Viscoelastic flow past a confined cylinder of a polyisobutylene solution

Abstract

SynopsisViscoelastic constitutive equations are evaluated using the benchmark problem of the planar flow past a confined cylinder for a well-characterized solution of S%(w/w) polyisobutylene in tetradecane. The ratio of channel height to cylinder diameter is equal to two. We compare finite element simulations with point-wise measured velocities and stresses obtained by means of laser Doppler anemometry and a flow-induced birefringence technique, respectively. The Deborah number (De) ranges from 0.25 to 2.32. In the case of the geometry with a symmetrically confined cylinder, computations were made with a generalized Newtonian model and with both a single-and a four-mode Phan-Thien and Tanner (PlT) model. All model parameters were determined in simple shear flow. A similar analysis is presented in case of an asymmetrically confined cylinder (with De = 1.87). Impressively good agreement was found between the predictions of the four-mode P'IT model and the measured velocities and stresses. The agreement was even excellent in the geometry with the asymmetrically confined cylinder. 0 I995 Society of Rheology.

Modelling of non-isothermal viscoelastic flows

“…This problem, recommended as a benchmark problem [17], was extensively studied in Refs. [13,29,30] to evaluate the performance of constitutive equations in complex flows for both polymer solutions and melts. Constitutive equations are tested by means of comparison of measured data of the velocity and/or stress field with finite element simulations.…”

“…The numerical methods used here have been tested by comparing results with other published work and with experimental results from flows of polymer solutions and polymer melts [12,13].…”

“…This is a benchmark flow extensively studied by our group [12][13][14]. It is one of the complex flows that is supplementary to the simple shear flows, commonly used for testing constitutive equations.…”

Mixed finite element methods for viscoelastic flow analysis: a review

“…To study the flow around a confined cylinder, Baaijens et al [137] and [138], apply the same PIB/C14 solution as Quinzani et al [132]. Velocities and stresses are identified by means of LDV and FIB, respectively.…”

Birefringence measurements on polymer melts in an axisymmetric flow cell

“…However, all numerical methods failed when reaching¯ow rates approximately half that of the minimum volumetric ow rate used in the experiments. However, as we wanted to make at least a qualitative comparison at this stage of the work, de-coupled simulations have been performed to calculate an approximate stress ®eld (Debae et al 1994;Douven et al 1995;Baaijens et al 1995). By this we mean that the velocity ®eld is ®rst calculated using a generalized Newtonian model, the Carreau-Yassuda model, for the viscosity,…”