Title: Two-dimensional compressible viscous flow around a circular cylinder,
Abstract: Direct numerical simulation is performed to study compressible, viscous flow
around a circular cylinder. The present study considers two-dimensional,
shock-free continuum flow by varying the Reynolds number between 20 and 100 and
the freestream Mach number between 0 and 0.5. The results indicate that
compressibility effects elongate the near wake for cases above and below the
critical Reynolds number for two-dimensional flow under shedding. The wake
elongation becomes more pronounced as the Reynolds number approaches this
critical value. Moreover, we determine the growth rate and frequency of linear
instability for cases above the critical Reynolds number. From the analysis, it
is observed that the frequency of the Bénard-von Kármán vortex street in
the time-periodic, fully-saturated flow increases from the dominant unstable
frequency found from the linear stability analysis as the Reynolds number
increases from its critical value, even for the low range of Reynolds numbers
considered. We also notice that the compressibility effects reduce the growth
rate and dominant frequency in the linear growth stage. Semi-empirical
functional relationships for the growth rate and the dominant frequency in
linearized flow around the cylinder in terms of the Reynolds number and
freestream Mach number are presented.