Continuum modeling of gas-particle flows across multiple scales

Abstract

A multi-scale strategy for the simulation of large scale gas-particle flows is presented that is based upon a combination of lattice-Boltzmann and volume-averaged (continuum) hydrodynamic model simulations. At the level of individual particles, the lattice-Boltzmann direct numerical simulation technique is employed to construct constitutive relationships for the fluid-particle drag force in the case of polydisperse, isotropic and monodisperse, anisotropic assemblies of spherical particles. At the meso-scale, the microscopic fluid-particle drag models developed via direct numerical simulation are incorporated into a continuum model description of gas-particle flow, and meso-scale flow instabilities are examined through a combination of finite volume simulation and linear stability analysis. For monodisperse gas-particle flows it is demonstrated via linear stability analysis that the incorporation of an anisotropic fluid-particle drag model into a continuum model framework produces a mixed mode as the dominant instability mechanism for intermediate Stokes number gas-particle flows. This is in contrast to the classical one-dimensional travelling wave instability that is obtained when an isotropic drag model is used in continuum model descriptions. For polydisperse systems, it is found through finite volume simulations that clustering phenomena are robust to changes in kinetic theory model frameworks that are commonly used to describe polydisperse gas-particle flows.

Due to the heavy computational demand associated with grid-independent simulation of gas-particle flows at the continuum level, it is of interest in many settings to devise an accurate coarse-grained description of gas-particle flow. It is demonstrated that the fine scale clustering patterns that occur in gas-particle flows at the meso-scale necessitate the development of filtered balance equations to accurately simulate gas-particle flows using coarse numerical grid resolution. In this work, the need for filtered models is illustrated by considering monodisperse, reacting and bidisperse non-reacting gas-particle flows. For monodisperse, reacting gas-particle flows, it is shown that filtered species balance equations must be developed in order to accurately describe species transport in solid-catalyzed, first order isothermal gas-phase reactions. Within the filtered species balance equations, constitutive models for the filtered reaction rate are constructed using fine-grid continuum model simulations. It is found that filtered reaction rates that can be as much as three times lower than what would be predicted via coarse grid simulation of the same flow problem. For the case of bidisperse gas-particle flows, it is found that filtered equations of motion must be developed to enable accurate coarse-grid simulation of bidisperse gas-particle flows. The sensitivity of the filtered fluid-particle drag coefficient, particle-particle drag coefficient, and particle phase pressure and viscosity to particle size ratio, volume fraction ratio and filter size is presented. Moreover, the volume fraction and filter size dependence of the fluid-particle drag coefficient and particle phase pressure and viscosity in bidisperse systems are compared to existing filtered models used to describe monodisperse gas-particle flows.

By coupling direct numerical simulation and continuum model simulation, the scales of motion ranging from particle level to the level of large meso-scale clusters can be united so that accurate coarse-grained continuum model descriptions of gas-particle flow can be constructed. The result is a computationally inexpensive design tool that can be used in the scale-up and design of multiphase flow devices without the inherent risk and expense of pilot plant testing.