A compressible single‐temperature conservative two‐phase model with phase transitions |
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| Authors: | G La Spina M de' Michieli Vitturi E Romenski |
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| Affiliation: | 1. Istituto Nazionale di Geofisica e Vulcanologia, Sezione di Pisa, Italy;2. Dipartimento di Matematica L.Tonelli, University of Pisa, Pisa, Italy;3. Sobolev Institute of Mathematics, Russian Academy of Sciences, Moscow, Russia |
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| Abstract: | A model for multidimensional compressible two‐phase flow with pressure and velocity relaxations based on the theory of thermodynamically compatible system is extended to study liquid–gas flows with cavitation. The model assumes for each phase its own pressure and velocity, while a common temperature is considered. The governing equations form a hyperbolic system in conservative form and are derived through the theory of a thermodynamically compatible system. The phase pressure‐equalizing process and the interfacial friction are taken into account in the balance laws for the volume fractions of one phase and for the relative velocity by adding two relaxation source terms, while the phase transition is introduced into the model considering in the balance equation for the mass of one phase the relaxation of the Gibbs free energies of the two phases. A modification of the central finite‐volume Kurganov–Noelle–Petrova method is adopted in this work to solve the homogeneous hyperbolic part, while the relaxation source terms are treated implicitly. In order to investigate the effect of the mass transfer in the solution, a 1D cavitation tube problem is presented. In addition, two 2D numerical simulations regarding cavitation problem are also studied: a cavitating Richtmyer–Meshkov instability and a laser‐induced cavitation problem. Copyright © 2014 John Wiley & Sons, Ltd. |
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| Keywords: | compressible flow finite volume hyperbolic partial differential equations two‐phase flows phase change |
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