We report progress on a task to model transformers in ALEGRA using the “Transient Magnetics” option. We specifically evaluate limits of the approach resolving individual coil wires. There are practical limits to the number of turns in a coil that can be numerically modeled, but calculated inductance can be scaled to the correct number of turns in a simple way. Our testing essentially confirmed this “turns scaling” hypothesis. We developed a conceptual transformer design, representative of practical designs of interest, and that focused our analysis. That design includes three coils wrapped around a rectangular ferromagnetic core. The secondary and tertiary coils have multiple layers. The tertiary has three layers of 13 turns each; the secondary has five layers of 44 turns; the primary has one layer of 20 turns. We validated the turns scaling of inductance for simple (one-layer) coils in air (no core) by comparison to available independent calculations for simple rectangular coils. These comparisons quantified the errors versus reduced number of turns modeled. For more than 3 turns, the errors are <5%. The magnetic field solver failed to converge (within 5000 iterations) for >10 turns. Including the core introduced some complications. It was necessary to capture the core surfaces in thin grid sheaths to minimize errors in computed magnetic energy. We do not yet have quantitative benchmarks with which to compare, but calculated results are qualitatively reasonable.
In this work we evaluated the effects that equations of state and strength models have on SCJ development using the Sandia National Laboratories multiphysics shock code, ALEGRA. Results were quantified using a Lagrangian tracer particle following liner collapse, passing through the compression zone, and flowing into the jet tip. We found consistent results among several EOS: 3320, 3331, and 3337. The 3325 EOS generated a measurable low density and hollow region near the jet tip which appears to be reflected in a lower internal energy of the jet. At this time, we cannot tell, experimentally, if such a hollow region exists. The 3337 EOS is recent, well documented [6], and produces results similar to 3320 [3]. The various strength models produced more noticeable differences. In terms of internal energy and temperature, SGL had the largest values followed by PTW, ZA, and finally JC and MTS, which were quite similar to each other. We looked at melt conditions in the SGL and JC models using the 3337 EOS. The SGL model reported a liquid region along the jet axis all the way to the tip-seemingly consistent with experiment-while the JC model does not indicate any phase transition. None of the other yield models indicated melt along the jet axis. For all EOS and strength models, we found similar results for the velocity history of the jet tip as measured against experiment using photon Dopper velocimetry.
A preliminary finite-element model has been developed using the ALEGRA-FE code for explosive- driven depoling of a PZT 95/5 ferroelectric generator. The ferroelectric material is characterized using hysteresis-loop and hydrostatic depoling tests. These characteristics are incorporated into ALEGRA-FE simulations that model the explosive drive mechanism and shock environment in the material leading to depoling, as well as the ferroelectric response and the behavior of a coupled circuit. The ferroelectric-to-antiferroelectric phase transition is captured, producing an output voltage pulse that matches experimental data to within 10% in rise time, and to within about 15% for the final voltage. Both experimental and modeled pulse magnitudes are less than the theoretical maximum output of the material. Observations from materials characterization suggest that unmodeled effects such as trapped charge in the stored FEG material may have influenced the experimentally observed output. ACKNOWLEDGEMENTS The authors are thankful to Mr. Peter Bartkowski and Mr. Paul Berning at ARL for initiating this work and providing critical insight along the way. Also, we thank Dr. Thomas Hughes and Dr. James Carleton at Sandia for important technical discussions and guidance. Finally, we wish to thank Tom Chavez at Sandia, who was heavily involved in conducting the laboratory materials characterization.
Use of insensitive high explosives (IHEs) has significantly improved ammunition safety because of their remarkable insensitivity to violent cook-off, shock and impact. Triamino-trinitrobenzene (TATB) is the IHE used in many modern munitions. Previously, lightning simulations in different test configurations have shown that the required detonation threshold for standard density TATB at ambient and elevated temperatures (250 C) has a sufficient margin over the shock caused by an arc from the most severe lightning. In this paper, the Braginskii model with Lee-More channel conductivity prescription is used to demonstrate how electrical arcs from lightning could cause detonation in TATB. The steep rise and slow decay in typical lightning pulse are used in demonstrating that the shock pressure from an electrical arc, after reaching the peak, falls off faster than the inverse of the arc radius. For detonation to occur, two necessary detonation conditions must be met: the Pop-Plot criterion and minimum spot size requirement. The relevant Pop-Plot for TATB at 250 C was converted into an empirical detonation criterion, which is applicable to explosives subject to shocks of variable pressure. The arc cross-section was required to meet the minimum detonation spot size reported in the literature. One caveat is that when the shock pressure exceeds the detonation pressure the Pop-Plot may not be applicable, and the minimum spot size requirement may be smaller.
This report introduces the concepts of Bayesian model selection, which provides a systematic means of calibrating and selecting an optimal model to represent a phenomenon. This has many potential applications, including for comparing constitutive models. The ideas described herein are applied to a model selection problem between different yield models for hardened steel under extreme loading conditions.
A closed-form solution is described here for the equilibrium configurations of the magnetic field in a simple heterogeneous domain. This problem and its solution are used for rigorous assessment of the accuracy of the ALEGRA code in the quasistatic limit. By the equilibrium configuration we understand the static condition, or the stationary states without macroscopic current. The analysis includes quite a general class of 2D solutions for which a linear isotropic metallic matrix is placed inside a stationary magnetic field approaching a constant value ° at infinity. The process of evolution of the magnetic fields inside and outside the inclusion and the parameters for which the quasi-static approach provides for self-consistent results is also explored. It is demonstrated that under spatial mesh refinement, ALEGRA converges to the analytic solution for the interior of the inclusion at the expected rate, for both body-fitted and regular rectangular meshes.
The growth of a cylindrical s park discharge channel in water and Lexan is studied using a series of one - dimensional simulations with the finite - element radiation - magnetohydrodynamics code ALEGRA. Computed solutions are analyzed in order to characterize the rate of growth and dynamics of the spark c hannels during the rising - current phase of the drive pulse. The current ramp rate is varied between 0.2 and 3.0 kA/ns, and values of the mechanical coupling coefficient K p are extracted for each case. The simulations predict spark channel expansion veloc ities primarily in the range of 2000 to 3500 m/s, channel pressures primarily in the range 10 - 40 GPa, and K p values primarily between 1.1 and 1.4. When Lexan is preheated, slightly larger expansion velocities and smaller K p values are predicted , but the o verall behavior is unchanged.
2016 IEEE/ACES International Conference on Wireless Information Technology, ICWITS 2016 and System and Applied Computational Electromagnetics, ACES 2016 - Proceedings
We explore how reliable the ALEGRA MHD code is in its static limit. Also, we explore (in the quasi-static approximation) the process of evolution of the magnetic fields inside and outside an inclusion and the parameters for which the quasi-static approach provides for self-consistent results.
We present a verification and validation analysis of a coordinate-transformation-based numerical solution method for the two-dimensional axisymmetric magnetic diffusion equation, implemented in the finite-element simulation code ALEGRA. The transformation, suggested by Melissen and Simkin, yields an equation set perfectly suited for linear finite elements and for problems with large jumps in material conductivity near the axis. The verification analysis examines transient magnetic diffusion in a rod or wire in a very low conductivity background by first deriving an approximate analytic solution using perturbation theory. This approach for generating a reference solution is shown to be not fully satisfactory. A specialized approach for manufacturing an exact solution is then used to demonstrate second-order convergence under spatial refinement and tem- poral refinement. For this new implementation, a significant improvement relative to previously available formulations is observed. Benefits in accuracy for computed current density and Joule heating are also demonstrated. The validation analysis examines the circuit-driven explosion of a copper wire using resistive magnetohydrodynamics modeling, in comparison to experimental tests. The new implementation matches the accuracy of the existing formulation, with both formulations capturing the experimental burst time and action to within approximately 2%.
Weak scaling studies were performed for the explicit solid dynamics component of the ALEGRA code on two Cray supercomputer platforms during the period 2012-2015, involving a production-oriented hypervelocity impact problem. Results from these studies are presented, with analysis of the performance, scaling, and throughput of the code on these machines. The analysis demonstrates logarithmic scaling of the average CPU time per cycle up to core counts on the order of 10,000. At higher core counts, variable performance is observed, with significant upward excursions in compute time from the logarithmic trend. However, for core counts less than 10,000, the results show a 3 × improvement in simulation throughput, and a 2 × improvement in logarithmic scaling. This improvement is linked to improved memory performance on the Cray platforms, and to significant improvements made over this period to the data layout used by ALEGRA.
The finite-element shock hydrodynamics code ALEGRA has recently been upgraded to include an X-FEM implementation in 2D for simulating impact, sliding, and release between materials in the Eulerian frame. For validation testing purposes, the problem of long-rod penetration in semi-infinite targets is considered in this report, at velocities of 500 to 3000 m/s. We describe testing simulations done using ALEGRA with and without the X-FEM capability, in order to verify its adequacy by showing X-FEM recovers the good results found with the standard ALEGRA formulation. The X-FEM results for depth of penetration differ from previously measured experimental data by less than 2%, and from the standard formulation results by less than 1%. They converge monotonically under mesh refinement at first order. Sensitivities to domain size and rear boundary condition are investigated and shown to be small. Aside from some simulation stability issues, X-FEM is found to produce good results for this classical impact and penetration problem.