Publications

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Compressible wall-modeled large-eddy simulations of Mach 8 turbulent boundary-layer flows over a flat plate were carried out for the conditions of the hypersonic wind tunnel at Sandia National Laboratories. The simulations provide new insight into the effect of wall cooling on the aero-optical path distortions for hypersonic turbulent boundary-layer flows. Four different wall-to-recovery temperature ratios, 0.3, 0.48, 0.71, and 0.89, are considered. Despite the much lower grid resolution, the mean velocity, temperature, and resolved Reynolds stress profiles from the simulation for a temperature ratio of 0.48 are in good agreement with those from a reference direct numerical simulation. The normalized root-mean-square optical path difference obtained from the present simulations is compared with that from reference direct numerical simulations, Sandia experiments, as well as predictions obtained with a semi-analytical model by Notre Dame University. The present analysis focuses on the effect of wall cooling on the wall-normal density correlations, on key underlying assumptions of the aforementioned model such as the strong Reynolds analogy, and on the elevation angle effect on the optical path difference. Wall cooling is found to increase the velocity fluctuations and decrease the density fluctuations, resulting in an overall reduction of the normalized optical path distortion. Compared to the simulations, the basic strong Reynolds analogy overpredicts the temperature fluctuations for cooled walls. Also different from the strong Reynolds analogy, the velocity and temperature fluctuations are not perfectly anticorrelated. Finally, as the wall temperature is raised, the density correlation length, away from the wall but inside the boundary layer, increases significantly for beam paths tilted in the downstream direction.

A wall-modeled large-eddy simulation of a Mach 14 boundary layer flow over a flat plate was carried out for the conditions of the Arnold Engineering Development Complex Hypervelocity Tunnel 9. Adequate agreement of the mean velocity and temperature, as well as Reynolds stress profiles with a reference direct numerical simulation is obtained at much reduced grid resolution. The normalized root-mean-square optical path difference obtained from the present wall-modeled large-eddy simulations and reference direct nu- merical simulation are in good agreement with each other but below a prediction obtained from a semi-analytical relationship by Notre Dame University. This motivates an evalua- tion of the underlying assumptions of the Notre Dame model at high Mach number. For the analysis, recourse is taken to previously published wall-modeled large-eddy simulations of a Mach eight turbulent boundary layer. The analysis of the underlying assumptions focuses on the root-mean-square fluctuations of the thermodynamic quantities, on the strong Reynolds analogy, two-point correlations, and the linking equation. It is found that with increasing Mach number, the pressure fluctuations increase and the strong Reynolds anal- ogy over-predicts the temperature fluctuations. In addition, the peak of the correlation length shifts towards the boundary layer edge.

We report 100-kHz burst-mode planar laser-induced fluorescence imaging of the nitricoxide molecule in the free-piston facility at Sandia National Laboratories. Cylinder wakestartup transients are visualized in high-temperature (T ~ 3000 K) post-shock flow with the facility in the shock-tube mode of operation. In the reflected shock-tunnel mode, NO PLIF visualization of a 4.6-MJ/kg, 3 km/s startup flow over a cylinder is presented, and free-stream molecular-tagging velocimetry exploiting the long fluorescence lifetime of free-stream NO is demonstrated.

Accurately measuring aero-optical properties of non-equilibrium gases is critical for characterizing compressible flow dynamics and plasmas. At thermochemical non-equilibrium conditions, excited molecules begin to dissociate, causing optical distortion and non-constant Gladstone-Dale behavior. These regions typically occur behind a strong shock at high temperatures and pressures. Currently, no experimental data exists in the literature due to the small number of facilities capable of reaching such conditions and a lack of diagnostic techniques that can measure index of refraction across large, nearly-discrete gradients. In this work, a quadrature fringe imaging interferometer is applied at the Sandia free-piston high temperature shock tube for high temperature and pressure Gladstone-Dale measurements. This diagnostic resolves high-gradient density changes using a narrowband analog quadrature and broadband reference fringes. Initial simulations for target conditions show large deviations from constant Gladstone-Dale coefficient models and good matches with high temperature and pressure Gladstone-Dale models above 5000 K. Experimental results at 7653 K and 7.87 bar indicate that the index of refraction approaches high temperature and pressure theory, but significant flow bifurcation effects are noted in reflected shock.

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.

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X-ray stereo digital image correlation (DIC) measurements were performed at 10 kHz on the internal surface of a jointed structure in a shock tube at a shock Mach number of 1.42 and compared with optical stereo DIC measurements on the outer, visible surface of the structure. The shock tube environment introduces temperature and density gradients in the gas through which the structure was imaged, resulting in spatial and temporal index of refraction variations. These variations cause bias errors in optical DIC measurements due to beam-steering but have minimal influence on x-ray DIC measurements. These results demonstrate the utility of time-resolved x-ray DIC measurements in complicated environments where optical measurements suffer severe errors and/or are precluded by lack of optical access.

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.

Aero-optics refers to optical distortions due to index-of-refraction gradients that are induced by aerodynamic density gradients. At hypersonic flow conditions, the bulk velocity is many times the speed of sound and density gradients may originate from shock waves, compressible turbulent structures, acoustic waves, thermal variations, etc. Due to the combination of these factors, aero-optic distortions are expected to differ from those common to sub-sonic and lower super-sonic speeds. This report summarizes the results from a 2019-2022 Laboratory Directed Research and Development (LDRD) project led by Sandia National Laboratories in collaboration with the University of Notre Dame, New Mexico State University, and the Georgia Institute of Technology. Efforts extended experimental and simulation methodologies for the study of turbulent hypersonic boundary layers. Notable experimental advancements include development of spectral de-aliasing techniques for highspeed wavefront measurements, a Spatially Selective Wavefront Sensor (SSWFS) technique, new experimental data at Mach 8 and 14, a Quadrature Fringe Imaging Interferometer (QFII) technique for time-resolved index-of-refraction measures, and application of QFII to shock-heated air. At the same time, model advancements include aero-optic analysis of several Direct Numerical Simulation (DNS) datasets from Mach 0.5 to 14 and development of wall-modeled Large Eddy Simulation (LES) techniques for aero-optic predictions. At Mach 8 measured and predicted root mean square Optical Path Differences agree within confidence bounds but are higher than semi-empirical trends extrapolated from lower Mach conditions. Overall, results show that aero-optic effects in the hypersonic flow regime are not simple extensions from prior knowledge at lower speeds and instead reflect the added complexity of compressible hypersonic flow physics.

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