## Abstract

This paper presents a summary of some recent work on the systematic closure of disperse-flow averaged-equations models on the basis of direct numerical simulations. Since the average pressure is found by solving the equations rather than prescribed as a closure relation, it is important first to identify the pressure part of the average stress. This objective is achieved by examining the transformation properties of the average stress under the gauge transformation

pc + pc +ψ, where PC is the continuous-phase pressure and ~ the potential of the body forces. After this step, the stress is expressed in terms of computable quantities. A strategy to derive closure relations is then described. It is also shown that the theological behavior of spatially non-uniform suspensions is described by a non-Newtonian constitutive equation.

pc + pc +ψ, where PC is the continuous-phase pressure and ~ the potential of the body forces. After this step, the stress is expressed in terms of computable quantities. A strategy to derive closure relations is then described. It is also shown that the theological behavior of spatially non-uniform suspensions is described by a non-Newtonian constitutive equation.

Original language | English |
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Title of host publication | Proceedings of the 17th Symposium on Energy Engineering Sciences |

Subtitle of host publication | May 13-14, 1999, Argonne National Laboratory, Argonne, Illinois |

Pages | 199-206 |

Publication status | Published - 1999 |

Event | 17th Symposium on Energy Engineering Sciences 1999 - Argonne National Laboratory, Lemont, United States Duration: 13 May 1999 → 14 May 1999 Conference number: 17 |

### Conference

Conference | 17th Symposium on Energy Engineering Sciences 1999 |
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Country | United States |

City | Lemont |

Period | 13/05/99 → 14/05/99 |