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.
Abraham, Purdue University.
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