## 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. As an example, it is shown how the effective viscosity for anon-uniform suspension can be obtained. This quantityu is found to be robust in the sense that it takes on the same values for the three specific flows considered. 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. As an example, it is shown how the effective viscosity for anon-uniform suspension can be obtained. This quantityu is found to be robust in the sense that it takes on the same values for the three specific flows considered. 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 30th Fluid Dynamics Conference |

Subtitle of host publication | 28 June 1999 - 1 July 1999, Norfolk, VA, U.S.A |

Publisher | AIAA Aerospace Sciences |

DOIs | |

Publication status | Published - 1999 |

Event | 30th AIAA Fluid Dynamics Conference 1999 - Norfolk, United States Duration: 28 Jun 1999 → 1 Jul 1999 Conference number: 30 |

### Conference

Conference | 30th AIAA Fluid Dynamics Conference 1999 |
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Country/Territory | United States |

City | Norfolk |

Period | 28/06/99 → 1/07/99 |