CFD Models of Shocks and Flow Fields Associated with Decelerating Spheres in Terms of Flow History and Inertial Effects

The bow shock stand-off distances of a sphere decelerating in air under its own drag were determined through numerical simulations using Fluent. Three cases were investigated with three different initial velocities. These results were then compared to steady-state numerical results obtained from the same CFD code in order to identify differences between the steady and unsteady cases at given Mach numbers. The initial Mach numbers used were 1.13, 1.19 and 1.25. A two-dimensional axisymmetric model was used in conjunction with a viscous turbulence model suitable for analysing transonic external aerodynamic problems. Numerically determined shock stand-off distances were compared to previous experimental results from literature for the steady and unsteady cases. There is a very good agreement between the steady-state numerical and experimental results, which confirms that a suitable numerical model was used. In the unsteady scenario, the numerical results follow the same trend as the experimental results, but the agreement is not as good. Some explanation for this is given. It was found that the shock stand-off distance for the unsteady cases was generally smaller than for the steady-state cases. Also, for the unsteady cases, a bow shock that was formed in supersonic flight transforms into a wave and persists well into the subsonic regime. In the steady-state cases, it is of course well known that no such phenomenon exists in flow at sonic and subsonic Mach numbers. The differences in the flow field and consequently in the drag in the steady and unsteady cases are explained using the concepts of flow history and fluid inertia.