Singularity of Inertial Particle Concentration in the Viscous Sublayer of Wall-bounded Turbulent Flows

Sikovsky, Dmitrii Ph.

doi:10.1007/s10494-013-9521-5

Cited by 25 publications

(37 citation statements)

References 39 publications

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“…(5)) the non-local contribution (which gives rise to caustics) is also related to the spatial clustering through ρ. In general the GT predicts a bi-fractal behavior for the longitudinal relative velocities ∝ ∥ − S r [ ] N p N dd min , 2 and we note that a similar behavior has recently been derived for the behavior of the wall-normal particle velocities in wall-bounded turbulent flows [35].…”

Section: Gustavsson Et Al Theorysupporting

confidence: 79%

New insights from comparing statistical theories for inertial particles in turbulence: II. Relative velocities

Bragg

Collins

2014

New J. Phys.

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Part I of this two-part series compared two theories for the radial distribution function (RDF), a statistical measure of the clustering of inertial particles in isotropic turbulence. In Part II, we will contrast three theoretical models for the relative velocities of inertial particles in isotropic turbulence, one by Zaichik et al (2009 New. J. Phys. 11 103018), the second by Pan et al (2010 J. Fluid Mech. 661 73) and the third by Gustavsson et al (2011 Phys. Rev. E. 84 045304).We find that in general they describe the relative velocities in qualitatively similar ways, capturing the influence of the non-local dynamics on the formation of caustics and non-smooth scaling behavior in the dissipation range. We then compare the theoretical predictions with direct numerical simulation data and find that although they capture the qualitative behavior of the data consistently, they differ quantitatively, and we discuss the possible sources of error in each of the theories. Finally, we consider how the Zaichik et al theory predicts that the formation of caustics modifies the form of the RDF, and show that the theory describes the behavior of the RDF for particles whose response time scales with the inertial range time scales of the turbulence.

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Section: Gustavsson Et Al Theorysupporting

confidence: 79%

New insights from comparing statistical theories for inertial particles in turbulence: II. Relative velocities

Bragg

Collins

2014

New J. Phys.

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“…Consequently in a boundary layer, the leading order contribution to the inward drift velocity is proportional to St w not St w 2 . As the diffusion coefficient in the boundary layer too is independent of St w , the near-wall particle concentration grows as a power law with an exponent ∝ St w , as suggested by [34,72]. This difference in the scaling arises solely due to the lack of spherical symmetry in the turbulent boundary layer.…”

Section: Non-centrifuge Mechanismsmentioning

confidence: 95%

New insights from comparing statistical theories for inertial particles in turbulence: I. Spatial distribution of particles

2014

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In this paper, we contrast two theoretical models for the spatial clustering of inertial particles in isotropic turbulence, one by Chun et al (2005 J. Fluid Mech. 536 219) and the other by Zaichik et al (2007 Phys. Fluids 19 113308). Although their predictions for the radial distribution function are similar in the regime ≪ St 1, they appear to describe the physical mechanism responsible for the clustering in quite different ways. We demonstrate why the theories generate such similar results in the regime ≪ St 1 by showing that the clustering mechanism in the Chun et al theory captures the leading order effects of the clustering mechanism in the Zaichik et al theory for ≪ St 1. However, outside of this regime, the similarity between the predictions of the theories breaks down, and we consider the sources of the differences as well as the physical meaning and implications of the differences. Using DNS data we then show that the clustering mechanism described by the Zaichik et al theory accurately describes the clustering up to ≈ St 1, and we identify a possible source of error for some of the slight quantitative discrepancies at larger St. We then compare these theories with others in the literature and attempt to reconcile as many of the physical explanations for clustering as we can. Finally, we consider the relationship between clustering in isotropic turbulence and the near-wall accumulation of Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. inertial particles in a turbulent boundary layer, and how they scale with the Stokes number in the weak inertia limit. New J. Phys. 16 (2014) 055013 A D Bragg and L R Collins 2 particle inertia. Here and throughout, τ τ = η St pwhere τ p is the particle response time and τ η is the Kolmogorov time scale. There are two aspects of clustering that are important to keep in mind. First, clustering peaks at Stokes numbers near unity and rapidly falls off for smaller or larger values. Second, clustering continues to increase at separation distances below the Kolmogorov length scale (the smallest scale of motion of the turbulence), implying no inner cutoff of the mechanism driving the particles together.Theories that describe and predict inertial particle clustering are simultaneously under development. Some, based on a phenomenological description of the process, capture clustering reasonably well [28,29], but do not yield new physical insights into the phenomenon. Others make assumptions about the turbulence that cannot be fully justified, such as white noise in time [30] or finite-time correlations that are significantly shorter than in real turbulence [31]. Two theories by Chun et al [32] and Zaichik et al [33] (hereafter CT and ZT, respectively) are based on similar descriptions of the turbulence, focus on sub-Kolmogorov scale clustering, and for small particles yield similar predictions in ...

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“…Particles are rapidly dispersed throughout most of the turbulent flow but are 'trapped' near the wall for longer durations. This results in higher particle concentrations in a thin layer adjacent to the wall and interactions between particles and near wall coherent structures become important (Marchioli and Soldati, 2002;Sikovsky, 2014).…”

Section: Introductionmentioning

confidence: 99%

Predicting the impact of particle-particle collisions on turbophoresis with a reduced number of computational particles

Johnson

2020

International Journal of Multiphase Flow

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A common feature of wall-bounded turbulent particle-laden flows is enhanced particle concentrations in a thin layer near the wall due to a phenomenon known as turbophoresis. Even at relatively low bulk volume fractions, particleparticle collisions regulate turbophoresis in a critical way, making simulations sensitive to collisional effects. Lagrangian tracking of every particle in the flow can become computationally expensive when the physical number of particles in the system is large. Artificially reducing the number of particles in the simulation can mitigate the computational cost. When particle-particle collisions are an important aspect determining the simulation outcome, as in the case when turbophoresis plays an active role, simply reducing the number of particles in the simulation significantly alters the computed particle statistics. This paper introduces a computational particle treatment for particle-particle collisions which reproduces the results of a full simulation with a reduced number of particles. This is accomplished by artificially enhancing the particle collision radius based on scaling laws for the collision rates. The proposed method retains the use of deterministic collision models and is applicable for both low and high Stokes number regimes.

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Singularity of Inertial Particle Concentration in the Viscous Sublayer of Wall-bounded Turbulent Flows

Cited by 25 publications

References 39 publications

New insights from comparing statistical theories for inertial particles in turbulence: II. Relative velocities

New insights from comparing statistical theories for inertial particles in turbulence: II. Relative velocities

New insights from comparing statistical theories for inertial particles in turbulence: I. Spatial distribution of particles

Predicting the impact of particle-particle collisions on turbophoresis with a reduced number of computational particles

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