Acta Mechanica Sinica

, Volume 34, Issue 1, pp 22–36 | Cite as

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

Research Paper
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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 \({ St}_\mathrm{k }<3.0\).

Keywords

Particle-laden turbulence Homogenous isotropic turbulence Large eddy simulation Particle collisions 

List of symbols

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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Notes

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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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.State Key Laboratory of Coal Combustion, School of Energy and Power EngineeringHuazhong University of Science and TechnologyWuhanChina

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