Flow modeling and stability analysis of viscoelastic flows using the finite element method.

摘要

Viscoelastic flows play a major role in many fields of science and engineering. Considering the complex rheological behavior exhibited by polymeric fluids, it is not surprising that very complex flow patterns are observed in many processes that make use of viscoelastic fluids. Hence, in order to design, optimize and control various polymer and composite material processing operations, robust and accurate simulation models are needed. In addition, it is well known that viscoelastic flows are prone to purely elastic instabilities. Existence of purely elastic instabilities suggests that all polymeric flows, however slow they may be, are susceptible to hydrodynamic instabilities. The onset of these instabilities imposes a limit on the throughput of many polymer processing operations. For this reason, understanding the influence of fluid elasticity on stability of prototypical processing flows is crucial.; Numerical computations using an adaptive finite element technique have been performed to examine the effect of fluid elasticity in prototypical processing flows. In particular, we have investigated a nonhomogeneous axisymmetric stagnant flow (in both forward and reverse directions) of a moderately concentrated polystyrene solution and a dilute polystyrene Boger fluid. The simulations were performed with various constitutive models and the results were compared with experimentally measured stresses in order to determine the level of model complexity needed for quantitative prediction of flow quantities. These comparisons have shown that the Giesekus model can accurately capture the flow kinetics and stress field in flows with single acceleration and deceleration of the fluid elements.; A benchmark problem—sedimentation of a sphere in a viscoelastic fluid, has also been modeled using various molecular based constitutive models. Through comparison of model predictions with experimentally measured drag on the sphere we have shown that molecular based constitutive models based on the single segment elastic dumbbell do not contain all the underlying physics required for describing the fluid dynamics of dilute polymeric solutions in complex flows with multiple acceleration and deceleration of the fluid elements.; A time dependent integration technique has been implemented for linear and nonlinear stability analysis of viscoelastic flows in complex geometries. This simulation technique has been validated in plane Couette flow of an Oldroyd-B fluid to show that it can capture the most dangerous eigenvalues of the flow system. In turn, this validated simulation technique has been used to examine the stability of the viscoelastic flow of an Oldroyd-B fluid through a bank of cylinders. The simulation results compare favorably with experimental findings both in terms of conditions for onset of the flow instability as well as the mechanism of the instability. Finally the nonlinear stability analysis is carried out to examine the dynamic structure of this flow system.