Photon Doppler Velocimetry Measurements Research Articles

Technology and times scales in Photonic Doppler Velocimetry (PDV)

Photonic Doppler Velocimetry (PDV) is a fiber-based measurement amenable to a wide range of experimental conditions. Interference between two optical signals—one Doppler shifted and the other not—is the essential principle in these measurements. A confluence of commercial technologies, largely driven by the telecommunication industry, makes PDV particularly convenient at near-infrared wavelengths. This discussion considers how measurement time scales of interest relate to the design, operation, and analysis of a PDV measurement, starting from the steady state through nanosecond resolution. Benefits and outstanding challenges of PDV are summarized, with comparisons to related diagnostics.

Characterization of ejecta in shock experiments with multiple light scattering

Upon impact, the free surface of a solid metal may eject a cloud of fast and fine particles. Photon Doppler Velocimetry (PDV) is one of the optical diagnostics used to characterize these ejecta. Although the technique provides a direct way to estimate the particle velocities in the single scattering regime, it has been shown that multiple scattering cannot be neglected in real ejecta. Here, we derive a model for PDV measurements starting from the first principles of wave scattering. We establish rigorously the relationship between the specific intensity and the measured signal, as well as the Radiative Transport Equation (RTE) that describes the evolution of the specific intensity upon scattering and absorption in dynamic ejecta, including the effects of inelastic scattering and inhomogeneities in the optical properties. We also establish rigorously the connection between the Monte Carlo scheme used for numerical simulations and the solution to the RTE. Using numerical simulations, we demonstrate the crucial contribution of multiple scattering to PDV spectrograms as well as the effect of statistical inhomogeneities in particle size distribution. These results could substantially impact the analysis of ejecta by PDV.

Uncovering the fracture behavior of metallic cylindrical shells under internal explosive loadings via careful design of densely-arranged multi-point photon Doppler velocimetry measurements

While the expanding process of cylindrical shells under internal explosive loadings is fundamental and ubiquitous in engineering applications, the comprehensive understanding of the underlying mechanism is still a challenge due to the limitation of the spatial resolution on the current diagnostic techniques. To address this issue, an improved densely-arranged multi-point photon Doppler velocimetry (DMPDV) technique with enough spatial resolution to capture the local dynamical evolution was carefully designed. The DMPDV technique was then applied to investigate the expanding behavior of an explosively driven 304 L stainless steel cylindrical shell. As a step beyond the coarse understanding of the overall dynamical response, the expanding process can then be demonstrated comprehensively with more exact concentrations on one fragment. By the combination of DMPDV and high-speed photography, we uncovered the evolution of the expanding process which can be divided into three stages: (1) In the beginning, due to the symmetries of the specimen and the loading, the cylinder expands uniformly and all the velocity-time curves at different hoop positions are coincide with each other. (2) after the emergence of cracks at the outer surface of the cylinder, the velocity-time curves start to separate from each other and are regularly arranged according to their test positions. (3) following the penetration of the crack through the thickness of the cylinder, there is a reverse in the velocity-time curves and the fragments begin to rotate, the rotation angle can be estimated using the velocity difference. The hidden mechanism is then revealed with the help of unloading wave theory and rigid body dynamics. Here the second stage is dominated by unloading wave while the last stage is controlled by the denotation products. These experimental results provide deep insight into the detailed fracture behavior of expanding cylindrical shell and are further validated by the Mott wave models as well as numerical simulations, respectively.

Structural Response of Double-Layer Steel Cylinders under Inside-Explosion Loading

The research on the structural response of explosive vessel is an important basis for the design of explosive vessels. Double-layer cylinder structures are widely used in the design of various explosive vessels. This paper studied the deformation of a steel cylindrical shell under internal explosion and proposes a new method for measuring shell deformation by PDV (photonic Doppler velocimetry). We carried out many spherical explosive experiments and obtained useful results that show displacement of the double-layer cylinders and the explosion time. The above process is a simulated LS-DYNA with a finite element numerical simulation. The vibration period of the outer cylindrical shell and the time for reflection of the stress wave in the outer cylindrical shell were obtained by numerical simulation and PDV measurement, respectively. The results of both can be verified against each other. Through the above research, the structural response of the multilayer cylinders can be obtained, which can provide further help with research of the structural design of multilayer cylinders.

High-Strain Rate Spall Strength Measurement for CoCrFeMnNi High-Entropy Alloy

In this study, we experimentally investigate the high stain rate and spall behavior of Cantor high-entropy alloy (HEA), CoCrFeMnNi. First, the Hugoniot equations of state (EOS) for the samples are determined using laser-driven CoCrFeMnNi flyers launched into known Lithium Fluoride (LiF) windows. Photon Doppler Velocimetry (PDV) recordings of the velocity profiles find the EOS coefficients using an impedance mismatch technique. Following this set of measurements, laser-driven aluminum flyer plates are accelerated to velocities of 0.5–1.0 km/s using a high-energy pulse laser. Upon impact with CoCrFeMnNi samples, the shock response is found through PDV measurements of the free surface velocities. From this second set of measurements, the spall strength of the alloy is found for pressures up to 5 GPa and strain rates in excess of 106 s−1. Further analysis of the failure mechanisms behind the spallation is conducted using fractography revealing the occurrence of ductile fracture at voids presumed to be caused by chromium oxide deposits created during the manufacturing process.

Development and integration of photonic Doppler velocimetry as a diagnostic for radiation driven experiments on the Z-machine.

Plasma density measurements are key to a wide variety of high-energy-density (HED) and laboratory astrophysics experiments. We present a creative application of photonic Doppler velocimetry (PDV) from which time- and spatially resolved electron density measurements can be made. PDV has been implemented for the first time in close proximity, ∼6 cm, to the high-intensity radiation flux produced by a z-pinch dynamic hohlraum on the Z-machine. Multiple PDV probes were incorporated into the photoionized gas cell platform. Two probes, spaced 4 mm apart, were used to assess plasma density and uniformity in the central region of the gas cell during the formation of the plasma. Electron density time histories with subnanosecond resolution were extracted from PDV measurements taken from the gas cells fielded with neon at 15 Torr. As well, a null shot with no gas fill in the cell was fielded. A major achievement was the low noise high-quality measurements made in the harsh environment produced by the mega-joules of x-ray energy emitted at the collapse of the z-pinch implosion. To evaluate time dependent radiation induced effects in the fiber optic system, two PDV noise probes were included on either side of the gas cell. The success of this alternative use of PDV demonstrates that it is a reliable, precise, and affordable new electron density diagnostic for radiation driven experiments and more generally HED experiments.

Pressure amplification and modelization in laser shock peening of Ti-6Al-4V and AA7085 with adhesive-backed opaque overlays

The effects of adhesive-backed overlays, specifically vinyl tape and aluminum tape, on the peak pressures generated by laser shock peening (LSP) of 7085 aluminum alloy and Ti-6Al-4V were investigated and the results are reported. Peak pressures were determined from photon doppler velocimetry measurements of rear surface velocity. Incorporating adhesive-backed opaque overlays in LSP provided up to 50 % pressure enhancement compared to processing without the overlays. Contrary to processing without the overlays, the temporal characteristics of LSP impulses with adhesive-backed overlays are shown to be independent of the laser pulse width in the range studied. This finding is an important impulse consideration in LSP parameter selection and has not been investigated or reported in the literature. A novel physics-based analytical model to predict shockwave pressures is proposed and validated with experimental data agreeing nominally within 15 % of the predicted values across the parameter space. The results provide insight into the improved residual stresses and enhanced material properties of published opaque overlay studies. Moreover, the results provide vital information for selecting LSP parameters for optimizing component performance and potential extension into previously unreachable pressure regimes.

Photon Doppler velocimetry measurements of impact-induced surface waves in glass and their role in fracture initiation and damage evolution

Ballistic experiments involving the impact of cylindrical Lexan® projectiles, with nominal velocities of 400 and 800 m/s, on borosilicate glass targets were conducted using a single-stage gas gun. The objective of the experiments was to develop a technique involving multiplexed photon Doppler velocimetry (PDV) to observe the distal surface motion due to the propagation of impact-induced elastic waves. Comparison of the recorded signals to finite-element simulations of the experiment allowed for the identification of the signature of fracture initiation and subsequent damage evolution in the material. By directing PDV probes through the rear surface of the target it was also found that the surface motion within the impact zone could be measured. In addition, it was discovered that two distinct velocity signals could be consistently measured beneath the impact site. One of these signals was identified as the particle velocity of the impact surface. The other signal is presently of unknown origin.

Photon Doppler velocimetry measurements of the impact velocity during electromagnetic pulse welding of copper-steel tubular joints

Tubular copper to steel joints were manufactured by electromagnetic pulse welding, during which the impact velocity was measured with photon Doppler velocimetry. The reduction in inner diameter and the remaining cross-sectional area of the target tube were determined after welding. Tube-to-tube configurations with an internal support exhibited a larger remaining cross-sectional area, compared to the configuration without internal support. Moreover, for the tube-to-rod configuration, the initial velocity drop immediately after impact dropped down to zero, whereas for the tube-to-tube configurations, a velocity drop to an intermediate level was found. The velocity and acceleration increased with an increase of the discharge energy. The acceleration was positive up to at least 9 μs, with an expected turning point situated between 9 μs and 11 μs. The acceleration was still positive at the moment of impact at a stand off distance of 1.0 mm and 1.5 mm, but was likely negative at 2.0 mm.

Effects of equations of state and constitutive models on simulating copper shaped charge jets in ALEGRA

We investigate the effects of copper equations of state and constitutive models on simulations of shaped charge jets using the Sandia National Laboratories’ multiphysics hydrocode, ALEGRA. Specifically, we compare (1) the 3320, 3325, 3331, and 3337 SESAME copper equations of state (EOS), and (2) Johnson–Cook, Zerilli–Armstrong, Preston–Tonks–Wallace, Steinberg–Guinan–Lund, and Mechanical Threshold Stress constitutive models. Several of these cases are also compared against photon Doppler velocimetry measurements of the tip velocity. Lagrangian tracer particles are used to follow a part of the jet's evolution in state space for the various models. We monitored the jet topology and found that the various EOS produce similar results, although the 3325 model generates a cavity near the jet tip whose size decreases with increasing mesh resolution. Constitutive models generated more noticeable differences. We found the SGL and PTW models produced higher temperatures while the MTS and JC models returned very similar results at lower temperatures. The SGL model was the only strength model that reported a liquid region along the axis of the jet. For all material models, we found similar results for the velocity history of the jet tip as measured against experiment using photon Doppler velocimetry.

Hugoniot Measurements Utilizing In Situ Synchrotron X-ray Radiation

Pressure–density relationships derived from the experimentally obtained shock and particle velocities are critical to define a material’s equation of state (EOS). Typically, impact experiments coupled with velocimetry are used to map a material’s Hugoniot. Limitations such as sample geometry and varying indices of refraction may prevent proper characterization using traditional techniques such as photon doppler velocimetry (PDV) or velocity interferometer system for any reflector (VISAR). Here, traditional Hugoniot measurements using PDV are compared to dynamic x-ray imaging encompassing two different sample geometries on the gas gun platform. Through each of these methods an experimentally derived Hugoniot is determined for a previously uncharacterized polymeric material, Somos Watershed XC11122, that is used 3D printed stereolithography parts. A Us–up relationship was determined to be Us = 2.93 us + 1.73 mm/μs through traditional PDV. Slope and sound speed values determined from x-ray imaging methods varied 11% from PDV measurements. Each method yielded a Hugoniot with densities similar to poly(methyl methacrylate) (PMMA). The similarity shows the viability of such analyses for dynamic properties and Hugoniot data. The performance and analysis of both PDV and dynamic x-ray measurements are laid out in this work. Comparing PDV and x-ray imaging highlights distinct advantages and disadvantages among each method. PDV provides less uncertainty for velocity measurements, however x-ray imaging is more spatially resolved allowing for shock steadiness observations of value when studying heterogeneous materials. Additionally, x-ray imaging provides greater insight into the shape and heterogeneity of the shock front as well as uniaxial strain state (1D zone) assumptions.

Hydrodynamic disassembly and expansion of electron-beam-heated warm dense copper

Cu foils, $200\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{m}$ in thickness, were heated in two stages by a $\ensuremath{\sim}100$-ns-long monoenergetic electron bunch at 19.8 MeV and a current of 1.7 kA ($8.5\ifmmode\times\else\texttimes\fi{}{10}^{14} {e}^{\ensuremath{-}}$) in a 2-mm-spot to ${T}_{e}\ensuremath{\sim}1$ eV. After 45 ns of isochoric heating, the pressure in the foil builds up to $g20$ GPa (200 kbar), it begins to hydrodynamically disassemble, and a velocity spread is measured. Near the end of the electron pulse, the 1550 nm probe is cut off or absorbed. Photonic Doppler velocimetry measurements were made to quantify the expansion velocity, hydrodynamic disassembly time, and pressure of the foil prior to cutoff. Measurements indicate foil motion begins the instant electrons pass through the foil and continues until the particle velocity approaches the ambient sound velocity of Cu and the bulk density exceeds the critical density of the probe. Once the density of the plasma drops below the critical threshold and begins reflecting again, an expansion velocity of the classical plasma is also measured, similar to the point-source solution.

Application of photon Doppler velocimetry for characterization of ejecta from shock-loaded samples

We consider the problem of recovering the physical parameters of ejecta from data of photon Doppler velocimetry (PDV). The results of PDV measurements of ejecta production from shock-loaded Pb samples are presented. Shockwaves in the samples were generated by an accelerated flyer-plate. Depending on the sample thickness, the shock-breakout pressure varied from 27.5 to 43 GPa. The ejecta transport occurred in the air. The spectral profile J(ω) of heterodyne beats underlies our analysis of the experiments. The noise-free component of |J(ω)|2 is shown to obey the transport equation which accounts for multiple scattering and absorption of the probing beam in the cloud of moving particles. This provides a means for theoretical modeling of PDV data. Varying the values of the free-surface velocity and the parameters of the velocity distribution of ejecta, we fit the calculated spectrum to the PDV-measured one. We apply this method to time-resolved PDV spectra and, based on the ejecta optical model, recover the values of the free-surface velocity, the areal density, and the density-velocity distribution of ejecta.

Photon Doppler velocimetry measurements of transverse surface velocities.

The goal of this work was to develop a technique for making transverse surface velocity measures utilizing Photon Doppler Velocimetry (PDV). Such a task is achieved by transmitting light and collecting Doppler-shifted light at an angle relative to the normal axis, where measured velocities are representative of a component of the transverse velocity. Because surface characteristics have an intrinsic effect on light scatter, different surface preparations were explored to direct reflectivity, including diffusion by means of sandpapering, or increasing retroreflectivity by coating with microspheres, milling v-cuts, and electrochemically etching grooves. Testing of these surface preparations was performed using an experiment featuring a 30 mm diameter aluminum disk rotating at 6000 or 6600 RPM. A single PDV collimator was positioned along the rotational axis of the disk at various angles, resolving the apparent transverse velocity. To characterize surface preparations, light return and velocities were recorded as a function of probe angle ranging from 0° to 51° from the surface normal for each preparation. Polished and electrochemically etched surfaces did not provide enough reflected light to resolve a beat frequency; however, sandpapered surfaces, retroreflective microspheres, and milled v-cuts provided adequate reflected light for incidence angles up to 51°. Applications of the surface preparations were then studied in gas gun experiments. Retroreflective microspheres were studied in a planar impact experiment, and milled v-cuts were studied in an oblique impact experiment. A normal and transverse profile of particle velocity was resolved in the oblique impact experiment.

Multiple light scattering in metallic ejecta produced under intense shockwave compression.

A roughened metallic plate, subjected to intense shock wave compression, gives rise to an expanding ejecta particle cloud. Photonic Doppler velocimetry (PDV), a fiber-based heterodyne velocimeter, is often used to track ejecta velocities in dynamic compression experiments and on nanosecond time scales. Shortly after shock breakout at the metal-vacuum interface, a particular feature observed in many experiments in the velocity spectrograms is what appear to be slow-moving ejecta, below the free-surface velocity. Using Doppler Monte Carlo simulations incorporating the transport of polarization in the ejecta, we show that this feature is likely to be explained by the multiple scattering of light, rather than by possible collisions among particles, slowing down the ejecta. As the cloud expands in a vacuum, the contribution of multiple scattering decreases due to the limited field of view of the pigtailed collimator used to probe the ejecta, showing that the whole geometry of the system must be taken into account in the calculations to interpret and predict PDV measurements.

Microstructure Based Failure Criterion For Ductile Materials

For ductile metals, the process of dynamic fracture occurs through nucleation, growth and coalescence of voids. The stress required to nucleate these voids is inferred from the velocimetry data (using the acoustic approach) and termed as the spall strength. This is a key parameter that is used to evaluate a material’s susceptibility to damage and failure. However, it is also well recognized that the dynamic parameters used to generate the shock state such as pulse duration, tensile strain-rate and peak stress coupled with material microstructure itself affect the material response in a complex manner. Yet, it is impossible to capture all this information by assessing only the spall strength measured from simple one-dimensional Photon Doppler Velocimetry measurements. Although, there exist widely used corrections proposed by Kanel et. al. that allow for the inclusion of some of these complexities into the measured spall strength but still does not take the microstructure into account. In this work, we propose another scheme for normalization of spall strength with a damage area to capture the complexities included in the damage and failure process especially pertaining to microstructure. We will also demonstrate the application of this scheme by applying to examples of materials such as Copper, Copper-24 wt%Ag, Copper-15 wt% Nb and additively manufactured 316L SS.

Dynamic fragmentation of Al-W granular rings with different mesostructures

Explosively driven fragmentation mechanisms of Al-W particulate composite rings were investigated. The effect of mesostructures (particulate Al and W, particulate Al and W fibers) and bonding between Al particles (processing via cold isostatic and cold isostatic + hot isostatic pressing) were determined. The kinematics of the expansion process was monitored using Photon Doppler Velocimetry measurements of the velocity of the outer surface of the rings. Numerical simulations of the expansion velocity of rings were in agreement with experimental data. Agglomerated fragments larger than sizes of initial Al particles were observed in experiments. The characteristic size of these agglomerates is most likely determined by the spacing between W inclusions. The simulations show that the dynamically expanded rings had clusters of particulates between shear bands (developing into macrocracks), which expand without significant plastic deformation, generating agglomerated fragments with sizes larger than initial Al particles, as observed in experiments. It was also demonstrated that debris has a measurable fraction of particles with sizes below the original particle sizes. The mesostructure of the fragments demonstrated that Al particles were heavily deformed within the regions having locally high strain plastic flow, which may result in fragments sizes below initial Al particle diameter. Simulations agree with experiments in that Al particles between neighboring W particles/fibers are heavily plastically deformed in comparison with Al particles away from W inclusions. Simulations also demonstrated that increasing initial porosity increases the plastic straining of Al particles between W particles/fibers. Thus, initial porosity may cause an increase in temperature of the Al fragments and cracking their surface oxide layers, therefore increasing the chance of subsequent rapid oxidation in air.

Detection of an anomalous pressure on a magneto-inertial-fusion load current diagnostic

Recent Magnetized Liner Inertial Fusion experiments at the Sandia National Laboratories Z pulsed power facility have featured a PDV (Photonic Doppler Velocimetry) diagnostic in the final power feed section for measuring load current. In this paper, we report on an anomalous pressure that is detected on this PDV diagnostic very early in time during the current ramp. Early time load currents that are greater than both B-dot upstream current measurements and existing Z machine circuit models by at least 1 MA would be necessary to describe the measured early time velocity of the PDV flyer. This leads us to infer that the pressure producing the early time PDV flyer motion cannot be attributed to the magnetic pressure of the load current but rather to an anomalous pressure. Using the MHD code ALEGRA, we are able to compute a time-dependent anomalous pressure function, which when added to the magnetic pressure of the load current, yields simulated flyer velocities that are in excellent agreement with the PDV measurement. We also provide plausible explanations for what could be the origin of the anomalous pressure.

Analysis of Fiber Optic Sensor to Measure Velocities During High Deformation Rate Material Forming Processes

Previous methods of measuring high velocities, e.g., during electromagnetic forming (EMF) and magnetic pulse welding processes where the workpiece is deforming, include photon Doppler velocimetry (PDV), laser micrometers, and high speed photography. In this paper, an alternative method is presented, implementing a fiber optic, reflectance dependent sensor. The sensor is shown to be an attractive, low purchase cost solution to measure high velocities. Data are shown with respect to sensor characterization including various surface reflectivity values, curvatures, and misalignments; implementation in two EMF/welding processes; and verification with high velocity PDV measurements. The sensor system is one twentieth the purchase cost of a PDV system, and yet measures velocities accurately (using PDV measurements as the reference) to at least 150 m/s provided that local curvature is not extreme and the displacement is less than approximately 27 mm. Sensor performance is also enhanced by the use of retroreflective tape, which is shown to increase the displacement range by 9×, decrease sensitivity to misalignment, and increase repeatability and ease of implementation.

In-situ Raman spectroscopy and high-speed photography of a shocked triaminotrinitrobenzene based explosive

We have developed a single-shot Raman spectroscopy experiment to study at the molecular level the initiation mechanisms that can lead to sustained detonation of a triaminotrinitrobenzene-based explosive. Shocks up to 30 GPa were generated using a two-stage laser-driven flyer plate generator. The samples were confined by an optical window and shock pressure was maintained for at least 30 ns. Photon Doppler Velocimetry measurements were performed at the explosive/window interface to determine the shock pressure profile. Raman spectra were recorded as a function of shock pressure and the shifts of the principal modes were compared to static high-pressure measurements performed in a diamond anvil cell. Our shock data indicate the role of temperature effects. Our Raman spectra also show a progressive extinction of the signal which disappears around 9 GPa. High-speed photography images reveal a simultaneous progressive darkening of the sample surface up to total opacity at 9 GPa. Reflectivity measurements under shock compression show that this opacity is due to a broadening of the absorption spectrum over the entire visible region.