### Abstract

Numerical flow simulation utilising a full multiphase
model is impractical for a suspension possessing wide
distributions in the particle size or density. Various
approximations are usually made to simplify the
computational task. In the simplest approach, the
suspension is represented by a homogeneous single-phase
system and the influence of the particles is taken into
account in the values of the physical properties. The
multiphase nature of the flow cannot, however, be avoided
when the concentration gradients are large and the
dispersed phases alter the hydrodynamic behaviour of the
mixture or when the distributions of the particles are
studied. In many practical applications of multiphase
flow, the mixture model is a sufficiently accurate
approximation, with only a moderate increase in the
computational effort compared to a single-phase
simulation.
This study concentrates on the derivation and closing of
the model equations. The validity of the mixture model is
also carefully analysed. Starting from the continuity and
momentum equations written for each phase in a multiphase
system, the field equations for the mixture are derived.
The mixture equations largely resemble those for a
single-phase flow but are represented in terms of the
mixture density and velocity. However, an additional term
in the mixture momentum equation arises from the slip of
the dispersed phases relative to the continuous phase.
The volume fraction for each dispersed phase is solved
from a phase continuity equation.
Various approaches applied in closing the mixture model
equations are reviewed. An algebraic equation is derived
for the velocity of a dispersed phase relative to the
continuous phase. Simplifications made in calculating the
relative velocity restrict the applicability of the
mixture model to cases in which the particles reach the
terminal velocity in a short time period compared to the
characteristic time scale of the flow of the mixture. The
terms for the viscous and turbulent stresses in the
mixture momentum equation are usually combined to a
generalised stress.
The mixture model applications reported in the literature
are briefly summarised. The areas of application include
gravity settling, rotational flows and turbulent flows.
The multiphase models in three commercial codes,
PHOENICS, FLUENT and CFX 4, are reviewed. The mixture
model approach, in a simplified form, is implemented only
in PHOENICS.

Original language | English |
---|---|

Place of Publication | Espoo |

Publisher | VTT Technical Research Centre of Finland |

Number of pages | 67 |

ISBN (Print) | 951-38-4946-5 |

Publication status | Published - 1996 |

MoE publication type | Not Eligible |

### Publication series

Series | VTT Publications |
---|---|

Number | 288 |

ISSN | 1235-0621 |

### Keywords

- multiphase flow
- mixtures
- models
- flow
- flow control
- simulation
- dispersions
- mathematical models
- equations
- computers

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## Cite this

Manninen, M., Taivassalo, V., & Kallio, S. (1996).

*On the mixture model for multiphase flow*. VTT Technical Research Centre of Finland. VTT Publications, No. 288 http://www.vtt.fi/inf/pdf/publications/1996/P288.pdf