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The influence of sub-grid scale motions on particle collision in homogeneous isotropic turbulence

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Abstract

The absence of sub-grid scale (SGS) motions leads to severe errors in particle pair dynamics, which represents a great challenge to the large eddy simulation of particle-laden turbulent flow. In order to address this issue, data from direct numerical simulation (DNS) of homogenous isotropic turbulence coupled with Lagrangian particle tracking are used as a benchmark to evaluate the corresponding results of filtered DNS (FDNS). It is found that the filtering process in FDNS will lead to a non-monotonic variation of the particle collision statistics, including radial distribution function, radial relative velocity, and the collision kernel. The peak of radial distribution function shifts to the large-inertia region due to the lack of SGS motions, and the analysis of the local flowstructure characteristic variable at particle position indicates that the most effective interaction scale between particles and fluid eddies is increased in FDNS. Moreover, this scale shifting has an obvious effect on the odd-order moments of the probability density function of radial relative velocity, i.e. the skewness, which exhibits a strong correlation to the variance of radial distribution function in FDNS. As a whole, the radial distribution function, together with radial relative velocity, can compensate the SGS effects for the collision kernel in FDNS when the Stokes number based on the Kolmogorov time scale is greater than 3.0. However, it still leaves considerable errors for \({ St}_\mathrm{k }<3.0\).

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Abbreviations

DPM:

Discrete particle model

FDNS:

Filtered direct numerical simulation

HIT:

Homogeneous isotropic turbulence

LES:

Large eddy simulation

PDF:

Probability density function

RDF (g):

Radial distribution function (dimensionless)

SGS:

Sub-grid scale

SPS:

Satellite particle simulation

L :

Length of the simulation domain

\(N_{\mathrm{cell} }\) :

Number of cells in the simulation field

\(N_{\mathrm{p} }\) :

Number of particles

d :

Diameter of particle

R :

Separation distance of particle pair at collision radius

r :

Separation distance of particle pair

\(V_\mathrm{field} \) :

Volume of the domain

\(V_s \) :

Volume of the annulus with radius r

\({ St}_\mathrm{k }\) :

Particle Stokes number based on the Kolmogorov scale

\(S_{ij,\mathrm{p}} \) :

Strain tensor rate of the flow at particle location

\(R_{ij,\mathrm{p}} \) :

Rotation tensor rate of the flow at particle location

r.m.s.:

Root mean square

\(w_\mathrm{r}\) :

Radial relative velocity (dimensionless)

\(w_\mathrm{r}^- \) :

Radial relative velocity in inward direction

\(\beta \) :

Particle collision kernel

\(\tau _\mathrm{p} \) :

Particle relaxation time

\(\tau _\mathrm{k}\) :

Kolmogorov time scale of turbulence

\({{\varvec{T}}}_{\mathrm{E }}\) :

Eulerian integral time scale of turbulence

\(\eta \) :

Kolmogorov length scale of turbulence

\(\nu _\mathrm{k} \) :

Kolmogorov velocity of the turbulence

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grants 51390494, 51306065, and 51276076), the Foundation of State Key Laboratory of Coal Combustion (Grant FSKLCCB1702).

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Authors and Affiliations

  1. State Key Laboratory of Coal Combustion, School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China

    Yan Xiong, Jing Li, Zhaohui Liu & Chuguang Zheng

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  1. Yan Xiong
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Correspondence to Jing Li or Zhaohui Liu.

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Xiong, Y., Li, J., Liu, Z. et al. The influence of sub-grid scale motions on particle collision in homogeneous isotropic turbulence. Acta Mech. Sin. 34, 22–36 (2018). https://doi.org/10.1007/s10409-017-0720-5

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