This work presents an experimental investigation of the deformation and breakup of water drops behind conical shock waves. A conical shock is generated by firing a bullet at Mach 4.5 past a vertical column of drops with a mean initial diameter of 192 µm. The time-resolved drop position and maximum transverse dimension are characterized using backlit stereo videos taken at 500 kHz. A Reynolds-Averaged Navier Stokes (RANS) simulation of the bullet is used to estimate the gas density and velocity fields experienced by the drops. Classical correlations for breakup times derived from planar-shock/drop interactions are evaluated. Predicted drop breakup times are found to be in error by a factor of three or more, indicating that existing correlations are inadequate for predicting the response to the three-dimensional relaxation of the velocity and thermodynamic properties downstream of the conical shock. Next, the Taylor Analogy Breakup (TAB) model, which solves a transient equation for drop deformation, is evaluated. TAB predictions for drop diameter calculated using a dimensionless constant of C2 = 2, as compared to the accepted value of C2 = 2/3, are found to agree within the confidence bounds of the ensemble averaged experimental values for all drops studied. These results suggest the three-dimensional relaxation effects behind conical shock waves alter the drop response in comparison to a step change across a planar shock, and that future models describing the interaction between a drop and a non-planar shock wave should account for flow field variations.
Measurements of gas-phase pressure and temperature in hypersonic flows are important to understanding fluid–structure interactions on vehicle surfaces, and to develop compressible flow turbulence models. To achieve this measurement capability, femtosecond coherent anti-Stokes Raman scattering (fs CARS) is applied at Sandia National Laboratories’ hypersonic wind tunnel. After excitation of rotational Raman transitions by a broadband femtosecond laser pulse, two probe pulses are used: one at an early time where the collisional environment has largely not affected the Raman coherence, and another at a later time after the collisional environment has led to significant J-dependent dephasing of the Raman coherence. CARS spectra from the early probe are fit for temperature, while the later CARS spectra are fit for pressure. Challenges related to implementing fs CARS in cold-flow hypersonic facilities are discussed. Excessive fs pump energy can lead to flow perturbations. The output of a second-harmonic bandwidth compressor (SHBC) is spectrally filtered using a volume Bragg grating to provide the narrowband ps probe pulses and enable single-shot CARS measurements at 1 kHz. Measurements are demonstrated at temperatures and pressures relevant to cold-flow hypersonic wind tunnels in a low-pressure cryostat with an initial demonstration in the hypersonic wind tunnel.
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.
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.
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.
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.
