Modeling the compressible flow field of an impulsively started circular cylinder with refined potential flow theory

Understanding compressible flows over bluff bodies, such as circular cylinders, is critical for applications in aerospace engineering, space exploration, and astrophysics. However, the complexity of viscous and unsteady flows, compounded by compressibility effects, remains a challenge for experimental and computational methods. This study explores the compressible flow field of an impulsively started circular cylinder using Refined Potential Flow Theory (RPT), an analytical model that extends classical potential flow theory to include compressibility effects. The governing equations, boundary conditions, and refined stream function are developed to capture the density, velocity, and pressure fields in subsonic and transonic regimes. The results demonstrate that compressibility marginally increases vortex enstrophy at low Reynolds numbers, while its influence on wake flow stability diminishes at higher values. The study reveals that compressibility suppresses shear layer instability, reduces wake velocity deficits, and introduces smaller-scale structures that disrupt the inertial range of turbulence in the low subsonic regime. At higher Mach numbers (M∞≥0.6), local supersonic pockets and shock waves emerge, forming complex λ-shock systems and bow shocks. The predictions of the Strouhal number from RPT show marginal changes for 0.2≤M∞≤0.5, consistent with experimental and computational trends. Although RPT aligns with existing methods to capture key flow features, discrepancies in wake stability and recirculation zone dimensions highlight areas for further refinement. This research underscores the potential of RPT in developing optimization tools that complement experimental and numerical studies, offering valuable insights into compressible flow physics for engineering applications in high-altitude flight and space exploration.