Numerical study of viscoelastic flow around an oscillating circular cylinder

The viscoelasticity-induced fluid-structure interaction studies have a significant influence on practical applications. To clarify the lock-in phenomenon and the wake topology of the vibrating cylinder placed in the viscoelastic flow, the Oldroyd-B fluid flows around an oscillating circular cylinder have been numerically investigated at Re=10 and Re=60, respectively. The governing equations are solved by the coupling of the square-root-conformation representation approach and the discontinuous Galerkin method in framework of the high-order dual splitting scheme. In addition, the arbitrary Lagrangian-Eulerian formulation is implemented in the coupling procedure in order to account for the interaction between the fluid and the oscillating body in the flow field. With this, complex boundary movements can be tackled simply and efficiently. In numerical simulation, the force coefficients and the wake structures of vortex and stress are discussed in some detail. At Re=10, when the frequency of cylinder is small, it is obvious that the vortex shedding takes place in the wake. As the frequency increases, almost no obvious vortex shedding is observed. Also, the wake still oscillates at the same frequency of the cylinder for all cases, even for high Wi numbers. However, different wake modes of vortex and stress are found for various frequencies at Re=60 and Wi=0.1. In the lock-in region, the 2S mode of wake type are observed. Beyond the lock-in region, the wake type is no longer 2S, but the formation of vortex shedding and stress distribution in the far wake recovers to its natural mode. These numerical results open up a new field of study for viscoelastic fluids.