Particle pair statistics of inertial particles at small separation using stereoscopic particle tracking

Particle pair statistics of inertial particles having average Stokes numbers of 2.1 and 14 are measured in isotropic turbulence at a Reynolds number of Reλ = 240. The radial distribution function (RDF) and mean relative approach velocity are obtained at small separation distances using 2-frame stereoscopic particle tracking velocimetry (stereo-PTV). At small separation distance, the RDF varies by an order of magnitude in the range of Stokes numbers investigated. However, the mean relative approach velocity is found to have a weak dependence on Stokes number. The results are shown to have high accuracy when compared to analogous mono-PTV datasets, and can be used to provide a more reliable estimate of the inter-particle collision rate. The main limitation of the measurement is observed at separation distances less than the laser sheet thickness, where the technique tended to underestimate the mean relative approach velocity.

The Development and Application of a Kinetic Theory for Modelling Dispersed Particle Flows

This Freeman Scholar article reviews the formulation and application of a kinetic theory for modeling the transport and dispersion of small particles in turbulent gas-flows, highlighting the insights and understanding it has provided and some of the long standing problems in the modeling of dispersed flows it has resolved. The theory has been developed and refined by numerous authors and now forms a rational basis for modeling complex particle laden flows. The formalism and methodology of this approach are discussed and the choice of closure of the kinetic equations involved which ensures realizability and well posedness with exact closure for Gaussian carrier flow fields. The historical development is presented and how single particle kinetic equations resolve the problem of closure of the transport equations for particle mass, momentum and kinetic energy /stress (the so called continuum equations) and the treatment of the dispersed phase as a fluid. The mass fluxes associated with the turbulent aerodynamic driving forces and interfacial stresses are shown to be both dispersive and convective in inhomogeneous turbulence with implications for the build up of particles concentration in near wall turbulent boundary layers and particle pair concentration at small separation. It is shown how this approach deals with the natural wall boundary conditions for a flowing particle suspension and examples are given of partially absorbing surfaces with particle scattering, and gravitational settling; how this approach has revealed the existence of contra gradient diffusion in a developing shear flow and the influence of the turbulence on gravitational settling (the Maxey effect). Particular consideration is given to the general problem of particle transport and deposition in turbulent boundary layers and near wall behavior including particle resuspension. Finally the application of a particle pair formulation for both monodisperse and bidisperse particle flows is reviewed where the differences between the two are compared through the influence of collisions on the particle continuum equations and on the particle collision kernel for the clustering of particles and the degree of random uncorrelated motion (RUM) at the small scales of the turbulence. The inclusion of bidisperse particle suspensions implies the application to polydisperse flows and the evolution of particle size distribution.

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

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.

From the particle pair production to the Hawking–Unruh radiation in the maximal acceleration hypothesis

Starting from a nonstandard approach to the Unruh effect, we present a description of the emission of radiation from a black hole that avoids quantization of scalar fields and Bogoliubov transformations, but assumes the existence of a maximal acceleration. In this framework, the description appears closer to the original heuristic Hawking’s point of view, with respect to the standard scenario.