Fully appreciating the impossibility of shock wave regular reflection from the axis of symmetry in axisymmetric internal flows.

This article focuses on the theoretical investigation of shock wave reflection in internal axisymmetric supersonic flows, specifically addressing the longstanding question of whether regular reflection can occur over the axis of symmetry. Using the curved shock theory (CST), the study derives explicit relations between flow gradients and shock curvatures, demonstrating that the flow near the reflection point is locally conical and governed by the Taylor–Maccoll equation. A detailed analysis of the singularity inherent in the Taylor–Maccoll equation shows that a smooth transition through this singularity—necessary for regular reflection—is impossible under physically realistic conditions, thereby proving that regular reflection cannot occur on the axis of symmetry in internal axisymmetric flows. This conclusion has implications for the design and prediction of shock structures in air-breathing propulsion systems and related devices.