Passive flow control and wake stabilization using pentad rod configurations around a square cylinder

This study investigates 2D fluid flow past a main square cylinder (C[Formula: see text] with four smaller control rods (C 1 –C[Formula: see text] arranged in two distinct pentad configurations within a 50[Formula: see text] channel. The finite volume method (FVM), accelerated by a full multigrid technique, is used to simulate flow behavior across [Formula: see text]. Boundaries comprise a uniform inlet, no-slip surfaces, and a convective outlet. Results reveal that viscous forces dominate at Re[Formula: see text] [Formula: see text] [Formula: see text]1, yielding attached streamlines and symmetric vorticity bubbles. When Re increases, the wake evolves from a steady regime (two recirculation lobes) to a complex multi-lobe structure, with pentad arrangements delaying the transition to unsteady flow compared to the single cylinder case. The critical Reynolds number increased from approximately Re [Formula: see text] 48 for the single square cylinder to Re[Formula: see text] [Formula: see text] [Formula: see text]85–92 for pentad I and Re [Formula: see text] 87–93 for pentad II. The time-averaged drag coefficient of the main cylinder decreased significantly in both pentad arrangements at low Re, with pentad II providing the best drag mitigation across [Formula: see text]. Similarly, lift fluctuations were suppressed more effectively in pentad II, yielding nearly neutral lift across the range. At [Formula: see text], both arrangements promoted orderly, laminar vortex shedding, underscoring their efficacy in delaying unsteady wake formation and reducing aerodynamic forces.