Development of an implicit framework for the two-fluid model on unstructured grids

Abstract

The two-fluid model is an efficient method for simulating multiphase flows, based on an averaged description of the phases as interpenetrating and interacting continua. It is particularly attractive for the simulation of dispersed gas-solid flows in which the large number of particles in practical devices can impose an insurmountable computational burden for particle tracking methods, given currently available computing resources. Whilst the two-fluid model is more efficient than particle tracking methods, it results in large, strongly coupled and highly non-linear systems of equations, placing a premium on efficient solution algorithms. Additionally, the constitutive models used to describe the solid phase introduce stiff source terms, requiring a robust solution algorithm to handle them. In this thesis a fully-coupled algorithm is developed for the two-fluid model, based on a Newton linearisation of the underlying equation system, resulting in an algorithm treating all inter-equation couplings implicitly. For comparison, a semi-coupled algorithm, based on a Picard linearisation of the two-fluid model is also implemented, yielding a smaller implicitly coupled pressure-velocity system and a segregated system for the transport of phase concentrations. Motivating this work is the highly non-linear nature of the two-fluid model and the stiff source terms arising in the models of the dispersed phase, these are treated explicitly in the semi-coupled algorithm and may impose stability limits on the algorithm. By treating these terms implicitly, it is expected that the fully-coupled solution algorithm will be more robust. The algorithms are compared by application to test cases ranging from academic problems to problems representative of industrial applications of the two-fluid model. These comparisons show that with increasing problem complexity, the robustness of the fully-coupled algorithm leads to an overall more efficient solution than the semi-coupled algorithm.