Numerical study of vortex-induced vibrations of a cylinder in shear-thinning and shear-thickening power-law fluids*

Vortex-induced Vibration (VIV) of a cylinder in Newtonian fluid is a model problem in Fluid-Structure Interactions (FSI) and has been studied extensively. In this work, we study the influence of shear-thinning and shear-thickening fluids on the VIV response of a 1DOF flexibly-mounted cylinder with a mass ratio of m^* = 2 at Re₀ = 15 and Re₀ = 200, respectively, defined based on the zero-shear-rate viscosity. We investigate how the VIV amplitude and frequency, flow forces, and vorticity contours change as the reduced velocity, U*, and fluid’s time constant, λ, change. When the results are compared based on Re₀, shear-thinning fluids enhance the oscillations while shear-thickening fluids suppress them. If, however, we define a characteristic Reynolds number, Re_char, based on a viscosity evaluated at the characteristic shear rate, U/D, then at a constant Re_char, the amplitude of response stays very similar for the shear-thinning, shear-thickening, and Newtonian fluids. Despite this similarity, the observed far wake is different: shear thinning amplifies the vorticity generation and reduces the extent of the wake, whereas shear thickening limits the vorticity generation and extends the wake.