A Hierarchy of NonEquilibrium TwoPhase Flow Models
Abstract
We consider a hierarchy of relaxation models for twophase flow. The models are derived from the nonequilibrium BaerNunziato model, which is endowed with relaxation source terms to drive it towards equilibrium. The source terms cause transfer of volume, heat, mass and momentum due to differences between the phases in pressure, temperature, chemical potential and velocity, respectively. The subcharacteristic condition is closely linked to the stability of such relaxation systems, and in the context of twophase flow models, it implies that the sound speed of an equilibrium system can never exceed that of the relaxation system. Here, previous work by Flåtten and Lund [Math. Models Methods Appl. Sci., 21 (12), 2011, 23792407] and Lund [SIAM J. Appl. Math. 72, 2012, 17131741] is extended to encompass twofluid models, i.e. models with separately governed velocities for the two phases. Each remaining model in the hierarchy is derived, and analytical expressions for the sound speeds are presented. Given only physically fundamental assumptions, the subcharacteristic condition is shown to be satisfied in the entire hierarchy, either in a weak or in a strong sense.
 Publication:

arXiv eprints
 Pub Date:
 April 2018
 arXiv:
 arXiv:1804.05241
 Bibcode:
 2018arXiv180405241L
 Keywords:

 Physics  Fluid Dynamics;
 76Txx;
 93C20
 EPrint:
 32 pages, 3 figures