## Abstract

Numerical experiments have been performed to study the geometric collision rate of heavy particles with finite inertia. The turbulent flow was generated by integrating numerically the full Navier-Stokes equations directly. We found that the collision kernel reached a peak at a particle response time larger than the Kolmogorov time but less than the large-eddy turnover timeΓimplying that both the large-scale and small-scale fluid motion can contributeΓalthough in very different mannersΓto the collision rate. Both numerical results and a stochastic theory show that the collision kernel approaches very slowly to the kinetic theory of Abrahamson (1975) at large τ_{p}/T_{e}Γwhere τ_{p} is the particle response time and T_{e} is the flow integral time scale. A rapid increase of the collision kernel with the particle response time was observed for small τ_{p}/τ_{k}Γwhere τ_{k} is the flow Kolmogorov time scale. A small inertia of τ_{p}/τ_{k} = 0.5 can lead to an order of magnitude increase in the collision kernel relative to the zero-inertia particles. A scaling law for the collision kernel at small τ_{p}/τ_{k} was proposed and confirmed numerically by varying the particle sizeΓinertial response timeΓand flow Reynolds number. A leading-order theory for small τ_{p}/τ_{k} was developedΓshowing that the enhanced collision is mainly a result of the nonuniform particle concentration due to the interaction of heavy particles with local flow microstructures.

Original language | English (US) |
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Title of host publication | American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FED |

Place of Publication | New York, NY, United States |

Publisher | ASME |

Volume | 17 |

State | Published - 1997 |

Externally published | Yes |

Event | Proceedings of the 1997 ASME Fluids Engineering Division Summer Meeting, FEDSM'97. Part 24 (of 24) - Vancouver, Can Duration: Jun 22 1997 → Jun 26 1997 |

### Other

Other | Proceedings of the 1997 ASME Fluids Engineering Division Summer Meeting, FEDSM'97. Part 24 (of 24) |
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City | Vancouver, Can |

Period | 6/22/97 → 6/26/97 |

## ASJC Scopus subject areas

- Engineering(all)