Abstract
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.
Highlights
The prominent role played by phase transitions in various natural and technological processes is well documented in the scientific literature
The formulation is presented in a fairly general setting that is independent of any particular material, 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
II, which enables the integration of solidification kinetics via homogeneous nucleation with phasebehavior computations, all in the context of continuum-scale hydrodynamic simulations oriented toward high-pressure applications
Summary
Scitation.org/journal/adv design and analysis of dynamic-compression (e.g., shock-loading) experiments. Fluid–solid transitions are a more natural starting point than solid–solid transitions because a proper treatment of the latter requires a consideration of complex dislocation-related phenomena that are absent in the former We have applied this combination of CNT-based models and hydrodynamic simulations to provide an a posteriori analysis of the solidification kinetics observed in dynamic-compression experiments on water and gallium. The description above illustrates the close coupling between the solidification kinetics and the phasebehavior computations: within a zone at a particular instance in time, the phase-behavior computations apply the EOS to determine P and T for a given set of V, E, and Φ; these P and T are used by the kinetic models to calculate the phase fractions Φ at the time step; in addition, the governing hydrodynamic equations in the form of mass, energy, and momentum balances are solved to find V and E at the time step.
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