Steady Two-Phase Choked Flow in Channels of Variable Cross Sectional Area

A Thermodynamically Consistent Relaxation Model for Turbulent Binary Mixture Undergoing Phase Transition

“…Hence, we obtain an evolution equation [1][2][3][4][5][6][7]12,16,[30][31][32][37][38][39][40][41]44,58,59] of the relaxation type…”

“…For example, the evolution equation for the slip vector u has the following form [4]: (2.13) or the Chan-Hillard-type, Eq.…”

“…(5.5) (t -is a time-like parameter) represents the recoverable microinertia contribution [4] and f is calculated as the Basset-like force [16,62]. (5.5) (t -is a time-like parameter) represents the recoverable microinertia contribution [4] and f is calculated as the Basset-like force [16,62].…”

“…In this case the sources s j 0 vanish since no phase change is observed, and J j ijk 0 since a flux-less evolution of shape of the bubble flow into slug flow is usually observed [4,64]. Then the internal variables can be reduced to a ¼ fj; k; eg and a ij ¼ fj ij ; 0; 0g.…”

“…Starting with the interpretation of the turbulent flux of momentum as an internal forces interchanging momentum between laminar and turbulent fluid within a continuum particle [44], we have endeavoured to deduce from analytical considerations the model for the thermodynamically consistent laws of transport of mass, momentum and energy between the phasic, turbulent and diffusive microstructures. On the basis of our work on non-equilibrium phase transitions, [1][2][3][4][5][6][7]16,32,[37][38][39][40][41]44,58,59], an approach from the opposite direction has been presented here -from thermodynamically substantiated models of a laminar flow Such a line of reasoning omits a specificity of phase transition phenomena.…”