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.
A new reflected shock tunnel has been commissioned at Sandia capable of generating hypersonic environments at realistic flight enthalpies. The tunnel uses an existing free-piston driver and shock tube coupled to a conical nozzle to accelerate the flow to approximately Mach 9. The facility design process is outlined and compared to other ground test facilities. A representative flight enthalpy condition is designed using an in-house state-to-state solver and piston dynamics model and evaluated using quasi-1D modeling with the University of Queensland L1d code. This condition is demonstrated using canonical models and a calibration rake. A 25 cm core flow with 4.6 MJ/kg total enthalpy is achieved over an approximately 1 millisecond test time. Analysis shows that increasing piston mass should extend test time by a factor of 2-3.
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.
A high-speed temperature diagnostic based on spontaneous Raman scattering (SRS) was demonstrated using a pulse-burst laser. The technique was first benchmarked in near-adiabatic H2-air flames at a data-acquisition rate of 5 kHz using an integrated pulse energy of 1.0 J per realization. Both the measurement precision and accuracy in the flame were within 3% of adiabatic predictions. This technique was then evaluated in a challenging free-piston shock tube environment operated at a shock Mach number of 3.5. SRS thermometry resolved the temperature in post-incident and post-reflected shock flows at a repetition rate of 3 kHz and clearly showed cooling associated with driver expansion waves. Collectively, this Letter represents a major advancement for SRS in impulsive facilities, which had previously been limited to steady state regions or single-shot acquisition.
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.
This paper validates the concept of a spatially filtered wavefront sensor, which uses a convergent-divergent beam to reduce sensitivity to aero-optical distortions near the focal point while retaining sensitivity at large beam diameters. This sensor was used to perform wavefront measurements in a cavity flow test section. The focal point was traversed to various spanwise locations across the test section, and the overall OPDRMS levels and aperture-averaged spectra of wavefronts were computed. It was demonstrated that the sensor was able to effectively suppress the stronger aero-optical signal from the cavity flow and recover the aero-optical signal from the boundary layer when the focal point was placed inside the shear region of the cavity flow. To model these measured quantities, additional collimated beam wavefronts were taken at various subsonic speeds in a wind tunnel test section with two turbulent boundary layers, and then in the cavity flow test section, where the signal from the cavity was dominant. The results from the experimental model agree with the measured convergent-divergent beam results, confirming that the spatial filtering properties of the proposed sensor are due to attenuating effects at small apertures.
A high-speed thermometry diagnostic based on spontaneous Raman scattering (SRS) was demonstrated using a pulse-burst laser at a 3-kHz data acquisition rate, with a pulse duration of 200 ns and wavelength of 532 nm. The technique was evaluated in a challenging free-piston shock tube environment operated at conditions up to 1653 K and 112 bar following an incident shock Mach number of 3.5 and a reflected shock Mach number of 2.2. The SRS thermometry resolved the temperature in post-incident and post-reflected shock flows and clearly showed cooling associated with driver expansion waves. A detailed spectral physics model inferred temperatures within 1% of the predicted post-shock temperatures, when SNR was greater than 2.0. This was a significant advancement of spontaneous Raman vibrational thermometry.
Measurements of bifurcated reflected shocks over a wide range of incident shock Mach numbers, 2.9 < Ms < 9.4, are carried out in Sandia’s high temperature shock tube. The size of the non-uniform flow region associated with the bifurcation is measured using high speed schlieren imaging. Measurements of the bifurcation height are compared to historical data from the literature. A correlation for the bifurcation height from Petersen et al. [1] is examined and found to over estimate the bifurcation height for Ms > 6. An improved correlation is introduced that can predict the bifurcation height over the range 2.15 < Ms < 9.4. The time required for the non-uniform flow region to pass over a stationary sensor is also examined. A non-dimensional time related to the induced velocity behind the shock and the distance to the endwall is introduced. This non-dimensional time collapses the data and yields a new correlation that predicts the temporal duration of the bifurcation.
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.
X-ray stereo digital image correlation (DIC) measurements were performed at 10 kHz on a jointed-structure in a shock tube at a shock Mach number of 1.42. The X-ray results were compared to optical DIC using visible light. In the X-ray measurements, an internal surface with a tantalum-epoxy DIC pattern was imaged, whereas the optical DIC imaged an external surface. The environment within the shock tube caused temperature and density gradients in the gas through which the structure was imaged, therefore leading to spatial and temporal index of refraction variations. These variations caused beam-steering effects that resulted in bias error in optical DIC measurements. X-rays were used to mitigate the effects of beam-steering caused by the shock tube environment. Beam displacements measured using X-ray DIC followed similar trends (slopes, oscillations amplitudes and frequencies) as optical DIC data while ignoring beam-steering effects. Power spectral densities of both measurements showed peaks at the natural frequencies of the structure. X-ray DIC also has the advantage of being able to image internal structural responses, whereas optical DIC is only capable of measurements on the outer surface of objects.
A new capability has been added to study shock-particle interactions in the Sandia High-Temperature Shock Tube (HST). The apparatus to do so featured a high-speed pneumatic actuator with high-pressure engineered seals. Like previous studies in a lower-strength facility, the particle curtain was comprised of 100-micron glass spheres at an initial volume fraction of approximately 20%. A shock-particle interaction was investigated using 210 kHz Schlieren imaging where the incident shock Mach number was 3.3. The initially uniform curtain was distorted by recoil in the HST. Nevertheless, the interaction dynamics were observed to be qualitatively similar to those in previous studies. Future efforts will work to decouple the recoil from the curtain formation and push the interaction towards stronger shocks.
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.
Conventional particle image velocimetry (PIV) configurations require a minimum of two optical access ports, inherently restricting the technique to a limited class of flows. Here, the development and application of a novel method of backscattered time-gated PIV requiring a single-optical-access port is described along with preliminary results. The light backscattered from a seeded flow is imaged over a narrow optical depth selected by an optical Kerr effect (OKE) time gate. The picosecond duration of the OKE time gate essentially replicates the width of the laser sheet of conventional PIV by limiting detected photons to a narrow time-of-flight within the flow. Thus, scattering noise from outside the measurement volume is eliminated. This PIV via the optical time-of-flight sectioning technique can be useful in systems with limited optical access and in flows near walls or other scattering surfaces.
Backscatter Particle Image Velocimetry via Optical Time-of-flight Sectioning (PIVOTS) is a novel method of performing PIV in situations where conventional PIV presents difficulties. The PIVOTS technique is introduced along with recent applications and results.
Simultaneous pressure sensitive paint (PSP) and stereo digital image correlation (DIC) measurements on a jointed beam structure are presented. Tests are conducted in a shock tube, providing an impulsive starting condition followed by approximately uniform high-speed flow conditions for 5.0 msec. The unsteady pressure loading generated by shock waves and vortex shedding results in the excitation of various structural modes in the beam. The combined data characterizes the structural loading input (pressure) and the resulting structural behavior output (deformation). Time-series filtering is used to remove external bias errors such as shock tube motion, and proper orthogonal decomposition (POD) is used to extract mode shapes from the deformation data. This demonstrates the utility of using fast-response PSP together with stereo digital image correlation (DIC), which provides a valuable capability for validating structural dynamics simulations.
The spanwise variation of resonance dynamics in the Mach 0.94 flow over a finite-span cavity was explored using stereoscopic time-resolved particle image velocimetry (TR-PIV) and time-resolved pressure sensitive paint (TR-PSP). The TR-PSP data were obtained along the cavity floor, whereas the TR-PIV measurements were made in a planform plane just above the cavity lip line. The pressure data showed relatively coherent distributions across the span. In contrast, the PIV showed a significant variation in resonance dynamics to occur across the span in the plane above the cavity. A substantial influence of the sidewalls appears to stem from spillage vortices. At the first cavity mode frequency, streamwise velocity fluctuations were several times higher near the sidewalls in comparison to the centerline values. Importantly, PSDs of streamwise velocity in the region of the spillage vortices showed a large peak to occur at mode one, indicating velocity fluctuations in these regions can have a preferred frequency. The resonance fluctuations in the velocity fields at modes two and three demonstrated a complex spatial dependence that varied with spanwise location.