This study presents an advanced numerical model for predicting a two-dimensional coupled galloping and vortex-induced vibration (VIV) in cross-flow and in-line directions of square cylinders under symmetric and asymmetric flow orientations. The present model combines the quasi-steady theory for the galloping with the nonlinear structure-wake oscillators simulating VIV, capturing the time-varying drag and lift hydrodynamic forces with the time-averaged and fluctuating components. By placing a flexibly mounted square cylinder in uniform flow at an initial angle of incidence, the cylinder is subject to instantaneous changes in the dynamic angle of attack accounting for relative flow-structure velocities. Modelling of such features in cross-flow and in-line directions for low and high mass ratio systems extends previous studies which have mostly focused on cross-flow responses of square cylinders with high mass ratios at a zero angle of incidence. New sets of empirical coefficients governing the drag and lift fluid forces for both the quasi-steady and wake oscillator approaches are introduced by calibrating with available experimental data in the literature, applicable to predict several flow-induced vibration phenomena under arbitrary flow-structure orientations. Mathematical criteria for the onset of twoand one-dimensional galloping instability are presented, verifying the likelihood of galloping occurrence. Parametric investigations are carried out to highlight the important effects of flow incidence angle, mass-damping ratio (Scruton number) and in-line response on the prediction of galloping and VIV in comparison with experimental results. By varying the reduced velocity parameter, the present model captures key qualitative features of the dominant galloping, interfering galloping-VIV and dominant VIV through the response amplitudes, mean drift displacements, oscillation frequencies, fluid force components and motion trajectories. Contributions from in-line responses are found to be meaningful for the interfering galloping-VIV system with a low mass-damping ratio and for an asymmetric flow orientation. The present model could be further calibrated and applied to other fluid-structure interaction applications with noncircular cross-sectional geometries under omnidirectional flow directions.
