Multi-scale modeling of particle-laden flows

Particle-laden flow occur in a wide range of engineering applications such as combustors, gasifiers, fluidized beds and pollution control systems. Particle-flow interactions are complex, especially in turbulent and confined flows. A proper understanding of these interactions is critical in designing devices with better performance characteristics. In this work, particle-laden flows in channels are numerically investigated with the lattice-Boltzmann method (LBM). A three-dimensional parallelized lattice-Boltzmann method code is developed to carry out these studies. The code resolves the particle surface and the boundary layer surrounding it to gain fundamental insights into particle-flow interactions. The lattice-Boltzmann method is assessed for its accuracy in solving several standard single-phase and multi-phase, laminar and turbulent flows. Direct numerical simulations (DNS) of particle-laden channel flows are then performed. When the particle diameter is smaller than the Kolmogorov length scale, direct numerical simulations (DNS) with the point-particle approximation show that the Stokes number, St, mass loading of particles, i.e. ratio of mass of dispersed to carried phase, and particle diameter, are important parameters that determine the distribution of the particles across the channel cross-section and the impact of the particles on the flow field. When the St is infinitesimally small, the particles are uniformly distributed across the cross-section of the channel. As St is increased, the particle concentration near the wall increases. At even higher St, the particle concentration near the wall decreases, but it increases at the center of the channel. These changes in concentration are attributed to turbophoresis which causes preferential movement of the particles. The impact of the turbophoretic force is affected by St and particle diameter. The parameters that influence the mean flow field of the carrier phase is primarily the mass loading. To further improve the understanding of the physics of the flow, particle-resolved direct numerical simulations (PR-DNS) are carried out. Particle motion in a laminar channel flow is initially studied. The trajectory of a single particle is examined. It is shown that the mean equilibrium position of the particle in the channel depends on the St. Particles with low St reach an equilibrium position that lies between the wall and the center of the channel (Segre-Silberberg effect) while those with high St begin to oscillate about the center of the channel as they are transported by the fluid. The particle location and motion are determined by the interplay of three forces acting on the particle in the wall normal direction: the Saffman lift, Magnus lift and wall repulsion. Saffman lift and Magnus lift act to move the particle towards the wall while wall-repulsion opposes this motion. Direct numerical simulations of turbulent flow past stationary particles in a channel are then carried out. These simulations provide information about particle-flow interactions when the particle is near the wall and at the center. Multiple particles fixed in a cross-sectional plane are also considered. The position of the particles in the channel, the particle size, the Reynolds number and the number of particles are varied. The details of the flow field are analyzed to provide insight into the factors that control the distance of influence of the fixed particle on the flow field. With a single particle case, the effect of the particle is felt for about 20 diameters downstream. When multiple particles are present, interaction between the vortices shed by the particles lengthens the distance to about 40 diameters downstream. The results suggest that in a particle-laden flow, if particles are separated by an average distance greater than 40 diameters, particle-fluid-particle interactions can be neglected. At shorter distances, these interactions become important. Next particle-resolved direct numerical simulations (PR-DNS) in a turbulent channel flow are carried out to study the particle motion when the particle diameter is larger than the Kolmogorov length scale. It is shown that in a turbulent channel flow, the dominant forces are the Saffman lift and the turbophoresis. When the particle is larger than the Kolmogorov length scale, turbophoresis can act in a local sense whereby the more intense exchange of momentum of eddies on the side of the particle with higher turbulent kinetic energy relative to the opposite side move the particle toward the lower turbulent kinetic energy region or in a global sense whereby even when the particles do not directly feel the effect of eddies, particles tend to diffuse down gradients of turbulent kinetic energy. The simulations show that particles with relatively lower St move preferentially toward the wall while those with higher St exhibit a relatively uniform concentration. This is consistent with the conclusion from the point-particle simulations. As particle size is increased, the St at which uniform distribution is reached increases. The likely reason is that the effect of local turbophoresis and Saffman lift increases for larger particles and these forces tend to concentrate particles near the wall. Higher St, i.e. higher inertia, is needed to overcome these forces

Analytical modeling for the heat transfer in sheared flows of nanofluids

We developed a model for the enhancement of the heat flux by spherical and elongated nano- particles in sheared laminar flows of nano-fluids. Besides the heat flux carried by the nanoparticles the model accounts for the contribution of their rotation to the heat flux inside and outside the particles. The rotation of the nanoparticles has a twofold effect, it induces a fluid advection around the particle and it strongly influences the statistical distribution of particle orientations. These dynamical effects, which were not included in existing thermal models, are responsible for changing the thermal properties of flowing fluids as compared to quiescent fluids. The proposed model is strongly supported by extensive numerical simulations, demonstrating a potential increase of the heat flux far beyond the Maxwell-Garnet limit for the spherical nanoparticles. The road ahead which should lead towards robust predictive models of heat flux enhancement is discussed.Comment: 14 pages, 10 figures, submitted to PR

Simulations of slip flow on nanobubble-laden surfaces

On microstructured hydrophobic surfaces, geometrical patterns may lead to the appearance of a superhydrophobic state, where gas bubbles at the surface can have a strong impact on the fluid flow along such surfaces. In particular, they can strongly influence a detected slip at the surface. We present two-phase lattice Boltzmann simulations of a flow over structured surfaces with attached gas bubbles and demonstrate how the detected slip depends on the pattern geometry, the bulk pressure, or the shear rate. Since a large slip leads to reduced friction, our results allow to assist in the optimization of microchannel flows for large throughput.Comment: 22 pages, 12 figure

Inertial Coupling Method for particles in an incompressible fluctuating fluid

We develop an inertial coupling method for modeling the dynamics of point-like 'blob' particles immersed in an incompressible fluid, generalizing previous work for compressible fluids. The coupling consistently includes excess (positive or negative) inertia of the particles relative to the displaced fluid, and accounts for thermal fluctuations in the fluid momentum equation. The coupling between the fluid and the blob is based on a no-slip constraint equating the particle velocity with the local average of the fluid velocity, and conserves momentum and energy. We demonstrate that the formulation obeys a fluctuation-dissipation balance, owing to the non-dissipative nature of the no-slip coupling. We develop a spatio-temporal discretization that preserves, as best as possible, these properties of the continuum formulation. In the spatial discretization, the local averaging and spreading operations are accomplished using compact kernels commonly used in immersed boundary methods. We find that the special properties of these kernels make the discrete blob a particle with surprisingly physically-consistent volume, mass, and hydrodynamic properties. We develop a second-order semi-implicit temporal integrator that maintains discrete fluctuation-dissipation balance, and is not limited in stability by viscosity. Furthermore, the temporal scheme requires only constant-coefficient Poisson and Helmholtz linear solvers, enabling a very efficient and simple FFT-based implementation on GPUs. We numerically investigate the performance of the method on several standard test problems...Comment: Contains a number of corrections and an additional Figure 7 (and associated discussion) relative to published versio

Channel flow of rigid sphere suspensions: particle dynamics in the inertial regime

We consider suspensions of neutrally-buoyant finite-size rigid spherical particles in channel flow and investigate the relation between the particle dynamics and the mean bulk behavior of the mixture for Reynolds numbers $500 \le Re \le 5000$ and particle volume fraction $0\le \Phi \le 0.3$, via fully resolved numerical simulations. Analysis of the momentum balance reveals the existence of three different regimes: laminar, turbulent and inertial shear-thickening depending on which of the stress terms, viscous, Reynolds or particle stress, is the major responsible for the momentum transfer across the channel. We show that both Reynolds and particle stress dominated flows fall into the Bagnoldian inertial regime and that the Bagnold number can predict the bulk behavior although this is due to two distinct physical mechanisms. A turbulent flow is characterized by larger particle dispersion and a more uniform particle distribution, whereas the particulate-dominated flows is associated with a significant particle migration towards the channel center where the flow is smooth laminar-like and dispersion low.Interestingly, the collision kernel shows similar values in the different regimes, although the relative particle velocity and clustering clearly vary with inertia and particle concentration.Comment: 36 Pages, 12 figure

A Review on Contact and Collision Methods for Multi-body Hydrodynamic problems in Complex Flows

Modeling and direct numerical simulation of particle-laden flows have a tremendous variety of applications in science and engineering across a vast spectrum of scales from pollution dispersion in the atmosphere, to fluidization in the combustion process, to aerosol deposition in spray medication, along with many others. Due to their strongly nonlinear and multiscale nature, the above complex phenomena still raise a very steep challenge to the most computational methods. In this review, we provide comprehensive coverage of multibody hydrodynamic (MBH) problems focusing on particulate suspensions in complex fluidic systems that have been simulated using hybrid Eulerian-Lagrangian particulate flow models. Among these hybrid models, the Immersed Boundary-Lattice Boltzmann Method (IB-LBM) provides mathematically simple and computationally-efficient algorithms for solid-fluid hydrodynamic interactions in MBH simulations. This paper elaborates on the mathematical framework, applicability, and limitations of various 'simple to complex' representations of close-contact interparticle interactions and collision methods, including short-range inter-particle and particle-wall steric interactions, spring and lubrication forces, normal and oblique collisions, and mesoscale molecular models for deformable particle collisions based on hard-sphere and soft-sphere models in MBH models to simulate settling or flow of nonuniform particles of different geometric shapes and sizes in diverse fluidic systems.Comment: 37 pages, 12 Figure

Turbulent channel flow of dense suspensions of neutrally-buoyant spheres

Dense particle suspensions are widely encountered in many applications and in environmental flows. While many previous studies investigate their rheological properties in laminar flows, little is known on the behaviour of these suspensions in the turbulent/inertial regime. The present study aims to fill this gap by investigating the turbulent flow of a Newtonian fluid laden with solid neutrally-buoyant spheres at relatively high volume fractions in a plane channel. Direct Numerical Simulation are performed in the range of volume fractions Phi=0-0.2 with an Immersed Boundary Method used to account for the dispersed phase. The results show that the mean velocity profiles are significantly altered by the presence of a solid phase with a decrease of the von Karman constant in the log-law. The overall drag is found to increase with the volume fraction, more than one would expect just considering the increase of the system viscosity due to the presence of the particles. At the highest volume fraction here investigated, Phi=0.2, the velocity fluctuation intensities and the Reynolds shear stress are found to decrease. The analysis of the mean momentum balance shows that the particle-induced stresses govern the dynamics at high Phi and are the main responsible of the overall drag increase. In the dense limit, we therefore find a decrease of the turbulence activity and a growth of the particle induced stress, where the latter dominates for the Reynolds numbers considered here.Comment: Journal of Fluid Mechanics, 201

Diffusion-Based Coarse Graining in Hybrid Continuum-Discrete Solvers: Applications in CFD-DEM

In this work, a coarse-graining method previously proposed by the authors in a companion paper based on solving diffusion equations is applied to CFD-DEM simulations, where coarse graining is used to obtain solid volume fraction, particle phase velocity, and fluid-particle interaction forces. By examining the conservation requirements, the variables to solve diffusion equations for in CFD-DEM simulations are identified. The algorithm is then implemented into a CFD-DEM solver based on OpenFOAM and LAMMPS, the former being a general-purpose, three-dimensional CFD solver based on unstructured meshes. Numerical simulations are performed for a fluidized bed by using the CFD-DEM solver with the diffusion-based coarse-graining algorithm. Converged results are obtained on successively refined meshes, even for meshes with cell sizes comparable to or smaller than the particle diameter. This is a critical advantage of the proposed method over many existing coarse-graining methods, and would be particularly valuable when small cells are required in part of the CFD mesh to resolve certain flow features such as boundary layers in wall bounded flows and shear layers in jets and wakes. Moreover, we demonstrate that the overhead computational costs incurred by the proposed coarse-graining procedure are a small portion of the total costs in typical CFD-DEM simulations as long as the number of particles per cell is reasonably large, although admittedly the computational overhead of the coarse graining often exceeds that of the CFD solver. Other advantages of the present algorithm include more robust and physically realistic results, flexibility and easy implementation in almost any CFD solvers, and clear physical interpretation of the computational parameter needed in the algorithm. In summary, the diffusion-based method is a theoretically elegant and practically viable option for CFD-DEM simulations