Detonation-based propulsion systems are known for their high efficiency and energy release when compared to deflagrative systems, making them an ideal candidate in hypersonic propulsion applications. One such engine is the Oblique Detonation Wave (ODW) engine, which has a similar architecture to traditional scramjets but shortens the combustor and isolator to an anchored ODW after fuel injection. Previous research has focused on using a two-dimensional wedge to induce an ODW while limiting total losses through the combustor. In this configuration, a two-dimensional wedge-based architecture entails a rectangular duct, limiting potential inlet design and increasing overall skin friction. However, an inward-turning axisymmetric ODW wedge architecture, where a two-dimensional wedge is revolved around a central axis, has yet to be examined in detail. The work at present aims to investigate the fundamental physics required to predict the Oblique Shock Wave (OSW) for an inward-turning axisymmetric flow, which is critical for designing a circular ODW engine combustor. Multiple steady simulations of inviscid and ideal air at Mach 4, 6, and 8 were performed over a 1-inch wedge with wedge angles of 16°, 18°, and 20°. The radius of the inlet boundary was also varied between 1, 3, and 5 inches to examine the effect of increasing the blockage ratio. The results showed that the shock angle for an inward-turning axisymmetric flow was up to 8% steeper than the analytical, two-dimensional wedge solution. Additionally, it was found that the OSW diverged further from the two-dimensional solution when the blockage ratio was increased. These findings provide insight into the flow physics that must be considered when designing inward-turning axisymmetric ODW engines.