Chaotic rotation of a finite-size spheroidal particle in oscillating shear flows with fluid inertia

Abstract

Rotational dynamics of a prolate spheroid in oscillating shear flows is studied by fully resolved direct numerical simulations with an immersed boundary method. In this flow configuration, we extend the work of Nilsen and Andersson [“Chaotic rotation of inertial spheroids in oscillating shear flow,” Phys. Fluids 25, 013303 (2013)] with focusing on the fluid inertia effect. We observe that the spheroid could rotate in chaotic and nonchaotic modes, which are identified by the sign of a largest Lyapunov exponent of the dynamic system. These two distinct rotation modes depend on both particle Reynolds number and oscillation frequency. For a certain Reynolds number, chaotic rotation appears when oscillation frequency is lower than a critical value, which decreases linearly with the increase of the particle Reynolds number. Based on this finding, we propose an empirical expression to predict the rotation mode. We, furthermore, discuss the mechanism of the emergence of the chaotic rotation, which is ascribed to a nonlinear interaction between time-varying orientation of the inertial spheroid and the oscillation of the shear rate.