Numerical Simulations of the Oldroyd-B Fluid Flow Around Triangular Cylinders with Different Orientations

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 = pi/4 and 3 pi/4, and from vortex shedding to steady state at theta = 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 = 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 >= 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 <= Re <= 120 and 0.125 <= Wi <= 4) are given in this study.