Understanding the transport and break up of reactive ejecta

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Highlights

  • Rapid heating of Ce ejecta transporting in shock-heated D2 and H2 was observed.

  • The rapid heating can only be explained by reactions of the Ce with the gases.

  • Reactive breakup dynamics showed increasing ejecta diameters with increasing time.

  • Hydrodynamic breakup showed large diameters stabilize to small sizes, as expected.

  • We propose a method to determine the masses and sizes below diagnostic resolution.

Abstract

This manuscript investigates reactive- versus hydrodynamic-breakup processes of ejecta. For this study, the reactive metal is cerium (Ce) and the nonreactive metal is tin (Sn), the nonreactive gas is helium (He) and the reactive gas is deuterium (D2) or hydrogen (H2). Experiments were performed in vacuum and the reactive- and nonreactive-gases at various pressures, where we endeavored to match the post-shock gas densities to differentiate between reactive- versus hydrodynamic-breakup processes. Hydrodynamic breakup sensitively links to the Weber number (gas density, liquid fragment diameter, surface tension, and the square of the relative velocity between the fragment and the gas), whereas reactive breakup links to the reactive dynamics which includes two processes. In one case the reactive metal breaks up into smaller fragments as rapidly as the reaction rate, and in the other a crust grows on the liquid fragments as the reactions occur, a diffusion limited process. In the latter case, the particle diameters increase with time as the crust grows. In this process, which is indicated by the data, particles breakup as the CeD2 loses strength with increasing temperature, leaving an exponentially increasing diameter.

Introduction

Ejecta form as a spray of dense particles ejected from the back surface of metals into a vacuum or gas when the metal is subjected to strong shocks. The interest in ejecta centers on military and industrial applications, including the physics of fusion.

The earliest available technical report on ejecta is from research by the Atomic Weapons Research Establishment, Aldermaston (UK). In their report [1], Bristow and Hyde characterized temporal ejecta (surface spray) phenomena as a dense-spray, or background-spray, which they distinguished as grass (dense spray), or as an increasingly darkening region (background spray). They further observed bush-like features, and grain boundary effects, and they also described spray from surface flaws, such as cracks and pinholes, which they portrayed as mushrooms, crown-spikes and rings. The general conclusions of their research identified surface-spray as an indicator of melting of the metal.

The physics of ejecta are now understood as a special limiting case of impulse driven Richtmyer–Meshkov (RM) [2], [3] unstable phenomena with an Atwood number At=(ρ1ρ2)(ρ1+ρ2)1, where ρ1 is the density of the medium beyond the surface and ρ2 is the density of the metal post-shock. In situations where At=1, the shockwave proceeds through the metal and interacts with the perturbations, causing them to invert and unstably grow into the lower density medium beyond the surface. If the metal is solid post-shock, the unstable growth will either arrest [4], [5], or it will transition to fully unstable growth to form solid ejecta [6], [7], the (RM) dynamics of which depend on the viscosity and yield-strength of the metal [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], the morphology of the perturbations [9], and the peak loading stress (PL) of the shockwave [17]. In contrast, if the metal is liquid post-shock, the RM unstable growth causes liquid ejecta that transports into the lower density medium beyond the surface. In both the solid and liquid situations the reflected shockwave transmits into the metal as a rarefaction wave that scatters into a fan at the speed of sound in the shocked metal. The dynamics of the rarefaction wave with the compressed metal releases the post-shock metal (solid or liquid) into tension, or to zero pressure post-shock, depending on the characteristics of the shockwave impulse. If tension is present, subsequent damage manifests as spall in solids, but as cavitation in liquids.

It is interesting to note the dates of Richtmyer’s and Meshkov’s publications (1960 and 1969, respectively). These dates imply interest in impulse (shockwave) driven surface-defect phenomena in the 1960s, and as early as the 1950s. Indeed, two of the authors in [18] (A.P. Tolochko and V.A. Golubev) personally communicate that their ejecta-research began in the 1950s (at Sarov, Ru.). Furthermore, while Richtmyer’s instability work was formally published in 1960 [2], it was reported internally earlier at the Los Alamos Scientific Laboratory (LASL) in 1955 [19]. Consequently, it is unsurprising that the first experiments done at the LASL PHERMEX x-radiography facility, when it came online in 1963, were devoted to the jetting and ejection of mass from surface features on explosively driven experiments [20]. The PHERMEX x-radiography facility was designed to study explosively driven hydrodynamic phenomena, such as jetting and spall, on diverse materials, as well as various high-explosive (HE) geometries. The PHERMEX experiments from 1963 to 1975, with x-radiography data and experiment design descriptions, are included in LASL PHERMEX Data Volumes I, II and II [20], [21], [22]. These volumes include multiple, single shot experiments from which a time series of radiographs from otherwise identical experiments can be constructed.

From these foundations ejecta research expanded at an increasingly rapid pace. For example, 1970s research on new experimental ejecta mass diagnostics developed at Sandia National Laboratories – notably what is now known as the Asay-foil [23], [24] — were published. Further, Asay, et al. used their new foil diagnostic to study ejecta formation from Al, Au, Cu, Pb and W on flyer-plate (gun) experiments [25], [26], [27]. Results from that research were used to build a prescriptive ejecta model that Asay and Bertholf describe in [27].

Also around this time, researchers at the Los Alamos National Laboratory (LANL) developed a capacitive ejecta mass diagnostic [28]. These novel ejecta diagnostics – the Asay-foil and the capacitive diagnostic – are positioned in the path of the ejecta flow field, and they collect the ejecta onto a momentum-transfer surface. Such in situ diagnostics return the density of the ejecta (spray) versus time (ρ(t)), and areal masses (ρA), longitudinal to the surface and ejecta motion. In this geometry, ρ(t) is the reduced density of the ejecta fragments, relative to the full density of the metal. In contrast x-radiographs return the spatial distribution ρA(x) transverse to the surface motion at a moment in time.

Subsequently, from the 1980s up until the late 1990s, multiple efforts were reported from national laboratories around the world about their efforts to develop, validate and verify techniques to study and quantify total ejected mass and mass-velocity distributions [29], [30], [31], and size-velocity distributions with Mie-scattering [32] and holography [33], [34]. The quantitative benchmark for ejecta sizing is holography, and for ρ(t) the benchmark is x-radiography. Comparisons of in situ diagnostics with x-radiography requires the transformation of ρ(t) to ρ(x), as described in [35], [36].

By the 2000s, many techniques to quantify ejecta properties were established, including soft-radiography [18], [30], [37], [38], the Asay foil  [23], [29], [37], [38], and the newer piezoelectric diagnostic [39], and x-radiography is being used to validate the quantitative capability of Asay foils [37], [38] and piezoelectric pins [40], [41], [42], [43].

With mature diagnostic techniques available, work at LANL to understand the physics of ejecta accelerated. Our initial experiments fielded in situ single-crystal lithium-niobate (LN), and periodically polled lead-zirconate–titanate (PZT), piezoelectric pins coincidently with x-radiography on explosively driven ejecta diagnostic validation studies [40], [41], [42], [43], [44], [45]; the material we studied was Sn. These Sn ejecta studies demonstrated that the LN-pin technology returned quantitative results [42], [43], [45], whereas results from the PZT-pin technology were only qualitative [42], [46].

We next expanded our Sn ejecta studies to understand the variables that affect ejecta production, variables that include material phase post shock [1], [23], the surface roughness [1], [23], and the shape of the shockwave loading profile.1 Specifically, the variables we considered were:

  • (1)

    the shockwave loading profile S, which is either supported (S), a square-shockwave as caused by flyer-plate impact (guns), or unsupported (S), a Taylor- or triangular-shockwave as caused by explosive loading,

  • (2)

    the surface roughness Ra of metals, as caused by machine tooling marks, which are usually continuous and regular in amplitude (h0), and periodic in frequency (wavelength λ), and

  • (3)

    the phase of the material post-shock, which is directly related to the equation of state (EOS) of the metal, and PL, independent of S.

Therefore, on our initial, single-shock ejecta experiments on Sn, we carefully controlled λ and h0, while we varied PL versus S: PL(S). This series of experiments fixed λ and the peak-to-valley depth 2h0 of the target finishes to (λ,2h0)(42,3.2)μm, and (λ,2h0)(30,1.8)μm (Ra18μin); Ra=32μin2h0=3.2μm. Results for the PL() experiments are in [17], [43], [44], and the results for the PL() experiments are in [47], [48], with PL() and PL() both summarized in [49], [50]. These fixed finish studies versus PL(S) returned two important results: namely that ρA increased linearly with increasing PL(), but that ρA and ρ(t) saturated above a critical pressure with increasing PL(), which for Sn was PL()23.5GPa. This saturation for S(), which has always been attributed to S() versus S(), was elegantly demonstrated to be so by Georgievskaya and Rayevsky in [51].

We then studied ρA and ρ(t) from explosively driven Sn at PL()28GPa, e.g., see results reported in [17], [40], [43], [52]. The collection of these data, our Tin ejecta set, revealed that the critical parameters for predicting ejecta formation directly link to the wavenumber (k=2πλ) amplitude product kh0. This data set established LANL RM ejecta models [7], [53], [54], and has been used to validate RM instability models elsewhere [51]. Other physics relevant to RM-based ejecta production were subsequently elaborated on in [55], [56], [57]. A broad and vast review of RM physics is found in [58], [59].

Ejecta transport studies had also begun around the world [18], [60], [61] and at LANL [62]. During this period, at LANL we further developed our dynamic Mie-scattering (particle sizing) diagnostics [63], [64], validating the quantitative results of the Mie-scattering approach in comparisons with holography in vacuum and gases [64], [65]. Others have applied hydrodynamic particle-drag models to laser Doppler velocimetry (LDV) data from ejecta transport experiments to estimate ejecta sizes as the ejecta apparently slow down and couple to the post-shock gas [18], [66], [67], [68], [69], [70], [71]; we apply similar techniques as well in comparisons with Mie scattering results in this manuscript.

Importantly, all who study ejecta around the world are primarily interested in quantifying how much ejecta (mass) stays in a gas, versus how much ejecta may recollect onto the shocked surface if it is subjected to another shock to the material and gas. The prevailing consensus for the hydrodynamic breakup of ejecta is that liquid fragments will hydrodynamically breakup and stabilize in gases at diameters dO(1μm), where this final diameter directly links to the surface tension of the metal and Weber number (as seen in [64], [65], for Sn we observed d2μm in He). Our understanding is that particles of dO(1μm) do not couple to the gas but rather are recollected onto the surface in subsequent shock loading events. Therefore, we have endeavored to address whether other previously unaccounted for processes can lead to the rapid breakup of ejecta into sizes that would couple to (remain in) post-shock gases even in the presence of additional shock-loading events, i.e., dO(100nm). Thus began our study of hydrodynamic- versus reactive-breakup of ejecta. In our investigations, we studied Ce transporting in D2 (and H2) as the reactive breakup process, and for hydrodynamic breakup processes we studied Sn and Ce transporting in He, and Sn transporting in D2.

In the next section we describe the details of our experimental geometries, including the diagnostic packages and the diagnostics we used to examine hydrodynamic- and reactive-breakup processes. Sections 3 2017 and 2018 LDV, LN-pins, IR-imaging and Mie-scattering — solid Ce and liquid Sn, 4 2019 LDV, LN-pin, IR-imaging and Mie-scattering experiments — liquid Ce and liquid Sn include diagnostics and analysis of our initial and most recent reactive-versus non-reactive-transport experiments. We then discuss important observations on what we in the ejecta community have missed with respect to quantifying the amount of ejecta mass that couples to a gas, and we propose approaches to address this fundamental question about the final disposition of ejecta. Finally we close with our general conclusions from this work in Section 6.

Section snippets

Experimental details

In shock driven ejecta studies, our targets are usually designed to include continuously periodic perturbations on the back-sides of metal-coupons. In this situation, when the coupons are explosively driven, RM unstable sheets source mass beyond the surface into the vacuum or gas that interfaces with the targets.

In our reactive- versus nonreactive-transport studies, our desire is that the ejecta form in a liquid state, and to match the mass-velocity distributions of the nonreactive Sn to that

2017 and 2018 LDV, LN-pins, IR-imaging and Mie-scattering — solid Ce and liquid Sn

The December 2017 series were 1P experiments with packages and targets as described in Section 2. These 1P experiments shock-loaded 3 mm of Ce, and 2 mm of Sn, to PL18- and 29-GPa, respectively, ejecting Ce- and Sn-fragments into He or D2 at various initial gas pressures (P0), or vacuum. Diagnostics on each experiment included three IR cameras, two LDV probes and three LN-pins at a 23 mm height above the target surface (zp).

2019 LDV, LN-pin, IR-imaging and Mie-scattering experiments — liquid Ce and liquid Sn

Because we were confident that we understood the Sn and Ce non-reactive metal- and gas-mixture dynamics, in 2019 we mainly focused on Ce ejecta transporting in D2 and H2. The 2019 campaigns included 22 IR experiments (2 in vacuum, 14 in D2, 5 in H2 and 1 into He), and 6 Mie experiments (1 in vacuum, 1 in He, and 4 in D2); the targets and finishes are described in Section 2.1 in Table 3. All of the experiments were in the 2P geometry (PL25GPa) except for two that included a vacuum and D2

Mass partition concept

We are aware of no diagnostic — as presently applied, including holography, Mie scattering, multiwavelength extinction, microscopy, atomic spectroscopy, etc., that can describe with any detail the partition of mass below the lower resolution limits of that diagnostic. Holography can quantify the detected mass by summation, and if total mass is known it quantifies the residual mass below its lower resolution limit, without specifying the size- and mass-velocity distributions. Similarly, the Mie

Conclusions

The experimental results reported here support our particle reaction and breakup hypothesis. That is, we have seen rapid heating of Ce ejecta transporting in D2 and H2 gases. Further, the velocimetry and Mie-scattering results imply that rapid breakup events accompany the reactions. We also realized that while we affirm the rapid breakup, we cannot quantify the partition of ejecta mass below the lower resolution limit of our optical diagnostic. These experimental results demonstrate the need to

CRediT authorship contribution statement

William T. Buttler: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Writing, Visualization, Supervision, Project administration, Funding acquisition. Roland K. Schulze: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, writing. John J. Charonko: Methodology, Software, Validation, Formal analysis, Investigation, Writing, Visualization. Jason C. Cooley: Conceptualization, Writing, Project administration, Funding

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

Research presented in this article was supported by the Laboratory Directed Research and Development program of Los Alamos National Laboratory under project number [20070082DR]. We acknowledge additional support from the US Department of Energy’s National Nuclear Security Administration[http://dx.doi.org/10.13039/100006168] through the Office of Experimental Sciences, (Campaigns 1 and 2) and its Advanced Simulation and Computing (ASC) program for Physics and Engineering Models (PEM) .

This work

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