Single and two-particle motion of heavy particles in turbulence (original) (raw)
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Separation of Heavy Particles in Turbulence
Physical Review Letters, 2008
We study motion of small particles in turbulence when the particle relaxation time falls in the range of inertial time scales of the flow. Because of inertia, particles drift relative to the fluid. We demonstrate that the collective drift of two close particles makes them see local velocity increments fluctuate fast. This allows us to introduce Langevin description for separation dynamics. We describe the behavior of the Lyapunov exponent and give the analogue of Richardson's law for separation above viscous scale.
Quantifying Turbulence-Induced Segregation of Inertial Particles
Physical Review Letters, 2008
Particles with density different from that of the advecting fluid cluster due to the different response of light/heavy particles to turbulent fluctuations. This study focuses on the quantitative characterization of the segregation of dilute poly-disperse inertial particles evolving in turbulent flow, as obtained from Direct Numerical Simulation of homogeneous isotropic turbulence. We introduce an indicator of segregation amongst particles of different inertia and/or size, from which a length scale rseg, quantifying the segregation degree between two particle types, is deduced. The ability of efficiently mixing transported substances is one of the most distinctive properties of turbulence, which is ubiquitous in geophysical and astrophysical fluids. New features appear when turbulent flows are seeded with finite-size particulate matter having density ρ p different from the carrier fluid density ρ f . Due to inertia, measured by the Stokes time τ = a 2 /(3βν) (a being the particle radius and ν the fluid viscosity; β = 3ρ f /(2ρ p + ρ f )), such particles detach from fluid parcels' paths and distribute inhomogeneously [1, 2, 3]. Although this phenomenon of preferential concentration [4] has been known for a long time , it continues to attract much attention (see and ref. therein). It is important for drag reduction by microbubbles , for the effects of microbubbles on the small scales of turbulence [13], for aerosol physics which is critical for climatological models , or to understand the patchiness of chemical and biological agents in the oceans . The key issue is the tendency of inertial particles to form clusters with the consequent enhancement of the particle interaction rate.
Measuring segregation of inertial particles in turbulence by a full Lagrangian approach
Physical Review E, 2009
Preferential concentration of inertial particles in turbulence is studied numerically by evaluating the Lagrangian compressibility of the particle velocity field using the "full Lagrangian method." This is compared with the "mesoscopic Eulerian particle velocity field" both in a direct numerical simulation of turbulence and in a synthetic flow field. We demonstrate that the Lagrangian method, in contrast to the Eulerian, accurately predicts the compressibility of the particle velocity field even when the latter is characterized by singularities. In particular we use the method to evaluate the growth rates of spatial moments of the particle number density which reflect the fractal structure of segregation and the occurrence of singularities.
On the collision rate of small particles in isotropic turbulence. I. Zero-inertia case
Physics of Fluids, 1998
Numerical experiments have been performed to study the geometric collision rate of heavy particles with finite inertia. The turbulent flow was generated by direct numerical integration of the full Navier-Stokes equations. The collision kernel peaked at a particle response time between the Kolmogorov and the large-eddy turnover times, implying that both the large-scale and small-scale fluid motions contribute, although in very different manners, to the collision rate. Both numerical results for frozen turbulent fields and a stochastic theory show that the collision kernel approaches the kinetic theory of Abrahamson ͓Chem. Eng. Sci. 30, 1371 ͑1975͔͒ only at very large p /T e , where p is the particle response time and T e is the flow integral time scale. Our results agree with those of Sundaram and Collins ͓J. Fluid Mech. 335, 75 ͑1997͔͒ for an evolving flow. A rapid increase of the collision kernel with the particle response time was observed for small p / k , where k is the flow Kolmogorov time scale. A small inertia of p / k ϭ0.5 can lead to an order of magnitude increase in the collision kernel relative to the zero-inertia particles. A scaling law for the collision kernel at small p / k was proposed and confirmed numerically by varying the particle size, inertial response time, and flow Reynolds number. A leading-order theory for small p / k was developed, showing that the enhanced collision is mainly a result of the nonuniform particle concentration that results from the interaction of heavy particles with local flow microstructures.
On the collision rate of small particles in isotropic turbulence. II. Finite inertia case
Physics of Fluids, 1998
Numerical experiments have been performed to study the geometric collision rate of heavy particles with finite inertia. The turbulent flow was generated by direct numerical integration of the full Navier-Stokes equations. The collision kernel peaked at a particle response time between the Kolmogorov and the large-eddy turnover times, implying that both the large-scale and small-scale fluid motions contribute, although in very different manners, to the collision rate. Both numerical results for frozen turbulent fields and a stochastic theory show that the collision kernel approaches the kinetic theory of Abrahamson ͓Chem. Eng. Sci. 30, 1371 ͑1975͔͒ only at very large p /T e , where p is the particle response time and T e is the flow integral time scale. Our results agree with those of Sundaram and Collins ͓J. Fluid Mech. 335, 75 ͑1997͔͒ for an evolving flow. A rapid increase of the collision kernel with the particle response time was observed for small p / k , where k is the flow Kolmogorov time scale. A small inertia of p / k ϭ0.5 can lead to an order of magnitude increase in the collision kernel relative to the zero-inertia particles. A scaling law for the collision kernel at small p / k was proposed and confirmed numerically by varying the particle size, inertial response time, and flow Reynolds number. A leading-order theory for small p / k was developed, showing that the enhanced collision is mainly a result of the nonuniform particle concentration that results from the interaction of heavy particles with local flow microstructures.
Relative Diffusion of a Pair of Fluid Particles in Turbulence
Journal of the Physical Society of Japan, 1989
Turbulent diffusion of a pair of fluid particles in 3-dimensional homogeneous and isotropic turbulence was studied using a high-resolution direct numerical simulation ͑DNS͒ with 1024 3 grid points. The DNS showed that the mean square of the distance ␦x between the two fluid particles grows with time t as ͉͗␦x͉ 2 ͘ϳC⑀t 3 in the inertial subrange, which is in agreement with Richardson ͑1926͒ and Obukhov ͑1941͒, where CϷ0.7 and ⑀ is the mean dissipation rate per unit mass. A simple Lagrangian closure approximation for ͉͗␦x͉ 2 ͘ is shown to be in good agreement with the DNS.
Particle drift in turbulent flows: the influence of local structure and inhomogeneity
The way particles interact with turbulent structures, particularly in regions of high vorticity and strain rate, has been investigated in simulations of homogeneous turbulence and in simple flows which have a periodic or persistent structure e.g. separating flows and mixing layers. The influence on both settling under gravity and diffusion has been reported and the divergence (compressibility) of the underlying particle velocity field along a particle trajectory has been recognized as an important quantity in quantifying these features. This paper shows how these features can be incorporated in a formal way into a two-fluid model of the dispersed particle phase. In particular the PDF equation for the particle velocity and position is formerly derived on the basis of a stochastic process that involves the statistics of both the particle velocity and local compressibility along particle trajectories. The PDF equation gives rise to contributions to both the drift and particle diffusion...
2012
We consider a dilute gas of inertial particles transported by the turbulent flow. Due to inertia the particles concentrate preferentially outside vortices. The pair-correlation function of the particles' concentration is known to obey at small separations a power-law with a negative exponent, if the hydrodynamic interactions between the particles are neglected. The divergence at zero separation is the signature of the random attractor asymptoted by the particles' trajectories at large times. However the hydrodynamic interactions produce a repulsion between the particles that is non-negligible at small separations. We introduce equations governing the repulsion and show it smoothens the singular attractor near the particles where the pair correlation function saturates. The effect is most essential at the Stokes number of order one, where the correlations decrease by a factor of a few.
Lagrangian statistics of particle pairs in homogeneous isotropic turbulence
Physics of Fluids, 2005
We present a detailed investigation of the particle pair separation process in homogeneous isotropic turbulence. We use data from direct numerical simulations up to R λ ∼ 280 following the evolution of about two million passive tracers advected by the flow over a time span of about three decades. We present data for both the separation distance and the relative velocity statistics. Statistics are measured along the particle pair trajectories both as a function of time and as a function of their separation, i.e. at fixed scales. We compare and contrast both sets of statistics in order to gain an insight into the mechanisms governing the separation process. We find very high levels of intermittency in the early stages, that is, for travel times up to order ten Kolmogorov time scales. The fixed scale statistics allow us to quantify anomalous corrections to Richardson diffusion in the inertial range of scales for those pairs that separate rapidly. It also allows a quantitative analysis of intermittency corrections for the relative velocity statistics.
Physical Review Letters, 2012
We present a numerical study of two-particle dispersion from point-sources in 3D incompressible Homogeneous and Isotropic turbulence, at Reynolds number Re ≃ 300. Tracer particles are emitted in bunches from localized sources smaller than the Kolmogorov scale. We report the first quantitative evidence, supported by an unprecedented statistics, of the deviations of relative dispersion from Richardson's picture. Deviations are due to extreme events of pairs separating much faster than average, and of pairs remaining close for long times. The two classes of events are the fingerprint of complete different physics, the former being dominated by inertial subrange and large-scale fluctuations, while the latter by the dissipation subrange. A comparison of relative separation in surrogate white-in-time velocity field, with correct viscous-, inertial-and integral-scale properties allows us to assess the importance of temporal correlations along tracer trajectories.