Numerical Study of Flow Past Oscillatory Square Cylinders at Low Reynolds number

Abstract

The present work reports a numerical investigation of the flow past an oscillatory square cylinder atRe = 100. A fixed finite element immersed technique is proposed to solve the incompressible fluid–rigid body interaction problem. The study encompasses the analyses of the flow over a fixed cylinder andtransverse to the flow and streamwise oscillating cylinders. The dimensionless frequency fr , i.e., the ratiobetween cylinder’s oscillation and Strouhal frequencies, and motion amplitude are used to characterizethe flow pattern evolution and its action on the cylinder. First, to compute the flow over the cylinder, amesh size is determined from a mesh sensitivity analysis where the drag and lift coefficients computedusing the immersed method are compared with those obtained from a body-fitted mesh. A reasonablenumerical convergence is found from such analyses. Second, the oscillating square cylinder cases arestudied to describe the synchronization regions. To this end, an oscillating body motion is prescribedvarying the frequency of the imposed displacement with a constant amplitude. The synchronization zonesare determined when the aerodynamic coefficients exhibit the most significant variations. In particular,the lock-in phenomenon is observed at fr ≈ 1 for transversely oscillating square cylinders, confirmingsome aspects previously reported in the literature using other numerical techniques. In the present work,lock-in is determined at fr ≈ 2 for streamwise oscillating square cylinders, results is not longer found inthe literature.