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.
Four Direct Numerical Simulation (DNS) datasets covering effective freestream Mach numbers of 8 through 14 are used to investigate the behavior of turbulence-induced aero-optical distortions in hypersonic boundary layers. The datasets include two from simulations of flat plate boundary layers (Mach 8 and 14) and two from simulations of flow over a sharp cone (Mach 8 and 14). Instantaneous three-dimensional fields of density from each DNS are converted to refraction index and integrated to produce distributions of the Optical Path Differences (OPD) caused by turbulence. These values are then compared to experimental data from the literature and to an existing model for the root-mean-square of the OPD. Although the model was originally developed for flows with Mach ≤ 5, it provides a basis to which we compare the hypersonic data.
Compressible wall modeled large-eddy simulations of a Mach eight turbulent boundary layer over a flat plate were carried out for the conditions of the Hypersonic Wind Tunnel at Sandia National Laboratories. Overall good agreement of the velocity and temperature profiles is obtained with reference data from a direct numerical simulation and a theoretical relationship. Profiles of the resolved root-mean-square velocity fluctuations are in adequate agreement with the reference data. The refractive index is calculated from the density field and integrated along an expected beam path to calculate the optical path length. Then, by subtracting a bilinear fit of the instantaneous optical path length, the optical path difference is obtained. The computed aero-optical path difference shows a similar dependence on the aperture size as in the literature. The normalized root-mean-square optical path difference from the present wall-modeled large-eddy simulations and a reference direct numerical simulation and experiment are in good agreement. The optical path distortion is slightly above the value predicted by a semi-analytical relationship from the literature. Finally, instantaneous snapshots of the flow are analyzed via proper orthogonal decomposition and the optical path distortion is computed from subsets of the modes. The optical path distortion converges quickly with increasing number of modes which suggests that the main contribution comes from large energetic flow structures.
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.
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.
A blind CFD validation challenge is being organized for the unsteady transonic shock motion induced by the Sandia Axisymmetric Transonic Hump, which echoes the Bachalo-Johnson configuration. The wind tunnel and model geometry will be released at the start of the validation challenge along with flow boundary conditions. Primary data concerning the unsteady separation region will be released at the conclusion of the challenge after computational entrants have been submitted. This paper details the organization of the challenge, its schedule, and the metrics of comparison by which the models will be assessed.
An experimental characterization of the flow environment for the Sandia Axisymmetric Transonic Hump is presented. This is an axisymmetric model with a circular hump tested at a transonic Mach number, similar to the classic Bachalo-Johnson configuration. The flow is turbulent approaching the hump and becomes locally supersonic at the apex. This leads to a shock-wave/boundary-layer interaction, an unsteady separation bubble, and flow reattachment downstream. The characterization focuses on the quantities required to set proper boundary conditions for computational efforts described in the companion paper, including: 1) stagnation and test section pressure and temperature; 2) turbulence intensity; and 3) tunnel wall boundary layer profiles. Model characterization upstream of the hump includes: 1) surface shear stress; and 2) boundary layer profiles. Note: Numerical values characterizing the experiment have been redacted from this version of the paper. Model geometry and boundary conditions will be withheld until the official start of the Validation Challenge, at which time a revised version of this paper will become available. Data surrounding the hump are considered final results and will be withheld until completion of the Validation Challenge.
A new wind tunnel experiment is underway to provide a comprehensive CFD validation dataset of an unsteady, transonic flow. The experiment is based on the work of Bachalo and Johnson; an axisymmetric model with a spherical hump is tested at a transonic Mach number. The flow is turbulent approaching the hump and becomes locally supersonic at the apex. This leads to a shock-wave/boundary-layer interaction, an unsteady separation bubble, and flow reattachment downstream. A suite of diagnostics characterizes the flow: oil-flow surface visualization for shock and reattachment locations, particle image velocimetry for mean flow and turbulence properties, fast pressure-sensitive paint for model pressure distributions and unsteadiness, high-speed Schlieren for shock position and motion, and oil-film interferometry for surface shear stress. This will provide a new level of detail for validation studies; therefore, a blind comparison, or ‘CFD Challenge’ is proposed to the community. Participants are to be provided the geometry, incoming boundary layer, and boundary conditions, and are free to simulate with their method of choice and submit their results. A blind comparison will be made to the new experimental data, with the goal of evaluating the state of various CFD methods for use in unsteady, transonic flows.
Near-wall turbulence models in Large-Eddy Simulation (LES) typically approximate near-wall behavior using a solution to the mean flow equations. This approach inevitably leads to errors when the modeled flow does not satisfy the assumptions surrounding the use of a mean flow approximation for an unsteady boundary condition. Herein, modern machine learning (ML) techniques are utilized to implement a coordinate frame invariant model of the wall shear stress that is derived specifically for complex flows for which mean near-wall models are known to fail. The model operates on a set of scalar and vector invariants based on data taken from the first LES grid point off the wall. Neural networks were trained and validated on spatially filtered direct numerical simulation (DNS) data. The trained networks were then tested on data to which they were never previously exposed and comparisons of the accuracy of the networks’ predictions of wall-shear stress were made to both a standard mean wall model approach and to the true stress values taken from the DNS data. The ML approach showed considerable improvement in both the accuracy of individual shear stress predictions as well as produced a more accurate distribution of wall shear stress values than did the standard mean wall model. This result held both in regions where the standard mean approach typically performs satisfactorily as well as in regions where it is known to fail, and also in cases where the networks were trained and tested on data taken from the same flow type/region as well as when trained and tested on data from different respective flow topologies.