scholarly journals Single inertial particle statistics in turbulent flows from Lagrangian velocity models

2022 ◽  
Vol 7 (1) ◽  
Author(s):  
Jan Friedrich ◽  
Bianca Viggiano ◽  
Mickael Bourgoin ◽  
Raúl Bayoán Cal ◽  
Laurent Chevillard
Keyword(s):  
Turbulent Flows ◽  
Inertial Particle ◽  
Velocity Models ◽  
Lagrangian Velocity ◽  
Particle Statistics

scholarly journals Lagrangian Velocity Statistics in Turbulent Flows: Effects of Dissipation

2003 ◽  
Vol 91 (21) ◽  
Author(s):  
L. Chevillard ◽  
S. G. Roux ◽  
E. Levêque ◽  
N. Mordant ◽  
J.-F. Pinton ◽  
...  
Keyword(s):  
Turbulent Flows ◽  
Velocity Statistics ◽  
Lagrangian Velocity

scholarly journals TURBULENCE DRIVEN BY FARADAY SURFACE WAVES

2014 ◽  
Vol 34 ◽  
pp. 1460379 ◽  
Author(s):  
MICHAEL SHATS ◽  
NICOLAS FRANCOIS ◽  
HUA XIA ◽  
HORST PUNZMANN
Keyword(s):  
Turbulent Flows ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Spectral Energy ◽  
Vertical Acceleration ◽  
Faraday Waves ◽  
Frequency Spectra ◽  
Inverse Energy Cascade ◽  
Lagrangian Velocity ◽  
Measuring Frequency

We report experimental results which show that the particle motion on the surface perturbed by Faraday waves is similar to the fluid motion in 2D turbulence. It supports the inverse energy cascade or the spectral energy transfer from smaller to larger scales. The vertical acceleration ranges from the Faraday instability threshold up to the droplet nucleation threshold where the ripples are a couple of millimeters high. Such a configuration rules out any 2D assumption on the fluid motion. The motion of floaters on the surface of the Faraday waves is essentially three dimensional but its horizontal component shows unexpected analogy with two-dimensional turbulence. The presence of the inverse cascade is detected by measuring frequency spectra of the Lagrangian velocity and confirmed by computing the third moment of the horizontal Eulerian velocity fluctuations. This is a robust phenomenon observed in deep water in a broad range of flow energies and wavelengths. The emergence of such a phenomenology in Faraday waves broadens the applicability of features common to 2D turbulent flows to the context of surface wave phenomena which is prevalent in many systems.

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 Relative velocity of inertial particles in turbulent flows

2010 ◽  
Vol 661 ◽  
pp. 73-107 ◽  
Author(s):  
LIUBIN PAN ◽  
PAOLO PADOAN
Keyword(s):  
Turbulent Flows ◽  
Relative Velocity ◽  
Reynolds Numbers ◽  
Inertial Range ◽  
Inertial Particles ◽  
Inertial Particle ◽  
Two Phase ◽  
Time Dispersion ◽  
Particle Pairs ◽  
Acceleration Term

We present a model for the relative velocity of inertial particles in turbulent flows that provides new physical insight into this problem. Our general formulation shows that the relative velocity has contributions from two terms, referred to as the ‘generalized acceleration’ and ‘generalized shear’, because they reduce to the well-known acceleration and shear terms in the Saffman–Turner limit. The generalized shear term represents particles' memory of the flow velocity difference along their trajectories and depends on the inertial particle pair dispersion backward in time. The importance of this backward dispersion in determining the particle relative velocity is emphasized. We find that our model with a two-phase separation behaviour, an early ballistic phase and a later tracer-like phase, as found by recent simulations for the forward (in time) dispersion of inertial particle pairs, gives good fits to the measured relative speeds from simulations at low Reynolds numbers. In the monodisperse case with identical particles, the generalized acceleration term vanishes and the relative velocity is determined by the generalized shear term. At large Reynolds numbers, our model gives a St1/2-dependence of the relative velocity on the Stokes number St in the inertial range for both the ballistic behaviour and the Richardson separation law. This leads to the same inertial-range scaling for the two-phase separation that well fits the simulation results. Our calculations for the bidisperse case show that, with the friction timescale of one particle fixed, the relative speed as a function of the other particle's friction time has a dip when the two timescales are similar. This indicates that similar-size particles tend to have stronger velocity correlation than different ones. We find that the primary contribution at the dip, i.e. for similar particles, is from the generalized shear term, while the generalized acceleration term is dominant for particles of very different sizes. Future numerical studies are motivated to check the accuracy of the assumptions made in our model and to investigate the backward-in-time dispersion of inertial particle pairs in turbulent flows.

scholarly journals A phenomenological theory of Eulerian and Lagrangian velocity fluctuations in turbulent flows

2012 ◽  
Vol 13 (9-10) ◽  
pp. 899-928 ◽  
Author(s):  
Laurent Chevillard ◽  
Bernard Castaing ◽  
Alain Arneodo ◽  
Emmanuel Lévêque ◽  
Jean-François Pinton ◽  
...  
Keyword(s):  
Turbulent Flows ◽  
Phenomenological Theory ◽  
Velocity Fluctuations ◽  
Lagrangian Velocity
Sign in / Sign up

Export Citation Format

Share Document