Anisotropy in pair dispersion of inertial particles in turbulent channel flow

Pitton, Enrico; Marchioli, Cristian; Lavezzo, Valentina; Soldati, Alfredo; Toschi, Federico

doi:10.1063/1.4737655

Cited by 23 publications

(35 citation statements)

References 59 publications

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“…More recently, Pitton et al (2012) studied the separation of inertial particle pairs in a turbulent channel flow using DNS at a friction Reynolds number Re τ = 150. Results for inertial particles were compared to fluid tracers.…”

Section: Introductionmentioning

confidence: 99%

“…Arguably due to an insufficient separation of scales, Richardson's regime was not clearly identified. Pitton et al (2012) removed the effect of mean shear by tracking particles which follow the fluctuating velocity field. They found that, although pair separation is importantly reduced at long times compared to the case with mean shear, separation in the streamwise direction remains dominant over the wall-normal and spanwise separations.…”

Section: Introductionmentioning

confidence: 99%

“…The DNS of Pitton et al (2012) revealed the fundamental role played by inertial particle-turbulence interactions at small scales in the initial stages of pair separation. The authors found a superdiffusive pair dispersion of inertial particles in channel flow.…”

Section: Introductionmentioning

confidence: 99%

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Relative dispersion of particle pairs in turbulent channel flow

Polanco

Vinkovic

Stelzenmuller

et al. 2018

International Journal of Heat and Fluid Flow

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Lagrangian tracking of particle pairs is of fundamental interest in a large number of environmental applications dealing with contaminant dispersion and passive scalar mixing. The aim of the present study is to extend the observations available in the literature on relative dispersion of fluid particle pairs to wall-bounded turbulent flows, by means of particle pair tracking in direct numerical simulations (DNS) of a turbulent channel flow. The mean-square change of separation between particle pairs follows a clear ballistic regime at short times for all wall distances. The Eulerian structure functions governing this short-time separation are characterised in the channel, and allow to define a characteristic time scale for the ballistic regime, as well as a suitable normalisation of the mean-square separation leading to an overall collapse for different wall distances. Through fluid particle pair tracking backwards and forwards in time, the temporal asymmetry of relative dispersion is illustrated. At short times, this asymmetry is linked to the irreversibility of turbulence, as in previous studies on homogeneous isotropic flows. The influence of the initial separation (distance and orientation) as well as the influence of mean shear are addressed. By decomposing the mean-square separation into the dispersion by the fluctuating velocity field and by the average velocity, it is shown that the influence of mean shear becomes important at early stages of dispersion close to the wall but also near the channel centre. The relative dispersion tensor ∆ i j is also presented and particularly the sign and time evolution of the cross-term ∆ xy are discussed. Finally, a ballistic cascade model previously proposed for homogeneous isotropic turbulence is adapted here to turbulent channel flows. Preliminary results are given and compared to the DNS. Future developments and assumptions in two particle stochastic models can be gauged against the issues and results discussed in the present study.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Relative dispersion of particle pairs in turbulent channel flow

Polanco

Vinkovic

Stelzenmuller

et al. 2018

International Journal of Heat and Fluid Flow

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“…The LES prediction of other quantities related to particle separations such as the radial distribution function and the mean radial relative velocity between particles with the SGS-SDE model needs to be investigated in the future. In turbulent channel flows, the SGS timescale seen by particles changes with the distance from the wall due to the presence of strong shear rates and high flow anisotropy in the near-wall region [8,27,67]. The corresponding problem that should be studied is the effects of the shear rate on the SGS timescale seen by heavy particles.…”

Section: Discussionmentioning

confidence: 99%

“…For example, pollutant dispersion and warm rain droplet formation in the atmosphere, and fluidization and combustion in process engineering [2][3][4]. Understanding the relative dispersion of heavy particles in turbulence is vital for the processes of transport and mixing, since it is closely related to the fluctuation of local concentration, which determines reaction rates [5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

A nonlinear model for the subgrid timescale experienced by heavy particles in large eddy simulation of isotropic turbulence with a stochastic differential equation

Jin

2013

New J. Phys.

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The effects of subgrid scale (SGS) motions on the dispersion of heavy particles raise a challenge to the large-eddy method of simulation (LES). As a necessary first step, we propose the use of a stochastic differential equation (SDE) to represent the SGS contributions to the relative dispersions of heavy particles in LES of isotropic turbulence. The main difficulty is in closing the SGS-SDE model whilst accounting for the effects of particle inertia, filter width and gravity. The physics of the interaction between heavy particles and SGS turbulence is explored using the filtered direct numerical simulation method. It is found in the present work that (i) the ratio of the SGS Lagrangian and Eulerian timescales is different from that of the full-scale Lagrangian and Eulerian timescales. The ratios are also dependent on filter widths. (ii) In the absence of gravity, the SGS timescale seen by heavy particles non-monotonically changes with particle Stokes number and has a maximum at particle Stokes number (St = τ p /δT E ) near 0.5. (iii) In the presence of gravity, a similarity law exists between the SGS Lagrangian correlation function seen by a heavy particle within a timedelay τ and the SGS spatial correlation function with the displacement w τ , where w is the average settling velocity of a heavy particle. The joint effects of particle inertia and gravity are accounted for using the elliptic model for pair fluctuations to the dispersion of particles [9,10]. Chibbaro and Minier [10] addressed the importance of introducing specific features related to the near-wall coherent structure in pipe flows based on the Langevin probability density function (PDF) method. In the SDE, the Lagrangian integral timescale of fluid velocity seen by heavy particles (the fluid-particle interaction timescale), T Lp , is one of the key parameters and it determines the dispersion rates of heavy particles [11][12][13][14]. Direct numerical simulation (DNS) shows that T Lp does not vary monotonically with particle Stokes number St K from T L to T E , but has an 'N' shape with a maximum near St K = 1 due to the relative motion of particles near rotational vortical structures [15][16][17], where St K ≡ τ p /τ K , τ p is the particle Stokes response time and τ p = ρ p d 2 p /18µ, d p is the particle diameter, µ the dynamical viscosity, ρ p particle density and τ K the turbulent Kolmogorov timescale.The RANS method finds wide application in engineering calculations [9] and the DNS method has manifested its power in fundamental research [17][18][19][20]. However, DNS is still limited to flows at relatively low or moderate Reynolds numbers. RANS does not predict well the unsteady structures in turbulent flows which are of importance for turbulent dispersion of heavy particles. Motivated by the limitations of RANS and DNS, large-eddy simulation (LES) is becoming a potential method for future engineering calculations. In LES, large-scale velocitiesū(x, t) are resolved explicitly using the filtered Navier-Stokes equations. The smallscale velocities...

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Prediction of Lagrangian dispersion of fluid particles in isotropic turbulent flows using large-eddy simulation method

2017

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The single-, two-and multi-particle dispersions in isotropic turbulent flows are investigated using the direct numerical simulation (DNS), filtered DNS (FDNS) and large-eddy simulation (LES) with a spectral eddy viscosity subgrid scale (SGS) model. The contributions of filtering operation and SGS model to the dispersions are separately studied by comparing the statistics obtained from the three methods. The missing SGS motions in LES can be observed to significantly hinder two-particle and four-particle dispersions if the initial separations are less than or comparable to the filter width. A theoretical analysis of the non-monotonic behavior at short time of the one-time, two-point Lagrangian velocity correlation functions with large initial separations based on the Taylor expansion and the Kolmogorov similarity theory is derived, and the Reynolds number effect on the performance of the spectral eddy viscosity SGS model is also investigated. The results show that the SGS model used performs better with increasing Reynolds numbers. It is concluded that the particle SGS model is needed to be developed to correctly capture the Lagrangian two-and multi-point dispersion statistics of fluid particles.

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Anisotropy in pair dispersion of inertial particles in turbulent channel flow

Cited by 23 publications

References 59 publications

Relative dispersion of particle pairs in turbulent channel flow

Relative dispersion of particle pairs in turbulent channel flow

A nonlinear model for the subgrid timescale experienced by heavy particles in large eddy simulation of isotropic turbulence with a stochastic differential equation

Prediction of Lagrangian dispersion of fluid particles in isotropic turbulent flows using large-eddy simulation method

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