Dynamics and friction drag behavior of viscoelastic flows in complex geometries: A multiscale simulation approach.

摘要

Flows of viscoelastic polymeric fluids are of great fundamental and practical interest as polymeric materials for commodity and value-added products are processed typically in a fluid state. The nonlinear coupling between fluid motion and microstructure, which results in highly non-Newtonian theology, memory/relaxation and normal stress development or tension along streamlines, greatly complicates the analysis, design and control of such flows. This has posed tremendous challenges to researchers engaged in developing first principles models and simulations that can accurately and robustly predict the dynamical behavior of polymeric flows. Despite this, the past two decades have witnessed several significant advances towards accomplishing this goal. Yet a problem of fundamental and great pragmatic interest has defied solution to years of ardent research by several groups, namely the relationship between friction drag and flow rate in inertialess flows of highly elastic polymer solutions in complex kinematics flows. First principles-based solution of this long-standing problem in non-Newtonian fluid mechanics is the goal of this research.; To achieve our objective, it is essential to develop the capability to perform large-scale multiscale simulations, which integrate continuum-level finite element solvers for the conservation of mass and momentum with fast integrators of stochastic differential equations that describe the evolution of polymer configuration. Hence, in this research we have focused our attention on development of a parallel, multiscale simulation algorithm that is capable of robustly and efficiently simulating complex kinematics flows of dilute polymeric solutions using the first principles based bead-spring chain description of the polymer molecules. The fidelity and computational efficiency of the algorithm has been demonstrated via three benchmark flow problems, namely, the plane Couette flow, the Poiseuille flow and the 4:1:4 axisymmetric contraction and expansion flow. It has been found that the algorithm shows linear speed up with the number of processors used in the parallelization and more importantly with the number of segments used in the bead-spring chain. In addition, the algorithm is approximately 50 times faster in comparison to the only existing multiscale simulation algorithm for bead-spring chains.; Employing the above algorithm multiscale simulations of the 4:1:4 axisymmetric contraction and expansion flow, a prototypical complex kinematics flow have been performed using bead-spring models of varying degree of complexity. A direct comparison with the experimental measurements for this flow has shown that for the first time the pressure drop (friction drag) evolution with the flow rate is quantitatively predicted by the bead-spring models that closely capture the transient extensional viscosity of the fluid. Also, based on an energy dissipation analysis it has been shown that the variation of the pressure drop with the flow rate is controlled by the coupling between the flow and the microstructure in the extensional flow dominant region of the flow domain. This has also demonstrated that the stress conformation hysteresis behavior, which has been conjectured in previous experimental studies to play an important role in the enhancement of the pressure drop cannot always be treated as a measure of the energy dissipation that actually causes the pressure drop enhancement. The simulation results, depending on the model used to characterize the fluid, have also shown the hitherto known vortex growth pathways, including either the growth of the upstream corner vortex or the shrinkage of the upstream corner vortex coupled with the formation of a lip vortex that grows and merges with the upstream corner vortex, which then increases in size with the flow rate. Furthermore, it has been demonstrated that the upstream corner vortex as well as lip vortex growth is driven by the adverse pressure gradient resul