Suppression of flip-flopping wake instability behind two side-by-side cylinders using a passive control rod at subcritical Reynolds number

Flow around bluff bodies induces vortex shedding, leading to fluctuating forces and vortex-induced vibrations. In many engineering fields, this vibration response can lead to structure stress and even damage. This study numerically investigates the effect of a small control rod with diameter ratios d / D = 0.06 and 0.07 on the wake and aerodynamic forces of two side-by-side circular cylinders. The cylinders are spaced at a center-to-center spacing ratio ( T / D ) of 1.25, with a Reynolds number, Re D = 1.2 × 10 4 . The rod is placed in the center line behind the cylinders. The unsteady, incompressible two-dimensional turbulent flow is modeled using Reynolds-Averaged Navier-Stokes equations with the SST k − ω turbulence model. Numerical simulations are conducted using Ansys Fluent software. In the uncontrolled case, the flow exhibits strong flip-flopping behavior and large fluctuations in drag and lift, with distinct shedding frequencies of St = 0.173 for the upper cylinder and St = 0.128 for the lower cylinder. In addition, a low-frequency flip-flopping mode appears at St = 0.013 , indicates wake instability. For d / D = 0.06 , the drag coefficient fluctuation amplitude decreases by 38 % for the upper cylinder and 31 % for the lower cylinder, while the mean drag decreases by 10.2 % and 6.5 %, respectively. The corresponding lift fluctuation ranges are reduced by 60 % and 18 %, and the root mean square lift coefficient for both cylinders is almost doubled. Strouhal numbers of both cylinders converge to a common value of St = 0.13 . and the flip-flopping Strouhal number shifts to St = 0.022 , indicating that the rod modifies the stability of the flip-flopping motion. For d / D = 0.07 , the vortex shedding is significantly suppressed, and stable recirculation bubbles are formed behind the cylinders, eliminating the flip-flopping phenomenon. The drag and lift coefficients exhibit periodic fluctuations. These fluctuations are reduced by approximately 90 % compared to the uncontrolled case. The mean drag coefficient decreases by 9.7 % for the upper cylinder and 7 %, for the lower cylinder. The root-mean-square of the lift coefficient is approximately doubled for both cylinders. Spectral analysis confirmed that the secondary cylinder interaction frequencies are completely eliminated. The results demonstrate that a control rod with d / D = 0.07 provides an effective passive flow control strategy, promoting energy savings and improving structural safety.