Stability Analysis of Filtered Two-Fluid Models for Gas-Particle Flows

Abstract

Solution of two-fluid models for gas-particle flows in fluidized beds produces structures on the scale of a few particle diameters. Linear stability analysis of the homogeneously fluidized state indeed predicts this. These fine structures are too computationally expensive to resolve in simulations of large-scale fluidized beds. As such, researchers have developed filtered two-fluid models, which average over fine structures smaller than a given filter size. Developing constitutive relations appropriate for these filtered two-fluid models is a topic of active research. The constitutive relations are, in general, functions of the filter size. Conceptually, solution of properly formulated filtered two-fluid models and constitutive relations should not reveal fine structures smaller than the filter size. Systematic assessment as to whether the filtered models published in the literature satisfy this requirement has not been done before and is the principal goal of this thesis. Towards this end, linear stability analysis of homogeneously fluidized states, as predicted by the filtered two-fluid models augmented with filtered constitutive relations proposed by Igci et al. (2011) and Milioli et al. (2013), has been studied here. The analysis started with a hypothesis that the wavelength corresponding to marginal stability of homogeneously fluidized states should be comparable to the filter size in the constitutive models. It was found that this expectation was met for only a narrow range of particle volume fractions. Retaining the filtered constitutive models for drag and particle phase viscosity proposed by Igci et al. (2011), an alternate model for the filtered particle phase pressure that would satisfy the above-stated hypothesis was formulated, which was then used to simplify the expression for filtered particle phase viscosity. These refined models yield qualitatively reasonable results for all particle volume fractions considered when used in conjunction with the Igci et al. (2011) filtered drag coefficient model and for dilute and intermediate beds when used in conjunction with the Milioli et al. (2013) one.