Fluid-structure interactions of resonant cantilevers in liquids and liquid-solid suspensions near a solid wall.

摘要

An investigation on rectangular cantilevers oscillating in confined liquids and liquid-solid suspensions has been performed. The effects of the surroundings (liquids, solid walls, and liquid-solid suspensions) on the cantilever response are interpreted in terms of the added mass and viscous damping coefficients. These coefficients depend on several key non-dimensional parameters: the kinetic Reynolds number R_k, the cantilever aspect ratio of width to thickness b/h, and the non dimensional gap height d/b. In this study, these parameters were varied from R_k = 2.7 × 102–1.7 × 105, b/h = 2–12, d/b = 3.8–0.01.; The added mass and the viscous damping coefficients are determined experimentally by measuring the response spectrum of the cantilever in air and in liquid separately. Based on the dimensional analysis of the Navier-Stokes (N-S) equations, a ‘small perturbation theory’ is proposed to calculate the added mass coefficient, and a ‘lubrication theory’ is proposed to calculate the viscous damping coefficient. Also, these coefficients are computed numerically using a two-dimensional Arbitrary-Lagrangian-Eulerian Finite-Element-Method (ALE-FEM) simulation of the incompressible N-S equations.; The added mass coefficient increases linearly with increasing b/h, and is independent of R_k for R_k > 1000. Viscous damping increases from air to liquid. The normalized viscous damping coefficient increases with increasing R_k, and is independent of b/ h. Added mass and viscous damping coefficient both increase with decreasing d/b. The effect of gap height becomes significant when the gap height d is of the order of the cantilever width b. In general, the gap height has a stronger effect on the cantilever response (in terms of frequency shift and damping) than do the fluid properties (air vs. liquid).; The effects of liquid-solid suspensions (particle sizes 2–11 microns, and particle volume fractions 2–20%) on the cantilever response were also investigated experimentally. For flow induced by an oscillating cantilever, the effective viscosity increases with increasing volume fraction of the solid and increasing number density of the particles (for a given volume fraction). Furthermore, for flow induced by an oscillating cantilever, the effective viscosity was higher than that predicted by shear-flow models.