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.
Femtosecond laser electronic excitation tagging (FLEET) is a powerful unseeded velocimetry technique typically used to measure one component of velocity along a line, or two or three components from a dot. In this Letter, we demonstrate a dotted-line FLEET technique which combines the dense profile capability of a line with the ability to perform two-component velocimetry with a single camera on a dot. Our set-up uses a single beam path to create multiple simultaneous spots, more than previously achieved in other FLEET spot configurations. We perform dotted-line FLEET measurements downstream of a highly turbulent, supersonic nitrogen free jet. Dotted-line FLEET is created by focusing light transmitted by a periodic mask with rectangular slits of 1.6 × 40 mm2 and an edge-to-edge spacing of 0.5 mm, then focusing the imaged light at the measurement region. Up to seven symmetric dots spaced approximately 0.9 mm apart, with mean full-width at half maximum diameters between 150 and 350 µm, are simultaneously imaged. Both streamwise and radial velocities are computed and presented in this Letter.
Time-resolved particle image velocimetry (TR-PIV) has become widespread in fluid dynamics. Essentially a velocity field movie, the dynamic content provides temporal as well as spatial information, in contrast to conventional PIV offering only statistical ensembles of flow quantities. From these time series arise further analyses such as accelerometry, space-time correlations, frequency spectra of turbulence including spatial variability, and derivation of pressure fields and forces. The historical development of TR-PIV is chronicled, culminating in an assessment of the current state of technology in high-repetition-rate lasers and high-speed cameras. Commercialization of pulse-burst lasers has expanded TR-PIV into more flows, including the compressible regime, and has achieved MHz rates. Particle response times and peak locking during image interrogation require attention but generally are not impediments to success. Accuracy considerations are discussed, including the risks of noise and aliasing in spectral content. Oversampled TR-PIV measurements allow use of multi-frame image interrogation methods, which improve the precision of the correlation and raise the velocity dynamic range of PIV. In combination with volumetric methods and data assimilation, a full four-dimensional description of a flow is not only achievable but becoming standardized. A survey of exemplary applications is followed by a few predictions concerning the future of TR-PIV.
The development of new hypersonic flight vehicles is limited by the physical understanding that may be obtained from ground test facilities. This has motivated the present development of a temporally and spatially resolved velocimetry measurement for Sandia National Laboratories (SNL) Hypersonic Wind Tunnel (HWT) using Femtosecond Laser Electronic Excitation Tagging (FLEET). First, a multi-line FLEET technique has been created for the first time and tested in a supersonic jet, allowing simultaneous measurements of velocities along multiple profiles in a flow. Secondly, two different approaches have been demonstrated for generating dotted FLEET lines. One employs a slit mask pattern focused into points to yield a dotted line, allowing for two- or three-component velocity measurements free of contamination between components. The other dotted-line approach is based upon an optical wedge array and yields a grid of points rather than a dotted line. Two successful FLEET measurement campaigns have been conducted in SNL’s HWT. The first effort established optimal diagnostic configurations in the hypersonic environment based on earlier benchtop reproductions, including validation of the use of a 267 nm beam to boost the measurement signal-to-noise ratio (SNR) with minimal risk of perturbing the flow and greater simplicity than a comparable resonant technique at 202 nm. The same FLEET system subsequently was reconstituted to demonstrate the ability to make velocimetry measurements of hypersonic turbulence in a realistic flow field. Mean velocity profiles and turbulence intensity profiles of the shear layer in the wake of a hypersonic cone model were measured at several different downstream stations, proving the viability of FLEET as a hypersonic diagnostic.
This experimental study explores the fluid-structure interactions occurring between a control surface and the hypersonic flow deflected by it. The control surface is simplified for this work as a spanwise finite wedge placed on a longitudinally sliced part of the cone. The front surface of the wedge is a thin panel which is designed to respond to the unsteady fluid loading arising from the shock-wave/boundary layer interactions. Experiments have been conducted in the Sandia Hypersonic Wind Tunnel at Mach 5 and Mach 8 at wedge angles of 10◦, 20◦ and 30◦ . High-speed schlieren and backside panel accelerometer measurements capture the unsteady flow dynamics and structural response of the thin panel, respectively. For attached or small separation interactions, the transitional regime has the strongest panel fluctuations with convective shock undulations induced by the boundary layer disturbance shown to be associated with dominant panel vibrations. For large separated interactions, shear layer flapping can excite select panel modes. Heating of the panel causes a downward shift in natural mode frequencies.
This study seeks to simplify the optical requirements for multi-line FLEET (Femtosecond Laser Electronic Excitation Tagging) generation by focusing the image of a periodic slit-mask with a cylindrical and spherical lens. Geometry effects on the signal were analyzed over fifteen mask iterations. The signal for each mask was found to vary with mask standoff from the focusing optics, which was optimized based on maximizing the Signal-to-Noise Ratio (SNR) for each mask. The number of generated lines was found to decrease with slit spacing while the separation of the lines increased. FLEET line spacing was determined by a constant magnification value of the imaged masks’ slit spacing. From the geometry study, two masks that produced three to five lines spaced at 0.8–1 mm apart with SNR > 4 were chosen to demonstrate the multi-line technique in a supersonic free-jet. Velocity calculations from this data showed good agreement with schlieren imaging of compressible flow structures.
Multi-frame correlation algorithms for time-resolved PIV have been shown in previous studies to reduce noise and error levels in comparison with conventional two-frame correlations. However, none of these prior efforts tested the accuracy of the algorithms in spectral space. Even should a multi-frame algorithm reduce the error of vector computations summed over an entire data set, this does not imply that these improvements are observed at all frequencies. The present study examines the accuracy of velocity spectra in comparison with simultaneous hot-wire data. Results indicate that the high-frequency content of the spectrum is very sensitive to choice of the interrogation algorithm and may not return an accurate response. A top-hat-weighted sliding sum-of-correlation is contaminated by high-frequency ringing whereas Gaussian weighting is indistinguishable from a low-pass filtering effect. Some evidence suggests the pyramid correlation modestly increases bandwidth of the measurement at high frequencies. The apparent benefits of multi-frame interrogation algorithms may be limited in their ability to reveal additional spectral content of the flow.
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 simple linear configuration for multi-line femtosecond laser electronic excitation tagging (FLEET) velocimetry is used for the first time, to the best of our knowledge, to image an overexpanded unsteady supersonic jet. The FLEET lines are spaced 0.5-1.0mmapart, and up to six lines can be used simultaneously to visualize the flowfield. These lines are created using periodic masks, despite the mask blocking 25%-30%of the 10 mJ incident beam.Maps of mean singlecomponent velocity in the direction along the principal flow axis, and turbulence intensity in that same direction, are created using multi-line FLEET, and computed velocities agree well with those obtained from single-line (traditional) FLEET. Compared to traditional FLEET, multi-line FLEET offers increased simultaneous spatial coverage and the ability to produce spatial correlations in the streamwise direction. This FLEET permutation is especially well suited for short-duration test facilities.
Two techniques have extended the effective frequency limits of postage-stamp PIV, in which a pulse-burst laser and very small fields of view combine to achieve high repetition rates. An interpolation scheme reduced measurement noise, raising the effective frequency response of previous 400-kHz measurements from about 120 kHz to 200 kHz. The other technique increased the PIV acquisition rate to very nearly MHz rates (990 kHz) by using a faster camera. Charge leaked through the camera shift register at these framing rates but this was shown not to bias the measurements. The increased framing rate provided oversampled data and enabled use of multi-frame correlation algorithms for a lower noise floor, increasing the effective frequency response to 240 kHz where the interrogation window size begins to spatially filter the data. Good agreement between the interpolation technique and the MHz-rate PIV measurements was established. The velocity spectra suggest turbulence power-law scaling in the inertial subrange steeper than the theoretical-5/3 scaling, attributed to an absence of isotropy.
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.
Bench-top tests are conducted to characterize Femtosecond Laser Electronic Excitation Tagging (FLEET) in static low pressure (35 mTorr-760 Torr) conditions, and to measure the acoustic disturbance caused by the resulting filament as a function of tagging wavelength and energy. The FLEET line thickness as a function of pressure and delay is described by a simple diffusion model. Initial FLEET measurements in a Mach 8 flow show that gate times of ≥ 1µs can produce visible smearing of the FLEET emission and challenge the traditional Gaussian fitting methods used to find the line center. To minimize flow perturbations and uncertainty of the final line position, several recommendations are offered: using third harmonic FLEET at 267 nm for superior signal levels with lower energy deposition than both 800 nm and 400 nm FLEET, and short camera delays and exposure times to reduce fitting uncertainty. This guidance is implemented in a Mach 8 test condition and results are presented.