Numerical study of unsteady viscoelastic flow past two side-by-side circular cylinders

In this study, numerical simulation is conducted to understand the two-dimensional viscoelastic flows past two side-by-side circular cylinders at a Reynolds number of 100. The Peterlin approximation of the finitely extensible nonlinear elastic model is adopted to describe the non-linear modulus of elasticity and the finite extendibility of polymer macromolecules. The flow behavior and time-averaged forces that act on the two cylinders are investigated over a wide range of parameter space, i.e., the Weissenberg number (We), from 0 to 8, and the spacing between the two cylinders (L-D), from 0.1D to 3.0D (D denotes the diameter of each cylinder). Similar to the corresponding Newtonian flow, the viscoelastic flow gradually undergoes six transitions as L-D increases. However, these transitions are delayed in the viscoelastic flow, particularly at a high We. As a result, three distinct flow modes remain within the above-mentioned L-D range at a high We. With increasing We, the total drag acting on the two cylinders increases for all L-D values, and the repulsive force between the two cylinders gradually decreases for a lower L-D value but increases for a higher L-D value. Both the intensity and frequency of force fluctuation decrease as We increases. The findings of the present study may provide new insight into the multi-body wake dynamics in the viscoelastic flow.