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.

A robust approach for stability analysis of complex flows using high-order Navier-Stokes solvers

“…The former is thus more susceptible to instability than the latter, for which compressibility acts as a stabilizing agent by countering the vorticity generation through mechanisms such as vorticity dilation as well as baroclinic torque [27]. A more detailed assessment reveals that the wavelength of the modes increases with Mach number in consistent with the findings of Canuto and Taira [26]. This effect is due to compressibility, which is responsible for the elongation of the recirculation region as shown in Fig.…”

“…However, as the Mach number is increased to M = 0.5, the frequency of the most weakly damped mode decreases to ω = 0.2893. This decrease in frequency with increase in Mach number is also observed in cylinder wake study of Canuto and Taira [26]. However, the current reduction of around 24% is more drastic than the 9% obtained between M = 0 and M = 0.5 near the critical Re for the cylinder in their study.…”

“…However, the current reduction of around 24% is more drastic than the 9% obtained between M = 0 and M = 0.5 near the critical Re for the cylinder in their study. Canuto and Taira [26] also observe that compressibility reduces the vortex-shedding frequency while increasing the wavelength, and but this effect is less pronounced as Re increases towards and beyond the critical value. Thus, the current higher reduction in frequency may be attributed to the fact that Reynolds number is far below critical.…”

“…The compressible governing equations are more cumbersome to linearize and the subsequent discretization of the governing equations also requires more care. A key conclusion from recent compressible studies [6,26,27] concerns the stabilizing effects of compressibility.…”

High‐order ghost‐point immersed boundary method for viscous compressible flows based on summation‐by‐parts operators

“…A, Details of computational grid around circular cylinder; B, Definitions of the relevant geometrical parameters of the symmetric separation region behind the cylinder [Colour figure can be viewed at wileyonlinelibrary.com]…”