Paper Number
IN13 

Session
Flow-induced Instabilities in Non-Newtonian Fluids

Title
A Space-Time Galerkin/Least-Squares Method for the simulation of non-Newtonian fluid flows

Presentation Date and Time
October 12, 2022 (Wednesday) 1:30

Track / Room
Track 5 / Sheraton 2

Authors (Click on name to view author profile)

  1. Varchanis, Stylianos (Okinawa Institute of Science and Technology)
  2. Haward, Simon J. (Okinawa Institute of Science and Technology)
  3. Shen, Amy Q. (Okinawa Institute of Science and Technology)

Author and Affiliation Lines (in printed abstract book)
Stylianos Varchanis, Simon J. Haward and Amy Q. Shen
Okinawa Institute of Science and Technology, Onna-son, Okinawa 904-0495, Japan

Speaker / Presenter 
Varchanis, Stylianos

Keywords
computational methods; flow-induced instabilities; gels; polymer melts; polymer solutions

Text of Abstract
The Space-Time Galerkin/Least-Squares (ST-GLS) finite element method is usually employed to solve the Navier-Stokes equations for incompressible Newtonian fluids [1-2]. Based on the ST-GLS principle, we present a new, fully consistent and highly stable finite element method for non-Newtonian fluid flows. Space and time are discretized using finite elements and all flow variables (velocity-pressure-stresses) are interpolated with polynomials of the same degree. The positive definiteness of the conformation tensor is enforced by a square-root reformulation of the constitutive equation [3]. The method is enriched with a consistent shock-capturing scheme that suppresses numerical oscillations around singularities. The accuracy, robustness, and generality of the method are validated in various benchmark flows of viscoelastic and elasto-visco-plastic (EVP) fluids. Initially, we consider the creeping flow of an Oldroyd-B fluid past a cylinder in a straight channel. We then proceed to the flow of a Saramito/Herschel-Bulkley (EVP) fluid in a lid-driven cavity with finite inertia. The method is also tested in creeping flows where elastic instabilities occur. These benchmark tests include pitchfork and Hopf bifurcations in the flow of Phan-Thien-Tanner fluids past a cylinder in a straight channel. Finally, we present for the first time the symmetry breaking in 3-dimensional simulations of a falling sphere in a upper convected Maxwell fluid, under the creeping flow assumption. In all cases, we demonstrate that we can obtain numerically stable solutions for very high values of the Weissenberg number that have never been accessed before by existing numerical methods. [1] T. J. R. Hughes, L. P. Franca, G. M. Hulbert, Comp. meth. App. Mech. Eng., 73 (1989). [2] T. E. Tezduyar, Advances in applied mechanics 28 (1991). [3] N. Balci, B. Thomases, M. Renardy, C. R. Doering, J. Non-Newt. Fluid Mech., 166 (2011).