arXiv subjects

M. W. Reeks

Publications and source records attributed to M. W. Reeks.

5 recordsLinked to original sources

arXiv2025

Kinetic theory based solutions for particle clustering in turbulent flows

Kinetic theory provides an elegant framework for studying dispersed particles in turbulent flows. Here the application of such probability density function (PDF)-based descriptions is considered in the context of particle clustering. The approach provides a continuum representation for the particle phase in which momentum conservation identifies two fundamental contributions to the particle mass flux. These take the form of an additional body force, which emerges from inhomogeneities in the sampling of turbulence by particles, and a component of the particle phase stress tensor associated with turbophoresis. Remarkably, these contributions are frequently overlooked in the specification of mean-field models for dispersed particle flows. To assess the relative importance of these mass flux contributions a kinematic simulation study has been performed, making use of a specially constructed inhomogeneous flow field designed to mimic the dynamics of particle pair behaviour. Whilst the turbophoretic contribution always acts to increase the clustering of particles, both the direction in which the additional body force acts and the relative importance of the two mass flux contributions are found to vary with particle inertia and turbulence intensity. In some regimes the body force is also the dominant mechanism responsible for particle clustering, demonstrating its importance within model formulations. It is further highlighted that the evolution of the radial distribution function which describes particle clustering is represented as a balance between convection and diffusion, and only inclusion of the identified mass flux contributions within this balance enables correct prediction of the particle pair concentration profile observed in simulations.

physics.flu-dyn↗

arXiv2017

Is the kinetic equation for turbulent gas-particle flows ill-posed?

This paper is about well-posedness and realizability of the kinetic equation for gas-particle flows and its relationship to the Generalized Langevin Model (GLM) PDF equation. Previous analyses claim that this kinetic equation is ill-posed, that in particular it has the properties of a backward heat equation and as a consequence, its solutions will in the course of time exhibit finite-time singularities. We show that the analysis leading to this conclusion is fundamentally incorrect because it ignores the coupling between the phase space variables in the kinetic equation and the time and particle inertia dependence of the phase space diffusion tensor. This contributes an extra $+ve$ diffusion that always outweighs the contribution from the$-ve$ diffusion associated with the dispersion along one of the principal axes of the phase space diffusion tensor. This is confirmed by a numerical evaluation of analytic solutions of these $+ve$ and $-ve$ contributions to the particle diffusion coefficient along this principal axis. We also examine other erroneous claims and assumptions made in previous studies that demonstrate the apparent superiority of the GLM PDF approach over the kinetic approach. In so doing we have drawn attention to the limitations of the GLM approach which these studies have ignored or not properly considered, to give a more balanced appraisal of the benefits of both PDF approaches.

physics.flu-dyn↗

arXiv2016

A simple stochastic quadrant model for the transport and deposition of particles in turbulent boundary layers

We present a simple stochastic quadrant model for calculating the transport and de- position of heavy particles in a fully developed turbulent boundary layer based on the statistics of wall-normal fluid velocity fluctuations obtained from a fully developed channel flow. Individual particles are tracked through the boundary layer via their interactions with a succession of random eddies found in each of the quadrants of the fluid Reynolds shear stress domain in a homogeneous Markov chain process. In this way we are able to account directly for the influence of ejection and sweeping events as others have done but without resorting to the use of adjustable parameters. Deposition rate predictions for a wide range of heavy particles predicted by the model compare well with benchmark experimental measurements. In addition deposition rates are compared with those obtained from continuous random walk (CRW) models and Langevin equation based ejection and sweep models which noticeably give sig- nificantly lower deposition rates. Various statistics related to the particle near wall behavior are also presented. Finally we consider the model limitations in using the model to calculate deposition in more complex flows where the near wall turbulence may be significantly different.

physics.flu-dyn↗

arXiv2016

A large eddy simulation (LES) study of inertial deposition of particles onto in-line tube-banks

We study deposition and impact of heavy particles onto an in-line tube-banks within a turbulent cross flow through Lagrangian particle tracking coupled with an LES modelling framework. The flow Reynolds number based on the cylinder diameter D and flow velocity between the gap of two vertically adjacent cylinders is 33960. We examine the flow structures across the tube bank and report surface pressure characteristics on cylinders. Taking into account particle-wall impact and bounce, we study dispersion and deposition of three sets of particles (St = 0.35, 0.086, 0.0075) based on 107 particles tracked through the turbulent flow resolved by LES. The deposition efficiency for the three sets of particles are reported across the tube-banks. Positions of particle deposited onto tube-banks shows that significantly more of smaller particles deposit onto the back-side of the back-banks. This suggests that the smaller particles are easier to be entrained into the wake and impact onto the back-side of cylinders.

physics.flu-dyn↗

arXiv2016

An LES study of turbulent flow over in-line tube-banks and comparison with experimental measurements

Turbulent flow across an in-line array of tube-banks with transverse and longitudinal pitch PT /D = 2.67, and PL /D = 2.31, has been simulated successfully by Large Eddy Simulation (LES) based on the dynamic Smagorinsky subgrid scale model (SGS), in which a wall-layer model is used to reduce the computational cost. The flow structures across the tube-banks were examined through the normalized Q criterion. The surface pressure characteristics from the middle cylinder within each column of cylinders are found to agree well with the existing experimental data, as did also the values of drag and lift coefficients. These results indicate that cylinders from the second column experience the minimum drag force and maximum lift force fluctuation. Spectral analyses were performed for velocity signals sampled behind each middle cylinder axis, which show that the dominant vortex shedding frequency does not vary across the tube-banks. On this basis, we also examined the shear layer instability. Finally, we report auto-correlation functions for streamwise and cross velocity fluctuations as a function of the spanwise length.

physics.flu-dyn↗