Galloping of square cylinders in cross-flow at low Reynolds numbers

Abstract Galloping of square cylinders is studied at low values of the Reynolds number using a two-dimensional finite element method. A sinusoidal quasi-steady model allows determination of the occurrence of galloping and its amplitude. Parameters of this model are obtained via FEM unsteady simulations at different angles of incidence between 0° and 10°. The model efficiency is validated by comparing its predictions to those of unsteady simulations of fluid–structure interaction of a spring mounted square constrained to move in the direction transverse to the flow. Results show that the model yields good predictions of both the onset of galloping and its amplitude as a function of the Reynolds number at high values of the mass ratio. However, the quasi-steady model fails to reproduce the sudden change of amplitudes observed in finite element simulations at mass ratios below a critical value. Modifications to the model are introduced to reproduce this low mass ratio effect.