Lamb-Vector-Based Analysis of Fluid Force Contributing to Vortex-Induced Vibration

In this study, the Lamb-vector-based theory is used to quantify the contribution of local flow structures to vortex-induced vibration of a cylinder and an airfoil at a high attack angle at a low Reynolds number based on the two-dimensional unsteady fluid–structure interaction simulations. The fluid force terms calculated by the Lamb-vector-based formula in mixed inertial–noninertial form agree well with the near-field method (stress integration on the body) for both the stationary and high vibration amplitude conditions. The control volume is properly chosen to illustrate physical mechanisms of each term. The energy transfer of vibrating cylinders and airfoils is explored and compared to make a direct connection between various force generation mechanisms and the self-excited/self-limited nature of vortex-induced vibration. The quantitative contributions of a single vortex under different reduced natural frequencies are investigated. The lift amplitudes of all decomposed terms significantly increase within the lock-in regime compared with the forced vibration conditions. The difference in phase of different terms leads to distinct effects on sustaining flow-induced vibrations. For both the vibrating cylinder and airfoil, the main energy source for sustaining high-amplitude vortex-induced vibrations is associated with the dynamic process of formation of shear layer and shedding vortices, while the concentrated vortices shed into the wake tend to suppress vortex-induced vibration. Specifically, the unsteady term and vortex force term dominate the cyclic work on the cylinder and airfoil during vortex-induced vibrations, respectively.