Nonlinear modelling of unsteady wake galloping forces on a circular cylinder in the wake of a fixed cylinder

This paper aims at developing a nonlinear mathematical model for the unsteady wake galloping forces (UWGF) acting on a circular cylinder in the wake of a fixed identical circular cylinder, which is always neglected in quasi steady analysis. Numerical simulations are conducted to obtain the synchronous unsteady aerodynamic lift forces and displacements of wake galloping at Reynolds numbers (Re) of 1640-8420. The downstream cylinder is free to vibrate in the cross-flow direction with a mass-damping m*zeta = 0.267. The spacing ratio is fixed at L/D = 4 (where L is the center-to-center distance between the cylinders and D is the cylinder diameter). The UWGF model is built by combining the self-excited force and the vortex-induced force based on the spectra of the aerodynamic lift forces. Using an energy equivalent principle, the self-excited force can be divided into three parts: aerodynamic damping terms, aerodynamic stiffness terms and pure force terms. The identified aerodynamic parameters show that the aerodynamic damping terms are key factors determining the stable amplitude of wake galloping. The vortex-induced forces trigger an initial displacement to excite vibration in the early stage and have no influence on the stable amplitude. The proposed UWGF model is verified by experimental results and can calculate wake galloping responses better than the quasi-steady theory.