a channel and their results will be compared with the analytical solutions for this problem. The goal is simulate several confined and free surface problems using the algebraic model and compare them with the numerical results obtained by differential model. In these simulations, it is intended to investigate how the numerical responses are similar to ensure the viability of using the algebraic model. Furthermore, it is intended to compare the CPU time between the algebraic and differential models and also to investigate numerically, for a specific problem, whether the restriction of the Weissenberg number (Wi) is the same for both models and whether the algebraic model is able to simulate this problem for Wi higher than that employed in differential model. The numerical methodology to solve the algebraic PTT model is based on finite difference technique on a staggered grid. The fluid will be modelled by a Marker-and-Cell type method and an accurate representation of the fluid surface will be employed. (AU)