The present article aims to study the suppression of vortex shedding using a passive flow control technique (slit through a circular cylinder) in the laminar regime (Re $=100\text{–}500$). The slit width ratio S/D (slit width/diameter) on the modified cylinder plays an essential role to control the vortex shedding. The additional flow through the slit leads to the suppression of the global instability and vortex shedding, whereas a large amount of flow through the slit drastically alters the behavior of vortex shedding. The nature of vortex shedding remains periodic for all S/D, and the root mean square (rms) value of the lift coefficient decreases (in turn, vortex shedding suppression) with S/D up to Re $\le$ 300. For the range Re > 300, the root mean square (rms) value of the lift coefficient decreases up to S/D < 0.15, and the flow exhibits periodic vortex shedding, while the root mean square (rms) increases beyond S/D > 0.15 due to irregular vortex shedding downstream of cylinder. The variation of the Re for the S/D $=0.20$ shows bifurcation points where the flow changes its behavior from symmetric to asymmetric solution at Re$=$232 and again becomes symmetric at Re$=$304. The unsteady flow analysis over the modified cylinder also indicates the suppression in the vortex shedding; however, the analysis provides the qualitative property of suppression. The reduced-order modeling, i.e. Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD), is utilized to quantify suppression and investigate the dominant vortical structure for slit through the cylinder.

本文旨在研究在层流状态 (Re $=100\text{——}500$）。改进后的圆柱体上的狭缝宽度比 S/D（狭缝宽度/直径）对控制涡流脱落起着至关重要的作用。通过狭缝的额外流量导致全局不稳定性和涡旋脱落的抑制，而通过狭缝的大量流量会显着改变涡旋脱落的行为。涡流脱落的性质对于所有 S/D 保持周期性，升力系数的均方根 (rms) 值随着 S/D 的增加而减小（反过来，涡流脱落抑制）达到 Re$\le$300. 对于 Re > 300 的范围，升力系数的均方根 (rms) 值下降到 S/D < 0.15，并且流动表现出周期性的涡旋脱落，而均方根 (rms) 增加超过 S/ D > 0.15 由于圆柱体下游不规则的涡流脱落。S/D 的 Re 变化$=0.20$ 显示分岔点，其中流在 Re 处将其行为从对称解变为非对称解$=$232 并且在 Re 处再次变得对称$=$304. 修改后的圆柱体上的非定常流动分析也表明涡旋脱落受到抑制；然而，分析提供了抑制的定性特性。降阶建模，即适当正交分解 (POD) 和动态模式分解 (DMD)，用于量化抑制并研究穿过圆柱体的狭缝的主要涡流结构。