Generalized van der Waals equation of state for in-line use in hydrodynamic codes

Basko, M. M.

doi:10.20948/prepr-2018-112-e

Cited by 3 publications

(4 citation statements)

References 15 publications

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“…All the numerical results in this paper are obtained with a generalized version of the van der Waals equation of state (GWEOS), where the power exponent n in the attractive term is treated as a free parameter [10][11][12] . This variant of a two-phase EOS preserves the convenient property of the original van der Waals EOS that it can be cast in the universal reduced form, where the dimensionless quantities ρ, θ and p are, respectively, the density, temperature and pressure normalized by their values ρ cr , T cr and P cr at the critical point; the latter can be considered as three independent free parameters of GWEOS taken, for example, from experiment.…”

Section: Liquid-gas Phase Diagram For the Generalized Van Der Waamentioning

confidence: 99%

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Centered rarefaction wave with a liquid-gas phase transition in the approximation of “phase-flip” hydrodynamics

Basko

2018

Physics of Fluids

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It is proposed to evaluate the effects of thermodynamic metastability on fluid dynamics by comparing two different ideal-hydrodynamics solutions -one obtained with the fully equilibrium equation of state using the Maxwell construction, and the other in what we call the phase-flip approximation. The latter is based on the assumption of instantaneous decay of metastable states upon reaching the spinodal. The proposed method is applied to the classical problem of the centered rarefaction wave by expansion into vacuum, for which exact analytical solutions exist in both approximations. It is shown that the rapid decay of metastable states leads to the formation of a rarefaction shock in the expanding flow. Implications for the laser-heating experiments are discussed.

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Section: Liquid-gas Phase Diagram For the Generalized Van Der Waamentioning

confidence: 99%

“…The full set of formulae for calculating the EQ GWEOS is given in Ref. 12. Note that one always has v bi,l (p) < v sp,l (p) and v bi,g (p) > v sp,g (p).…”

Section: Liquid-gas Phase Diagram For the Generalized Van Der Waamentioning

confidence: 99%

Centered rarefaction wave with a liquid-gas phase transition in the approximation of “phase-flip” hydrodynamics

Basko

2018

Physics of Fluids

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“…The employed two-phase EOS Conceptually, the thermodynamics of a liquid-gas phase transition is adequately represented by the classical van der Waals EOS. In this work we make use of one of the simplest generalizations of this EOS (termed GWEOS) [23][24][25] in the form…”

Section: The Phase-flip Model Of Spall Fracture In Liquidsmentioning

confidence: 99%

“…The dimensional quantities P cr , V cr , T cr make up additional three free parameters of GWEOS; for more details see Ref. 25. The main motivation for using GWEOS in this work is its mathematical simplicity, which allows the in-line use of its both the metastable (MS) and the equilibrium (EQ) branches in hydrodynamic codes with the rounding-error accuracy -thus excluding numerical errors due to imperfect EOS.…”

Section: The Phase-flip Model Of Spall Fracture In Liquidsmentioning

confidence: 99%

On the theory and numerical modeling of spall fracture in pure liquids

Basko

2021

Preprint

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A novel phase-flip model is proposed for thermodynamically consistent and computationally efficient description of spallation and cavitation in pure liquids within the framework of ideal hydrodynamics. Aiming at ultra-fast dynamic loads, the spall failure of a liquid under tension is approximated as an instantaneous decomposition of metastable states upon reaching the spinodal stability limit of an appropriate two-phase liquid-gas equation of state. The spall energy dissipation occurs as entropy jumps in two types of discontinuous solutions, namely, in hypersonic spall fronts and in pull-back compression shocks. Practical application of the proposed model is illustrated with numerical simulations and a detailed analysis of a particular problem of symmetric plate impact. The numerical results are found to be in good agreement with the previously published molecular-dynamics simulations. Also, new approximate nonlinear formulae are derived for evaluation of the strain rate, fractured mass, and spall strength in terms of the observed variation of the free-surface velocity. The new formula for the spall strength clarifies complex interplay of the three first-order nonlinear correction terms and establishes a universal value of the correction factor for attenuation of the spall pulse, which in the limit of weak initial loads is independent of the equation of state.

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]Numerical method for simulating rarefaction shocks in the approximation of phase-flip hydrodynamics

Basko

2021

Appl. Math. Mech.-Engl. Ed.

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Generalized van der Waals equation of state for in-line use in hydrodynamic codes

Cited by 3 publications

References 15 publications

Centered rarefaction wave with a liquid-gas phase transition in the approximation of “phase-flip” hydrodynamics

Centered rarefaction wave with a liquid-gas phase transition in the approximation of “phase-flip” hydrodynamics

On the theory and numerical modeling of spall fracture in pure liquids

]Numerical method for simulating rarefaction shocks in the approximation of phase-flip hydrodynamics

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