Library Subscription: Guest
Begell Digital Portal Begell Digital Library eBooks Journals References & Proceedings Research Collections
Multiphase Science and Technology

ISSN Print: 0276-1459
ISSN Online: 1943-6181

Multiphase Science and Technology

DOI: 10.1615/MultScienTechn.v5.i1-4.10
pages 1-63


Mamoru Ishii
Therma-Hydraulics and Reactor Safety Laboratory, School of Nuclear Engineering, Purdue University, 400 Central Drive, West Lafayette, IN 47907, USA


The two-fluid model formulation is discussed in detail. The emphasis of the paper is on the three-dimensional formulation and the closure issues. The origin of the interfacial and turbulent transfer terms in the averaged formulation is explained and their original mathematical forms are examined. The interfacial transfer of mass, momentum, and energy is proportional to the interfacial area and driving force. This is not a postulate but a careful examination of the mathematical form of the exact interfacial terms. These two effects are considered separately. Since all the interfacial transfer terms involve the interfacial area concentration, the accurate modelling of the local interfacial is the first step to be taken for development of reliable two-fluid model closure relations. The interfacial momentum interaction has been studied in terms of the standard drag, lift, virtual mass, and Basset forces. Available analytical and semi-empirical correlations and closure relations are reviewed and existing shortcomings are pointed out. The other major area of importance is the modelling of turbulent transfer in two-phase flow. The two-phase turbulence cannot be understood without understanding the interfacial drag and lift forces accurately. There are some indications that the mixing length type model may not be sufficient to describe the three-dimensional turbulent and flow structures. Although it is a very difficult challenge, the two-phase flow turbulence should be investigated both experimentally and analytically with long time-scale research.