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Development of a 1D Lagrangian Hydrocode [Slides]
Abstract not provided.
The importance of electrothermal terms in Ohm's law for magnetized spherical implosions
The magnetohydrodynamics (MHD) of magnetic-field compression in laser-driven spherical targets is considered. Magnetic-field evolution is cast in terms of an effective fluid velocity, a convective term resulting from resistivity gradients, a resistive diffusion term, and a source term. Effective velocity is the sum of fluid velocity, drift velocity, and heat-flux velocity, given by electron heat flux divided by electron enthalpy density, which has two components: the perpendicular or Nernst velocity and the cross-field velocity. The Nernst velocity compresses the magnetic field as the heat front moves into gas. The cross-field velocity leads to dynamo generation of an azimuthal magnetic field. It is proposed that the heat-flux velocity should be flux limited using a “Nernst” flux limiter independent of the thermal flux limiter but should not exceed it. The addition of the MHD routines to the 1D, Lagrangian hydrocode LILAC and the Eulerian version of the 2D hydrocode DRACO is described, and the codes are used to model a magnetized spherical compression on the OMEGA laser. Thermal flux limiting at a shock front is found to cause unphysical electron temperature gradients that lead to large, unphysical magnetic fields caused by the resistivity gradient, so thermal flux limiting in the gas is removed. The Nernst term reduces the benefits of magnetization in inertial fusion. A Nernst flux limiter ≤0.12 is required in the gas in order to agree with measured neutron yield and increases in the neutron-averaged ion temperature caused by magnetization. This corresponds to preventing the Nernst velocity from exceeding the shock velocity, which prevents significant decoupling of the magnetic field and gas compression.
ZND Verification Tests for Reactive Burn Models in FLAG
The ZND theory, named after Zeldovich, von Neumann, and Doering, provides a simple model for one-dimensional ideal steady-state detonation. It assumes that the detonation wave front starts with a shock that is a discontinuous jump and is followed by a finite-length reaction zone. Reactive burn (also called reactive flow) models are based on ZND theory, as they model the shock initiation and detonation process with a finite reaction rate. The ZND wave propagation test is essentially the only available test case where an analytic solution exists for verification of reactive burn models in numerical codes. However, there are extensions and variants of the ZND test that have been devised for verification of multidimensional flows. The objective of this work is to provide verification of the reactive burn models currently implemented in the Lagrangian hydrocode FLAG and investigate the influence of mesh resolution, artificial viscosity models, and the Arbitrary Lagrangian-Eulerian (ALE) Euler relaxer on the simulation results. The burn models of interest are the Wescott-Stewart-Davis (WSD) model, the Scaled Uniform Reactive Flow (SURF) model (specifically with the SURFplus model extension), and the Arrhenius shock temperature state dependent WSD (AWSD) model. Previously, Ralph Menikoff has used ZND tests for verification of the SURF and SURFplus models in the Eulerian hydrocode xRAGE. The ZND tests here are somewhat different than the approach by Menikoff. In particular, we use a piston-driven ZND detonation wave (via a prescribed constant velocity boundary condition) in a Lagrangian framework whereas Menikoff had a ZND wave followed by a invariant rarefaction wave. The xRAGE simulations were carried out on uniform grids and adaptive mesh refinement (AMR) grids. Although AMR was recently implemented in FLAG and now fully functional for 2D simulations, it will not be evaluated with ZND tests at this time. Some work has been done previously for validating the reactive burn models in FLAG. For example, the validation studies of SURF with shock-to-detonation (SDT) tests, cylinder tests, and gap-stick tests. Further validation of the AWSD, WSD, and SURF models is described in for SDT, multi-shock, cylinder, and corner-turning tests. Recently, a large parameter study with approximately twenty SDT tests was performed to validate the AWSD, WSD, SURF, and SURFplus models while also investigating mesh resolution and artificial viscosity settings. To the best of our knowledge, the current work represents the first documented verification of these burn models in FLAG. The reader should note that many of the tables and figures in this report use units of cm/g/µs, which are the default units for FLAG. However, some lengths and velocities are expressed in µm and mm/µs, respectively, which are typical units for detonation analyses.
Verification Studies for the Noh Problem using Non-ideal Equations of State and Finite Strength Shocks
We present that the Noh verification test problem is extended beyond the commonly studied ideal gamma-law gas to more realistic equations of state (EOSs) including the stiff gas, the Noble-Abel gas, and the Carnahan-Starling EOS for hard-sphere fluids. Self-similarity methods are used to solve the Euler compressible flow equations, which in combination with the Rankine-Hugoniot jump conditions provide a tractable general solution. This solution can be applied to fluids with EOSs that meet criterion such as it being a convex function and having a corresponding bulk modulus. For the planar case the solution can be applied to shocks of arbitrary strength, but for cylindrical and spherical geometries it is required that the analysis be restricted to strong shocks. Finally, the exact solutions are used to perform a variety of quantitative code verification studies of the Los Alamos National Laboratory Lagrangian hydrocode FLAG.
Simulations of Sweeping Wave Propagation in a Boron Carbide Plate
In February 2020, experiments were conducted at Los Alamos National Laboratory measuring the propagation of a sweeping wave through a plate of boron carbide which was induced by detonating an adjacent charge of high explosive. Six such shots were red and in each case progress of the wave along the exposed surface of the plate was tracked using photon doppler velocimetry (PDV). In this report we discuss calculations performed using the Lagrangian hydrocode FLAG to model data taken from these experiments. We discuss the models chosen for the different experimental components, the choice of mesh (focusing on, both, two- and three-dimensional geometries), and compare the results from these calculations to experimentally-extracted PDV traces. Notably, we find that the PDV traces for this experiment are most faithfully reproduced using the full three-dimensional geometry, even when the mesh resolution for the three-dimensional calculations was significantly lower than the resolution for the corresponding two-dimensional calculations. We attribute this to the geometry of the experimental setup. Moreover, we find only negligible differences for the PDV traces obtained using the sesame table equation of state for boron carbide and the Gruneisen equation of state.
Constrained optimization framework for interface-aware sub-scale dynamics models for voids closure in Lagrangian hydrodynamics
In hydrocodes, voids are used to represent vacuum and model free boundaries between vacuum and real materials. We give a systematic description of a new treatment of void closure in the framework of the multimaterial arbitrary Lagrangian–Eulerian (ALE) methods. This includes a new formulation of the interface-aware sub-scale-dynamics (IA-SSD) closure model for multimaterial cells with voids, which is used in the Lagrangian stage of our indirect ALE scheme. The results of the comprehensive testing of the new model are presented for one- and two-dimensional multimaterial calculations in the presence of voids. Finally, we also present a sneak peek of a realistic shaped charge calculation in the presence of voids and solids.
Hydrodynamic modeling of laser interaction with micro-structured targets
A model is developed for numerical simulations of laser absorption in plasmas made of porous materials, with particular interest in low-density foams. Laser absorption is treated on two spatial scales simultaneously. At the microscale, the expansion of a thin solid pore wall is modeled in one dimension and the information obtained is used in the macroscale fluid simulations for the description of the plasma homogenization behind the ionization front. This two-scale laser absorption model is implemented in the arbitrary Lagrangian–Eulerian hydrocode PALE. In conclusion, the numerical simulations of laser penetration into low-density foams compare favorably with published experimental data.
Dependence of Dust Formation on the Supernova Explosion and nuDust
Dust is ubiquitous in the interstellar medium, serving as both a source of information and headaches to astronomers, depending on who you ask. The out-flows of core collapse supernovae (CCSNe) serve as a factory for dust nucleation and are one of a few known sources of dust in the universe. From observations of local CCSNe such as 1987A and Cassiopeia A, we know that dust is abundant in CCSN ejecta prior to interacting with the ISM. Furthermore, the explosion energy, explosive engine, metallicity, and progenitor mass of the CCSN will all impact the subsequent dust formation history and composition. Observations of the supernova ejecta probe the detailed composition of the ejecta which, in turn, can be used probe the properties of the progenitor star and the process of the explosion
Modeling the formation of Sedan Crater using the FLAG and HOSS codes
Numerical modeling of explosion crater formation requires accounting for complex physical processes. Numerical validation of explosion cratering is an important step in modeling and requires experimental data for comparison. Models using discrete elements and continuum models have both benefits and drawbacks to their approaches. In this work, we consider both an arbitrary Lagrangian–Eulerian (ALE) hydrocode and a finite discrete element method (FDEM) approach to modeling the formation of the Sedan crater, the largest human-made crater in the United States. The Sedan crater formed from an underground nuclear detonation in the Nevada desert as part of Project Plowshare. Our models show that the continuum approach of the hydrocode matched well compared to early test time prior to the mound rupture and subsequent fireball venting, when most of the alluvium exhibited fluid behavior. Our FDEM approach matched the final crater dimensions well, after material had settled back into the crater, when material strength and solid mechanics play key roles. Our work shows how leveraging the benefits of multiple numerical approaches can lead to better understanding of complex physical problems, especially problems with limited experimental data. By using a continuum approach to early-time hydrodynamics and an FDEM approach to later-time solid mechanics, we can better understand the different physical regimes of explosion crater formation.
Dust Formation and Growth in Supernovae Explosions
Dust is a multi-messenger probe able to explore the dynamics of the Supernova Engine. The yield and composition of grains formed in the supernova explosion are dependent on the initial explosion characteristics of the progenitor and on the explosion mechanism. Using dust as a prove, the dynamics of dust formation and growth is modeled in a diverse set of Core-Collapse Supernovae Explosions (CCSNe). The progenitor mass, explosion energy engine type, and composition are varied across 72 models. The explosion is evolved using a 1-D Lagrangian Hydro-dynamical code (hydrocodes) to roughly 3 years. A multigrain nucleation and dust growth model is used to post process the hydrocode results and model grain formation and growth. The results show an earlier onset of grain formation, a larger silicate grain abundance, and smaller grain sizes in high explosion energy models.
A High Resolution Simulation of a Single Shock-Accelerated Particle
We report particle drag models, which capture macroviscous and pressure effects, have been developed over the years for various flow regimes to enable cost effective simulations of particle-laden flows. The relatively recent derivation by Maxey and Riley has provided an exact equation of motion for spherical particles in a flow field based on the continuum assumption. Many models that have been simplified from these equations have provided reasonable approximations; however, the sensitivity of particle-laden flows to particle drag requires a very accurate model to simulate. To develop such a model, a two-dimensional axisymmetric Navier–Stokes direct numerical simulation of a single particle in a transient, shock-driven flow field was conducted using the hydrocode FLAG. FLAGs capability to run arbitrary Lagrangian-Eulerian hydrodynamics coupled with solid mechanic models makes it an ideal code to capture the physics of the flow field around and in the particle as it is shock-accelerated—a challenging regime to study. The goal of this work is twofold: to provide a validation for FLAGs Navier–Stokes and heat diffusion solutions and to provide a rationale for recent experimental particle drag measurements.
Hybrid Particle Method for Computational Shock Physics
A long-standing area of research for Eulerian shock wave physics codes has been the treatment of strength and damage for materials. Here we present a method that will aid in the analysis of strength and failure in shock physics applications where excessive diffusion of critical variables can occur and control the solution outcome. Eulerian methods excel for large deformation simulations in general but are inaccurate in capturing structural behavior. Lagrangian methods provide better structural response, but finite element meshes can become tangled. Therefore, a technique for merging Lagrangian and Eulerian treatments of material response, within a single numerical framework, was implemented in the Multiple Component computational shock physics hydrocode. The capability is a Lagrangian/Eulerian Particle Method (LEPM) that uses particles to interface a Lagrangian treatment of material strength with a more traditional Eulerian treatment of the Equation of State (EOS). Lagrangian numerical methods avoid the advection diffusion found in Eulerian methods, which typically strongly affects strength constitutive law internal variables, such as equivalent plastic strain, porosity and/or damage. The Lagrangian capability enhances existing capabilities and permits accurate predictions of high rate, large deformation and/or shock of mechanical structures.
A Numerical Simulation of a Single Shock-Accelerated Particle
Particle drag models, which capture macro viscous and pressure effects, have been developed over the years for various flow regimes to enable cost effective simulations of particle-laden flows. The relatively recent derivation by Maxey and Riley has provided an exact equation of motion for spherical particles in a flow field based on the continuum assumption. Many models that have been simplified from these equations have provided reasonable approximations; however, the sensitivity of particle-laden flows to particle drag requires a very accurate model to simulate. To develop such a model, a 2D axisymmetric Navier-Stokes direct numerical simulation of a single particle in a transient, shock-driven flow field was conducted in the hydrocode FLAG. FLAG’s capability to run arbitrary Lagrangian-Eulerian hydrodynamics coupled with solid mechanic models makes it an ideal code to capture the physics of the flow field around and in the particle as it is shock-accelerated – a challenging regime to study. The goal of this work is twofold: to provide a validation for FLAG’s Navier-Stokes and heat diffusion solutions, and to provide a rationale for recent experimental particle drag measurements.
Study of hypervelocity projectile impact on thick metal plates
Hypervelocity impacts generate extreme pressure and shock waves in impacted targets that undergo severe localized deformation within a few microseconds. These impact experiments pose unique challenges in terms of obtaining accurate measurements. Similarly, simulating these experiments is not straightforward. This paper proposed an approach to experimentally measure the velocity of the back surface of an A36 steel plate impacted by a projectile. All experiments used a combination of a two-stage light-gas gun and the photonic Doppler velocimetry (PDV) technique. The experimental data were used to benchmark and verify computational studies. Two different finite-element methods were used to simulate the experiments: Lagrangian-based smooth particle hydrodynamics (SPH) and Eulerian-based hydrocode. Both codes used the Johnson-Cook material model and the Mie-Grüneisen equation of state. Experiments and simulations were compared based on the physical damage area and the back surface velocity. Finally, the results of this study showed that the proposed simulation approaches could be used to reduce the need for expensive experiments.
Investigation of ALEGRA shock hydrocode algorithms using an exact free surface jet flow solution.
Computational testing of the arbitrary Lagrangian-Eulerian shock physics code, ALEGRA, is presented using an exact solution that is very similar to a shaped charge jet flow. The solution is a steady, isentropic, subsonic free surface flow with significant compression and release and is provided as a steady state initial condition. There should be no shocks and no entropy production throughout the problem. The purpose of this test problem is to present a detailed and challenging computation in order to provide evidence for algorithmic strengths and weaknesses in ALEGRA which should be examined further. The results of this work are intended to be used to guide future algorithmic improvements in the spirit of test-driven development processes.
Modeling Plastic Deformation of Steel Plates in Hypervelocity Impact Experiments
Hypervelocity impact experiments were done with a two-stage light gas gun to study the plastic deformation of metallic plates. Cylindrical Lexan projectiles were fired at A36 steel target plates with a velocity range of 4.5-6.0 km/s. Experiments were designed to produce a front side impact crater and a permanent bulging deformation on the back surface of the target while preventing complete perforation. Free surface velocities from the back surface of target plate were acquired using the newly developed Multiplexed Photonic Doppler Velocimetry (MPDV) system. Two different computational techniques were developed to simulate this type of experiment: Lagrangian-based smooth particle hydrodynamics (SPH) in LS-DYNA and the Eulerian-based hydrocode CTH. Parameters for material models including equation of state, compressive strength, and spall model were selected to obtain highest fidelity numerical results to compare with experiment.
Design of a Three-Layer Impactor for Material Strength Measurements at Multi-Megabar Pressures
Off-Hugoniot loading methods for dynamic compression have been a topic of interest for many years as a means of accessing high pressures without melting a material. Simulations and an initial test experiment of a three-layer gas-gun impactor suitable for use in measuring dynamic material strength at multi-megabar pressures are described. As shown through ARES hydrocode simulations, an impactor consisting of a low-, medium-, and high-impedance material, such as TPX, Al, and Ta or Pt, can produce a quasi-isentropic loading path up to 4.6 Mbar pressure with a low homologous temperature (T/T melt = 0.1–0.25). These impactors can also be tailored to create a pressure drive suitable for a Lagrangian sound speed experiment. Simulated in-situ velocities were analyzed to determine the change in calculated strength due to non-uniformity in the impactor, which provides a measure of error sensitivity. An initial test of a three-layer projectile onto a flat target at 4.4 km/s impact velocity is reported. Finally, while the impactor incurred some delamination during firing, the measured sample/window interface velocity generally agrees with the simulated peak velocity and subsequent release, indicating the feasibility of this approach for measuring material strength.