Parallel Simulation of Viscoelastic Flow Past an Array of Cylinders by a Unstructured FVM Algorithm

In this paper, the flow of an Oldroyd-B fluid past an array of circular cylinders in a channel is simulated by a parallelized pressure-based Finite Volume Method (FVM) using fine unstructured meshes. The numerical method is using the Discrete Elastic Viscous Split Stress vorticity (DEVSS-omega) formulation and the SIMPLER iteration algorithm. The spacing parameter between cylinders is selected L=6. The results show that the shear motion in the gap between the wall and the cylinder dominates the flow at high Deborah number. Closing of cylinders will alter the behaviour of wall shear layers and delay the occurrence of instability. Introduction Viscoelastic flows past an array of cylinders have been obtained much attention in the last decade due to its implicative applications in flows through porous media [3,8,10,11,14-16]. Experiments showed that this type of flows exhibits instability at high Deborah number [3,8,11]. Linear stability analysis also revealed the features of instability for various parameters [16,18]. Comparing to the flows past a single cylinder in a channel, it is well known that the extension in the wake of cylinders of array is reduced. How the shear behavior is changed is not clear. Experiments found that the critical Deborah number for instability increases with closing of the cylinders. Extension in the wake has been nominated as the mechanism for the instability initiation [2,11,12]. However, Dou and Phan-Thien [5] found that the mechanism for instability of viscoleastic flows past a single cylinder in a channel is generated by the strong shear on the cylinder rather than the elongation in the wake. The mechanism of instability in the case of array of cylinders needs to be carefully examined because of its importance in applications [6]. Fig.1 Sketch of the flow geometry In this study, the flow of an Oldroyd-B fluid past an array of cylinders in a channel with geometry h/R=2 (Figure 1) is simulated using a parallelized unstructured FVM method, with fine meshes. The Discrete Elastic Viscous Split Stress (DEVSS) formulation is employed in the implementation of the SIMPLER pressure-velocity coupling method. The computing results are compared with those of single cylinder. The results show that the velocity inflection on the cylinder is delayed with the cylinder closing. This should contributes to the increasing of the critical Debo qual litera