### Abstract

The collision rate of monodisperse solid particles in a turbulent gas is governed by a wide range of scales of motion in the flow. Recent studies have shown that large-scale energetic eddies are the dominant factor contributing to the relative velocity between two colliding particles (the turbulent transport effect), whereas small-scale dissipative eddies can enhance the collision rate significantly by inducing local non-uniform particle distribution (the accumulation effect). The turbulent transport effect is most noticeable when the particle inertial response time τ(p) is of the order of the flow integral timescale and the accumulation effect is most pronounced when τ(p) is comparable to the flow Kolmogorov time. We study these two contributions separately through direct numerical simulations. The two effects are quantified carefully with a numerical procedure that is independent of the computation of average collision rate. This facilitates the study of not only the statistical description of the collision kernel, but also the relative contributions and modelling of the two physical effects. Simulations at several flow Reynolds numbers were performed to suggest a model for the accumulation effect. The data show that the accumulation effect scales linearly with flow Taylor microscale Reynolds number R(λ), while the theory for fully developed turbulence indicates that the maximum level of the turbulent transport effect scales with R(λ)(1/2). Finally, an integrated model has been developed to predict the collision rate at arbitrary flow Reynolds numbers and particle inertia.

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

Pages (from-to) | 117-153 |

Number of pages | 37 |

Journal | Journal of Fluid Mechanics |

Volume | 415 |

State | Published - 2000 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mechanics of Materials
- Computational Mechanics
- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Journal of Fluid Mechanics*,

*415*, 117-153.

**Statistical mechanical description and modelling of turbulent collision of inertial particles.** / Wang, L. P.; Wexler, A. S.; Zhou, Y.

Research output: Contribution to journal › Article

*Journal of Fluid Mechanics*, vol. 415, pp. 117-153.

}

TY - JOUR

T1 - Statistical mechanical description and modelling of turbulent collision of inertial particles

AU - Wang, L. P.

AU - Wexler, A. S.

AU - Zhou, Y.

PY - 2000

Y1 - 2000

N2 - The collision rate of monodisperse solid particles in a turbulent gas is governed by a wide range of scales of motion in the flow. Recent studies have shown that large-scale energetic eddies are the dominant factor contributing to the relative velocity between two colliding particles (the turbulent transport effect), whereas small-scale dissipative eddies can enhance the collision rate significantly by inducing local non-uniform particle distribution (the accumulation effect). The turbulent transport effect is most noticeable when the particle inertial response time τ(p) is of the order of the flow integral timescale and the accumulation effect is most pronounced when τ(p) is comparable to the flow Kolmogorov time. We study these two contributions separately through direct numerical simulations. The two effects are quantified carefully with a numerical procedure that is independent of the computation of average collision rate. This facilitates the study of not only the statistical description of the collision kernel, but also the relative contributions and modelling of the two physical effects. Simulations at several flow Reynolds numbers were performed to suggest a model for the accumulation effect. The data show that the accumulation effect scales linearly with flow Taylor microscale Reynolds number R(λ), while the theory for fully developed turbulence indicates that the maximum level of the turbulent transport effect scales with R(λ)(1/2). Finally, an integrated model has been developed to predict the collision rate at arbitrary flow Reynolds numbers and particle inertia.

AB - The collision rate of monodisperse solid particles in a turbulent gas is governed by a wide range of scales of motion in the flow. Recent studies have shown that large-scale energetic eddies are the dominant factor contributing to the relative velocity between two colliding particles (the turbulent transport effect), whereas small-scale dissipative eddies can enhance the collision rate significantly by inducing local non-uniform particle distribution (the accumulation effect). The turbulent transport effect is most noticeable when the particle inertial response time τ(p) is of the order of the flow integral timescale and the accumulation effect is most pronounced when τ(p) is comparable to the flow Kolmogorov time. We study these two contributions separately through direct numerical simulations. The two effects are quantified carefully with a numerical procedure that is independent of the computation of average collision rate. This facilitates the study of not only the statistical description of the collision kernel, but also the relative contributions and modelling of the two physical effects. Simulations at several flow Reynolds numbers were performed to suggest a model for the accumulation effect. The data show that the accumulation effect scales linearly with flow Taylor microscale Reynolds number R(λ), while the theory for fully developed turbulence indicates that the maximum level of the turbulent transport effect scales with R(λ)(1/2). Finally, an integrated model has been developed to predict the collision rate at arbitrary flow Reynolds numbers and particle inertia.

UR - http://www.scopus.com/inward/record.url?scp=0033869053&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033869053&partnerID=8YFLogxK

M3 - Article

VL - 415

SP - 117

EP - 153

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -