Abstract Three-dimensional Large-Eddy Simulations (3D LES) are performed to study the separated and reattaching flow over a 5:1 rectangular cylinder in streamwise sinusoidal flow. The ratio of inflow frequency to natural vortex-shedding frequency is varied from 0 to 6 ​at five amplitudes up to 60% of the time-mean velocity. The effect on the two-dimensional (2D) and three-dimensional (3D) characteristics of the separation bubble and surface pressures are reported. The relationship between the time-averaged flow field and the statistics of the chordwise pressure distribution are obtained firstly. The flow-pressure relationships are qualitatively similar in uniform and sinusoidal flows. Then, the amplitude-frequency domain of the sinusoidal flow is divided into three regimes to describe the effects on the mean reattachment length. The simulations capture the interferences between leading-edge vortices and trailing edge vortices for longer separation bubbles. However, the interactions are not observed in shorter separation bubbles due to the diffusions of leading-edge vortices. Finally, the flow three-dimensionality is studied by performing proper orthogonal decomposition (POD) and spanwise correlation analysis on the surface pressures. The oncoming flow oscillations correspond to the most energetic structures dominating the pressure field, which are constant in the spanwise direction. While the local vortical structures mainly influence the 3D features of the flow dynamics.

Graphical abstract The physics of the 2D and 3D features of the separated flow are different between uniform and sinusoidal flow conditions. In the sinusoidal flows, the first two modes of the fluctuating pressures are dominated by the frequency of the oncoming flow oscillations. The corresponding eigenvectors are nearly constant along the spanwise direction. Therefore, the oncoming flow oscillations (POD modes 1 and 2) are the main contributors to the 2D flow field. In addition, the third mode is related to the frequency of the vortices formation, merging and shedding in the separation bubble. The eigenvector of the third mode shows variability along both the x and z directions in the upstream part of the lateral surface, reflecting the 3D features of the separation bubble. This indicates that the instantaneous 3D flow structures are dominated by the local vortical structures. The first to third POD eigenvectors along the upper surface of the cylinder for uniform flow (left column) and sinusoidal flow (right column) with the frequency equals the natural vortex shedding frequency and the amplitude of 60% of the time-mean velocity. Display Omitted

Highlights • Sinusoidal flows passing a 5:1 rectangular cylinder are numerically simulated. • The effects of inflow frequency and amplitude on the separation bubble are investigated. • The instantaneous flow dynamics are sensitive to the flow condition. • The contributions of flow fluctuations and local vortices to the overall flow dynamics are evaluated. • The relationships between flow topology and pressure statistics are provided.