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Steady one-dimensional nozzle flow solutions of liquid–gas mixtures

Published online by Cambridge University Press:  20 November 2013

S. LeMartelot ,
R. Saurel  and
O. Le Métayer
S. LeMartelot*
Affiliation:
Aix-Marseille Université, CNRS, IUSTI UMR 7343, 13013 Marseille, France
R. Saurel
Affiliation:
Aix-Marseille Université, CNRS, IUSTI UMR 7343, 13013 Marseille, France RS2N, Bastidon de la Caou, 13360 Roquevaire, France
O. Le Métayer
Affiliation:
Aix-Marseille Université, CNRS, IUSTI UMR 7343, 13013 Marseille, France
*
†Email address for correspondence: [email protected]
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Abstract

Exact compressible one-dimensional nozzle flow solutions at steady state are determined in various limit situations of two-phase liquid–gas mixtures. First, the exact solution for a pure liquid nozzle flow is determined in the context of fluids governed by the compressible Euler equations and the ‘stiffened gas’ equation of state. It is an extension of the well-known ideal-gas steady nozzle flow solution. Various two-phase flow models are then addressed, all corresponding to limit situations of partial equilibrium among the phases. The first limit situation corresponds to the two-phase flow model of Kapila et al. (Phys. Fluids, vol. 13, 2001, pp. 3002–3024), where both phases evolve in mechanical equilibrium only. This model contains two entropies, two temperatures and non-conventional shock relations. The second one corresponds to a two-phase model where the phases evolve in both mechanical and thermal equilibrium. The last one corresponds to a model describing a liquid–vapour mixture in thermodynamic equilibrium. They all correspond to two-phase mixtures where the various relaxation effects are either stiff or absent. In all instances, the various flow regimes (subsonic, subsonic–supersonic, and supersonic with shock) are unambiguously determined, as well as various nozzle solution profiles.

JFM classification

Compressible Flows: Compressible Flows Compressible Flows: Gas dynamics Multiphase and Particle-laden Flows: Multiphase flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 737 , 25 December 2013 , pp. 146 - 175
Copyright
©2013 Cambridge University Press 

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