Efficient Numerical Modeling of Oscillatory Fluid-Structure Interaction

We present a method to calculate the complex-valued coefficients of fluid loading of immersed mechanical resonators, used as sensors for density, viscosity, and viscoelastic properties. The approach is based on the eigenmode decomposition of structures of arbitrary geometry and the linearized Navier-Stokes equations in the surrounding fluid. A complete numerical solution with finite elements is computationally very expensive for most realistic cases. The critical part is the fine discretization in the boundary (Stokes) layer. In domains away from the oscillating structure, the velocity field can be well approximated by the potential flow solution, fulfilling the normal components of boundary motion but not the tangential components. The latter are accounted for by a superposition with appropriately scaled plane shear wave solutions. We introduce a novel reduced-order model for the fluid interaction which is based on the definitions of an effective added fluid volume, an effective area of shear-wave interaction, and an effective length scale of viscous dissipation. These LAV-parameters are characteristic for a specific resonator geometry and eigenmode, and only weakly dependent on the fluid properties and frequency, so they can be used as the sensor's calibration factors.