Hierarchical modelling of multiphase flows using fully resolved fixed mesh and PDF approaches

Abstract

Fully–resolved simulations of multiphase flow phenomena and in particular particulate flow simulations are computationally expensive and are only feasible on massively parallel computer clusters. A 3D SIMPLE type pressure correction algorithm is implemented and extensively tested and parallelized to exploit the power of massively parallel computing clusters currently available. Domain decomposition and communication schemes applicable to a general unstructured or structured multi–block CFD codes are discussed and algorithms are proposed, implemented and tested. Several high–performance linear solvers and a multi–grid strategy for the current framework are implemented and the best types of solvers are identified.

A 2D CFD code is developed by the author to test several possible fixed–mesh strategies. Variations of immersed boundary (IB) and fictitious domain (FD) methods are implemented and compared. FD methods are identified to have better properties especially if other transport phenomena are also considered. Therefore an FD method is adapted by the author for the SIMPLE type flow solvers and is extended to heat transfer problems. The method is extensively tested for the simulation of flow around stationary in addition to freely moving particles and forced motion where both natural and forced convection are considered. The method is used to study the flow and heat transfer around a stationary cylinder and a new high resolution correlation is devised for the estimation of the local Nusselt number curves. Free fall problem for a single circular cylinder is considered and the effects of internal heat generation and also long term behavior of single cold particle subject to natural convection are also studied in detail. A particle collision strategy is also adapted and tested for the particle–particle collision problems. The FD algorithm is extended to the 3D framework and the flow around single stationary sphere and also free fall of a single sphere are used to validate the FD algorithm in 3D.

A unique polydispersed fluid-particle turbulent modelling process is reviewed and the closure problem for this framework is studied in detail. Two methods for the closure of the non–integer moments which results from the polydispersity of the particles are proposed namely PDF reconstruction using Laguerre polynomials and a unique direct method named Direct Fractional Method of Moments (DFMM). The latter is derived using the results of the fractional calculus by writing an equation for the fractional derivatives of the moment generating function. The proposed methods are tested on a number of problems consisting of analytical, experimental and DNS simulations to asses their validity and viability which shows that both methods provide accurate results with DFMM having more desirable properties.

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