An examination of the one-fluid formulation for two-phase flows*

For direct numerical simulations of two-phase flow, the established methodology is the application of the one-fluid formulation, which applies everywhere in the domain, including at the gas-liquid interface. The physical consistency of this formulation is examined by considering whether it satisfies the governing equations in the bulk region of the domain and the jump conditions at the interface. An analysis of various versions of the momentum and energy one-field formulations published in the literature reveals a frequent inconsistency, particularly for problems involving phase change. The issue is in part attributed to a lack of equivalence between conservative and non-conservative forms of the equation, although other issues are also uncovered. A proposed generalized one-field formulation is advanced that is able to exhibit the desired level of physical consistency by satisfying interfacial and bulk phase relations.