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Title: Coupling solidification kinetics with phase-behavior computations in hydrodynamic simulations of high-pressure, dynamic-compression processes

Journal Article · · AIP Advances
DOI: https://doi.org/10.1063/5.0032973 · OSTI ID:1735803

In this study, we report a numerical scheme to integrate models for the kinetics of solidification processes together with phase-behavior computations in the context of continuum-scale hydrodynamic simulations. The objective of the phase-behavior computations is to determine the pressure and temperature, given the following three sets of inputs: (1) an appropriate equation of state to describe our system, (2) the phase fraction(s) produced by the kinetic models, (3) and the volume and internal energy obtained by solving the conservation equations that govern the hydrodynamic behavior. The kinetics are assumed to be governed by the Kolmogorov–Johnson–Mehl–Avrami equation, and the nucleation and growth rates that enter into that equation are functions of the pressure and temperature produced by the phase-behavior computations. Our formulation allows for the fluid and solid phases to be at different temperatures (thermal nonequilibrium) and pressures (arising from surface-tension-induced Laplace contributions). The formulation is presented in a fairly general setting that is independent of any particular material, although we demonstrate it in some examples related to high-energy-density science applications where materials are rapidly compressed to pressures exceeding several gigapascals in less than a microsecond. We conclude with a critical evaluation of our approach and provide suggestions for future work to improve the predictive capabilities and generality of the models.

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC52-07NA27344; NA0003960
OSTI ID:
1735803
Alternate ID(s):
OSTI ID: 1731020
Report Number(s):
LLNL-JRNL--806659; 1012046
Journal Information:
AIP Advances, Journal Name: AIP Advances Journal Issue: 12 Vol. 10; ISSN 2158-3226
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English

References (37)

Extended and accurate determination of the melting curves of argon, helium, ice ( H 2 O ) , and hydrogen ( H 2 ) journal March 2000
Nanosecond freezing of water under multiple shock wave compression: Continuum modeling and wave profile measurements journal August 2005
Local-Basis-Function Equation of State for Ice VII–X to 450 GPa at 300 K journal January 2020
A metastable limit for compressed liquid water journal March 2007
Drive-pressure optimization in ramp-wave compression experiments through differential evolution journal November 2020
Enthalpy diffusion in multicomponent flows journal May 2009
Onset of convection with fluid compressibility and interface movement journal September 2013
Material dynamics under extreme conditions of pressure and strain rate journal April 2006
A constitutive model for metals applicable at high‐strain rate journal March 1980
Solution of the non-steady state problem in nucleation kinetics journal March 1969
Strength of lithium fluoride under shockless compression to 114 GPa journal November 2009
Holistic Approach for Studying Planetary Hydrospheres: Gibbs Representation of Ices Thermodynamics, Elasticity, and the Water Phase Diagram to 2,300 MPa journal January 2020
Modern Crystallography III book January 1984
The thermodynamics of a liquid-solid interface at extreme conditions: A model close-packed system up to 100 GPa journal September 2018
Rapid freezing of water under dynamic compression journal May 2018
Numerical modeling of solid-cluster evolution applied to the nanosecond solidification of water near the metastable limit journal October 2019
Melting and refreezing of zirconium observed using ultrafast x-ray diffraction journal February 2020
Nanosecond Freezing of Water at High Pressures: Nucleation and Growth near the Metastability Limit journal October 2018
Phase Diagrams of H 2 O and D 2 O at High Pressures journal June 1968
A new equation of state for aluminum journal January 1986
A Gallium Multiphase Equation of State
  • Crockett, Scott D.; Greeff, Carl W.; Elert, Mark
  • SHOCK COMPRESSION OF CONDENSED MATTER 2009: Proceedings of the American Physical Society Topical Group on Shock Compression of Condensed Matter, AIP Conference Proceedings https://doi.org/10.1063/1.3295016
conference January 2009
High pressure-temperature Raman measurements of H[sub 2]O melting to 22 GPa and 900 K journal January 2004
Dissipative structures, dynamics and entropy journal January 1975
Kinetics of Phase Change. I General Theory journal December 1939
Temperature dependence of the crystal–melt interfacial energy of metals journal May 2012
Thermodynamics of flat thin liquid films journal August 2015
Observations on the nucleation of ice VII in compressed water
  • Stafford, Samuel J. P.; Chapman, David J.; Bland, Simon N.
  • SHOCK COMPRESSION OF CONDENSED MATTER - 2015: Proceedings of the Conference of the American Physical Society Topical Group on Shock Compression of Condensed Matter, AIP Conference Proceedings https://doi.org/10.1063/1.4971716
conference January 2017
Free energy models for ice VII and liquid water derived from pressure, entropy, and heat capacity relations journal August 2017
ALE3D: An Arbitrary Lagrangian-Eulerian Multi-Physics Code report May 2017
Modeling of Nucleation Processes book December 2009
Nanosecond freezing of water under multiple shock wave compression: Optical transmission and imaging measurements journal November 2004
The Effect of Droplet Size on Surface Tension journal March 1949
High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics journal January 2012
Artificial fluid properties for large-eddy simulation of compressible turbulent mixing journal May 2007
A study of ALE simulations of Rayleigh–Taylor instability journal March 2001
Kinetics of Phase Change. II Transformation‐Time Relations for Random Distribution of Nuclei journal February 1940
Formation of Crystal Nuclei in Liquid Metals journal October 1950