Hydrodynamics around long vibrating beams

The paper is devoted to the study of hydrodynamics around long cantilever beams that perform flexural vibrations in first natural mode in a viscous incompressible fluid. The study is based on the numerical three-dimensional simulation of flows induced by vibrations. The fluid motion is described by the full non-stationary system of Navier–Stokes equations and the oscillation profile of the beam is determined according to the Euler–Bernoulli theory. In the framework of the research, the analysis of the changes of hydrodynamics around the beams that are caused by an increase of the relative length, dimensionless frequency and amplitude of oscillations is made, in particular, the applicability of a quasi-two-dimensional theory is considered. According to the results of the study, the dynamic processes of vortex formation in a wide range of vibration frequencies and amplitudes are described, the map of the observed flow regimes is constructed, and analysis of the dependence of hydrodynamic forces on the vibration parameters is carried out.