Preferential concentration and relative velocity statistics of inertial particles in Navier–Stokes turbulence with and without filtering

2011 ◽  
Vol 680 ◽  
pp. 488-510 ◽  
Author(s):  
BAIDURJA RAY ◽  
LANCE R. COLLINS
Keyword(s):  
Velocity Field ◽  
Time Scale ◽  
Relative Velocity ◽  
Stokes Number ◽  
Separation Distance ◽  
Inertial Particles ◽  
Subgrid Scale ◽  
Preferential Concentration ◽  
P 75 ◽  
Particle Statistics

The radial distribution function (RDF, a statistical measure of preferential concentration), and the relative velocity measured along the line-of-centres of two particles are the key statistical inputs to the collision kernel for finite-inertia particles suspended in a turbulent flow Sundaram & Collins (J. Fluid Mech., vol. 335, 1997, p. 75). In this paper, we investigate the behaviour of these two-particle statistics using direct numerical simulation (DNS) of homogeneous isotropic turbulence. While it is known that the RDF for particles of any Stokes number (St) decreases with separation distance Sundaram & Collins (J. Fluid Mech., vol. 335, 1997, p. 75), Reade & Collins (Phys. Fluids, vol. 12, 2000, p. 2530), Salazar et al. (J. Fluid Mech., vol. 600, 2008, p. 245), we observe that the peak in the RDF versus St curve shifts to higher St as we increase the separation distance. Here, St is defined as the ratio of the particle's viscous relaxation time to the Kolmogorov time-scale of the flow. Furthermore, as found in a previous study Wang, Wexler, & Zhou (J. Fluid Mech., vol. 415, 2000, p. 117), the variance of the radial relative velocity (wr) is found to increase monotonically with increasing separation distance and increasing Stokes number; however, we show for the first time that the parameteric variation of the skewness of wr with St and r/η is qualitatively similar to that of the RDF, and points to a connection between the two. We then apply low-pass filters (using three different filter scales) on the DNS velocity field in wavenumber space in order to produce ‘perfect’ large-eddy simulation (LES) velocity fields without any errors associated with subgrid-scale modelling. We present visual evidence of the effect of sharp-spectral filtering on the flow structure and the particle field. We calculate the particle statistics in the filtered velocity field and find that the RDF decreases with filtering at low St and increases with filtering at high St, similar to Fede & Simonin (Phys. Fluids, vol. 18, 2006, p. 045103). We also find that the variation of the RDF with St shifts towards higher St with filtering at all separation distances. The variance of wr is found to decrease with filtering for all St and separation distances, but the skewness of wr shows a non-monotonic response to filtering that is qualitatively similar to the RDF. We consider the variation of the RDF and moments of wr with filter scale and find that they are approximately linear in the inertial range. We demonstrate that a simple model consisting of a redefinition of the St based on the time-scale of the filtered velocity field cannot recover the unfiltered statistics. Our findings provide insight on the effect of subgrid-scale eddies on the RDF and wr, and establish the requirements of a LES model for inertial particles that can correctly predict clustering and collisional behaviour.

Lift Force Effects on the Behavior of Bubbles in Homogeneous Isotropic Turbulence

2005 ◽  
Author(s):  
Mustapha Abbad ◽  
Benoiˆt Oesterle´
Keyword(s):  
Relative Velocity ◽  
Lift Force ◽  
Isotropic Turbulence ◽  
Stokes Number ◽  
Rise Velocity ◽  
Homogeneous Isotropic Turbulence ◽  
Preferential Concentration ◽  
Coupling Approximation ◽  
Lagrangian Tracking ◽  
Small Bubbles

The influence of lift forces on the dispersion of small bubbles is numerically studied in a homogeneous isotropic turbulence generated by random Fourier modes, under one-way coupling approximation. The effects of bubble Stokes number and mean relative velocity are investigated by computing the statistics from Lagrangian tracking of a large number of bubbles in many flow field realizations, and comparison is provided between the results obtained with and without taking the lift force into account. The effects of preferential concentration, which are known to reduce the terminal rise velocity of bubbles, are also investigated. The lift force is found to drastically modify the correlations and integral time scales of the fluid seen by the bubbles in their fluctuating motion, and to significantly enhance the accumulation of bubbles in high vorticity regions.

scholarly journals The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 1. Simulations without gravitational effects

2016 ◽  
Vol 796 ◽  
pp. 617-658 ◽  
Author(s):  
Peter J. Ireland ◽  
Andrew D. Bragg ◽  
Lance R. Collins
Keyword(s):  
Reynolds Number ◽  
Relative Velocity ◽  
Isotropic Turbulence ◽  
Reynolds Numbers ◽  
Inertial Particles ◽  
Inertial Particle ◽  
Physical Mechanisms ◽  
Preferential Sampling ◽  
Velocity Statistics ◽  
Particle Statistics

In this study, we analyse the statistics of both individual inertial particles and inertial particle pairs in direct numerical simulations of homogeneous isotropic turbulence in the absence of gravity. The effect of the Taylor microscale Reynolds number, $R_{{\it\lambda}}$, on the particle statistics is examined over the largest range to date (from $R_{{\it\lambda}}=88$ to 597), at small, intermediate and large Kolmogorov-scale Stokes numbers $St$. We first explore the effect of preferential sampling on the single-particle statistics and find that low-$St$ inertial particles are ejected from both vortex tubes and vortex sheets (the latter becoming increasingly prevalent at higher Reynolds numbers) and preferentially accumulate in regions of irrotational dissipation. We use this understanding of preferential sampling to provide a physical explanation for many of the trends in the particle velocity gradients, kinetic energies and accelerations at low $St$, which are well represented by the model of Chun et al. (J. Fluid Mech., vol. 536, 2005, pp. 219–251). As $St$ increases, inertial filtering effects become more important, causing the particle kinetic energies and accelerations to decrease. The effect of inertial filtering on the particle kinetic energies and accelerations diminishes with increasing Reynolds number and is well captured by the models of Abrahamson (Chem. Engng Sci., vol. 30, 1975, pp. 1371–1379) and Zaichik & Alipchenkov (Intl J. Multiphase Flow, vol. 34 (9), 2008, pp. 865–868), respectively. We then consider particle-pair statistics, and focus our attention on the relative velocities and radial distribution functions (RDFs) of the particles, with the aim of understanding the underlying physical mechanisms contributing to particle collisions. The relative velocity statistics indicate that preferential sampling effects are important for $St\lesssim 0.1$ and that path-history/non-local effects become increasingly important for $St\gtrsim 0.2$. While higher-order relative velocity statistics are influenced by the increased intermittency of the turbulence at high Reynolds numbers, the lower-order relative velocity statistics are only weakly sensitive to changes in Reynolds number at low $St$. The Reynolds-number trends in these quantities at intermediate and large $St$ are explained based on the influence of the available flow scales on the path-history and inertial filtering effects. We find that the RDFs peak near $St$ of order unity, that they exhibit power-law scaling for low and intermediate $St$ and that they are largely independent of Reynolds number for low and intermediate $St$. We use the model of Zaichik & Alipchenkov (New J. Phys., vol. 11, 2009, 103018) to explain the physical mechanisms responsible for these trends, and find that this model is able to capture the quantitative behaviour of the RDFs extremely well when direct numerical simulation data for the structure functions are specified, in agreement with Bragg & Collins (New J. Phys., vol. 16, 2014a, 055013). We also observe that at large $St$, changes in the RDF are related to changes in the scaling exponents of the relative velocity variances. The particle collision kernel closely matches that computed by Rosa et al. (New J. Phys., vol. 15, 2013, 045032) and is found to be largely insensitive to the flow Reynolds number. This suggests that relatively low-Reynolds-number simulations may be able to capture much of the relevant physics of droplet collisions and growth in the adiabatic cores of atmospheric clouds.

scholarly journals The effect of turbulence on mass transfer rates between inertial polydisperse particles and fluid

2019 ◽  
Vol 874 ◽  
pp. 1147-1168 ◽  
Author(s):  
Ewa Karchniwy ◽  
Adam Klimanek ◽  
Nils Erland L. Haugen
Keyword(s):  
Mass Transfer ◽  
Time Scale ◽  
Transfer Rate ◽  
Particle System ◽  
Mass Transfer Rate ◽  
Stokes Number ◽  
Flow Time ◽  
Inertial Particles ◽  
Integral Scale ◽  
Order Of Magnitude

The current work investigates how turbulence affects the mass transfer rate between inertial particles and fluid in a dilute, polydisperse particle system. Direct numerical simulations are performed in which all scales of turbulence are fully resolved and particles are represented in a Lagrangian reference frame. The results show that, similarly to a monodisperse system, the mass transfer rate between particles and fluid decreases as a result of particle clustering. This occurs when the flow time scale (based on the turbulence integral scale) is long relative to the chemical time scale, and is strongest when the particle time scale is one order of magnitude smaller than the flow time scale (i.e. the Stokes number is around 0.1). It is also found that for larger solid mass fractions, the clustering of the heavier particles is enhanced by the effect of drag force from the particles on the fluid (momentum back-reactions or two-way coupling). In particular, when two-way coupling is accounted for, locations of particles of different sizes are much more correlated, which leads to a stronger effect of clustering, and thus a greater reduction of the particle–fluid mass transfer rate.

Snowflakes in the atmospheric surface layer: observation of particle–turbulence dynamics

2017 ◽  
Vol 814 ◽  
pp. 592-613 ◽  
Author(s):  
Andras Nemes ◽  
Teja Dasari ◽  
Jiarong Hong ◽  
Michele Guala ◽  
Filippo Coletti
Keyword(s):  
Large Scale ◽  
Isotropic Turbulence ◽  
Volume Fraction ◽  
Response Times ◽  
Field Measurements ◽  
Stokes Number ◽  
Inertial Particles ◽  
Natural Setting ◽  
Scale Particle ◽  
Particle Imaging

We report on optical field measurements of snow settling in atmospheric turbulence at $Re_{\unicode[STIX]{x1D706}}=940$. It is found that the snowflakes exhibit hallmark features of inertial particles in turbulence. The snow motion is analysed in both Eulerian and Lagrangian frameworks by large-scale particle imaging, while sonic anemometry is used to characterize the flow field. Additionally, the snowflake size and morphology are assessed by digital in-line holography. The low volume fraction and mass loading imply a one-way interaction with the turbulent air. Acceleration probability density functions show wide exponential tails consistent with laboratory and numerical studies of homogeneous isotropic turbulence. Invoking the assumption that the particle acceleration has a stronger dependence on the Stokes number than on the specific features of the turbulence (e.g. precise Reynolds number and large-scale anisotropy), we make inferences on the snowflakes’ aerodynamic response time. In particular, we observe that their acceleration distribution is consistent with that of particles of Stokes number in the range $St=0.1{-}0.4$ based on the Kolmogorov time scale. The still-air terminal velocities estimated for the resulting range of aerodynamic response times are significantly smaller than the measured snow particle fall speed. This is interpreted as a manifestation of settling enhancement by turbulence, which is observed here for the first time in a natural setting.

scholarly journals Concentration and velocity statistics of inertial particles in upward and downward pipe flow

2017 ◽  
Vol 822 ◽  
pp. 640-663 ◽  
Author(s):  
J. L. G. Oliveira ◽  
C. W. M. van der Geld ◽  
J. G. M. Kuerten
Keyword(s):  
Liquid Velocity ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Stokes Number ◽  
Terminal Velocity ◽  
Point Particle ◽  
Inertial Particles ◽  
Carrier Fluid ◽  
Velocity Statistics ◽  
The Difference

Three-dimensional particle tracking velocimetry is applied to particle-laden turbulent pipe flows at a Reynolds number of 10 300, based on the bulk velocity and the pipe diameter, for developed fluid flow and not fully developed flow of inertial particles, which favours assessment of the radial migration of the inertial particles. Inertial particles with Stokes number ranging from 0.35 to 1.11, based on the particle relaxation time and the radial-dependent Kolmogorov time scale, and a ratio of the root-mean-square fluid velocity to the terminal velocity of order 1 have been used. Core peaking of the concentration of inertial particles in up-flow and wall peaking in down-flow have been found. The difference in mean particle and Eulerian mean liquid velocity is found to decrease to approximately zero near the wall in both flow directions. Although the carrier fluid has all of the characteristics of the corresponding turbulent single-phase flow, the Reynolds stress of the inertial particles is different near the wall in up-flow. These findings are explained from the preferential location of the inertial particles with the aid of direct numerical simulations with the point-particle approach.

Motion of Descending Solid Particles and Local Flow Around the Particles in Downward Turbulent Water Duct Flow (Keynote)

2011 ◽  
Author(s):  
Yoshimichi Hagiwara ◽  
Hideto Fujii ◽  
Katsutoshi Sakurai ◽  
Takashi Kuroda ◽  
Atsuhide Kitagawa
Keyword(s):  
Reynolds Number ◽  
Time Scale ◽  
High Speed ◽  
Fluid Velocity ◽  
Stokes Number ◽  
Solid Particles ◽  
Duct Flow ◽  
Local Flow ◽  
Particle Reynolds Number ◽  
Turbulent Water

The Stokes number, the ratio of the particle time scale to flow time scale, is a promising quantity for estimating changes in statistics of turbulence due to particles. First, we explored the Stokes numbers in some recent studies. Secondly, we discussed the results of our direct numerical simulation for turbulent flow with a high-density particle in a vertical duct. In the discussion, we defined the particle Reynolds number from the mean fluid velocity in the near-particle region at any time. We evaluated a new local Stokes number for the particle. It is found that the Stokes number is effective for the prediction of the distance between the particle center and one wall. Finally, we carried out experiments for turbulent water flow with aluminum balls of 1 mm in diameter in a vertical channel. The motions of aluminum balls and tracer particles in the flow were captured with a high-speed video camera. We found that the experimental results for the time changes in the wall-normal distance of the ball and the particle Reynolds number for the ball are similar to the predicted results.

Two-Fluid Large-Eddy Simulation Approach for Gas-Particle Turbulent Flows Using Equilibrium Assumption

2006 ◽  
Author(s):  
Babak Shotorban ◽  
S. Balachandar
Keyword(s):  
Velocity Field ◽  
Gas Phase ◽  
Turbulent Flows ◽  
Particle Concentration ◽  
Particle Flux ◽  
Subgrid Scale ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Scale Particle ◽  
Two Fluid

This article illustrates a two-fluid large-eddy simulation (LES) approach for gas-particle turbulent flows. The equilibrium assumption in which the velocity of particles is approximated in terms of the velocity and acceleration of the gas phase, is made for the development of gas-particle LES formulation in this study. A filtered Eulerian velocity field is defined for particles and expressed in terms of the temporal and spatial derivatives of the gas-phase filtered velocity field. Also, filtered particle concentration defined in the Eulerian framework is governed by a transport equation with a closure problem resulted from filtering the particle concentration nonlinear convection term and in the form of subgrid-scale particle flux. A Smagorinsky kind of formulation is used to model the subgrid-scale particle flux and close the transport equation of the filtered particle concentration. The developed gas-particle LES formulation is implemented in a homogeneous shear turbulence configuration and results are discussed. It is shown that the equilibrium assumption is valid for sufficiently small particle time constants through conducting the direct numerical simulation of the same configuration.

scholarly journals On the transition between turbulence regimes in particle-laden channel flows

2018 ◽  
Vol 845 ◽  
pp. 499-519 ◽  
Author(s):  
Jesse Capecelatro ◽  
Olivier Desjardins ◽  
Rodney O. Fox
Keyword(s):  
Reynolds Number ◽  
Fluid Phase ◽  
Stokes Number ◽  
Channel Flows ◽  
High Mass ◽  
Inertial Particles ◽  
Mass Loading ◽  
Two Phase ◽  
Phase Dynamics ◽  
Wide Range

Turbulent wall-bounded flows exhibit a wide range of regimes with significant interaction between scales. The fluid dynamics associated with single-phase channel flows is predominantly characterized by the Reynolds number. Meanwhile, vastly different behaviour exists in particle-laden channel flows, even at a fixed Reynolds number. Vertical turbulent channel flows seeded with a low concentration of inertial particles are known to exhibit segregation in the particle distribution without significant modification to the underlying turbulent kinetic energy (TKE). At moderate (but still low) concentrations, enhancement or attenuation of fluid-phase TKE results from increased dissipation and wakes past individual particles. Recent studies have shown that denser suspensions significantly alter the two-phase dynamics, where the majority of TKE is generated by interphase coupling (i.e.  drag) between the carrier gas and clusters of particles that fall near the channel wall. In the present study, a series of simulations of vertical particle-laden channel flows with increasing mass loading is conducted to analyse the transition from the dilute limit where classical mean-shear production is primarily responsible for generating fluid-phase TKE to high-mass-loading suspensions dominated by drag production. Eulerian–Lagrangian simulations are performed for a wide range of particle loadings at two values of the Stokes number, and the corresponding two-phase energy balances are reported to identify the mechanisms responsible for the observed transition.

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