Onset of Vortex Shedding in Flow Past Rankine Ovals

Journal article, 2026

Rankine ovals are fundamental to potential flow, yet their characteristics in viscous flows are rarely investigated. The geometry of Rankine ovals is defined by the parameter (Ua/m), with (U) the free-stream velocity, (a) the half-distance between the source and sink, and (m) the source strength. In this study, we use direct numerical simulations to investigate vortex shedding and the associated fluid dynamics for Reynolds numbers ((Re)) from 10 to 200 and (Ua/m) from 0 to 1. The results indicate a linear relationship between (Ua/m) and critical (Re). We further analyze the lift and drag coefficients, Strouhal number ((St)), and vortex formation mechanisms. Using data-driven dimensional analysis, we derive universal empirical relations for (St) and the friction drag coefficient that are independent of (Ua/m). We also demonstrate that for sufficiently large (Ua/m), the pressure drag can be predicted using potential flow theory. This approach enables reliable estimation of total hydrodynamic drag without the need for simulations. By investigating critical (Re), hydrodynamic coefficients, and wake characteristics of Rankine ovals across a range of geometries defined by the physically meaningful parameter (Ua/m), this study offers systematic hydrodynamic data and useful guidance for bluff-body research and related engineering applications.