Vortex-induced vibrations of a cylinder in inelastic shear-thinning and shear-thickening fluids

Vortex-induced vibrations (VIV) of a cylinder in a Newtonian fluid is a model problem in fluid–structure interactions 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 one-degree-of-freedom flexibly-mounted cylinder. We consider a system with a mass ratio of $m^*=2$ and zero structural damping in shear-thinning and shear-thickening power-law fluids at $Re_0 = 15$ and $Re_0 = 200$ , respectively, defined based on the zero-shear-rate viscosity of the fluids. We investigate how the VIV amplitude and frequency, flow forces, and the vorticity contours change as the reduced velocity, $U^*$ , and fluid's time constant, $\lambda$ , change. When the results are compared based on $Re_0$ , 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, $\dot {\gamma } = U/D$ , 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 generation of vorticity and reduces the extent of the wake, whereas shear thickening limits the generation of vorticity and extends the wake. Our findings show that the local apparent viscosity observed close to the cylinder placed in shear-thinning or shear-thickening fluids governs the VIV response of the cylinder.