Numerical simulations of the Oldroyd-B fluid flow around triangular cylinders with different orientations

Abstract

This study numerically simulates the two-dimensional flow of Oldroyd-B fluid around an isosceles right-angled triangular cylinder with five orientations. The log-conformation reformulation is employed to stabilize the numerical simulations. By adjusting the triangular orientation angle ($\theta$), three types of fluids development process can be observed: from steady to vortex shedding at $\theta =0$ and $\pi$, keeping the vortex shedding at $\theta =\frac{\pi }{4}$ and $\frac{3\pi }{4}$, and from vortex shedding to steady state at $\theta =\frac{\pi }{2}$. When the triangular cylinder faces the incoming stream with the inclined plane, the elastic effect acting on the cylinder is strong, otherwise it is weak. For $\theta =\frac{\pi }{2}$, the effects of the viscosity ratio ($\beta$), the Reynolds number ($Re$), and the Weissenberg number ($Wi$) are further investigated. When the elasticity is reduced by changing the viscosity ratio ($\beta$) that ranged from 0 to 0.9, the final flow state will transition from stable to vortex shedding state, which indicates the restraining effect of elasticity on wake instability. In the high elastic Oldroyd-B fluid, the critical Reynolds number for vortex shedding is about 110 for $Wi=1$. Besides, the Weissenberg numbers ($Wi$) ranged from 0.25 to 8 are discussed at $Re=100$. With the increase of $Wi$, four different flow states of the wake are observed: periodic vortex shedding at low Weissenberg number $Wi=0.25$, stabilizing for $Wi$ ranged from 0.5 to 1, semi-periodic strong vortex shedding for $Wi$ is about 2, and chaos when $Wi\ge 4$. The results indicate that excessively strong elastic effects may also lead to unstable flows. Finally, the flow states corresponding to each Reynolds number and Weissenberg number in a certain range ($90\le Re\le 120$ and $0.125\le Wi\le 4$) are given in this study.