Investigation of the asymmetric flow field around a spheroid using global stability analysis
Year: 2026
Type: article
Abstract: The first bifurcation of the flow around a spheroid is analysed using global stability analysis to understand the development of flow asymmetry despite the symmetry of the configuration. The base flow, perturbations, adjoint modes, vorticity fields, structural sensitivity and skin friction lines are analysed to characterise the flow. The study of aspect ratio effects at zero angle of attack establishes that the structure of the asymmetry is the same whether the axisymmetric body is bluff or more streamlined. Stability of the flow field around the 6 : 1 spheroid is then investigated for angles of attack $\alpha \in [0{-}90]^\circ$ as a function of Reynolds number. Comparison of the low angle of attack results with the DARPA SUBOFF experiments of Ashok et al. ( J. Fluid Mech., 2015, vol. 774, pp. 416–442) shows that the asymmetry observed in the experiments is similar to the global mode predicted by the stability calculations. It is conjectured that the experimental asymmetry is triggered by the weak cross-stream circulating flow. The leading eigenmode is a stationary asymmetric mode in the angle of attack $\alpha \in [0{-}65]^\circ$ range, while above $\alpha =65^\circ$ , the leading mode is an oscillatory shedding mode. The rapid decrease in the critical Reynolds number between cases $\alpha =49.25^\circ$ and $49.5^\circ$ is attributed to coexisting symmetric flow states that have different susceptibilities to asymmetry; there exists a symmetric stationary mode that does not become unstable first, but appears to be the difference between the base flows at the same Reynolds number at the two angles of attack. The change from a stationary to an oscillatory instability between $\alpha =65^\circ$ and $70^\circ$ is linked to the ability/inability of the vortex sheets to roll up and reattach to the body in the former/latter cases, respectively. The difference in the separation patterns and the similarity between the eigenmodes indicate that asymmetry of the flow field is governed by the same mechanism across a wide angle of attack range, regardless of whether the flow is like a bluff body wake, a streamlined body wake or a vortex wake. Previous studies have argued that the asymmetry of vortex pairs emerges either because of a vortex instability or a separation/reattachment related mechanism; since the development of the asymmetry cannot be linked to specific features in the separation pattern in the investigated configurations, our results support the former argument.
Source: Journal of Fluid Mechanics
Authors: András Szabó, Krishnan Mahesh
Institution: University of Michigan
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
Awards: G7452177136, G8876996369
OpenAlex ID: W7161636616