Particle transport in a turbulent boundary layer: Non-local closures for particle dispersion tensors accounting for particle-wall interactions

Bragg, Andrew D.; Swailes, David; Skartlien, R.

doi:10.1063/1.4757657

Cited by 16 publications

(18 citation statements)

References 31 publications

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“…However in contrast to the RDF, the non-local corrections have a relatively weak effect on the ZT predictions for S p 2 . The reason is that the equation for S p 2 is influenced by μ much more than λ, and μ, unlike λ, is only weakly non-local [39]. It is clear from the above results that while the theories are able to describe the qualitative features of S p 2 , there is still some way to go before they will be capable of making quantitatively accurate predictions.…”

Section: Comparing Theory With Dnsmentioning

confidence: 89%

“…A related error in the ZT results from the use of local closures for λ and μ even though they are inherently non-local due to the r dependence of the Δ t u r ( , ) statistics (see Part I for their unclosed definitions). Local closures for these dispersion tensors can be in considerable error [39]; for example, in Part I we introduced a non-local correction to the local closure for the diffusion coefficient λ in the RDF equation, and showed its importance for obtaining accurate predictions of the RDF. However in contrast to the RDF, the non-local corrections have a relatively weak effect on the ZT predictions for S p 2 .…”

Section: Comparing Theory With Dnsmentioning

confidence: 99%

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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: Comparing Theory With Dnsmentioning

confidence: 89%

Section: Comparing Theory With Dnsmentioning

confidence: 99%

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

Bragg

Collins

2014

New J. Phys.

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“…(See Minier & Peirano (2001) and Pai & Subramaniam (2012) for other approaches to modelling the fluid seen by the particles. An anisotropic version of (A 12) can be found in Bragg, Swailes & Skartlien (2012).) In terms of the RA moment equations, the unclosed terms arising due to fluid drag are …”

Section: Appendix a Moment Methods And Reynolds Averagingmentioning

confidence: 99%

On multiphase turbulence models for collisional fluid–particle flows

Fox¹

2014

J. Fluid Mech.

192

215

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Starting from a kinetic theory (KT) model for monodisperse granular flow, the exact Reynolds-averaged (RA) equations are derived for the particle phase in a collisional fluid-particle flow. The corresponding equations for a constant-density fluid phase are derived from a model that includes drag and buoyancy coupling with the particle phase. The fully coupled macroscale/hydrodynamic model, rigorously derived from a kinetic equation for the particles, is written in terms of the particle-phase volume fraction, the particle-phase velocity and the granular temperature (or total granular energy). As derived from the hydrodynamic model, the RA turbulence model solves for the RA particle-phase volume fraction, the phase-averaged (PA) particle-phase velocity, the PA granular temperature and the PA turbulent kinetic energy of the particle phase. Thus, unlike in most previous derivations of macroscale turbulence models for moderately dense granular flows, a clear distinction is made between the PA granular temperature Θ p , which appears in the KT constitutive relations, and the particle-phase turbulent kinetic energy k p , which appears in the turbulent transport coefficients. The exact RA equations contain unclosed terms due to nonlinearities in the hydrodynamic model and we briefly discuss the available closures for these terms. Finally, we demonstrate by comparing model predictions with direct numerical simulation results that even for non-collisional fluid-particle flows it is necessary to provide separate models for Θ p and k p in order to correctly account for the effect of the particle Stokes number and mass loading.

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“…This occurs for St ≫ 1 particles that move ballistically. It also occurs for fluid particles that are fully-mixed at t = 0 (Bragg et al 2012b), since their spatial distribution remains constant and uniform ∀t due to incompressibility. In fact, u z (x p (t), t) = 0 can only occur if δ(x p (t) − x) both fluctuates in time and is also correlated with u z (x, t).…”

Section: Theoretical Framework For Arbitrary Stmentioning

confidence: 99%

Multiscale preferential sweeping of particles settling in turbulence

Tom

Bragg

2019

J. Fluid Mech.

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In a seminal article, Maxey (1987, J. Fluid Mech., 174:441-465) presented a theoretical analysis showing that enhanced particle settling speeds in turbulence occur through the preferential sweeping mechanism, which depends on the preferential sampling of the fluid velocity gradient field by the inertial particles. However, recent Direct Numerical Simulation (DNS) results in Ireland et al. (2016b, J. Fluid Mech., 796:659-711) show that even in a portion of the parameter space where this preferential sampling is absent, the particles nevertheless exhibit enhanced settling velocities. Further, there are several outstanding questions concerning the role of different turbulent flow scales on the enhanced settling, and the role of the Taylor Reynolds number R λ . The analysis of Maxey does not explain these issues, partly since it was restricted to particle Stokes numbers St ≪ 1. To address these issues, we have developed a new theoretical result, valid for arbitrary St, that reveals the multiscale nature of the mechanism generating the enhanced settling speeds. In particular, it shows how the range of scales at which the preferential sweeping mechanism operates depends on St. This analysis is complemented by results from DNS where we examine the role of different flow scales on the particle settling speeds by coarse-graining the underlying flow. The results show how the flow scales that contribute to the enhanced settling depend on St, and that contrary to previous claims, there can be no single turbulent velocity scale that characterizes the enhanced settling speed. The results explain the dependence of the particle settling speeds on R λ , and show how the saturation of this dependence at sufficiently large R λ depends upon St.The results also show that as the Stokes settling velocity of the particles is increased, the flow scales of the turbulence responsible for enhancing the particle settling speed become larger. Finally, we explored the multiscale nature of the preferential sweeping mechanism by considering how particles preferentially sample the fluid velocity gradients coarsegrained at various scales. The results show that while rapidly settling particles do not preferentially sample the fluid velocity gradients, they do preferentially sample the fluid velocity gradients coarse-grained at scales outside of the dissipation range. This explains the findings of Ireland et al., and further illustrates the truly multiscale nature of the mechanism generating enhanced particle settling speeds in turbulence.

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Particle transport in a turbulent boundary layer: Non-local closures for particle dispersion tensors accounting for particle-wall interactions

Cited by 16 publications

References 31 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

On multiphase turbulence models for collisional fluid–particle flows

Multiscale preferential sweeping of particles settling in turbulence

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