### Abstract

Numerical experiments have been performed to study the geometric collision rate of heavy particles with finite inertia. The turbulent flow was generated by direct numerical integration of the full Navier-Stokes equations. The collision kernel peaked at a particle response time between the Kolmogorov and the large-eddy turnover times, implying that both the large-scale and small-scale fluid motions contribute, although in very different manners, to the collision rate. Both numerical results for frozen turbulent fields and a stochastic theory show that the collision kernel approaches the kinetic theory of Abrahamson [Chem. Eng. Sci. 30, 1371 (1975)] only at very large τ_{p}/T_{e}, where τ_{p} is the particle response time and T_{e} is the flow integral time scale. Our results agree with those of Sundaram and Collins [J. Fluid Mech. 335, 75 (1997)] for an evolving flow. A rapid increase of the collision kernel with the particle response time was observed for small τ_{p}/τ_{k}, where T_{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 size, inertial response time, and flow Reynolds number. A leading-order theory for small τ_{p}/τ_{k} was developed, showing that the enhanced collision is mainly a result of the nonuniform particle concentration that results from the interaction of heavy particles with local flow microstructures.

Original language | English (US) |
---|---|

Pages (from-to) | 1206-1216 |

Number of pages | 11 |

Journal | Physics of Fluids |

Volume | 10 |

Issue number | 5 |

State | Published - May 1998 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Fluid Flow and Transfer Processes
- Computational Mechanics
- Mechanics of Materials
- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Physics of Fluids*,

*10*(5), 1206-1216.

**On the collision rate of small particles in isotropic turbulence. II. Finite inertia case.** / Zhou, Yong; Wexler, Anthony S.; Wang, Lian Ping.

Research output: Contribution to journal › Article

*Physics of Fluids*, vol. 10, no. 5, pp. 1206-1216.

}

TY - JOUR

T1 - On the collision rate of small particles in isotropic turbulence. II. Finite inertia case

AU - Zhou, Yong

AU - Wexler, Anthony S.

AU - Wang, Lian Ping

PY - 1998/5

Y1 - 1998/5

N2 - Numerical experiments have been performed to study the geometric collision rate of heavy particles with finite inertia. The turbulent flow was generated by direct numerical integration of the full Navier-Stokes equations. The collision kernel peaked at a particle response time between the Kolmogorov and the large-eddy turnover times, implying that both the large-scale and small-scale fluid motions contribute, although in very different manners, to the collision rate. Both numerical results for frozen turbulent fields and a stochastic theory show that the collision kernel approaches the kinetic theory of Abrahamson [Chem. Eng. Sci. 30, 1371 (1975)] only at very large τp/Te, where τp is the particle response time and Te is the flow integral time scale. Our results agree with those of Sundaram and Collins [J. Fluid Mech. 335, 75 (1997)] for an evolving flow. A rapid increase of the collision kernel with the particle response time was observed for small τp/τk, where Tk is the flow Kolmogorov time scale. A small inertia of τp/τk = 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 τp/τk was proposed and confirmed numerically by varying the particle size, inertial response time, and flow Reynolds number. A leading-order theory for small τp/τk was developed, showing that the enhanced collision is mainly a result of the nonuniform particle concentration that results from the interaction of heavy particles with local flow microstructures.

AB - Numerical experiments have been performed to study the geometric collision rate of heavy particles with finite inertia. The turbulent flow was generated by direct numerical integration of the full Navier-Stokes equations. The collision kernel peaked at a particle response time between the Kolmogorov and the large-eddy turnover times, implying that both the large-scale and small-scale fluid motions contribute, although in very different manners, to the collision rate. Both numerical results for frozen turbulent fields and a stochastic theory show that the collision kernel approaches the kinetic theory of Abrahamson [Chem. Eng. Sci. 30, 1371 (1975)] only at very large τp/Te, where τp is the particle response time and Te is the flow integral time scale. Our results agree with those of Sundaram and Collins [J. Fluid Mech. 335, 75 (1997)] for an evolving flow. A rapid increase of the collision kernel with the particle response time was observed for small τp/τk, where Tk is the flow Kolmogorov time scale. A small inertia of τp/τk = 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 τp/τk was proposed and confirmed numerically by varying the particle size, inertial response time, and flow Reynolds number. A leading-order theory for small τp/τk was developed, showing that the enhanced collision is mainly a result of the nonuniform particle concentration that results from the interaction of heavy particles with local flow microstructures.

UR - http://www.scopus.com/inward/record.url?scp=0032075687&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032075687&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032075687

VL - 10

SP - 1206

EP - 1216

JO - Physics of Fluids

JF - Physics of Fluids

SN - 0031-9171

IS - 5

ER -