Michael W Reeks

• BSc,PhD
• Professor at Newcastle University

Kinetic theory provides an elegant framework for studying dispersed particles in turbulent flows. Here the application of such probability density function-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 fund...

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 tw...

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. 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 ap...

We show that in ADE type the trace of Webster's categorification of a tensor product of irreducibles for the quantum group is isomorphic to a tensor product of Weyl modules for the current algebra U˙(g[t]). This extends a result of Beliakova, Habiro, Lauda, and Webster who showed that the trace of the categorified quantum group U˙⁎(g) is isomorphic...

We establish an isomorphism between the center of the twisted Heisenberg category and the subalgebra of the symmetric functions $\Gamma$ generated by odd power sums. We give a graphical description of the factorial Schur $Q$-functions as closed diagrams in the twisted Heisenberg category and show that the bubble generators of the center correspond...

We show that in ADE type the trace of Webster's categorification of a tensor product of irreducibles for the quantum group is isomorphic to a tensor product of Weyl modules for the current algebra $\dot{U}(\mathfrak{g}[t])$. This extends a result of Beliakova, Habiro, Lauda, and Webster who showed that the trace of the categorified quantum group $\...

This paper is about well-posedness and realizability of the kinetic equation for gas-particle ows 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 i...

We establish an isomorphism between the center of the twisted Heisenberg category and the subalgebra of the symmetric functions $\Gamma$ generated by odd power sums. We give a graphical description of the factorial Schur $Q$-functions as closed diagrams in the twisted Heisenberg category and show that the bubble generators of the center correspond...

We show that the trace decategorification, or zeroth Hochschild homology, of the twisted Heisenberg category defined by Cautis and Sussan is isomorphic to a quotient of W-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \...

We formulate a type B extended nilHecke algebra, following the type A construction of Naisse and Vaz. We describe an action of this algebra on extended polynomials and describe some results on the structure on the extended symmetric polynomials. Finally, following Appel, Egilmez, Hogancamp, and Lauda, we prove a result analogous to a classical theo...

We formulate a type B extended nilHecke algebra, following the type A construction of Naisse and Vaz. We describe an action of this algebra on extended polynomials and describe some results on the structure on the extended symmetric polynomials. Finally, following Appel, Egilmez, Hogancamp, and Lauda, we prove a result analogous to a classical theo...

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...

We show that the trace decategorification, or zeroth Hochschild homology, of the twisted Heisenberg category defined by Cautis and Sussan is isomorphic to a quotient of $W^-$, a subalgebra of $W_{1+\infty}$ defined by Kac, Wang, and Yan. Our result is a twisted analogue of that by Cautis, Lauda, Licata, and Sussan relating $W_{1+\infty}$ and the tr...

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 struct...

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 tu...

We determine a basis of the cocenter (i.e., the zeroth Hochschild homology) of the degenerate affine Hecke-Clifford and spin Hecke algebras in classical types.

We analyze the escape of Brownian particles over potential barriers using the Fokker-Planck equation in a similar way to that of Chandrasekhar (Rev. Modern Phys., 1943), deriving a formula for the particle deposition velocity to a surface as a function of the particle response time. For very small particle response times, the particle deposition ve...

The Clausius Virial theorem of Classical Kinetic Theory is used to evaluate the pressure of a suspension of small particles at equilibrium in an isotropic homogeneous and stationary turbulent flow. It then follows a similar approach to the way Einstein (1905] evaluated the diffusion coefficient of Brownian particles (leading to the Stokes-Einstein...

This paper describes methods and approaches that have been used to simulate and model the transport, mixing and agglomeration of small particles in a flowing turbulent gas. The transported particles because of their inertia are assumed not to follow the motion of the large scales of the turbulence and or the motion of the small dissipating scales o...

We present a simple stochastic quadrant model for calculating the transport and deposition 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 interaction...

Agglomerate aerosols in a turbulent flow may be subjected to very high turbulent shear rates which through the generation of lift and drag can overcome the adhesive forces binding the constituents of an agglomerate together and cause it to break-up. This paper presents an analysis of the experimental measurements of the breakup of agglomerates betw...

DNS studies of dispersed particle motion in isotropic homogeneous turbulence [1] have revealed the existence of a component of random uncorrelated motion (RUM)dependent on the particle inertia {\tau}p(normalised particle response time or Stoke number). This paper reports the presence of RUM in a simple linear random smoothly varying flow field of c...

The way particles interact with turbulent structures, particularly in regions of high vorticity and strain rate, has been investigated in simulations of homogeneous turbulence and in simple flows which have a periodic or persistent structure e.g. separating flows and mixing layers. The influence on both settling under gravity and diffusion has been...

This book contains a collection of the main contributions from the first five workshops held by Ercoftac Special Interest Group on Synthetic Turbulence Models (SIG42. It is intended as an illustration of the sig’s activities and of the latest developments in the field. This volume investigates the use of Kinematic Simulation (KS) and other syntheti...

A full Lagrangian method (FLM) is used in direct numerical simulations (DNS) of incompressible homogeneous isotropic and statistically stationary turbulent flow to measure the statistical properties of the segregation of small inertial particles advected with Stokes drag by the flow. Qualitative good agreement is observed with previous kinematic si...

The results presented here are part of a long-term study in which we analyse the segregation of inertial particles in turbulent flows using the so called full Lagrangian method (FLM) to evaluate the ‘compressibility’ of the particle phase along a particle trajectory. In the present work, particles are advected by Stokes drag in a random flow field...

A theoretical model to predict the joint distribution of droplet size and charge density for an electrostatic spray is described based on the maximum entropy method. From known values of the electrostatic spray parameters, the model is used to evaluate the joint distribution of droplet size and charge density for a cone-jet mode electrostatic spray...

The condensation of microdroplets in model systems, reminiscent of atmospheric clouds, is investigated numerically and analytically. Droplets have been followed through a synthetic turbulent flow field composed of 200 random Fourier modes, with wave numbers ranging from the integral scales O10 2 m to the Kolmogorov scales O10 −3 m. As the influence...

This paper is concerned with the development and validation of a simple Lagrangian model for particle agglomeration in a turbulent flow involving the collision of particles in a sequence of correlated straining and vortical structures which simulate the Kolmogorov small scales of motion of the turbulence responsible for particle pair dispersion and...

The rupture of a tube in the Steam Generator (SG) represents a dominant accident risk of fission product release to the atmosphere because this release by-passes the reactor containment. Preliminary experiments reproducing the sonic flow conditions in the ruptured tube reveal a break-up of the agglomerated aerosol at the tube exit. Whilst this brea...

Planar micro-devices capable of continuously separating large volumes of dilute suspensions were designed and modeled using a commercial CFD package. The devices consist of a single high aspect ratio spiral micro channel with a bifurcation at the exit. The device exploits small inertial and hydrodynamic differences between particles of dissimilar s...

The combined effects of Brownian forcing and straining flow on the statistical description of particle dynamics are considered. Using a Fokker-Planck (pdf) model results are obtained for both instantaneous and continuous releases of particles into the flow. The approach shows that continuous sources generate true equilibrium distributions, and high...

The distribution of inertial particles in turbulent flows is strongly non-homogeneous and is driven by the structure of the underlying carrier flow field. In this work, we use DNS combined with Lagrangian particle tracking to characterize the effect of inertia on particle preferential accumulation. We compare the Eulerian statistics computed for fl...

Simultaneous diffusive and inertial motion of Brownian particles in laminar Couette flow is investigated via Lagrangian and Eulerian descriptions to determine the effect of particle inertia on diffusive transport in the long-time limit. The classical fluctuation dissipation theorem is used to calculate the amplitude of random-force correlations, th...

Comparisons are made between the Advection–Diffusion Equation (ADE) approach for particle transport and the two-fluid model approach based on the PDF method. In principle, the ADE approach offers a much simpler way of calculating the inertial deposition of particles in a turbulent boundary layer than that based on the PDF approach. However the ADE...

Simultaneous diffusive and inertial motion of Brownian particles in laminar Couette flow is investigated via Lagrangian and Eulerian descriptions to determine the effect of particle inertia on diffusive transport in the long-time. The classical fluctuation dissipation theorem is used to calculate the amplitude of random-force correlations, thereby...

The paper examines a fundamental discrepancy between two probability density function (PDF) models, the kinetic model (KM) and generalized Langevin model (GLM), currently used to model the dispersion of particles in turbulent flows. This discrepancy is manifest in particle dispersion in an unbounded simple shear flow where model predictions for the...

The Probabaility Density (PDF) approach for modelling dispersed particle flow is analogous to the classical kinetic theory gases. That is, there exists a master equation (analogous to the Maxwell Boltzmann equation of Kinetic Theory) which can be used in a formal way to derive the two-fluid model equations for both phases of the flow and the associ...

The paper addresses an apparent incompatibility between the two current formulations of the PDF approach for the dispersion of particles in a uniform shear flow. It is shown that this incompatibility arises through neglect of the inertial convection term in the transport equation for the mean carrier flow velocity local to a particle. Evaluating th...

Comparisons are made between the Advection-Diffusion Equation (ADE) approach for particle transport and the two fluid model approach based on the PDF method. In principal the ADE approach offers a simpler way of calculating the inertial deposition of particles in a turbulent boundary layer than that based on the PDF approach. However the ADE equati...

The recoilless fraction and second order Doppler shift of the Mossbauer line in iron 57 present as an impurity in Al, Rh, Pd, V, and Mo metals was measured in the range 4-1000 K. Values of the weighted mean lattice frequencies for the iron atoms were obtained and on the basis of a central force nearest neighbour model the iron-host force constant c...

The recent progress in the application of a kinetic approach to two-fluid modelling of dispersed particle flows is described. In particular, the behavior of solid particles settling under gravity in a homogeneous turbulent flow near a partially absorbing wall is described. This simple, somewhat idealized system approximates the deposition of large...

The steady‐state transport and deposition of ‘‘high inertia’’ particles in turbulent duct flow is studied. A relatively simple yet fundamental PDF (probability density function) equation (kinetic equation) is proposed as a model for such systems together with models describing perfectly and partially adsorbing boundaries. Using the idea of particle...

In this paper we consider numerical solutions to a kinetic equation for the dispersion of small particles in a turbulent flow. The solution represents the probability density that a particle has a certain velocity and position at a given time. These solutions are based on a mixed finite-difference spectral method. Computational results are presente...

A Lagrangian random-walk approach to modeling particle deposition in turbulent duct flows is presented. The inhomogeneous boundary layer turbulence is simulated by a discrete eddy field, characterized by a random normal velocity (drawn from a Gaussian probability distribution) and a random time scale (drawn from an exponential probability distribut...

A Master Transport equation is presented as a basis for the description of the statistical behaviour of discrete particles in inhomogeneous turbulence. Motion is considered in the particle phase space, and a contracted form of Lagrangian History Direct Interaction (LHDI) is used to represent the closure term in the averaged particle Liouville equat...

Eulerian direct interaction is used to close Liouville's equation central to the transport of particles in a turbulent fluid where the dominant drag force is derived from the particle and local fluid velocities. The reliability of the equation is then tested by comparison of solutions with those of a computer simulation of particle motion with Stok...

A solution to the dispersion of small particles suspended in a turbulent fluid is presented, based on the approximation proposed by Phythian for the dispersion of fluid points in an incompressible random fluid. Motion is considered in a frame moving with the mean velocity of the fluid, the forces acting on the particle being taken as gravity and a...

The distribution of inertial particles in turbulent flows is strongly non-homogeneous and is driven by the structure of the flow field. In this work, we examine the relationship between particle concentration and flow field in a turbulent channel (Reτ = 150). We use DNS combined with Lagrangian tracking of particles, with Stokes numbers equal to 0....