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

Abstract

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.

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

“…is the amplitude of the first dip in the u f s (t) profile. However, contrary to what might be expected, formula (17) never becomes asymptotically accurate even in the limit of an infinitely weak load because of the pb-shock attenuation: below we show its error to be 40% for the considered case of symmetric plate collision. The situation becomes even worse when the acoustic formulae 12,35 εsp,ac = ∆u f s 2c 0 (t pb − t 2 )…”

“…by fluid inertia and pressure gradients), the phase flip must occur at a constant ρ = v −1 whenever ε is finite. The only possibility where it could be accompanied by a density jump, would be inside a rarefaction shock 17 , which can be excluded in the context of spallation because relaxation of tension means growth of pressure. In addition, energy conservation requires the local value of the specific internal energy e to be preserved as well, which implies that the phase flip is always accompanied by a jump-like increase in pressure, temperature, and entropy.…”

“…Similar to the acoustic formula (17), our PA estimate of the spall strength is based on the measured free-surface velocity pullback ∆u f s . We begin by arguing that the outer boundary msp of the spall zone, represented by the pb-shock starting point M sp in Fig.…”

“…propagates without attenuation down to the free surface, where the well-known 43 ( § 11, Ch. XI) velocity doubling rule ∆u f s = −2u ′ sp applies; then (17) follows directly from Eq. ( 30) in the limit of b|ū ′ | ≪ 1.…”

“…A much simpler and computationally inexpensive alternative is to simply adopt the fully equilibrium (EQ) equation of state (EOS), obtained by applying Maxwell's rule to the primitive EOS of the van-der-Waals (vdW) type 9,[14][15][16] . However, because the EQ EOS allows no negative pressures, it cannot describe tensile states, pullback shocks, and only approximately reproduces mass distribution in the regions of spallation and cavitation 17 .…”