Effects of viscoelasticity on the onset of vortex shedding and forces applied on a cylinder in unsteady flow regime

Abstract

The present paper aims to investigate the effect of viscoelasticity on the onset of vortex shedding of a high concentration polymer solution over a cylinder using the finite volume method for the first time. To describe the behavior of the viscoelastic fluid, mathematically, the Phan–Thien–Tanner (PTT) model is employed. The convergence problems are resolved using the rheoFoam solver developed by previous researchers based on the log-conformation method. The exact critical Reynolds number (Recr), which corresponds to the onset of vortex shedding, is estimated by implementing numerous unsteady simulations at each elasticity number (El). The Recr is also calculated at every retardation ratio (β) and elongational viscosity. The results revealed a significant impact of viscoelasticity on Recr so that the flow of a high viscosity ratio PTT becomes unstable at higher Re (at very low El) or lower Re (at higher El), compared to a Newtonian fluid. In addition, Recr decreases linearly with β according to Recr=−34.5β+46.525 and increases with extensional viscosity. It is also found that β plays a vital role in the effect of viscoelasticity on the flow parameters. The averaged drag coefficient (CD¯) and the amplitude of lift coefficient (CLmax) do not have similar behaviors for low and high β. Moreover, viscoelasticity enlarges the vortices and increases the shedding frequency. A comprehensive physical analysis of flow structures is carried out using the distribution of time-averaged stress components and pressure over the cylinder. The numerical results demonstrated the three regimes of drag reduction at El < 0.015, drag enhancement at 0.015 < E1 < 1, and a Newtonian behavior at El > 1 that is an opposite trend compared to a steady regime. The variations of CLmax with El are also similar to CD¯, but at different critical elasticity numbers (El = 0.005 and 2). It is found that the normal stress changes the drag force by the variation of pressure distribution over the cylinder, while the shear stress directly affects the drag and lift forces. In addition, the viscoelasticity decreases the size of the vortices behind the cylinder and increases their vorticity, and changes the position of maximum normal stress, which leads to drag variations. It was also concluded that the higher the elongational viscosities, the lower the shedding frequency.