An experimental and numerical investigation of a viscoelastic flow around a cylinder

In this paper the plane flow of a shear thinning solution of 5 wt% polyisobutylene (PIB) in tetradecane (C14) (PIB/C14) around a cylinder placed between parallel plates is investigated numerically and experimentally. Both Laser Doppler Anemometry and Flow Induced Birefringence measurements are performed and compared with numerical results, using a Discontinuous Galerkin method and a one-mode Phan-Thien Tanner model. Previous work has shown a good agreement between measured and computed stress fields for the flow through a planar four-to-one contraction with this fluid. The flow around a cylinder, however, leads to some surprising differences

Viscoelastic flow past a confined cylinder of a polyisobutylene solution

Viscoelastic constitutive equations are evaluated using the benchmark problem of the planar flow past a confined cylinder for a well-characterized solution of 5%(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 (PTT) 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 PTT model and the measured velocities and stresses. The agreement was even excellent in the geometry with the asymmetrically confined cylinder. ©1995 Society of Rheolog

Viscoelastic flow past a confined cylinder of a low-density polyethylene melt

The capabilities of the exponential version of the Phan-Thien-Tanner (PTT) model and the Giesekus model to predict stress fields for the viscoelastic flow of a low density polyethylene melt around a confined cylinder are investigated. Computations are based on a newly developed version of the discontinuous Galerkin method. This method gives convergent results up to a Deborah number of 2.5 for the falling sphere in a tube benchmark problem. Moreover, the specific implicit-explicit implementation allows the efficient resolution of problems with multiple relaxation times which are mandatory for polymer melts. Experimentally, stress fields are related to birefringence distributions by means of the stress optical rule. Three different fits, of equal quality, to available viscometric shear data are used: two for the PTT model and one for the Giesekus model. Comparison of computed and measured fringes reveals that neither of the models is capable of describing the full birefringence pattern sufficiently well. In particular it appears difficult to predict both the birefringent tail at the wake of the cylinder that is dominated by elongational effects and the fringe pattern between cylinder and the walls where a combined shear-elongational flow is present