Harmonic oscillations of laminae in non-Newtonian fluids: A lattice Boltzmann-Immersed Boundary approach

In this paper, the fluid dynamics induced by a rigid lamina undergoing harmonic oscillations in a non-Newtonian calm fluid is investigated. The fluid is modelled through the lattice Boltzmann method and the flow is assumed to be nearly incompressible. An iterative viscosity-correction based procedure is proposed to properly account for the non-Newtonian fluid feature and its accuracy is evaluated. In order to handle the mutual interaction between the lamina and the encompassing fluid, the Immersed Boundary method is adopted. A numerical campaign is performed. In particular, the effect of the non-Newtonian feature is highlighted by investigating the fluid forces acting on a harmonically oscillating lamina for different values of the Reynolds number. The findings prove that the non-Newtonian feature can drastically influence the behaviour of the fluid and, as a consequence, the forces acting upon the lamina. Several considerations are carried out on the time history of the drag coefficient and the results are used to compute the added mass through the hydrodynamic function. Moreover, the computational cost involved in the numerical simulations is discussed. Finally, two applications concerning water resources are investigated: the flow through an obstructed channel and the particle sedimentation. Present findings highlight a strong coupling between the body shape, the Reynolds number, and the flow behaviour index.