Hydrocode Models Research Articles

Using Hydrodynamic Similarity as a Verification Method for Impact Cratering Simulations in the FLAG Hydrocode

Hydrodynamic codes (hydrocodes) are common tools for modeling hypervelocity impacts to provide insight into the physical phenomenon. Hydrocodes can simulate impacts from micrometer to kilometer spatial scales and reach impact velocities difficult to achieve in experimental settings. However, numerical models are approximations, and demonstrating that a numerical method is capable of providing physical results for these models is essential. In this work, we employ a hydrocode verification technique that leverages hydrodynamic similarity, a mathematical property of the conservation equations of fluid mechanics that form the basis for hydrocode models. Using the FLAG hydrocode, we simulate aluminum (Al) and basalt projectiles and targets at spatial scales spanning 7 orders of magnitude (hundreds of micrometers to kilometers). These materials were chosen because Al-6061 is a common material in spacecraft and satellites and basalt is a useful approximation of rocky astronomical bodies. Our results show that hydrodynamic similarity holds for each material model used and across spatial scales. We show that under certain conditions hydrodynamic similarity can apply in the presence of gravity and that similarity does not hold in the presence of strength models. We conclude that the FLAG hydrocode preserves important mathematical properties of fluid dynamics in hypervelocity impacts of Al-6061 and basalt.

Temperature and Density on the Forsterite Liquid-Vapor Phase Boundary.

The physical processes during planet formation span a large range of pressures and temperatures. Giant impacts, such as the one that formed the Moon, achieve peak pressures of 100s of GPa. The peak shock states generate sufficient entropy such that subsequent decompression to low pressures intersects the liquid‐vapor phase boundary. The entire shock‐and‐release thermodynamic path must be calculated accurately in order to predict the post‐impact structures of planetary bodies. Forsterite (Mg2SiO4) is a commonly used mineral to represent the mantles of differentiated bodies in hydrocode models of planetary collisions. Here, we performed shock experiments on the Sandia Z Machine to obtain the density and temperature of the liquid branch of the liquid‐vapor phase boundary of forsterite. This work is combined with previous work constraining pressure, density, temperature, and entropy of the forsterite principal Hugoniot. We find that the vapor curves in previous forsterite equation of state models used in giant impacts vary substantially from our experimental results, and we compare our results to a recently updated equation of state. We have also found that due to under‐predicted entropy production on the principal Hugoniot and elevated temperatures of the liquid vapor phase boundary of these past models, past impact studies may have underestimated vapor production. Furthermore, our results provide experimental support to the idea that giant impacts can transform much of the mantles of rocky planets into supercritical fluids.

Effects of underground explosions on soil and structures

Much effort has been dedicated to the study of underground explosions because they pose a major threat to people and structures below or above the ground. In this regard, it is especially important to model the propagation of blast waves in soil and their effects on structures. The main phenomena caused by underground explosive detonation that must be addressed are crater or camouflet formation, shock wave and elastic–plastic wave propagation in soil, and soil-structure interaction. These phenomena can be numerically simulated using hydrocodes, but much care must be taken to obtain reliable results. The objective of this study is to analyze the ability of a hydrocode and simple soil models that do not require much calibration to approximately reproduce experimental and empirical results related to different buried blast events and to provide general guidelines for the simulation of this type of phenomena. In this regard, crater formation, soil ejecta, blast wave propagation in soil, and their effects on structures below and above the ground are numerically simulated using different soil models and parameters; the results are analyzed. The properties of soil have a significant effect on structures, the ejecta, and the propagation of shock waves in soil. Thus, the model of the soil to study these phenomena must be carefully selected. However their effect on the diameter of a crater is insignificant.

A new constitutive model for steel fibre reinforced concrete subjected to dynamic loads

The use of steel fibre reinforced concrete (SFRC) in protective structures has gained worldwide interest due to its superior mechanical characteristics. At present, hydrocode material models have been frequently used to simulate the dynamic behaviour of SFRC subjected to impact and blast loads. However, as these material models are developed for normal concrete, much effort is required for model calibration, and their other drawbacks, such as the neglect of shear dilation and the inappropriate consideration of strain-rate effect, may lead to inaccuracies in numerical predictions. In this study, a new constitutive material model is developed for SFRC, in which the damage evolution, shear dilation and strain-rate dependent material properties are properly taken into account. The new material model could accurately capture the mechanical behaviours of SFRC (i.e. strain hardening and softening in both compression and tension) with simple input parameters. It is then incorporated into the commercial finite element code LS-DYNA to simulate the structural behaviour of SFRC components under various loading conditions. The effectiveness and accuracy of the new material model are validated against the reported experimental results.

Radial gravity anomalies associated with the ejecta of the Orientale basin

GRAIL gravity data shows small-scale gravity anomalies radiating out from the Orientale basin between distances of ∼550 km (average distance to the Cordillera ring) and ∼1000 km. These radial gravity lineations are sometimes associated with secondary crater chains or catenae, of which the specific details of formation and their relation to the basin ejecta remain unclear. However, many of the radial gravity anomalies have no clear topographic signature at all. Typical anomalies have an average width of about 20 km, with a magnitude of ± 20 mGal, and a length of 50–200 km. Here we use gravity inversions, hydrocode modeling, and observations to investigate the radial gravity anomalies in more detail. Density inversion models show that the gravity can be matched by solutions ranging from broad low-amplitude anomalies with density contrasts of ± 20 kg/m3 extending to depths of tens of kilometers, to shallow high-amplitude anomalies with density contrasts of about ± 200–400 kg/m3 confined to the top ∼1–2 km of the crust. Hydrocode models of the low-velocity secondary impacts of basin ejecta show that the impacting material does not disperse – as occurs for hypervelocity impacts – but instead remains as a thin layer within the secondary craters. This remaining secondary projectile material derived from Orientale ejecta can explain the linear gravity anomalies associated with secondary crater chains and catenae. However, this does not explain the majority of linear gravity features that are not associated with secondary crater chains. Therefore, we conclude that the majority of radial gravity anomalies represent the structure of the ejecta deposit. This density variability within the ejecta of basins likely contributes substantially to the density variability of the shallow upper crust as a whole.

Hydrocode modeling of the spallation process during hypervelocity impacts: Implications for the ejection of Martian meteorites

Hypervelocity ejection of material by impact spallation is considered a plausible mechanism for material exchange between two planetary bodies. We have modeled the spallation process during vertical impacts over a range of impact velocities from 6 to 21 km/s using both grid- and particle-based hydrocode models. The Tillotson equations of state, which are able to treat the nonlinear dependence of density on pressure and thermal pressure in strongly shocked matter, were used to study the hydrodynamic–thermodynamic response after impacts. The effects of material strength and gravitational acceleration were not considered. A two-dimensional time-dependent pressure field within a 1.5-fold projectile radius from the impact point was investigated in cylindrical coordinates to address the generation of spalled material. A resolution test was also performed to reject ejected materials with peak pressures that were too low due to artificial viscosity. The relationship between ejection velocity veject and peak pressure Ppeak was also derived. Our approach shows that “late-stage acceleration” in an ejecta curtain occurs due to the compressible nature of the ejecta, resulting in an ejection velocity that can be higher than the ideal maximum of the resultant particle velocity after passage of a shock wave. We also calculate the ejecta mass that can escape from a planet like Mars (i.e., veject > 5 km/s) that matches the petrographic constraints from Martian meteorites, and which occurs when Ppeak = 30–50 GPa. Although the mass of such ejecta is limited to 0.1–1 wt% of the projectile mass in vertical impacts, this is sufficient for spallation to have been a plausible mechanism for the ejection of Martian meteorites. Finally, we propose that impact spallation is a plausible mechanism for the generation of tektites.

Modelling of complex blast

There is an extensive hierarchy of models for the prediction of free-field blast wave propagation and loading. As one begins to move to more complex scenarios (e.g. near-field blast, non-ideal explosives, internal blast or buried charges), there is a need for more detailed understanding and modelling. In this article, we discuss a range of sub-models for the components of complex blast which can be used in hydrocode modelling of the loading of targets or structures. Many explosives are fuel-rich and thus have the capacity to undergo secondary combustion after detonation (afterburn). Even in the free field, this mechanism affects the wave profile and we illustrate the errors associated with simpler models, even for the case of detonation of a sphere of 2,4,6-trinitrotoluene (TNT) in the free field. We identify why these effects should be accounted for in any analysis of later time reflections in more complex targets and discuss how the effects of complex blast are also important in assessing human injury. We also report some engineering models which we have developed based on parameter studies using hydrocode models. The effects of any casing surrounding the explosive charge also influence the loading on a target, both by taking energy out of the blast wave and by accelerating fragments which produce a heterogeneous loading on a structure. Some blast mitigation concepts also make use of the transfer of energy to powder, liquid or foam surrounds. Buried charges can also behave in a similar manner to powder-based blast mitigants and lead to fast moving fingers of solid material which can produce localised loadings on structures. We identify how recent studies in these areas are influencing complex blast calculations.

Spatially resolved shock response at dry metallic multi-material interfaces

The high strain-rate behaviour of multi-component systems is often dominated by mediation at material interfaces. The extent to which a materials microstructure influences dynamic friction and relative sliding response remains an area of active study. Initial results from a study on the behaviour of dry metallic interfaces under the passage of a controlled loading wave are presented. Held in close contact along a single planar interface, oblique shock waves were generated along the boundary by direct copper flyer impact at velocities in the range 250 ms−1 – 300 ms−1. Both the 100 mm and 13 mm bore gas guns located at Imperial College London were utilised for this purpose. A line-imaging velocity interferometer system for any reflector (VISAR) system was used to directly record the velocity profile across the contact interface, providing a measure of any spatially dependent response while photon doppler velocimetry (PDV) was used to determine the far field response. Comparisons of these results against current generation hydrocode models are presented, with significant deviations from the computationally predicted results identified in the peak shock state immediately following shock breakout.

Formation of melt droplets, melt fragments, and accretionary impact lapilli during a hypervelocity impact

We present a model that describes the formation of melt droplets, melt fragments, and accretionary impact lapilli during a hypervelocity impact. Using the iSALE hydrocode, coupled to the ANEOS equation of state for silica, we create high-resolution two-dimensional impact models to track the motion of impact ejecta. We then estimate the size of the ejecta products using simple analytical expressions and information derived from our hydrocode models. Ultimately, our model makes predictions of how the size of the ejecta products depends on impactor size, impact velocity, and ejection velocity. In general, we find that larger impactor sizes result in larger ejecta products and higher ejection velocities result in smaller ejecta product sizes. We find that a 10km diameter impactor striking at a velocity of 20km/s creates millimeter scale melt droplets comparable to the melt droplets found in the Chicxulub ejecta curtain layer. Our model also predicts that melt droplets, melt fragments, and accretionary impact lapilli should be found together in well preserved ejecta curtain layers and that all three ejecta products can form even on airless bodies that lack significant volatile content. This prediction agrees with observations of ejecta from the Sudbury and Chicxulub impacts as well as the presence of accretionary impact lapilli in lunar breccia.

Stardust interstellar dust calibration: Hydrocode modeling of impacts on Al‐1100 foil at velocities up to 300 km s−1 and validation with experimental data

Abstract– We present initial results from hydrocode modeling of impacts on Al‐1100 foils, undertaken to aid the interstellar preliminary examination (ISPE) phase for the NASA Stardust mission interstellar dust collector tray. We used Ansys’ AUTODYN to model impacts of micrometer‐scale, and smaller projectiles onto Stardust foil (100 μm thick Al‐1100) at velocities up to 300 km s−1. It is thought that impacts onto the interstellar dust collector foils may have been made by a combination of interstellar dust particles (ISP), interplanetary dust particles (IDP) on comet, and asteroid derived orbits, β micrometeoroids, nanometer dust in the solar wind, and spacecraft derived secondary ejecta. The characteristic velocity of the potential impactors thus ranges from <<1 to a few km s−1 (secondary ejecta), approximately 4–25 km s−1 for ISP and IDP, up to hundreds of km s−1 for the nanoscale dust reported by Meyer‐Vernet et al. (2009). There are currently no extensive experimental calibrations for the higher velocity conditions, and the main focus of this work was therefore to use hydrocode models to investigate the morphometry of impact craters, as a means to determine an approximate impactor speed, and thus origin. The model was validated against existing experimental data for impact speeds up to approximately 30 km s−1 for particles ranging in density from 2.4 kg m−3 (glass) to 7.8 kg m−3 (iron). Interpolation equations are given to predict the crater depth and diameter for a solid impactor with any diameter between 100 nm and 4 μm and density between 2.4 and 7.8 kg m−3.

Correction to “Possible crippling of the core dynamo of Mars by Borealis impact”

[1] In the paper “Possible crippling of the core dynamo of Mars by Borealis impact” by Jafar Arkani‐Hamed (Journal of Geophysical Research, 115, E12021, doi:10.1029/ 2010JE003602, 2010) the impact heating of Mars by the Borealis impact, which likely created the northern lowland basin, was calculated. Using the crater scaling laws [Holsapple, 1993; Melosh, 1989] the basin diameter was related to the size of the impactor. Following the impact, a nearly uniform shock pressurewas generated inside an isobaric region in the mantle, outside which the shock pressure decreased exponentially with distance from the isobaric center following the average model of Pierazzo et al. [1997]. After crossing the core‐mantle boundary, the shock wave travelled in the core where the shock pressure again decayed with distance travelled from the isobaric center according to Pierazzo et al.’s average model but with the physical parameters of the core. The corresponding impact temperature increase is obtained using the Foundering model of Watters et al. [2009]. [2] The impact‐heated core stratified within a few tens of years and the possible pre‐existing core dynamo decayed with the characteristic time of 10–15 kyr [Arkani‐Hamed and Olson, 2010]. Shortly after the stratification, convection started in a thin layer in the outer core, the thickness of which increased in time as convection penetrated to deeper parts of the core until the entire core convected on a global scale. It took ∼60 Myr for the core to develop global convection and power a new core dynamo. [3] Here I describe a correction required in the calculation of the shock pressure distribution in the core. This correction is important because it increases the crippling time of the Martian core dynamo by a factor of larger than 4. The source of the required correction is the transmission coefficient of the shock wave across the core‐mantle boundary (CMB), the ratio of the shock pressure at the top of the core to that at the base of the mantle. The transmission coefficient was determined on the basis of seismic ray theory [Aki and Richards, 2002, section 5.2]. It resulted in a sudden drop of shock pressure as passing from the mantle to the core, in contrast to the sudden jump of the pressure according to recent Hydrocode models [Ivanov et al., 2010; Bierhaus et al., 2011].

Simulations of a comet impact on the Moon and associated ice deposition in polar cold traps

Modeling results of the water vapor plume produced by a comet impact on the Moon and of the resulting water ice deposits in the lunar cold traps are presented. The water vapor plume is simulated near the point of impact by the SOVA hydrocode and in the far field by the Direct Simulation Monte Carlo (DSMC) method using as input the SOVA hydrocode solution at a fixed hemispherical interface. The SOVA hydrocode models the physics of the impact event such as the surface deformation and material phase changes during the impact. The further transport and retention processes, including gravity, photodestruction processes, and variable surface temperature with local polar cold traps, are modeled by the DSMC method for months after impact. In order to follow the water from the near field of the impact to the full planetary induced atmosphere, the 3D parallel DSMC code used a collision limiting scheme and an unsteady multi-domain approach. 3D results for the 45° oblique impact of a 2 km in diameter comet on the surface of the Moon at 30 km/s are presented. Most of the cometary water is lost due to escape just after impact and only ∼3% of the cometary water is initially retained on the Moon. Early downrange focusing of the water vapor plume is observed but the later material that is moving more slowly takes on a more symmetric shape with time. Several locations for the point of impact were investigated and final retention rates of ∼0.1% of the comet mass were observed. Based on the surface area of the cold traps used in the present simulations, ∼1 mm of ice would have accumulated in the cold traps after such an impact. Estimates for the total mass of water accumulated in the polar cold traps over 1 byr are consistent with recent observations.

Exploring the role of shear in oblique impacts: A comparison of experimental and numerical results for planar targets

Oblique impacts produce asymmetric damage patterns due to asymmetric, directed shock waves; these patterns are seen for both laboratory and planetary scale craters [1,2]. Previous laboratory and computational studies of impact-induced damaged have focused mainly on tensile failure following hypervelocity impacts. Though extension plays a significant role in impact-induced damage, it is widely accepted that shear failure also occurs during hypervelocity impacts. Shear failure occurs over a variety of scales both during and after impacts [3–5]. Here we examine this process in more detail for oblique impacts. Experiments not only provide a general view of small-scale processes (including damage patterns in their final form), but also can be difficult to relate to larger impacts with confidence, even though similarities can be documented [e.g. 1]. Detailed computer models provide complementary information. Although they detail underlying processes during crater formation, they do not always contain adequate constitutive models, thereby requiring simplifying assumptions. A comprehensive model taking into account deformation following failure of rocks is still unavailable, which limits conclusions based solely on numerical simulations. Consequently, a combination of models and experiments must be used. Impact experiments into planar polymethylmethacrylate (PMMA) targets at small scale are examined in an attempt to constrain the sequence, location and style of failure. Two- and three-dimensional CTH models (with identical conditions to the experiments) were computed using a variety of failure criteria in order to determine the parameter set that best matches the experimental results. High-speed imaging recorded the sequence and location of failure within various PMMA targets, which was then compared with results from theoretical models. The CTH models provide critical details about specific failure style and indicate only minimal failure due to extension following the impact except for tensile failure at the base of the block. Instead, shear failure dominates below the crater. While the CTH hydrocode models generally match the extent of the damaged region, some differences remain. Projectile properties (density, composition, size) for impacts with the same kinetic energy affect the extent, style, and growth of damage in a given target. This includes differences in degree of uprange damage, subarcuate fractures, and sub-parallel failure planes. Comparisons between experiment and hydrocode results reveal that projectile failure (even at hypervelocity) contributes to the observed differences.

Characterizing the transient response of CFRP/Al HC spacecraft structures induced by space debris impact at hypervelocity

To quantify the disturbance induced by the impact of micrometeoroid and space debris particles at hypervelocity on vibration-sensitive CFRP/Al HC SP satellite platforms a method is presented which uses experimentally validated hydrocode models to characterize the impact-induced transient wave in the local structure. Key features of the transient waveform are simplified by a mathematical function which is expressed in terms of impactor momentum. Evolution of the transient waveform is characterized using multiple measurement gauges located on the sandwich panel facesheets outside the area of mechanical damage. The characterization is then used to extrapolate the elastic waveform back to the impact location. The elastic-equivalent excitation of a CFRP/Al HC SP is defined in terms of force with respect to time for application in finite element structural codes for propagation of the local disturbance to vibration-sensitive locations (i.e. measurement devices).

Yarkovsky/YORP chronology of asteroid families

Asteroid families are the byproducts of catastrophic collisions whose fragments form clusters in proper semimajor axis, eccentricity, and inclination space. Although many families have been observed in the main asteroid belt, only two very young families, Karin and Veritas, have well-determined ages. The ages of other families are needed, however, if we hope to infer information about their ejection velocity fields, space weathering processes, etc. In this paper, we developed a method that allows us to estimate the ages of moderately young asteroid families (approximately in between 0.1 and 1 Gyr). We apply it to four suitable cases—Erigone, Massalia, Merxia, and Astrid—and derive their likely ages and approximate ejection velocity fields. We find that Erigone and Merxia were produced by large catastrophic disruption events (i.e., parent body ⩾100 km) that occurred approximately 280 and 330 Myr ago, respectively. The Massalia family was likely produced by a cratering event on Asteroid (20) Massalia less than 200 Myr ago. Finally, the Astrid family, which was produced by the disruption of a 60–70 km asteroid, is 100–200 Myr old, though there is considerable uncertainty in this result. We estimate that the initial ejection velocities for these families were only a few tens of meters per second, consistent with numerical hydrocode models of asteroid impacts. Our results help to verify that asteroid families are constantly undergoing dynamical orbital evolution from thermal (Yarkovsky) forces and spin vector evolution from thermal (YORP) torques.

Asteroid impact tsunamis

A review of the known historic asteroid impacts generating huge tsunamis at the sea surface is provided. Different approaches from the linear theories to Navier–Stokes equations and hydrocode models are very briefly presented or referenced. The propagation and run-up stage of tsunamis is discussed and the important role of the sea bottom topography is emphasized. Further studies focusing on propagation and run-up are suggested to extend previous works on the subject. To cite this article: C. Kharif, E. Pelinovsky, C. R. Physique 6 (2005).

Observations at terrestrial impact structures: Their utility in constraining crater formation

Abstract— Hypervelocity impact involves the near instantaneous transfer of considerable energy from the impactor to a spatially limited near‐surface volume of the target body. Local geology of the target area tends to be of secondary importance, and the net result is that impacts of similar size on a given planetary body produce similar results. This is the essence of the utility of observations at impact craters, particularly terrestrial craters, in constraining impact processes. Unfortunately, there are few well‐documented results from systematic contemporaneous campaigns to characterize specific terrestrial impact structures with the full spectrum of geoscientific tools available at the time. Nevertheless, observations of the terrestrial impact record have contributed substantially to fundamental properties of impact. There is a beginning of convergence and mutual testing of observations at terrestrial impact structures and the results of modeling, in particular from recent hydrocode models. The terrestrial impact record provides few constraints on models of ejecta processes beyond a confirmation of the involvement of the local substrate in ejecta lithologies and shows that Z‐models are, at best, first order approximations. Observational evidence to date suggests that the formation of interior rings is an extension of the structural uplift process that occurs at smaller complex impact structures. There are, however, major observational gaps and cases, e.g., Vredefort, where current observations and hydrocode models are apparently inconsistent. It is, perhaps, time that the impact community as a whole considers documenting the existing observational and modeling knowledge gaps that are required to be filled to make the intellectual breakthroughs equivalent to those of the 1970s and 1980s, which were fueled by observations at terrestrial impact structures. Filling these knowledge gaps would likely be centered on the later stages of formation of complex and ring structures and on ejecta.

Collisional History of Gaspra

Interpretation of the impact record on Asteroid 951 Gaspra requires understanding of the effects of collisions on a target body of Gaspra's size and shape. Recent hydrocode models show that major impacts on Gaspra may leave craters larger than previously thought possible and that they can create substantial regolith and produce global jolting capable of erasing many smaller craters. A Gaspra-size body has a mean lifetime of about 109 years and is likely to have several impact craters of 4 km diameter or larger, which is consistent with the number of observed concavities on Gaspra. The steep size distribution of small craters on Gaspra implies an even steeper distribution for small asteroids, and the relative paucity of kilometer-size craters seems to require a twice-in-a-Gaspra-lifetime impact to have occurred about 50 myr ago. All of these considerations consistently point to a scenario in which several of the very large concavities (>4 km diameter) on Gaspra are probably impact craters.

Constraints on extragalactic-jet characteristics from lobe observations

We discuss Very Large Array spectral and polarimetric observations of the lobes of luminous, double radio galaxies. These observations can provide information on the (typically undetected) jets responsible for the sources. Spectral steepening is usually observed in the lobes, with the radio spectral index increasing with distance from the hot spot. These data can be used to infer a "speed of separation" of the hot spot and lobe material. These speeds, typically 1.0 × 104–3.0 × 104 km/s, are in agreement with hydrocode models of jets, which interpret the measured speed of separation as a combination of hot-spot motion and backflow. Polarimetric observations indicate that in at least some sources, there is an undetectably small amount of internal Faraday rotation, indicating upper limits to the thermal-plasma density of a few times 10−5 cm−3 or less. These measurements are also in agreement with the numerical beam models, provided that the beam density is substantially less than that of the background medium. We conclude that the lobe observations indicate that these sources are powered by light, high-Mach-number beams.