High Enthalpy Differential Equation-Based Estimates for Spherical/Cylindrical Forebody Shock Stand-off Distance

Here we consider the shock stand-off distance for blunt forebodies using a simplified differential-based approach with extensions for high enthalpy dissociative chemistry effects. Following Rasmussen [4], self-similar differential equations valid for spherical and cylindrical geometries that are modified to focus on the shock curvature induced vorticity in the immediate region of the shock are solved to provide a calorically perfect estimate for shock standoff distance that yields good agreement with classical theory. While useful as a limiting case, strong shock (high enthalpy) calorically perfect results required modification to include the effects of dissociative thermo-chemistry. Using a dissociative ideal gas model for dissociative equilibrium behavior combined with shock Hugoniot constraints we solve to provide thermodynamic modifications to the shock density jump thereby sensitizing the simpler result for high enthalpy effects. The resulting estimates are then compared to high enthalpy stand-off data from literature, recent dedicated high speed shock tunnel measurements and multi-temperature partitioned implementation CFD data sets. Generally, the theoretical results derived here compared well with these data sources, suggesting that the current formulation provides an approximate but useful estimate for shock stand-off distance.