Energy evolution in the Kármán vortex street of compressible flow around a circular cylinder

In this study, compressible flow around a circular cylinder is investigated at Reynolds number (Re = 50, 100, 150, 200) and Mach number (Ma = 0.1, 0.3, 0.5, 0.6) using direct numerical simulation. The energy evolution and vortex dynamics within the Kármán vortex street are discussed, with the case of Re = 150 and Ma = 0.5 serving as a representative example. The kinetic energy evolution involves three key regions: region E supplies energy to vortices, region I causes vortices deflection and expansion, and region S promotes vortex separation, with kinetic energy transport dominating the variation in kinetic energy. Through time-averaged statistical results, we divide the near wake into several zones, each revealing the impact of non-uniformity, unsteady effects, and viscous forces on energy redistribution. Unsteady effects are predominant in the main vortex passage, while non-uniformity prevails in areas swept by the vortex head and tail. Furthermore, the effects of Reynolds numbers and Mach numbers on vortex dynamics and energy evolution are further explored. The results reveal that as the Re increases, the strength of vortices and vortex-shedding frequency are enlarged, leading to an enhanced kinetic energy transport and energy redistribution. However, variations in Mach number have minimal impact on these processes. At higher Re, the unsteady effects become more pronounced, and low-energy regions shift closer to the cylinder.