scholarly journals Study of Colliding Particle-Pair Velocity Correlation in Homogeneous Isotropic Turbulence

2020 ◽  
Vol 10 (24) ◽  
pp. 9095
Author(s):  
Santiago Lain ◽  
Martin Ernst ◽  
Martin Sommerfeld
Keyword(s):  
Correlation Function ◽  
Turbulent Flow ◽  
Isotropic Turbulence ◽  
Volume Fraction ◽  
Pair Correlation ◽  
Average Kinetic Energy ◽  
Velocity Correlation ◽  
Particle Inertia ◽  
Particle Pair ◽  
Theoretical Approaches

This paper deals with the numerical analysis of the particle inertia and volume fraction effects on colliding particle-pair velocity correlation immersed in an unsteady isotropic homogeneous turbulent flow. Such correlation function is required to build reliable statistical models for inter-particle collisions, in the frame of the Euler–Lagrange approach, to be used in a broad range of two-phase flow applications. Computations of the turbulent flow have been carried out by means of Direct Numerical Simulation (DNS) by the Lattice Boltzmann Method (LBM). Moreover, the dependence of statistical properties of collisions on particle inertia and volumetric fraction is evaluated and quantified. It has been found that collision locations of particles of intermediate inertia, StK~1, occurs in regions where the fluid strain rate and dissipation are higher than the corresponding averaged values at particle positions. Connected with this fact, the average kinetic energy of colliding particles of intermediate inertia (i.e., Stokes number around 1) is lower than the value averaged over all particles. From the study of the particle-pair velocity correlation, it has been demonstrated that the colliding particle-pair velocity correlation function cannot be approximated by the Eulerian particle-pair correlation, obtained by theoretical approaches, as particle separation tends to zero, a fact related with the larger values of the relative radial velocity between colliding particles.

scholarly journals The Extended Symmetry Lie Algebra and the Asymptotic Expansion of the Transversal Correlation Function for the Isotropic Turbulence

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
V. N. Grebenev ◽  
A. N. Grishkov ◽  
M. Oberlack
Keyword(s):  
Correlation Function ◽  
Asymptotic Expansion ◽  
Lie Algebra ◽  
Degrees Of Freedom ◽  
Isotropic Turbulence ◽  
Central Charge ◽  
Riemannian Metrics ◽  
Equivalence Transformation ◽  
Velocity Correlation ◽  
Correlation Tensor

The extended symmetry of the functional of length determined in an affine spaceK3of the correlation vectors for homogeneous isotropic turbulence is studied. The two-point velocity-correlation tensor field (parametrized by the time variablet) of the velocity fluctuations is used to equip this space by a family of the pseudo-Riemannian metricsdl2(t)(Grebenev and Oberlack (2011)). First, we observe the results obtained by Grebenev and Oberlack (2011) and Grebenev et al. (2012) about a geometry of the correlation spaceK3and expose the Lie algebra associated with the equivalence transformation of the above-mentioned functional for the quadratic formdlD22(t)generated bydl2(t)which is similar to the Lie algebra constructed by Grebenev et al. (2012). Then, using the properties of this Lie algebra, we show that there exists a nontrivial central extension wherein the central charge is defined by the same bilinear skew-symmetric formcas for the Witt algebra which measures the number of internal degrees of freedom of the system. For the applications in turbulence, as the main result, we establish the asymptotic expansion of the transversal correlation function for large correlation distances in the frame ofdlD22(t).

DISSIPATIVE PROCESSES IN LOW DENSITY STRONGLY INTERACTING 2D ELECTRON SYSTEMS

2010 ◽  
Vol 24 (25n26) ◽  
pp. 4946-4960
Author(s):  
DAVID NEILSON
Keyword(s):  
Correlation Function ◽  
Pair Correlation Function ◽  
Mode Coupling ◽  
Glassy Phase ◽  
Pair Correlation ◽  
Low Density ◽  
Electron Systems ◽  
Electron Correlations ◽  
Electron Densities ◽  
Theoretical Approaches

A glassy phase in disordered two dimensional (2D) electron systems may exist at low temperatures for electron densities lying intermediate between the Fermi liquid and Wigner crystal limits. The glassy phase is generated by the combined effects of disorder and the strong electron-electron correlations arising from the repulsive Coulomb interactions. Our approach here is motivated by the observation that at low electron densities the electron pair correlation function, as numerically determined for a non-disordered 2D system from Monte Carlo simulations, is very similar to the pair correlation function for a 2D classical system of hard discs. This suggests that theoretical approaches to 2D classical systems of hard discs may be of use in studying the disordered, low density electron problem. We use this picture to study its dynamics on the electron-liquid side of a glass transition. At long times the major relaxation process in the electron-liquid will be a rearrangement of increasingly large groups of the discs, rather than the movement of the discs separately. Such systems have been studied numerically and they display all the characteristics of glassy behaviour. There is a slowing down of the dynamics and a limiting value of the retarded spatial correlations. Motivated by the success of mode-coupling theories for hard spheres and discs in reproducing experimental results in classical fluids, we use the Mori formalism within a mode-coupling theory to obtain semi-quantitative insight into the role of electron correlations as they affect the time response of the weakly disordered 2D electron system at low densities.

scholarly journals Decay of isotropic turbulence in the initial period

1948 ◽  
Vol 193 (1035) ◽  
pp. 539-558 ◽  
Keyword(s):  
Correlation Function ◽  
Isotropic Turbulence ◽  
Initial Period ◽  
Rate Of Change ◽  
Velocity Correlation ◽  
Integral Scale ◽  
Direct Measurements ◽  
Theoretical Predictions ◽  
History Of ◽  
Velocity Correlation Functions

In a previous paper the authors described direct measurements of all the terms in the equation for the rate of change of mean square vorticity in isotropic turbulence. The present paper is concerned with developments arising from the earlier work and with the experimental verification of some recent theoretical investigations. The results of measurements of the turbulent intensity u ' and of λ are presented; these establish that u' -2 and λ 2 are each proportional to the time of decay provided that the time is not too large. Within this initial period of the decay, the double and triple velocity correlation functions are found to maintain their form, i.e. to be self-preserving, for small values of the distance r between the two points at which the correlations are taken. For larger separations the double velocity correlation function changes its form slightly during decay and direct measurements of λ and of the integral scale L show that λ/ L increases during the decay. Theoretical predictions about the shape of the correlation function, for limited ranges of r , at high and at low Reynolds numbers are compared with measurements. Theory has shown that the above decay law cannot persist indefinitely, and the present experiments confirm that the decay law changes in the expected direction when the time is large. A division of the life-history of the turbulence into initial, transition and final periods is suggested; within the initial period, a classification based on the Reynblds number is also possible. Some speculations on the interpretation of the initial period are presented.

scholarly journals SPATIAL STATISTICS FOR SIMULATED PACKINGS OF SPHERES

2011 ◽  
Vol 20 (3) ◽  
pp. 203 ◽  
Author(s):  
Alexander Bezrukov ◽  
Dietrich Stoyan ◽  
Monika Bargieł
Keyword(s):  
Distribution Function ◽  
Correlation Function ◽  
Spatial Statistics ◽  
Volume Fraction ◽  
Pair Correlation ◽  
Simulation Methods ◽  
Coordination Numbers ◽  
Contact Distribution ◽  
Contact Distribution Function ◽  
Random Packings

This paper reports on spatial-statistical analyses for simulated random packings of spheres with random diameters. The simulation methods are the force-biased algorithm and the Jodrey-Tory sedimentation algorithm. The sphere diameters are taken as constant or following a bimodal or lognormal distribution. Standard characteristics of spatial statistics are used to describe these packings statistically, namely volume fraction, pair correlation function of the system of sphere centres and spherical contact distribution function of the set-theoretic union of all spheres. Furthermore, the coordination numbers are analysed.

scholarly journals SOME DENSE RANDOM PACKINGS GENERATED BY THE DEAD LEAVES MODEL

2019 ◽  
Vol 38 (1) ◽  
pp. 3
Author(s):  
Dominique Jeulin
Keyword(s):  
Correlation Function ◽  
Pair Correlation Function ◽  
Random Media ◽  
Volume Fraction ◽  
Pair Correlation ◽  
Sequential Model ◽  
Dead Leaves Model ◽  
The Dead ◽  
Dense Packings ◽  
Random Packings

The intact grains of the dead leaves model enables us to generate random media with non overlapping grains. Using the time non homogeneous sequential model with convex grains, theoretically very dense packings can be generated, up to a full covering of space. For these models, the theoretical volume fraction, the size distribution of grains, and the pair correlation function of centers of grains are given.

Sign in / Sign up

Export Citation Format

Share Document