Investigation of sub-Kolmogorov inertial particle pair dynamics in turbulence using novel satellite particle simulations

2013 ◽  
Vol 720 ◽  
pp. 192-211 ◽  
Author(s):  
Baidurja Ray ◽  
Lance R. Collins
Keyword(s):  
Structure Function ◽  
Power Law ◽  
Particle Motion ◽  
Relative Velocity ◽  
Velocity Structure ◽  
Inertial Particles ◽  
Particle Clustering ◽  
Particle Pair ◽  
Velocity Statistics ◽  
Particle Simulations

AbstractClustering (or preferential concentration) of weakly inertial particles suspended in a homogeneous isotropic turbulent flow is driven primarily by the smallest eddies at the so-called Kolmogorov scale. In particle-laden large-eddy simulations (LES), these small scales are not resolved by the grid and hence their effect on both the resolved flow scales and the particle motion have to be modelled. In order to predict clustering in a particle-laden LES, it is crucial that the subgrid model for the particles captures the mechanism by which the subgrid scales affect the particle motion (Ray & Collins, J. Fluid Mech., vol. 680, 2011, pp. 488–510). In this paper, we describe novel satellite particle simulations (SPS), in which we study the clustering and relative velocity statistics of inertial particles at separation distances well below the Kolmogorov length scale. SPS is designed to isolate pairwise interactions of particles, and is therefore well suited for developing two-particle models. We show that the power-law dependence of the radial distribution function (RDF), a statistical measure of clustering, is predicted by the SPS in excellent agreement with direct numerical simulations (DNS) for Stokes numbers up to 3, implying that no explicit information from the inertial range is required to accurately describe particle clustering. This result further explains our successful prediction of the RDF power using the drift-diffusion model of Chun et al. (J. Fluid Mech., vol. 536, 2005, pp. 219–251) for $\mathit{St}\leq 0. 4$. We also consider the second-order longitudinal relative velocity structure function for the particles; we show that the SPS is able to capture its power-law exponent for $\mathit{St}\leq 0. 5$ and attribute the disagreement at larger $\mathit{St}$ to the effect of the larger scales of motion not captured by the SPS. Further, the SPS is able to capture the ‘caustic activation’ of the structure function at zero separation and predict the critical $\mathit{St}$ and rate of activation in agreement with the DNS (Salazar & Collins, J. Fluid. Mech., vol. 696, 2012, pp. 45–66). We show comparisons between filtered DNS and equivalently filtered SPS, and the findings are similar to the unfiltered case. Overall, SPS is an efficient and accurate computational tool for investigating particle pair dynamics at small separations, as well as an interesting platform for developing LES subgrid models designed to accurately reproduce particle clustering.

Inertial particle relative velocity statistics in homogeneous isotropic turbulence

2012 ◽  
Vol 696 ◽  
pp. 45-66 ◽  
Author(s):  
Juan P. L. C. Salazar ◽  
Lance R. Collins
Keyword(s):  
Structure Function ◽  
Relative Velocity ◽  
Velocity Structure ◽  
Structure Functions ◽  
Inertial Subrange ◽  
Inertial Particles ◽  
Inertial Particle ◽  
Scaling Exponents ◽  
Velocity Statistics ◽  
Dissipation Range

AbstractIn the present study, we investigate the scaling of relative velocity structure functions, of order two and higher, for inertial particles, both in the dissipation range and the inertial subrange using direct numerical simulations (DNS). Within the inertial subrange our findings show that contrary to the well-known attenuation in the tails of the one-point acceleration probability density function (p.d.f.) with increasing inertia (Bec et al., J. Fluid Mech., vol. 550, 2006, pp. 349–358), the opposite occurs with the velocity structure function at sufficiently large Stokes numbers. We observe reduced scaling exponents for the structure function when compared to those of the fluid, and correspondingly broader p.d.f.s, similar to what occurs with a passive scalar. DNS allows us to isolate the two effects of inertia, namely biased sampling of the velocity field, a result of preferential concentration, and filtering, i.e. the tendency for the inertial particle velocity to attenuate the velocity fluctuations in the fluid. By isolating these effects, we show that sampling is playing the dominant role for low-order moments of the structure function, whereas filtering accounts for most of the scaling behaviour observed with the higher-order structure functions in the inertial subrange. In the dissipation range, we see evidence of so-called ‘crossing trajectories’, the ‘sling effect’ or ‘caustics’, and find good agreement with the theory put forth by Wilkinson et al. (Phys. Rev. Lett., vol. 97, 2006, 048501) and Falkovich & Pumir (J. Atmos. Sci., vol. 64, 2007, 4497) for Stokes numbers greater than 0.5. We also look at the scaling exponents within the context of the model proposed by Bec et al. (J. Fluid Mech., vol. 646, 2010, pp. 527–536). Another interesting finding is that inertial particles at low Stokes numbers sample regions of higher kinetic energy than the fluid particle field, the converse occurring at high Stokes numbers. The trend at low Stokes numbers is predicted by the theory of Chun et al. (J. Fluid Mech., vol. 536, 2005, 219–251). This work is relevant to modelling the particle collision rate (Sundaram & Collins, J. Fluid Mech., vol. 335, 1997, pp. 75–109), and highlights the interesting array of phenomena induced by inertia.

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.

High-order velocity structure functions in turbulent shear flows

1984 ◽  
Vol 140 ◽  
pp. 63-89 ◽  
Author(s):  
F. Anselmet ◽  
Y. Gagne ◽  
E. J. Hopfinger ◽  
R. A. Antonia
Keyword(s):  
Structure Function ◽  
Power Law ◽  
Lognormal Distribution ◽  
Velocity Structure ◽  
Inertial Range ◽  
Turbulent Shear ◽  
Strict Sense ◽  
Duct Flow ◽  
Power Law Exponent ◽  
Turbulent Duct Flow

Measurements are presented of the velocity structure function on the axis of a turbulent jet at Reynolds numbers Rλ ≤ 852 and in a turbulent duct flow at Rλ = 515. Moments of the structure function up to the eighteenth order were calculated, primarily with a view to establish accurately the dependence on the order of the inertial range power-law exponent and to draw conclusions about the distribution of energy transfer in the inertial range. Adequate definition of the probability density of the structure function was achieved only for moments of order n ≤ 10. It is shown, however, that, although the values of moments of n > 10 diverges from their true values, the dependence of the moment of the structure function on the separation r is still given to a fair accuracy for moments up to n ≈ 18. The results demonstrate that the inertial-range power-law exponent is closely approximated by a quadratic dependence on the power which for lower-order moments (n [lsim ] 12) would be consistent with a lognormal distribution. Higher-order moments diverge, however, from a lognormal distribution, which gives weight to Mandelbrot's (1971) conjecture that ‘Kolmogorov's third hypothesis’ is untenable in the strict sense. The intermittency parameter μ, appearing in the power-law exponent, has been determined from sixth-order moments 〈(δμ)6〉 ∼ r2−μ to be μ = 0.2 ± 0.05. This value coincides with that determined from non-centred dissipation correlations measured in identical conditions.

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.

MULTIFRACTAL CASCADE SYMMETRY MODEL FOR FULLY DEVELOPED TURBULENCE

Fractals ◽  
2018 ◽  
Vol 26 (04) ◽  
pp. 1850070
Author(s):  
G. C. LAYEK ◽  
SUNITA
Keyword(s):  
Structure Function ◽  
Symmetry Group ◽  
Velocity Structure ◽  
Random Parameter ◽  
Continuous Symmetry ◽  
Space Filling ◽  
Support Set ◽  
Developed Turbulence ◽  
Symmetry Model ◽  
Velocity Structure Function

We report a symmetry model for turbulence intermittency. This is obtained by the compositions of continuous symmetry group transformations of statistical turbulent spectral equation at infinite Reynolds number limit. Flow evolution under group compositions yields velocity structure function exponents that depend on the dilation symmetry group parameter [Formula: see text] [Formula: see text] and a random parameter [Formula: see text]. The random parameter [Formula: see text] is associated with energy distribution. Since the correction to the space-filling Kolmogorov cascade is small, the value of [Formula: see text]. The asymptotic structures are filaments having dimension one, so [Formula: see text] is found to be related with [Formula: see text] by [Formula: see text]. The present model therefore depends only on [Formula: see text], and [Formula: see text] can be ascertained uniquely for [Formula: see text]. It is found that the velocity structure function exponents [Formula: see text], [Formula: see text] in present symmetry model agree well with the existing experimental, direct numerical simulation results and different phenomenological models for [Formula: see text]. For these values of [Formula: see text], the correction to Kolmogorov space-filling, universal [Formula: see text] law, belongs to the range [Formula: see text], and the fractal dimension for the support set lies in [Formula: see text].

Doppler lidar alerting algorithm of low-level turbulence based on velocity structure function

2017 ◽  
Vol 46 (10) ◽  
pp. 1030005
Author(s):  
熊兴隆 Xiong Xinglong ◽  
韩永安 Han Yong′an ◽  
蒋立辉 Jiang Lihui ◽  
陈柏纬 Chen Bowei ◽  
陈 星 Chen Xing
Keyword(s):  
Structure Function ◽  
Velocity Structure ◽  
Doppler Lidar ◽  
Low Level ◽  
Velocity Structure Function
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