Variations in wake structures and fluid forces around a square cylinder with four small control square rods at low Reynolds number

Abstract

Numerical prediction of fluid flow past a square cylinder with 4 control square rods placed in a channel is carried out using an in-house code based on finite volume method (FVM) and a full multi-grid technique (FMG). The flow features are extracted in terms of streamlines, iso-vortices, and drag (CD) and lift (CL) coefficients evolutions for steady and unsteady regimes. Numerical results demonstrated significant effect due to the addition of control rods by delaying the onset of flow instability, increasing the critical Reynolds number (Re_c) from 50 to 80. For instance, at Re = 10, the flow around the square cylinder with control rods exhibits two large recirculation lobes, while higher Reynolds numbers lead to six elongated lobes. On another hand, at unsteady regime for the square cylinder without control rods, the critical Reynolds number for vortex shedding is predicted to be approximately 48.064. The flow remains steady up to Re ≈ 87 with control rods, transitioning to unsteady flow at Re ≈ 93, indicating a substantial delay compared to the cylinder without rods. It is also seen that oscillatory flow with rods is aperiodic, whereas it is periodic without rods. Moreover, the impact of control square rods on time averaged drag and lift coefficients is analyzed and discussed. It is found that Strouhal number (St) variation shows an enhancement up to Re ≈ 140 without rods, followed by a decline, while control rods lead to a drop in St despite increased frequencies. Additionally, drag coefficient is reduced by up to 58.31% with control rods, and lift coefficient peaks at Re = 1 without rods, declining with higher Re.