Parametric Vibration of Elastic Cavitating Wing in Unsteady Flow

Abstract

A two-dimensional unsteady potential flow outside an elastic partially cavitating wing is analyzed numerically by using the Birnbaum equation on hydrofoil chord and the Lagrange-Cauchy integral on the cavity. An angle of attack has a small periodic perturbation, and cavity thickness and length have got perturbations too. Wing vibration is considered as vibration of a variable thickness beam with two clamp bolts near the beam center. A mono-frequency flow perturbation induces mono-frequency flexural vibration of a non-cavitating wing, but the vibration of a cavitating wing is multy-frequency one, and a spectrum of a cavitating wing response can depend on an amplitude of the incoming flow perturbation. Numerical simulation of NACA-16009 hydrofoil vibration was made for various free-stream speeds, module of elasticity, fluid and wing densities, and as a result, three frequency bands of a vibration increase are found. The low-frequency band is connected with a cavity volume oscillation. There is a considerable effect of cavity length, therefore the cavitation number influences on vibration as a parameter. The high-frequency band is connected with elastic resonances of wing. Besides, resonance-like frequencies were found in the middle band. This phenomenon has not a dependence on cavity dimensions and wing elasticity, but appears as a result of an interaction between hydrodynamic damping and media inertia forces.