Magnus force reduction in a shear-thinning fluid

This study aims to investigate the impact of fluid shear-thinning on the Magnus forces acting on a rotating cylinder or a sphere immersed in an unbounded flow using direct numerical simulation. The Carreau model is employed to represent the shear-thinning fluid, with the considered Reynolds number (Re) ranging from 0.01 to 100, Carreau number (Cu) from 0 to 100, power-law index (n) from 0.1 to 1, and viscosity ratio (β) from 0.001 to 0.5. The rotation rate (α) is fixed at 6. A characteristic Reynolds number, Rec, based on a viscosity evaluated at the characteristic shear rate, γ˙α=αU∞/2a, is introduced. It is found that, at a constant Rec, compared to that in a Newtonian fluid, the Magnus force exerted on the rotating cylinder or sphere in the shear-thinning fluid is reduced. This reduction results from the difference in viscosity distribution between the upper and lower sides of the cylinder or sphere. Furthermore, our analysis demonstrates that the logarithmic reduction in the Magnus force coefficient can be expressed as a linear combination of the logarithm of the strain rate difference and the logarithm of the shear strain rate sensitive function at two limit states, Cu→0 or Cu→∞. This work may be helpful to deepen the understanding of complex rheological behavior encountered in swirling flow hydrodynamics.