1. Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA Slide 1 Ejecta source and transport modeling in the FLAG hydrocode Jimmy Fung Alan K. Harrison, Shirish Chitanvis, Jeremy Margulies Los Alamos National Laboratory Acknowledgments: William T. Buttler and Russell T. Olson International Conference on Numerical Methods For Multi-Material Fluid Flows Arcachon FR 5-9 September 2011 LA-UR 11-04992

2. Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA Slide 2 Outline of this talk Motivation: Ejecta and modeling ejecta experiments. The FLAG hydrocode Features General hydro step Ejecta modeling in FLAG A PIC-like formulation Source modeling Transport modeling Modeling the experiment General simulation parameters for hydrodynamics and ejecta Results

3. Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA Motivation: Ejecta and modeling ejecta experiments Extreme shock loading may cause damage and failure at material free surfaces, producing particulate fragmentation known as ejecta. Theories, experiments, and modeling involve a wide range of solid and fluid mechanics at relevant spatial and temporal scales. Slide 3 Surface finish Buttler, Olson, Zellner: 2007+

4. Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA The FLAG hydrocode is well suited to model the experiment. Slide 4  Compressibility  Strength, damage, failure  High strain rates  Impact/contact  Mixtures Bement / Kenamond

5. Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA The FLAG hydro scheme follows from finite volume formulation of compatible hydrodynamics on a staggered grid Slide 5 Velocities live on nodes Pressure, material “states” live in zones Momentum, energy equations are solved in a predictor-corrector step Hydrodynamics: Discrete hydrodynamics: mesh cell dual mesh cell momentum energy Burton, Caramana, Shashkov…

6. Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA An MP-PIC formulation is used to model ejecta in FLAG. (Super) particles represent packets of multiple physical particles. Tracking individual physical particles is expensive, so allowing computational particles to represent “many” reduces cost. The tradeoff is the statistical resolution. While FLAG hydro advances the continuum equations of motion, a distinct solver is implemented to advance particle equations of motion. Positions and velocities in space and time Positions relative to the hydrodynamics mesh Particle-fluid coupling involves Averaging particle quantities over zones Interpolating continuum information from mesh zones and points to particles How is the formulation integrated with FLAG hydro? 1.Predictor step for continuum momentum and energy 2.Corrector step for momentum 3.Ejecta tracking and transport 4.Ejecta sourcing 5.Corrector step for energy Slide 6 Andrews, M.J. and O'Rourke, P.J. : MP-PIC

7. Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA Ejecta source modeling involves heuristics for triggering generation and statistical sampling for particle initialization. Ejecta particle generation is dependent on material properties (melt, damage) as well as kinematic quantities (free surface acceleration) and statistical distributions Triggering can be always-on or dependent on the shock loading profile Power-law and exponential distributions are included for sampling particle mass and velocity Slide 7

8. Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA Ejecta transport includes particle kinematics and drag effects. Slide 8 particle fluid velocity Particle positions are updated explicitly Particle velocities are updated using a predictor-corrector method Drag is a Reynolds-number based formulation (assuming spherical particles) using end-of-time-step fluid velocities Deceleration/acceleration and entrainment phenomena are captured with this formulation time

9. Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA FLAG particle transport in quiescent fluid matches well with analytical solution. Slide 9 L. D. Cloutman time (  sec) velocity (cm/  sec) position (cm) Re > 1000 Re ≤ 1000

10. Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA With constant accelerating fluid, particle drag can model deceleration and reacceleration. Slide 10 time (  sec) velocity (cm/  sec) position (cm)

11. Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA “Sloshing”: phase-locking is a phenomenon that is similar to entrainment. Slide 11 time (  sec) velocity (cm/  sec) position (cm)

12. Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA The general setup for the experiment applies slidelines, Lagrange and ALE over a dendritic mesh. Slide 12 air plastic HE Al Sn ALE on in HE/plastic/air Lagrange in Sn, Al dendritic mesh slideline air Al Sn HE

13. Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA FLAG captures the general hydrodynamics of the Al-Sn experiment. Slide 13 0 microseconds2 microseconds6 microseconds air plastic HE Al Sn detonation wave ejecta shocks

14. Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA How do we do? Shock breakout pressure and velocity match the experiment. Experimental data are being used to calibrate the FLAG simulation. Slide 14 velocity (cm/  sec) experiment measures 0.22 cm/  sec acceleration/10 (cm/  sec 2 ) tin free surface time (microsecond)

15. Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA Experimental data are being used to calibrate the FLAG ejecta model. Parameters used in the ejecta model Acceleration threshold: 0.7 cm/  sec Mean particle mass: 2.73e-09 g Average relative particle velocity: 0.0175 cm/  sec Each computational particle represents 100 physical particles How do we do? With particles recorded within the coverage area of a hypothetical piezo pin probe, the calculation produces an areal mass of 26.0 mg/cm 2, similar to the experimental value of 24.6 mg/cm 2. Slide 15 3.5 microseconds5 microseconds

16. Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA

17. Ejecta movie Slide 17

18. Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA Concluding remarks This work continues an effort to develop an MP-PIC particle package in FLAG to facilitate ejecta modeling Current work is focused on source and transport models Calculations match well against analytic solutions for drag in quiescent flow Demonstrations with fluid acceleration show deceleration / reacceleration stages as well as dependencies on particle size Preliminary testing and calibration efforts using actual experimental data is encouraging FLAG produces shock-breakout pressures and velocities as well as ejecta areal masses that are similar to experiment Future work should include ongoing development of source and transport models, time step algorithms and controllers, breakup and collision models as well as additional calibration Slide 18

19. Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA Questions? References A.K. Harrison and J. Fung, “Ejecta in the FLAG Hydrocode”, presented at Numerical Methods for Multi-Material Fluids and Structures, Pavia (2009). E.J. Caramana, D.E. Burton, M.J. Shashkov, P.P. Whalen, “The construction of compatible hydrodynamics algorithms utilizing conservation of total energy”, J. Comp. Phys. 142, 521 (1998). Andrews, M.J. and O'Rourke, P.J. (1996). The Multiphase Particle-in-Cell (MP-PIC) Method for Dense Particle Flows. International Journal of Multiphase Flow, 22(2):379–402. L. D. Cloutman, “Analytical solutions for the trajectories and thermal histories of unforced particulates”, Am. J. Phys 56:7, 1998. Zellner et al, “Effects of shock-breakout pressure on ejection of micron-scale material from shocked tin surfaces”, J. Appl. Phys. 102, 013522 (2007). Slide 19