Flow-Induced Locomotion of a Flexible Filament in the Wake of a Cylinder in Non-Newtonian Flows

Abstract

The problem of a flapping filament mounted to a free cylinder provides insight into computational fluid dynamics. We study the extent to which the length of the flexible filament and the non-Newtonian power-law fluids should be implemented to stabilize the flapping of an immersed structure in the flow with the Reynolds number of 100. We propose a hybrid model that includes an explicit Lattice Spring Model and Immersed Boundary non-Newtonian Lattice Boltzmann Method to simulate the behavior of the filament in the vicinity of a fluid flow. We validate this hybrid model using bench-marked problems, where a non-Newtonian fluid flow passes over a fixed cylinder in an unconfined channel and in a Newtonian flow over a cylinder containing a flexible fin. In the result section, we study the effects of fluid and structural characteristics on the motion of the filament and cylinder. When shear-thinning, Newtonian, and shear-thickening fluids are used, the results show that the cylinder keeps its minimum distance to the channel centerline at a specific length. This is due to the flapping of the filament generating the low-pressure region downstream from the cylinder and filament structure. We also analyze the effects of the bending stiffness. We find that from the lowest bending stiffness of 0.003 to the highest of 0.007, flexibility has no impact on the cylinder's center of mass, when the filament length is set as large as the critical length. The vibration amplitude and frequency of the filaments are also measured in different fluids and in varied filament stiffnesses. When n = 0.7, the bending stiffness of 0.007 causes a high-frequency vibration with the highest amplitude, whereas a bending stiffness of 0.005 achieves the minimum amplitude.