Rarefaction waves in van der Waals fluids with an arbitrary number of degrees of freedom

Abstract

The isentropic expansion of an instantaneously and homogeneously heated foil is calculated using a 1D fluid model. The initial temperature and density are assumed to be in the vicinity of the critical temperature and solid density, respectively. The fluid is assumed to satisfy the van der Waals equation of state with an arbitrary number of degrees of freedom. Self-similar Riemann solutions are found. With a larger number of degrees of freedom f, depending on the initial dimensionless entropy s[over ̃]_{0}, a richer family of foil expansion behaviors have been found. We calculate the domain in parameter space where these behaviors occur. In total, eight types of rarefaction waves are found and described.

Characterization of rarefaction waves in van der Waals fluids

“…The fluid is modeled by the VDW EOS with three degrees of freedom [25], in contrast to the arbitrary number of degrees of freedom in Ref. [16], meaning that only the rarefaction waves of case 3 and 6 of Ref. [16] out of the eight possible cases will be encountered:…”

“…[16], meaning that only the rarefaction waves of case 3 and 6 of Ref. [16] out of the eight possible cases will be encountered:…”

“…In Ref. [16], such plateaus of constant density (and pressure, temperature, energy density, velocity) during the phase transition from a single-phase to the twophase regime are found in van der Waals (VDW) fluids with an arbitrary number of degrees of freedom. In the present paper, we extend the semi-analytical formalism of Ref.…”

“…In the present paper, we extend the semi-analytical formalism of Ref. [16] for the specific case of a VDW equation of state (EOS) with three degrees of freedom supplemented with the Maxwell construction: we use Riemann's solution [17,18] in 1D to describe the dynamics of the heated target, modeled by a semi-infinite slab of material that initially extends from z = −∞ to z = 0. This effectively restricts the scope of this paper to the early stage of the foil expansion before the rarefaction waves from both sides of a given thin foil meet, coined as the simple wave regime in Ref.…”

“…the structure and properties of molecular liquids, liquid metals and crystals, their freezing and melting, and their critical behaviors [20]. With three degrees of freedom, the VDW EOS also corresponds to a monatomic gas at low density and does not yield rarefaction shockwaves [16,18,[21][22][23]. Nevertheless, the quantitative application of the VDW EOS must be checked and several directly measurable quantities can help us confirm, improve or reject the VDW model.…”