Numerical Solutions to Blunt Body Re-entry Problem

This report describes how using the Navier-Stokes equations to numerically calculate a shock wave will more accurately depict a realistic and observed shock wave. Earlier related inviscid shock capturing studies that have attempted to numerically calculate the shock wave and downstream field surrounding a blunt body re-entering the atmosphere have exhibited an instability known as the carbuncle phenomenon, which is not observed in nature. The use of high order shock-capturing methods has induced this instability in which the shock wave exhibits non-physical behavior. This study provides a new approach at calculating a numerical solution of the blunt body re-entry problem. Instead of using the Euler equations, the Navier-Stokes equations will be used, thus including physical damping in the problem. With the Navier-Stokes equations, the physical properties of the flow around the blunt body will be preserved in the numerical solution providing a solution in greater harmony with that seen in nature. In order to obtain this solution, the spatial and temporal resolution must be sufficiently fine to capture the shock. Since the shock wave is so thin, in the nanometer scale, the grid size in the domain surrounding the blunt body must be sufficiently small to capture the shock and not have the solution become unstable. The numerical solutions were calculated using OpenFOAM, a free, open source software system where the blunt body was a cylinder of radius 0.1 mm so that the computations are manageable.