  The present study investigates the passive flow control phenomena over a
two-dimensional circular cylinder using numerical simulations in the laminar
regime. The aim is to explore one of the passive control techniques, which
involves the introduction of a slit to the geometry of the cylinder. The two
parameters, slit width ratio S/D (slit width/diameter) and slit angle (measured
with respect to the incoming flow direction), play an essential role in
determining the trend of critical Reynolds number (Rec). Most of the analysis
invokes flow visualization and saturation amplitude methods to obtain the
critical Reynolds number (indicative of the onset of vortex shedding) for
different cases. Further, Hopf bifurcation analysis using Stuart-Landau
equation and global stability analysis confirm the accuracy and consistency in
the predicted solutions. The additional amount of flow through slit increases
the pressure downstream of the cylinder, which consequently leads to an
increase in Rec of the modified cylinder. The critical Reynolds number
increases with S/D of the modified cylinder at 0 deg slit angle (as an
additional amount of flow grows with S/D). The critical Reynolds number shows
an increasing trend with the slit angle in the range of S/D (0.05-0.15) as the
fluctuation intensity reduces with slit angle in this range. For S/D=
0.15-0.25, the extra amount of flow through slit induces the instability in
wake which causes a decrease in Rec with slit angle. A correlation is obtained
that estimates the critical Reynolds number for a given S/D and slit angle.
