During hypersonic flight, compressional and viscous heating of the air can form a plasma layer which encases the aircraft. If the boundary layer becomes turbulent, then the electron density fluctuations can effect a parasitic modulation in microwave signals transmitted through the plasma. We developed an approach for studying the interaction of microwave signals with a turbulent, hypersonic plasma layer. The approach affords a great deal of flexibility in both the plasma layer model and the antenna configuration. We then analyzed a situation in which microwaves, transmitted from a rectangular aperture antenna, propagate through a turbulent plasma layer to a distant receiver. We characterized the first- and second-order statistics of the computed parasitic modulation and quantified the depolarization of the signal. The amplitude fluctuations are lognormally distributed at low frequencies and Rice-distributed at high frequencies. Fluctuations in the copolarized phase and amplitude of the far-field signal are strongly anticorrelated. We used a multioutput Gaussian process (MOGP) to model these quantities. The efficacy of the MOGP model is demonstrated by recovering the time evolution of the copolarized phase given the copolarized amplitude and occasional measurements of the phase.
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.
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.
Previous efforts determined a set of calibrated, optimal model parameter values for Reynolds-averaged Navier–Stokes (RANS) simulations of a compressible jet in crossflow (JIC) using a $k–ε$ turbulence model. These parameters were derived by comparing simulation results to particle image velocimetry (PIV) data of a complementary JIC experiment under a limited set of flow conditions. Here, a $k–ε$ model using both nominal and calibrated parameters is validated against PIV data acquired from a much wider variety of JIC cases, including a realistic flight vehicle. The results from the simulations using the calibrated model parameters showed considerable improvements over those using the nominal values, even for cases that were not used in the calibration procedure that defined the optimal parameters. This improvement is demonstrated using a number of quality metrics that test the spatial alignment of the jet core, the magnitudes of multiple flow variables, and the location and strengths of vortices in the counter-rotating vortex cores on the PIV planes. These results suggest that the calibrated parameters have applicability well outside the specific flow case used in defining them and that with the right model parameters, RANS solutions for the JIC can be improved significantly over those obtained from the nominal model.
Density fluctuations in compressible turbulent boundary layers cause aero-optical distortions that affect the performance of optical systems such as sensors and lasers. The development of models for predicting the aero-optical distortions relies on theory and reference data that can be obtained from experiments and time-resolved simulations. This paper reports on wall-modeled large-eddy simulations of turbulent boundary layers over a flat plate at Mach 3.5, 7.87, and 13.64. The conditions for the Mach 3.5 case match those for the DNS presented by Miller et al.1 The Mach 7.87 simulation match those inside the Hypersonic Wind Tunnel at Sandia National Laboratories. For the Mach 13.64, the conditions inside the Arnold Engineering Development Complex Hypervelocity Tunnel 9 are matched. Overall, adequate agreement of the velocity and temperature as well as Reynolds stress profiles with reference data from direct numerical simulations is obtained for the different Mach numbers. For all three cases, the normalized root-mean-square optical path difference was computed and compared with data obtained from the reference direct numerical simulations and experiments, as well as predictions obtained with a semi-analytical relationship by Notre Dame University. Above Mach five, the normalized path difference obtained from the simulations is above the model prediction. This provides motivation for future work aimed at evaluating the assumptions behind the Notre Dame model for hypersonic boundary layer flows.
The character of aero-optical distortions produced by turbulence is investigated for subsonic, supersonic, and hypersonic boundary layers. Data from four Direct Numerical Simulations (DNS) of boundary layers with nominal Mach numbers ranging from 0.5 to 8 are used. The DNS data for the subsonic and supersonic boundary layers are of flow over flat plates. Two hypersonic boundary layers are both from flows with a Mach 8 inlet condition, one of which is flow over a flat plate while the other is a boundary layer on a sharp cone. Density fields from these datasets are converted to index-of-refraction fields which are integrated along an expected beam path to determine the effective Optical Path Lengths that a beam would experience while passing through the refractions of the turbulent field. By then accounting for the mean path length and tip/tilt issues related to bulk boundary layer effects, the distribution of Optical Path Differences (OPD s) is determined. Comparisons of the root-mean-squares of the OPDs are made to an existing model. The OPDr m s values determined from the subsonic and supersonic data were found to match the existing model well. As could be expected, the hypersonic data does not match as well due to assumptions like the Strong Reynold Analogy that were made in the derivation of the model. Until now, the model has never been compared to flows with Mach numbers as high as included herein or to flow over a sharp cone geometry.
The primary parameter of a standard k-ϵ model, Cμ, was calculated from stereoscopic particle image velocimetry (PIV) data for a supersonic jet exhausting into a transonic crossflow. This required the determination of turbulent kinetic energy, turbulent eddy viscosity, and turbulent energy dissipation rate. Image interrogation was optimized, with different procedures used for mean strain rates and Reynolds stresses, to produce useful turbulent eddy viscosity fields. The eddy viscosity was calculated by a least-squares fit to all components of the three-dimensional strain-rate tensor that were available from the PIV data. This eliminated artifacts and noise observed when using a single strain component. Local dissipation rates were determined via Kolmogorov’s similarity hypotheses and the second-order structure function. The eddy viscosity and dissipation rates were then combined to determine Cμ. Considerable spatial variation was observed in Cμ, with the highest values found in regions where turbulent kinetic energy was relatively ow but where turbulent mixing was important, e.g., along the high-strain jet edges and in the wake region. This suggests that use of a constant Cμ in modeling may lead to poor Reynolds stress predictions at mixing interfaces. A data-driven modeling approach that can predict this spatial variation of Cμ based on known state variables may lead to improved simulation results without the need for calibration.
Measurements are presented of the aero-optic distortion produced by a Mach 8 turbulent boundary layer in the Sandia Hypersonic Wind Tunnel. Flat optical inserts installed in the test section walls enabled a double-pass arrangement of a collimated laser beam. The distortion of this beam was imaged by a high-speed Shack-Hartmann sensor at a sampling rate of up to 1 MHz. Analysis is performed using two processing methods to extract the aero-optic distortion from the data. A novel de-aliasing algorithm is proposed to extract convective-only spectra and is demonstrated to correctly quantify the physical spectra even in case of relatively low sampling rates. The results are compared with an existing theoretical model, and it is shown that this model under-predicts the experimentally measured distortions regardless of the processing method used. Possible explanations for this discrepancy are presented. The presented results represent to-date the highest Mach number for which aero-optic boundary layer distortion measurements are available.