Modelling of two-phase flow based on separation of the flow according to velocity: Dissertation

Timo Narumo

Research output: ThesisDissertationCollection of Articles


This thesis concentrates on the development work of a physical one-dimensional two-fluid model that is based on Separation of the Flow According to Velocity (SFAV). The conventional way to model one-dimensional two-phase flow is to derive conservation equations for mass, momentum and energy over the regions occupied by the phases. This approach results in seemingly sensible equations but they need extra vague "virtual-mass" terms to form a hyperbolic system or a mathematically well-posed initial value problem. Furthermore, the interface between the phases is unavoidably very complicated geometrically, which especially makes the modelling of interfacial momentum transfer between the phases highly problematic. In the SFAV approach, the two-phase mixture is divided into two subflows, with as distinct average velocities as possible, and momentum conservation equations are derived over their domains. Mass and energy conservation are treated equally with the conventional model because they are distributed very accurately according to the phases, but momentum fluctuations follow better the flow velocity. Submodels for non-uniform transverse prole of velocity and density, slip between the phases within each subflow and turbulence between the subflows have been derived. The model system is hyperbolic in any sensible flow conditions over the whole range of void fraction. Thus, it can be solved with accurate numerical methods utilizing the characteristics. The characteristics agree well with the used experimental data on two-phase flow wave phenomena. Furthermore, the characteristics of the SFAV model are as well in accordance with their physical counterparts as of the best virtual-mass models that are typically optimized for special flow regimes like bubbly flow. The SFAV subflows enable easier interfacial momentum transfer modelling than in the conventional model because the interface between the subflows is geometrically much simpler than the interface between the phases. The SFAV model has proved to be applicable in describing two-phase flow physically correctly because both the dynamics and steady-state behaviour of the model has been considered and found to agree well with experimental data. This makes the SFAV model especially suitable for the calculation of fast transients, taking place in versatile form e.g. in nuclear reactors.
Original languageEnglish
QualificationDoctor Degree
Awarding Institution
  • Helsinki University of Technology
Award date19 Sept 1997
Place of PublicationEspoo
Print ISBNs951-38-5071-4
Publication statusPublished - 1997
MoE publication typeG5 Doctoral dissertation (article)


  • two-phase flow
  • flow velocity
  • fluid flow
  • SFAV
  • subflow


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