Admissible shock waves and shock-induced phase transitions in a van der Waals fluid

Abstract

A complete classification of shock waves in a van der Waals fluid is undertaken. This is in order to gain a theoretical understanding of those shock-related phenomena as observed in real fluids which cannot be accounted for by the ideal gas model. These relate to admissibility of rarefaction shock waves, shock-splitting phenomena, and shock-induced phase transitions. The crucial role played by the nature of the gaseous state before the shock (the unperturbed state), and how it affects the features of the shock wave are elucidated. A full description is given of the characteristics of shock waves propagating in a van der Waals fluid. The strength of these shock waves may range from weak to strong. The study is carried out by means of the theory of hyperbolic systems supported by numerical calculations.

Shock Wave Formation in the Collapse of a Vapor Nanobubble

“…with δ =R/c v ,R the gas constant, c v the constant volume specific heat, a and b the van der Waals coefficients, with K a suitable constant [23]. The evolution is governed by the conservation equations for mass …”

“…Away from the bubble, the shock propagates in the still liquid that, after the expansion wave, relaxed back to p ∞ , θ ∞ = θ e . The shock speed w is determined by the state ahead of the shock (p ∞ , ρ ∞ , u ∞ = 0) and by an additional parameter, the density ρ b behind the shock, say, see [28] and [23] for details concerning a van der Waals fluid. The small compressibility of the liquid…”

“…with δ =R/c v ,R the gas constant, c v the constant volume specific heat, a and b the van der Waals coefficients, with K a suitable constant [23]. The evolution is governed by the conservation equations for mass ∂ t ρ + ∇ · (ρu) = 0, momentum ∂ t (ρu) + ∇ · (ρu ⊗ u) = ∇ · τ , and total energy, ∂ t E + ∇ · (uE) = ∇ · [τ · u − λρ∇ · u∇ρ + k∇θ], where k is the thermal conductivity.…”

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

“…(3.45); it corresponds to the limiting case of c V = ∞. Because we treat all the metastable states between the binodal and the spinodal on equal basis with the absolutely stable ones, we are interested in a broader region of negative non-linearity that would lie above the spinodal curve -in contrast to the one above the binodal analyzed by previous authors [17,18,19]. The boundary Γ = 0 of the NNL region in GWEOS is obtained by setting the numerator in Eq.…”

Growth and Decay Behaviour of a Sawtooth Profile in Non-Ideal Gas

“…Recently [11] have studied evolutionary behaviour of acceleration waves in a perfectly conducting inviscid radiating gas permeated by a transverse magnetic field. Zhao et al [15], has shown that the shock waves in a van der Waal's fluid exhibit a richer behaviour than that predicted by the ideal gas model, characterizing compressive shocks, rarefaction shocks, and shock splitting phenomena together with their admissibility; the physical meaning of van der Waals gas and its influence on wave motion may be seen in the papers [17][18][19]. Ambika et al [20] have used the theory of progressive waves and some related procedures to study the attenuation and geometrical spreading of waves of finite and moderately small amplitudes influenced by the effects of non-linear convection in a non-ideal gas.…”