Modeling of viscoelastic lid driven cavity flow using finite element simulations

In this study we have used a convergent and highly accurate mixed finite el ement technique to model the effect of fluid elasticity on the flow kinemat ics and the stress distribution in lid driven cavity flow. Our work is moti vated by the desire to capture the important physical aspects of the basic flow and thus to better understand the purely elastic instability in recirc ulating flows which has been reported in the literature elsewhere [A.M. Gri llet, E.S.G. Shaqfeh, Observations of viscoelastic instabilities in recircu lation flows of Boger fluids, J. Non-Newtonian Fluid Mech. 64 (1996) 141-15 5; P. Pakdel, G.H. McKinley, Cavity flows of elastic liquids: purely elasti c instablities, Phys. Fluids 10 (5) (1998) 1058-1070]. In our numerical inv estigations we have treated the corner singularities by incorporating a con trolled amount of leakage which allows the computation of fully elastic mes h converged solutions. We begin by validating our Newtonian cavity results against previous work to show that the introduction of leakage does not app reciably modify the cavity recirculation flow. Then we examine the polymer stresses to understand how elasticity changes the flow kinematics, slowing the primary recirculation vortex and causing the vortex center to shift opp osite of the direction of Lid motion. Variations of the cavity aspect ratio are also explored. Focusing on the corners we find that the leakage reliev es the corner singularities and moreover, finite leakage helps explain the unusual behavior seen in the radial velocity in experiments. Finally, we ha ve reexamined the previously proposed mechanisms for elastic instability in this flow and put forth a new instability mechanism. Together, these mecha nisms may better explain the complex aspect ratio dependence of the onset o f elastic instability in lid driven cavity flow. (C) 1999 Elsevier Science B.V. All rights reserved.