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.
High-enthalpy hypersonic flight represents an application space of significant concern within the current national-security landscape. The hypersonic environment is characterized by high-speed compressible fluid mechanics and complex reacting flow physics, which may present both thermal and chemical nonequilibrium effects. We report on the results of a three-year LDRD effort, funded by the Engineering Sciences Research Foundation (ESRF) investment area, which has been focused on the development and deployment of new high-speed thermochemical diagnostics capabilities for measurements in the high-enthalpy hypersonic environment posed by Sandia's free-piston shock tunnel. The project has additionally sponsored model development efforts, which have added thermal nonequilibrium modeling capabilities to Sandia codes for subsequent design of many of our shock-tunnel experiments. We have cultivated high-speed, chemically specific, laser-diagnostic approaches that are uniquely co-located with Sandia's high-enthalpy hypersonic test facilities. These tools include picosecond and nanosecond coherent anti-Stokes Raman scattering at 100-kHz rates for time-resolved thermometry, including thermal nonequilibrium conditions, and 100-kHz planar laser-induced fluorescence of nitric oxide for chemically specific imaging and velocimetry. Key results from this LDRD project have been documented in a number of journal submissions and conference proceedings, which are cited here. The body of this report is, therefore, concise and summarizes the key results of the project. The reader is directed toward these reference materials and appendices for more detailed discussions of the project results and findings.
A new cell-centered third-order entropy stable Weighted Essentially Non-Oscillatory (SS-WENO) finite difference scheme in multi-block domains is developed for compressible flows. This new scheme overcomes shortcomings of the conventional SSWENO finite difference scheme in multi-domain problems by incorporating non-dissipative Simultaneous Approximation Term (SAT) penalties into the construction of a dual flux. The stencil of the generalized dual flux allows for full stencil biasing across the interface while maintaining the nonlinear stability estimate. We demonstrate the shock capturing improvement across multi-block domain interfaces using the generalized SSWENO in comparison to the conventional entropy stable high-order finite difference with interface penalty in shock problems. Furthermore, we test the new scheme in multi-dimensional turbulent flow problems to assess the accuracy and stability of the multi-block domain formulation.
A new cell-centered third-order entropy stable Weighted Essentially Non-Oscillatory (SS-WENO) finite difference scheme in multi-block domains is developed for compressible flows. This new scheme overcomes shortcomings of the conventional SSWENO finite difference scheme in multi-domain problems by incorporating non-dissipative Simultaneous Approximation Term (SAT) penalties into the construction of a dual flux. The stencil of the generalized dual flux allows for full stencil biasing across the interface while maintaining the nonlinear stability estimate. We demonstrate the shock capturing improvement across multi-block domain interfaces using the generalized SSWENO in comparison to the conventional entropy stable high-order finite difference with interface penalty in shock problems. Furthermore, we test the new scheme in multi-dimensional turbulent flow problems to assess the accuracy and stability of the multi-block domain formulation.